University of Ljubljana Faculty of Electrical Engineering Tomazˇ Vrtovec Automatic analysis of three-dimensional spine images PhD thesis Supervisor: Prof. Dr. Franjo Pernusˇ Ljubljana, 2007 Univerza v Ljubljani Fakulteta za elektrotehniko Tomazˇ Vrtovec Avtomatska analiza tridimenzionalnih slik hrbtenice Doktorska disertacija Mentor: prof. dr. Franjo Pernusˇ Ljubljana, 2007 The juice was worth the squeeze. ¦ Sokje bil vreden stiska. Contents Statement / Izjava .................................. xiii Abbreviations ...................................... xvii Abstract / Povzetek ................................. 1 P.1 Prikazovanje in kvantitativno vrednotenje slik .................. 5 P.1.1 Prikazovanje medicinskih slik ...................... 5 P.1.2 Kvantitativno vrednotenje medicinskih slik ............... 7 P.2 Prikazovanje in kvantitativno vrednotenje slik hrbtenice ............. 8 P.2.1 Prikazovanje slik hrbtenice ........................ 8 P.2.2 Kvantitativno vrednotenje slik hrbtenice ................. 10 P.3 Motivacija ..................................... 15 P.4 Izvirni prispevki k znanosti ............................ 15 P.4.1 Definicija hrbtenici lastnega koordinatnega sistema ........... 15 P.4.2 Razvoj postopka za avtomatsko prikazovanje CT slik hrbtenice z ukrivljenimi prerezi ............................... 16 P.4.3 Razvoj postopka za avtomatsko prikazovanje MR slik hrbtenice z ukrivljenimi prerezi ............................ 16 P.4.4 Razvoj postopka za kvantitativno vrednotenje ukrivljenosti hrbtenice v 3D ..................................... 17 vii viii Contents P.4.5 Razvoj postopka za avtomatsko dolocˇanje polozˇaja in rotacije vretenc v CT in MR slikah hrbtenice ........................ 17 1 Introduction and Summary .......................... 19 1.1 Visualization and quantitative evaluation of images ............... 21 1.1.1 Visualization of medical images ..................... 21 1.1.2 Quantitative evaluation of medical images ................ 26 1.2 Visualization and quantitative evaluation of spine images ............ 27 1.2.1 Visualization of spine images ....................... 27 1.2.2 Quantitative evaluation of spine images ................. 31 1.3 Motivation ..................................... 42 1.4 Contributions ................................... 42 1.4.1 Definition of the spine-based coordinate system ............. 42 1.4.2 Development of an automated technique for curved planar reformation of computed tomography (CT) spine images ............... 43 1.4.3 Development of an automated technique for curved planar reformation of magnetic resonance (MR) spine images ................ 43 1.4.4 Development of a framework for quantitative evaluation of spinal curvature in 3D ................................ 44 1.4.5 Development of an automated technique for the determination of the position and rotation of vertebra in CT and MR spine images ...... 45 2 Automated curved planar reformation of 3D spine images ...... 47 Abstract ......................................... 48 2.1 Introduction .................................... 48 2.2 Method ...................................... 50 2.2.1 Spine-based coordinate system ...................... 50 2.2.2 Coordinate system parametrization .................... 52 2.2.3 Estimation of spine curve parameters ................... 53 2.2.4 Estimation of rotational parameters .................... 53 2.2.5 Additional spine features ......................... 55 2.3 Experiments .................................... 56 2.3.1 Experimental data ............................. 56 2.3.2 Implementation details .......................... 56 2.4 Results ....................................... 57 Contents ix 2.4.1 Qualitative results ............................. 57 2.4.2 Quantitative results ............................ 57 2.5 Discussion ..................................... 60 2.6 Conclusion .................................... 62 Acknowledgments .................................... 62 3 Automated generation of curved planar reformations from MR images of the spine .................................. 63 Abstract ......................................... 64 3.1 Introduction .................................... 64 3.2 Problem description ................................ 67 3.3 Methods ...................................... 67 3.3.1 Initial estimation of centres and rotations of vertebrae .......... 68 3.3.2 Robust refinement of centres and rotations of vertebrae ......... 70 3.3.3 Curved planar reformation ........................ 71 3.4 Experiments and results .............................. 72 3.4.1 MR spine images ............................. 72 3.4.2 Implementation details .......................... 72 3.4.3 Results .................................. 73 3.5 Discussion and conclusion ............................ 76 Acknowledgments .................................... 80 4 Quantitative analysis of spinal curvature in 3D: Application to CT images of normal spine ............................. 81 Abstract ......................................... 82 4.1 Introduction .................................... 82 4.2 Materials and Methods .............................. 83 4.2.1 Subjects .................................. 83 4.2.2 Three-dimensional (3D) vertebral body line ............... 83 4.2.3 Geometric curvature and curvature angle ................. 85 4.3 Results ....................................... 85 4.4 Discussion ..................................... 87 Appendix ........................................ 93 X Contents Acknowledgments .................................... 94 5 Determination of 3D location and rotation of lumbar vertebrae in CT images by symmetry-based auto-registration ............ 95 Abstract ......................................... 96 5.1 Introduction .................................... 96 5.2 Methodology ................................... 98 5.2.1 Vertebral parameters ........................... 98 5.2.2 Symmetry of the vertebral anatomy ................... 98 5.2.3 Symmetry-based auto-registration .................... 99 5.3 Experiments and results .............................. 100 5.3.1 Experimental data ............................. 100 5.3.2 Implementation details .......................... 101 5.3.3 Experiments ................................ 101 5.3.4 Results .................................. 102 5.4 Conclusions .................................... 107 Acknowledgments .................................... 110 6 Modality-independent determination of vertebral position and rotation in 3D ..................................... 111 Abstract ......................................... 112 6.1 Introduction .................................... 112 6.2 Method ...................................... 113 6.2.1 Vertebral parameters and natural vertebral symmetry .......... 113 6.2.2 Registration of symmetrical vertebral parts ................ 114 6.3 Experiments and results .............................. 115 6.3.1 Data and experiments ........................... 115 6.3.2 Results .................................. 116 6.4 Discussion ..................................... 118 7 Conclusion ...................................... 121 Appendix ......................................... 125 A Reprint permissions ................................ 125 Contents xi Bibliography ...................................... 127 Publications ....................................... xix Papers in journals .................................... xix Papers in conference proceedings ............................ xx Monographs and other completed works ........................ xxi About the author / O avtorju ........................... xxiii Acknowledgments / Zahvala ........................... xxvii Index ........................................... xxxi Statement I undersigned Tomazˇ Vrtovec hereby state that I have prepared the PhD thesis independently under the supervision of Prof. Dr. Franjo Pernusˇ. Contribution from other collaborators is entirely quoted in acknowledgments or/and at individual chapters. Ljubljana, June 26th 2007 Tomazˇ Vrtovec, B.Sc. xiii Izjava Podpisani Tomazˇ Vrtovec izjavljam, da sem doktorsko disertacijo izdelal samostojno pod mentorstvom prof. dr. Franja Pernusˇa. Izkazano pomocˇ drugih sodelavcev sem v celoti navedel v zahvali in/ali pri posameznih poglavjih. Ljubljana, 26. junij 2007 Tomaž Vrtovec, univ.dipl.inž.el. XV I have made this longer, because I have not had the time to make it shorter. Blaise Pascal, 1623 - 1662 (Provincial Letters: Letter XVI, 1657) Abbreviations 1D one dimension, one-dimensional 2D two dimensions, two-dimensional 3D three dimensions, three-dimensional 6D six dimensions, six-dimensional CA curvature angle CAD computer-aided diagnosis CPR curved planar reformation CT computed tomography EDO edge distance optimization GC geometric curvature MIP maximum intensity projection MR magnetic resonance LL lumbar lordosis LSF least squares fitting LTS least trimmed squares pixel picture element SNR signal-to-noise ratio TJ thoracolumbar junction TK thoracic kyphosis voxel volume element xvii There are no facts, only interpretations. Friedrich W. Nietzsche, 1844 - 1900 (Notebooks, 1887) Abstract Medical images are of extreme importance for diagnosing and understanding of normal and pathological conditions of the human body. To some extent, the quality of image-assisted medical examinations depends on the acquisition of images, interpretation of the information present in images and on the research activity and clinical environment that stimulate image formation and its application. In the past decades, advances in medical imaging technology and computerized medical image processing led to the development of new three-dimensional (3D) image acquisition techniques that have become important clinical tools in modern diagnostic radiology and medical health care. Although two-dimensional (2D) images, especially radiographic (X-ray) images, are still widely present in clinical examination due to relatively low acquisition price and wide area of application, they are slowly being replaced by 3D images. The continuous increase in the number of acquired cross-sections, reduction in cross-sectional thickness and relatively short acquisition time led to the expansion of 3D imaging techniques. Among the most important 3D techniques are computed tomography (CT) and magnetic resonance (MR) imaging, which provide qualitative data of the imaged structures. However, characteristic features of these techniques and variable positioning of the patient during image acquisition still represent a major source of variability that causes errors in the interpretation of image information. On the other hand, human capability of discovering and diagnosing diseases by proper interpretation of medical images is limited due to our non-systematic search patterns. Moreover, the presence of noise may conceal the natural anatomical background, such as actual geometrical relationship between anatomical structures, which may further hamper mental reconstruction of the 3D image information. Errors in interpretation may also be caused by similar characteristics of normal and pathological conditions and by the natural biological variability in human anatomy. Image 1 2 Abstract interpretation therefore depends to a great extent on adequate presentation and measurement of the information about anatomical structures or physiological processes. As the information of interest is often associated with characteristic features of the selected structure or process, it is crucial to use specially designed image processing techniques for visualization and quantitative evaluation. Techniques for visualization and quantitative evaluation of medical images are therefore extremely valuable in the development of image-assisted diagnosis, planning of surgical interventions and assessment of medical treatment outcomes. This thesis concentrates on the design, development and validation of automated techniques that aim to improve the visualization of 3D spine images, and techniques for an improved quantitative evaluation of the most important parameters of the spine in 3D, such as the spinal curvature and vertebral rotation. The fields of visualization and quantitative evaluation of spine images are closely related, as knowledge of spine parameters may provide a more effective spine visualization, and, on the other hand, proper spine visualization may allow a more effective measurement of spine parameters. Dejstev ni, so samo interpretacije. Friedrich W. Nietzsche, 1844 - 1900 (Zvezki, 1887) Povzetek Informacijska vsebina medicinskih slik je kljucˇnega pomena za odkrivanje in razumevanje normalnih in bolezenskih stanj cˇlovesˇkega organizma. Kakovost slikovno podprtih medicinskih preiskav je v veliki meri odvisna od tehnike zajema slik, interpretacije informacijske vsebine slik ter od raziskovalnega oziroma medicinskega okolja, ki spodbuja zajemanje slik in njihovo uporabo. Napredek na podrocˇju medicinskih slikovnih tehnik ter na podrocˇju racˇunalnisˇke obdelave medicinskih slik je v zadnjih desetletjih privedel do razvoja novih tridimenzionalnih (3D) tehnik zajema slik, ki so nepogresˇljive v sodobni zdravstveni oskrbi. 3D slike so pricˇele nadomesˇcˇati dvodimenzionalne (2D) slike, predvsem rentgenske, ki pa so sˇe vedno mocˇno prisotne pri medicinskih preiskavah zaradi nizke cene zajema ter sˇirokega podrocˇja uporabe. Neprestano povecˇevanje sˇtevila slikovnih rezin v enem zajemu, zmanjsˇevanje debeline slikovnih rezin ter cˇasa, potrebnega za zajem slike (tabela 1.1, str. 20), je namrecˇ povzrocˇilo razmah uporabe 3D slikovnih tehnik (Sakas, 2002). Med najpomembnejsˇimi 3D slikovnimi tehnikami sta predvsem racˇunalnisˇka tomografija (CT) in magnetna resonanca (MR), ki dajeta kakovostne podatke o slikanih anatomskih strukturah. Spremenljive lastnosti uporabljenih tehnik kot tudi spremenljiva lega pacienta med postopkom zajema pa so sˇe vedno vir napak pri interpretaciji informacijske vsebine slik. Po drugi strani smo ljudje pri interpretaciji medicinskih slik v smislu sposobnosti odkrivanja in diagnosticiranja obolenj omejeni zaradi nasˇih nesistematicˇnih iskalnih vzorcev, poleg tega pa prisotnost sˇuma v slikah lahko povzrocˇi prikrivanje naravnega anatomskega ozadja, kot so na primer dejanski geometrijski odnosi med anatomskimi strukturami, kar lahko ovira miselno rekonstrukcijo slikovne informacije v 3D. Nenazadnje pa lahko 3 4 Povzetek napake pri interpretaciji povzročijo tudi podobne značilnosti nekaterih normalnih in bolezenskih stanj ter naravna biološka variabilnost človeške anatomije in fiziologije. Interpretacija slik je torej močno odvisna od načina predstavitve ter merjenja informacije o anatomskih strukturah ali o fizioloških procesih. Ker je informacija o določeni strukturi ali procesu pogosto povezana s karakterističnimi lastnostmi te strukture ali procesa, je uporaba specifičnih tehnik prikazovanja ter kvantitativnega vrednotenja medicinskih slik ključnega pomena za razvoj slikovno podprte medicinske diagnostike, načrtovanje terapevtskih posegov ter vrednotenje učinkov zdravljenja. Poškodbe in degeneracijska obolenja hrbtenice predstavljajo področje v medicini, kjer trenutni načini zdravljenja kljub doseganju pričakovanih kliničnih rezultatov še niso povsem primerni (Toyone in dr., 2005). Bolečine v hrbtenici se ponavadi zdravijo s kombinacijo sredstev proti bolečinam ter fizioterapije, v primeru akutnih obolenj ali travmatičnih poškodb hrbtenice pa se ponavadi opravi kirurški poseg. Kljub temu pa so rezultati zdravljenja pri velikem številu pacientov nezadovoljivi. S trenutnim znanjem o fizičnih ter biomehaničnih lastnostih hrbtenice je namreč nemogoče natančno napovedati rezultate zdravljenja, poleg tega pa je odkrivanje, prikazovanje ter kvantitativno vrednotenje obolenj hrbtenice oteženo zaradi kompleksnosti in členjene sestave hrbtenice. Po drugi strani pa sodobne tehnike zajema slik omogočajo kakovosten vpogled v celotno anatomijo hrbtenice. Tehnika CT je primerna za opazovanje hrbteničnih kosti, medtem ko tehnika MR omogoča vpogled v mehka tkiva in je torej primerna za opazovanje medvretenčnih ploščic1, hrbtenjače2 ter korenin živcev3'4, ki izhajajo iz hrbtenjače. Razvoj sodobnih tehnik prikazovanja ter kvantitativnega vrednotenja lahko torej pripomore k natančnejši medicinski diagnozi ter načrtovanju učinkovitejših strategij zdravljenja hrbteničnih obolenj. V doktorski disertaciji smo načrtovali, razvili ter vrednotili izvirne avtomatske (samodejne) postopke za izboljšanje prikazovanja 3D medicinskih slik hrbtenice ter avtomatske postopke za kvantitativno vrednotenje nekaterih najpomembnejših parametrov hrbtenice v 3D, kot sta ukrivljenost hrbtenice ter rotacija vretenc. Področji prikazovanja ter kvantitativnega vrednotenja sta v primeru slik hrbtenice tesno povezani, saj poznavanje najpomembnejših parametrov hrbtenice omogoča učinkovitejše prikazovanje hrbtenice kot anatomske strukture, po drugi strani pa ustrezno prikazovanje hrbtenice omogoča pravilnejše kvantitativno vrednotenje parametrov hrbtenice. medvretenčna ploščica: ploščica med telesoma sosednjih vretenc, ki sestoji iz vezivne hrustančevine in notranjega pulpoznega jedra; intervertebralni diskus (slika 1.4, str. 28) 2hrbtenjača: del centralnega živčevja iz centralne sive in periferne bele možganovine, ki leži v hrbteničnem kanalu; hrbtni mozeg 3 sprednja korenina spinalnega živca: motorični del spinalnega živca, ki izstopa iz sprednjega stebra hrbtnega mozga in se ob medvretenčni odprtini združi z zadajšnjo korenino v spinalni živec 4zadaj šnja korenina spinalnega živca: senzorični del spinalnega živca, ki vstopa v zadajšnji del hrbtnega mozga Povzetek 5 P.1 Prikazovanje in kvantitativno vrednotenje slik Proces nastajanja slike lahko pojmujemo kot preslikavo dolocˇenih lastnosti slikanega objekta v prostorsko domeno slike, ki je osnova za prikazovanje slikanega objekta in njegovih lastnosti, za nadaljnje kvantitativno vrednotenje strukture ali funkcije slikanega objekta ter nenazadnje za pravilno interpretacijo informacije o slikanem objektu. Osnovni namen prikazovanja slik je ucˇinkovita izraba informacijske vsebine v slikah, od katere je odvisno nadaljnje kvantitativno vrednotenje ter interpretacija slik. Na podrocˇju razvoja tehnik za prikazovanje medicinskih slik je najpomembnejsˇe izlusˇcˇevanje klinicˇno pomenljive informacije, kar omogocˇa razvoj natancˇne ter neinvazivne medicinske diagnostike ter zdravljenja. Prostorsko prikazovanje slik je definirano kot preslikava slikovne informacije iz 3D prostorske domene slike na 2D napravo za prikazovanje (Rubin in dr., 1996, Robb, 2000, Udupa, 2000). Tehnike prikazovanja so naslednje: • 2D prikazovanje slik zdruzˇuje tiste tehnike prikazovanja, kjer so na osnovi 3D slike dolocˇeni tisti 2D prerezi, ki najugodneje prikazujejo izbrane znacˇilnosti slik: - Originalni prerezi prikazujejo originalne slikovne elemente vzolzˇ primarnih ravnin rekonstrukcije. Pri CT so te ravnine ponavadi orientirane precˇno, medtem ko so pri MR orientirane vzporedno z izbrano vzbujevalno ravnino (slika 1.1a, str. 23). - Vecˇravninski prerezi prikazujejo originalne slikovne elemente vzdolzˇ ravnin, ki so pravokotne na primarno ravnino rekonstrukcije. Glede na orientacijo teh ravnin locˇimo precˇne5, stranske6 in cˇelne7 prereze (slika 1.1b, str. 23). - Posˇevni prerezi prikazujejo originalne slikovne elemente vzdolzˇ ravnin, ki oklepajo poljuben kot s primarno ravnino rekonstrukcije (slika 1.1c, str. 23). - Ukrivljeni prerezi (CPR; ang. curved planar reformation) prikazujejo originalne slikovne elemente vzdolzˇ poljubnih ukrivljenih ploskev, ki so raztegnjene in prikazane kot ravnine (slika 1.1d, str. 23). • 3D prikazovanje slik zdruzˇuje tiste tehnike prikazovanja, kjer so na osnovi 3D slike dolocˇene tiste 2D projekcije, ki najugodneje prikazujejo izbrane 3D strukture v sliki: P.1.1 Prikazovanje medicinskih slik 5precˇni prerez: prerez, ki pod pravim kotom precˇka vzdolzˇno os telesa, organa ali strukture; transverzalni, aksialni prerez (slika 1.3, str. 26) 6stranski prerez: prerez, ki poteka vzporedno z ravnino, ki deli telo, organ ali strukturo na leve in desne dele; lateralni, sagitalni prerez (slika 1.3, str. 26) 7cˇelni prerez: prerez, ki poteka vzporedno z ravnino, ki deli telo, organ ali strukturo na anteriorne in posteriorne dele; frontalni, koronalni prerez (slika 1.3, str. 26) 6 Povzetek - Projekcije maksimalne intenzitete (MIP; ang. maximum intensity projection) prikazujejo najvecˇje intenzitete originalnih slikovnih elementov vzdolzˇ vzporednih projekcijskih zˇarkov, ki so pravokotni na poljubno orientirano ravnino projekcije (slika 1.2a, str. 24). - Upodabljanje povrsˇine je prikazovanje povrsˇine strukture v sliki s kombinacijo projekcije geometrijskih primitivov (tocˇka, daljica, trikotnik, poligon) in modelov prikazovanja (barvni model, model sencˇenja). Povrsˇino strukture je potrebo predhodno razgraditi, notranjost strukture pa med prikazovanjem ni vidna (slika 1.2b, str. 24). - Upodabljanje prostornine je neposredno prikazovanje strukture v sliki s kombinacijo projekcije potekov slikovne intenzitete vzdolzˇ projekcijskih zˇarkov ter modelov prikazovanja (barvni model, model sencˇenja, model prosojnosti). Razgradnja povrsˇine strukture ni potrebna, notranjost strukture pa je med prikazovanjem vidna (slika 1.2c, str. 24). Uveljavljene tehnike 2D prikazovanja anatomskih struktur temeljijo na ravninskih (vecˇravninskih in posˇevnih) prerezih 3D slik. Z ravninskimi prerezi pa ne moremo vedno slediti ukrivljenim anatomskim strukturam ali anatomskim strukturam cevaste oblike (npr. hrbtenica, zˇile, cˇrevesje), zato je prikazovanje teh struktur velikokrat nezadovoljivo, saj vsi pomembni deli struktur niso hkrati vidni v enem samem ravninskem prerezu. Posledica tega je lahko nezadostna kakovost diagnosticˇne informacije o opazovanih ukrivljenih strukturah. Resˇitev tega problema je uporaba tehnike prikazovanja z ukrivljenimi prerezi, ki so pravokotni ali tangentni na krivuljo vzdolzˇ strukture. Koordinatni sistem, ki ga dolocˇa 3D slika, je tako preslikan v koordinatni sistem, ki ga dolocˇa opazovana 3D anatomska struktura. Rocˇno orisovanje krivulje, ki sledi ukrivljeni anatomski strukturi, je najenostavnejsˇi nacˇin prikazovanja ukrivljenih prerezov. Tak pristop pa je cˇasovno zamuden ter tezˇaven zaradi kompleksne navigacije v 3D prostoru. Ukrivljeni prerezi se kot tehnika prikazovanja uporabljajo na podrocˇju angiografije8 za prikazovanje zˇil ter za vrednotenje bolezenskih znakov na zˇilah (He in dr., 2001, Kanitsar in dr., 2002, 2003, Maddah in dr., 2003, Ochi in dr., 1999, Raman in dr., 2002, 2003, Saroul in dr., 2003), na podrocˇju pankreatografije9 za prikazovanje in vrednotenje bolezni trebusˇne slinavke (Gong in Xu, 2004, Prokesch in dr., 2002a, 2002b), za prikazovanje mozˇganov (Leonardi in dr., 1991) ter na podrocˇjih bronhoskopije10 (Law in Heng, 2000, Perchet in dr., 2004) in kolonoskopije11 (Ge in dr., 1999, Samara in dr., 1999, Wan in dr., 2002). Natancˇno dolocˇanje krivulje oziroma sredinskega poteka opazovane cevaste strukture (Aylward in Bullitt, 2002, Bitter in dr., 2000) je bistvenega pomena pri vseh pristopih prikazovanja z ukrivljenimi prerezi. Prikazovanje ukrivl- 8angiografija: rentgenski prikaz ozˇilja z vbrizganjem kontrastnega sredstva za diagnosticˇne namene 9pankreatografija: rentgenski prikaz izvodil trebusˇne slinavke z vbrizganjem kontrastnega sredstva 10bronhoskopija: pregled sapnika in bronhialnega vejevja z bronhoskopom, to je opticˇno napravo za opazovanje notranjosti sapnika 11kolonoskopija: vizualni pregled celotnega cˇrevesja s koloskopom, to je podaljsˇanim upogljivim en-doskopom; koloskopija Povzetek 7 jenih prerezov sicer omogocˇajo tudi namenski racˇunalnisˇki programi ter programski paketi proizvajalcev CT in MR skenerjev, vendar pa to zahteva rocˇno orisovanje krivulje, ki sledi ukrivljeni anatomski strukturi. Cˇ eprav MR skenerji omogocˇajo poljubno orientacijo vzbuje-valne ravnine in torej lahko posnemanjo prikazovanje s posˇevnimi prerezi, je tako prikazovanje sˇe vedno odvisno od operaterja, ki orientacijo ravnine nastavi, ter od lege pacienta v skenerju. Poleg tega obstaja tudi mozˇnost pridobivanja ukrivljenih prerezov neposredno iz MR skenerja (Bo¨rnert, 2003, Bo¨rnert in Scha¨ffter, 1996, Jochimsen in Norris, 2002), vendar pa kakovost tako pridobljenih slik, ki so sicer ukrivljene le v eni dimenziji (1D), ni zadovoljiva zaradi nizke prostorske locˇljivosti ter prisotnosti artefaktov intenzitetne modulacije. Razvoj avtomatskih tehnik za prikazovanje slik z ukrivljenimi prerezi lahko torej pomembno prispeva k interpretaciji 3D informacije v medicinskih slikah. P.1.2 Kvantitativno vrednotenje medicinskih slik Kvantitativno vrednotenje slik je izrazˇanje slikovne informacije izbranih merljivih lastnosti slik z numericˇnimi vrednostmi, ki so opremljene z ustreznimi merskimi enotami (Bankman in dr., 2000, Brown in McNitt-Gray, 2000). Znacˇilni primeri so racˇunanje razdalje med tocˇkami ter plosˇcˇine ali prostornine obmocˇja v sliki. Pri obdelavi medicinskih slik kvantitativno vrednotenje obsega merjenje geometrijskih lastnosti izbranih anatomskih struktur (npr. premer krvne zˇile) ali lastnosti, ki so iz teh geometrijskih lastnosti izpeljane (npr. pretok krvi skozi zˇilo). Pomembna podrocˇja uporabe vkljucˇujejo morfometrijo12, racˇunalnisˇko podprto diagnostiko (CAD, ang. computer-aided diagnosis), nacˇrtovanje ter analizo rezultatov zdravljenja, slikovno podprte kirursˇke posege ter posnemanje strukture in funkcije normalnih in patolosˇkih tkiv. Postopki za kvantitativno vrednotenje so najbolj uporabni takrat, kadar so popolnoma avtomatski oziroma zahtevajo cˇim manj rocˇnega poseganja. Poleg racˇunalnisˇkih algoritmov pa so pomembne tudi tehnike za preverjanje tocˇnosti ter zanesljivosti teh algoritmov, saj je potrebno pokazati njihovo klinicˇno vrednost in mozˇnost uporabe. Algoritem je zato potrebno preizkusiti na resnicˇnih slikah, rezultate pa primerjati z referencˇnimi meritvami iste lastnosti, ki jih v istih slikah opravijo strokovnjaki ali posamezniki z ustreznimi izkusˇnjami na izbranem podrocˇju, ali z drugimi referencˇnimi meritvami. Zanesljivost delovanja avtomatskega postopka mora biti primerljiva ali vecˇja od referencˇnih meritev, kar je potrebno potrditi z ustreznimi eksperimenti ter statisticˇno analizo rezultatov. Kvantitativno vrednotenje je bistvenega pomena za objektivno primerjanje merjenih lastnosti med pacienti. Nenazadnje je pa pomembno uposˇtevati tudi ustreznost dobljenih rezultatov v medicinskem okolju. 12morfometrija: merjenje organizma in njegovih delov 8 Povzetek P.2 Prikazovanje in kvantitativno vrednotenje slik hrbtenice P.2.1 Prikazovanje slik hrbtenice Pri pregledovanju 3D slike hrbtenice s tehnikami prikazovanja na osnovi ravninskih prerezov lahko hrbtenica seka stranske ali čelne ravnine, medtem ko prečna ravnina ni vedno postavljena na isto višino vretenčnih teles13 ali medvretenčnih ploščic. Vsi pomembni strukturni deli hrbtenice torej ne morejo biti prikazani hkrati v enem samem prerezu, kar je prisotno že pri prikazovanju normalne hrbtenice zaradi njene naravne ukrivljenosti v obliki črke “S”, bolj pa je poudarjeno v primeru bolezenske ukrivljenosti hrbtenice, na primer pri skoliozi14 ali povečani kifozi15 oziroma lordozi16. Doslej je bilo predstavljenih že veliko načinov prikazovanja CT slik hrbtenice, katerih namen je bil izboljšati kvantitativno ter kvalitativno vrednotenje deformacij hrbtenice. Z uporabo stransko orientiranih poševnih prerezov so Rabassa in dr. (1993) pokazali, da se je prikazovanje medvretenčnih sklepov17 izboljšalo, medtem ko so prečno orientirani poševni prerezi omogočali opazovanje ravnin, vzporednih z medvretenčnimi ploščicami. Čeprav je bilo prikazovanje omejeno na poševne prereze, so avtorji priporočili, da bi le-ti v določenih kliničnih primerih lahko nadomestili uveljavljene večravninske CT prereze, na primer pri vrednotenju stenoze18 medvretenčne odprtine19 ali pri določanju mesta poškodbe hrbtenice. Poševne prereze v vratnem predelu hrbtenice, ki so bili pravokotni na daljšo os leve in desne medvretenčne odprtine, so uporabljali tudi Roberts in dr. (2003a). Z njihovo pomočjo so izboljšali doslednost ter ponovljivost pri interpretaciji stenoze medvretenčne odprtine med različnimi opazovalci ter priporočili uporabo poševnih prerezov v rutinskem vrednotenju tega obolenja (slika 1.5a, str. 29). Rothman in dr. (1984) so pokazali, da so ukrivljeni prerezi, ki so jih pridobili z ročnim povezovanjem točk v krivuljo, zelo uporabni pri določanju dejanskih anatomskih odnosov med strukturami vratnega predela hrbtenice. V posameznem ukrivljenem prerezu so lahko namreč hkrati opazovali hrbtenjačo, korenine živcev, ki izhajajo iz hrbtenjače, ter medvretenčne sklepe. Newton in dr. (2002) so izboljšali prepoznavo ter interpretacijo kongenitalnih20 deformacij hrbtenice s pomočjo ukrivljenih prerezov, določenih z ročnim orisovanjem hrbtenice v večravninskih prerezih. Prednost ukrivljenih v primerjavi z večravninskimi prerezi je bila najbolj izrazita pri hrbtenicah z znatno stransko ali čelno ukrivljenostjo (slika 1.5b, str. 29). Menten in dr. (2005) 13telo vretenca: masivni del vretenca, ki nosi tezˇo in iz njega izhajajo odrastki (slika 1.4, str. 28) 14skolioza: nefiziolosˇka ukrivljenost hrbtenice vstran zaradi misˇicˇnih ali kostnih okvar 15kifoza: ukrivljenost hrbtenice navzad (slika 1.6, str. 30) 16lordoza: ukrivljenost hrbtenice v sprednji smeri (slika 1.6, str. 30) 17medvretencˇni sklep: sklep, sestavljen iz zgornjih in spodnjih sklepnih odrastkov vretenca, ki tvorijo stik s sosednjim vretencem (slika 1.4, str. 28) 18 hrbtenična stenoza: zožitev hrbteničnega kanala z okvaro živčevja zaradi degenerativnih sprememb na hrbtenici 19medvretenčna odprtina: parna stranska odprtina med vretencema za prehod spinalnega živca; interver-tebralni foramen (slika 1.4, str. 28) 20kongenitalen: tisti, ki obstaja že ob rojstvu (deden ali nastal zaradi škodljivih vplivov v nosečnosti) Povzetek 9 so predstavili posebno metodo prikazovanja slik hrbtenice, ki ravno tako temelji na tehniki prikazovanja z ukrivljenimi prerezi. Posebnost je v tem, da so bili ukrivljeni prerezi določeni preko krivulj, ki v slikah prečnih CT prerezov približno sledijo robu hrbteničnega kanala21. Strukture na prednjem ter zadnjem delu hrbtenice so bile na ta način prikazane hkrati, s čimer seje izboljšalo vrednotenje kongenitalnih deformacij hrbtenice. Ročno določanje točk oziroma krivulj, ki določajo potek ukrivljenih prerezov, je skupna lastnost vseh predstavljenih načinov prikazovanja. S polavtomatsko metodo so Kaminsky in dr. (2004) razgrajevali hrbtenico v ukrivljenih prerezih ter se tako izognili težavam z orientacijo v standardih večravninskih prerezih. Preslikava je bila določena s 3D zlepki22, ki so opisovali centralno krivuljo hrbtenice. Krivuljo so določili ročno v stranskih in čelnih prerezih ali pa avtomatsko z iskanjem največjega premera navideznih krogel, postavljenih v telesa vretenc ali vzdolž hrbteničnega kanala. V zadnjih letih je MR postala uveljavljena tehnika zajema slik hrbtenice, saj omogoča pridobivanje 3D slik tako mehkih tkiv kot tudi določenih kostnih struktur hrbtenice z ustrezno nastavitvijo parametrov slikanja (Brown in Semelka, 1999, Grenier in dr., 2005, 2006). Namenske večkanalne tuljave za slikanje hrbtenice pa še dodatno izboljšajo ločljivost ter razmerje signal-šum v slikah (SNR, ang. signal-to-noise ratio). V prikazovanju hrbteničnih nepravilnosti, poškodb ter obolenj MR velikokrat prekaša druge slikovne tehnike, kot sta na primer CT tehnika ali precej invazivna mielografija23. Poleg tega pa je MR še posebej primerna za longitudinalne raziskave ter analize rezultatov zdravljenja, saj pacient ni izpostavljen ionizacijskemu sevanju. Uporaba različnih tehnik prikazovanja se je tudi na področju obdelave MR slik hrbtenice izkazala kot učinkovita. Apicella in Mirowitz (1995) sta poročala, da se večravninski MR prerezi lahko uporabijo za kompenzacijo navidezne asimetrije 3D anatomskih struktur, ki jo povzroči spremenljiva lega pacienta med postopkom zajema, ter da se tak način prikazovanja lahko uporabi pri različnih anatomskih strukturah. V primeru slik hrbtenice bi se lahko uporabili za izboljšanje prikazovanja hrbteničnega kanala ali medvretenčnih odprtin. Da bi se izognili napakam pri merjenju rotacije vretenc, so Birchall in dr. (1997) ter Adam in Askin (2006) na podlagi stranskih in čelnih prerezov ročno določili poševne prereze, ki so potekali vzporedno z zgornjo ali spodnjo vretenčno ploščico24 oziroma vzporedno z vretenčnimi ploščicami skozi središče telesa vsakega vretenca. Liljenqvist in dr. (2002) so se osredotočili na morfologijo25 vretenca, ki je zelo pomembna pri vstavljanju vijakov v pediMe vretenca26 kot dela kirurškega posega pri zdravljenju skolioze (Kuklo in dr., 2005a). Merjenje dolžine, širine ter kota pedikla je potekalo v ročno določenih poševnih MR prerezih, ki so potekali pravokotno na telesa vretenc. hrbtenični kanal: kanal, ki ga oklepajo telesa in loki vretenc ter vsebuje hrbtenjačo in njene ovojnice; vretenčni kanal (slika 1.4, str. 28) 22zlepek: matematična funkcija, določena s odsekoma zveznimi polinomi 23mielografija: rentgenska preiskava prostora hrbtnega mozga s kontrastnim sredstvom 24vretenčna ploščica: tanek sloj hrustanca med površino telesa vretenca ter medvretenčno ploščico na zgornjem ali spodnjem delu telesa vretenca 25morfologija: veda o zgradbi normalnih ali patološko spremenjenih celic, tkiv, organov ali organizmov 26pedikel vretenca: ožji del vretenčnega loka, ki izhaja iz telesa vretenca (slika 1.4, str. 28) 10 Povzetek P.2.2 Kvantitativno vrednotenje slik hrbtenice Kvantitativno vrednotenje parametrov hrbtenice lahko pomembno prispeva k načrtovanju kirurških posegov (Aronsson in dr., 1996, Duke in dr., 2005, Herring in dr., 1998, Tamura in dr., 2005), analizi rezultatov kirurških posegov (Kuklo in dr., 2005b, Lee in dr., 2004, Petit in dr., 2004), spremljanju poteka zdravljenja hrbteničnih obolenj (Asazuma in dr., 2004, Stokes in Aronsson, 2001) ter pri določanju referenčnih vrednosti normalnih ter bolezenskih stanj (Cyteval in dr., 2002, Sevastik in dr., 1995). Med najpomembnejšimi parametri vrednotenja hrbtenice so ukrivljenost hrbtenice, dolžina hrbtenične krivulje, Cobbov kot, položaj središčnih točk teles vretenc ter prečni, stranski in čelni kot rotacije vretenc (Stokes, 1994) (slika 1.7, str. 31). Pri vrednotenju skoliotičnih deformacij pa sta v ospredju predvsem dva parametra, in sicer ukrivljenost hrbtenice ter rotacija vretenc. Ker vzroki za nastanek ter razvoj skolioze, tako kongenitalne kot idiopatične27, še vedno niso povsem znani, je poleg ugotavljanja primernosti obstoječih slikovnih tehnik (Cassar-Pullicino in Eisenstein, 2002, Do in dr., 2001, Schmitz in dr., 2001, Wright, 2000) pomemben tudi razvoj sistemov za razvrščanje skoliotičnih deformacij (Ajemba in dr., 2005, King in dr., 1983, Lenke in dr., 2001, Poncet in dr., 2001, Ramirez in dr., 2006). Nenazadnje je pa pomembno tudi dokazati klinično vrednost takih sistemov razvrščanja (Arlet in dr., 2003, Coonrad in dr., 1998, Edgar, 2002, Ogon in dr., 2002, Richards in dr., 2003). Metode vrednotenja ukrivljenosti hrbtenice so bile najprej razvite za uporabo v čelno orientiranih rentgenskih slikah, saj le-te prikazujejo najpomembnejši del deformacije v primeru skolioze. Ena najstarejših metod merjenja ukrivljenosti, ki je sicer še vedno v uporabi, je Fer-gusonova metoda (Ferguson, 1930). Stopnja deformacije je določena s kotom med premi-cama, ki povezujeta središče apikalnega vretenca s središčema vretenc na konceh deformacije29 (slika 1.8a, str. 33). Greenspanov indeks (Greenspan in dr., 1978) omogoča merjenje ukrivljenosti posameznih vretenc in je zato uporaben za merjenje kratkih segmentov ter relativno šibkih hrbteničnih krivulj. Središči vretenc na konceh deformacije določata hrbtenično premico, na katero se pravokotno določijo dodatne premice skozi središča vretenc na krivulji hrbtenice (slika 1.8b, str. 33). Razmerje vsote dolžin teh premic proti dolžini hrbtenične premice predstavlja merilo (indeks) za deformacijo, ki zavzame pri normalni hrbtenici vrednost nič. Najbolj uveljavljena metoda za vrednotenje ukrivljenosti hrbtenice v čelnih rentgenskih slikah je Cobbova metoda (Cobb, 1948). Stopnjo deformacije določa Cobbov kot, izmerjen med premicama, ki potekata vzporedno z zgornjo vretenčno ploščico na zgornjem koncu deformacije ter vzporedno s spodnjo vretenčno ploščico na spodnjem koncu deformacije (slika 1.8c, str. 33). Hrbtenične krivulje, ki imajo Cobbov kot večji od 10 stopinj, se pojmujejo kot skoliotične. Kljub temu, da so široko v uporabi, vse predstavljene metode temeljijo na ročnem določanju vretenc ter drugih lastnosti hrbtenice, kar se kaže v njihovi relativno visoki variabilnosti ter 27idiopaticˇen: tisti, ki nastane zaradi neznanega vzroka ali neodvisno od drugih bolezni 28apikalno vretence: vretence, ki se nahaja v konici (sredisˇcˇu) deformacije hrbtenice 29vretenci na konceh deformacije: vretenci, ki sta najbolj nagnjeni proti konkavnemu delu deformacije hrbtenice Povzetek 11 nezanesljivosti (Beekman in Hall, 1979, Carman in dr., 1990, Deacon in dr., 1984, Diab in dr., 1995, Morrissy in dr., 1990, Shea in dr., 1998, Stokes in dr., 1993, Wills in dr., 2007, Zmurko in dr., 2003). Po drugi strani pa so bile predstavljene sˇtevilne sˇtudije, kjer so ukrivljenost hrbtenice zaradi njenega zveznega poteka skusˇali opisati z razlicˇnimi matematicˇnimi funkcijami, kot so npr. sinusne funkcije (Drerup in Hierholzer, 1996), zlepki (Kaminsky in dr., 2004, Verdonck in dr., 1998, Yang in dr., 2007), polinomske funkcije (Patwardhan in dr., 1996, Peng in dr., 2005), ter tudi s statisticˇnimi metodami, kot je npr. kriging interpolacija30 (Poncet in dr., 1999). Zanesljivost ter natancˇnost merjenja Cobbovega kota ter sistemov za razvrsˇcˇanje skolioticˇnih deformacij so poskusˇali izboljsˇati s pomocˇjo racˇunalnisˇkih algoritmov (Chockalingam in dr., 2002, Goh in dr., 2000a, Stokes in Aronsson, 2006). Vendar pa je najvecˇji vzrok za nenatancˇnost metode ta, da se relativno zapletena 3D deformacija hrbtenice vrednoti z relativno enostavno meritvijo v enem 2D prerezu, in sicer v cˇelni rentgenski sliki. Cheung in dr. (2002) so poskusˇali izboljsˇati meritve z ugotavljanjem poteka sredinske krivulje hrbtenice na podlagi kombiniranja cˇelne in stransko orientirane rentgenske slike. Poleg rentgenskih slik so ukrivljenost hrbtenice skusˇali vrednotiti tudi v slikah, pridobljenih z drugimi slikovnimi tehnikami, na primer v stereo-radiografskih31 slikah ter stereofotografijah32 hrbta (Asamoah in dr., 2000, Bendels in dr., 2005, Bergeron in dr., 2005, Drerup in Hierholzer, 1994, Gille in dr., 2007, Liljenqvist in dr., 1998, Stokes in dr., 1988, Tredwell in dr., 1999, Zubairi, 2002), v stereoradiografskih slikah prsnega kosˇa (Aykroyd in Mardia, 2003, Boisvert in dr., 2006, Jaremko in dr., 2001) ali v moire´ovih33 ter drugih topografskih slikah hrbta (Kim in dr., 2001, Knott in dr., 2006), ter celo z razlicˇnimi neinvazivnimi primomocˇki, kot je na primer elektrogoniometer34 (Campbell-Kyureghyan in dr., 2005) ali skoliometer35 (Amendt in dr., 1990). Vrednotenje ukrivljenosti hrbtenice je bilo seveda opravljeno tudi v precˇnih CT prerezih slik hrbtenice (Adam in dr., 2005, Verdonck in dr., 1998), ki omogocˇajo kakovostne prikaze 3D geometrije hrbtenice. Slikanje celotne dolzˇine hrbtenice s CT tehniko pa predstavlja precej invaziven pristop zaradi izpostavljanja relativno visoki kolicˇini ionizacijskega sevanja (Brant-Zawadzki, 2002). Pristop, ki temelji na CT slikanju, torej ne pride v posˇtev v primerih, kjer se zahteva vecˇkratni zajem slik (npr. pri spremljanju poteka deformacije ali zdravljenja). Ker pri tehniki MR ionizacijskega sevanja ni, lahko le-ta predstavlja alternativo pri dolocˇanju hrbtenicˇne krivulje (Wessberg in dr., 2006). Vrednotenje rotacij vretenc je bilo najvecˇkrat omejeno na precˇne rotacije, to je rotacije vretenca okoli vzdolzˇne osi hrbtenice. To je v veliki meri tudi vzrok, da je sinonim za precˇno rotacijo 30kriging interpolacija: skupina geostatisticˇnih metod za prostorsko linearno interpolacijo vrednosti nakljucˇnega polja 31stereoradiografija: tehnika zajemanja parov rentgenskih slik, preko katerih se lahko rekonstruira lastnosti objektov v 3D 32stereofotografija: tehinka zajemanja fotografij mrezˇe, ki je projicirana na opazovani objekt pod ra-zlicˇnimi koti, kar omogocˇa opazovanje globine objekta 33moire´ove topografske slike: slike opisujejo obliko 3D objekta na podlagi progastih svetlobnih vzorcev; svetlobo, ki je projicirana na objekt, opazujemo s posebno kamero, svetlostna intenziteta progastih vzorcev pa dolocˇa ekvidistancˇna podrocˇja oddaljenosti od kamere 34elektrogoniometer: naprava za zvezno merjenje kotov v sklepih med okoncˇinami 35skoliometer: naprava za merjenje kota asimetrije trupa 12 Povzetek velikokrat kar izraz “rotacija”. Glede na razpoložljivost tehnologije za zajemanje slik so se razvili različni pristopi k merjenju prečne rotacije v čelnih, stranskih in prečnih ravninskih prerezih. Določanje prečne rotacije v čelnih rentgenskih slikah je med prvimi predstavil Cobb (1948). Metoda je temeljila na določanju položaja trnastega odrastka vretenca36, ki ponavadi lezi na sredini telesa vretenca. Z naraščajočo rotacijo pa se trnasti odrastek prične sukati proti konkavni strani hrbtenične krivulje. Na podlagi delitve telesa vretenca na šest enakih odsekov je bila stopnja prečne rotacije določena z odsekom, ki je vseboval trnasti odrastek (slika 1.9a, str. 35). Podobnega principa se poslužuje metoda, ki sta jo predstavila Nash in Moe (1969), saj temelji na določanju položaja pediklov vretenca. Pedikli, ki ponavadi ležijo na zunanji strani telesa vretenca, se namreč z naraščajočo rotacijo pričnejo premikati proti konveksni strani hrbtenične krivulje (slika 1.9b, str. 35). Predstavljeni metodi sta spodbudili nastanek številnih študij, ki so poskušale vpeljati različne geometrijske principe za kar najbolj natančen opis anatomskih lastnosti vretenc v čelnih rentgenskih slikah ter različne polavtomatske računalniške pristope za izboljšanje natančnosti meritev prečne rotacije vretenc (Benson in dr., 1976, Chi in dr., 2006, Coetsier in dr., 1977, Deacon in dr., 1984, Drerup, 1984, 1985, 1992, Mehta, 1973, Perdriolle in Vidal, 1985, Stokes in dr., 1986). Analiza natančnosti raznovrstnih pristopov (Drerup in Hierholzer, 1992a, 1992b, Ho in dr., 1993, Omeroglu in dr., 1996, Russell in dr., 1990, Skalli in dr., 1995, Weiss, 1995) je pokazala, da je vrednotenje prečne rotacije v čelnih rentgenskih slikah nezanesljivo. Razlog za to je največkrat v tem, da rentgenske projekcije ne dajejo zadovoljive ali dovolj kakovostne informacije o opazovanih anatomskih strukturah. Kljub temu, da stranske rentgenske slike niso primerne za merjenje prečnih rotacij vretenc, se lahko v njih meri stranska rotacija vretenc, to je rotacija okrog osi, ki poteka od leve do desne strani telesa. Na podlagi stranske rotacije se lahko določijo maskimalne vrednosti kifoze in lordoze, naklon križnega predela hrbtenice ter razlike v naklonu med sosednjimi vretenci. Največkrat se je uporabila kar Cobbova metoda (Bernhardt in Bridwell, 1989, Cote in dr., 1997, Korovessis in dr., 1998, Stagnara in dr., 1982) (slika 1.10a, str. 36). Zaradi že omenjenih pomanjkljivosti tega postopka pa so bili predlagani alternativni pristopi. Določanje Cobbovega kota v stereoradiografskih slikah so na primer predstavili De Smet in dr. (1980), Stokes (1989), Dumas in dr. (2004) ter Poncet in dr. (2001). Harrison in dr. (2000) so merili rotacijo na podlagi premic, ki so bile ročno določene tangentno na zadnjo stran izbranih teles vretenc (slika 1.10b, str. 36). V delu Goh in dr. (2000a) je merilo za stransko rotacijo predstavljal povprečni polmer ukrivljenosti dveh krožnih lokov, ki sta potekala skozi ročno določene točke na vogalih vretenčnih teles (slika 1.10c, str. 36). Pinel-Giroux in dr. (2006) so sestavili krivuljo hrbtenice iz štirih krožnih lokov, tangentnih na središča izbranih teles vretenc. Izmerjena rotacija je bila določena s kotom med premicami, ki so povezovale središča krožnih lokov s središči vretenčnih teles, ter referenčno vodoravno premico (slika l.lOd, str. 36). Podoben pristop so predstavili Janik 36trnasti odrastek vretenca: odrastek, ki štrli iz loka mišicam; spinozni procesus vretenca (slika 1.4, str. 28) vretenca navzad in je pripenjališče nekaterim hrbtnim Povzetek 13 in dr. (1998) za ledveno lordozo ter Harrison in dr. (1998, 2002, 2004) za prsno kifozo, kjer so kote določali s pomočjo elips, ki so se kar najbolje prilegale točkam v vogalih vretenčnih teles (slika l.lOe, str. 36). Prince in dr. (2007) so vrednotili stransko rotacijo vretenc z indeksom ki- C v v C v v lože, ki je bil določen kot razmerje med največjo razdaljo hrbtenice do relerencne čelne ravnine ter dolžino premice, ki je povezovala merjeni točki na hrbtenici. Najbolj intuitiven način merjenja prečne rotacije vretenc je vrednotenje v prečnih prerezih (Hei-thoff in Herzog, 1991), vendar je to postalo mogoče šele z razvojem 3D slikovnih tehnik. Izkazalo seje, daje mogoče prečno rotacijo vretenc najbolj natančno določiti v CT slikah (Kris-mer in dr., 1996, Kuklo in dr., 2005b). Prvi poskus merjenja rotacije v prečnih CT prerezih sta predstavila Aaro in Dahlborn (1981). Prečna rotacija je bila določena s kotom med premico, ki V • V V V V v ^7 ^ R v v je potekala skozi stičišče obeh plosc vretencnega loka ' in skozi središče telesa vretenca, ter referenčno stransko ravnino (slika 1.1 la, str. 38). Na podoben način so prečno rotacijo definirali Ho in dr. (1993). Kot, ki sta ga določali premici skozi stičišče vsake plosce vretencnega loka V • V V V V v s pediklom in skozi stičišče obeh plosc vretencnega loka, je bil najprej razpolovljen z dodatno premico. Prečna rotacija je bila nato določena s kotom med to premico ter med referenčno stransko ravnino (slika 1.1 lb, str. 38). Še bolj kompleksna je metoda, ki temelji na ročnem določanju petih značilnih točk anatomije vretenca (Krismer in dr., 1996), in sicer točk v središču telesa vretenca, na koncu trnastega odrastka vretenca, v središču hrbteničnega kanala med obema ploščama vretencnega loka ter točk na najbolj posteriorni in anteriorni39 strani hrbteničnega kanala. Tako izbrane točke so tvorile premice, ki so glede na referenčno stransko krivuljo določale različne kote prečne rotacije (slika 1.1 le, str. 38). Gocen in dr. (1999) so rotacijo definirali s kotom med premico, ki je potekala skozi najbolj posteriorni točki obeh pediklov vretenca, ter referenčno stransko ravnino CT slike (slika 1.1 Id, str. 38). Kljub zelo natančno podanim metodam vrednotenja prečne rotacije so opisane študije zanemarjale dejstvo, da so lahko vretenca zaradi deformacije hrbtenice rotirana tudi v stranski in čelni smeri, kar lahko povzroči napako pri meritvah v obliki “navidezne” prečne rotacije. Skalli in dr. (1995) so primerjali vrednosti, izmerjene v 3D, z vrednostmi, izmerjenimi v 2D, ter ugotovili, da je merjenje prečne rotacije vretenc v prečnih prerezih lahko nenatančno, še posebej v primeru izrazitih stranskih ali čelnih rotacij vretenc. Krismer in dr. (1996) so poročali, da lahko napake pri merjenju nastopijo tudi v primeru popolnoma simetričnih vretenc ter tudi pri v v '•'" v nadomeščanju prečnih prerezov s poševnimi prerezi. Yazici in dr. (2001) so primerjali meritve v prečnih CT prerezih z meritvami v čelnih rentgenskih slikah, pridobljenih pri stoječem in V V v v ležečem položaju pacienta. Ugotovili so, da lega pacienta vpliva na meritve tako v prečnih kot tudi v čelnih prerezih, kar je seveda lahko pojmovano kot dodatna rotacija v 3D. Predlagane računalniško podprte metode za vrednotenje prečne rotacije vretenc v CT slikah plošča vretencnega loka: zadajšnji del vretencnega loka, iz katerega navzad izhaja trnasti odrastek vretenca; lamina arkusa vretenca (slika 1.4, str. 28) 38vretenčni lok: koščeni lok na zadajšnji strani vre- tenca; arkus vretenca 39anterioren: tisti, ki je v telesu pred cˇim ali v sprednjem delu organa; sprednji, ventralen 14 Povzetek so zaradi precejšnjega ročnega poseganja zgolj polavtomatske. Metoda, ki so jo predstavili v v v" v Rogers in dr. (2005), je temeljila na ročnem določanju za meritve najprimernejšega prečnega prereza ter središčne točke rotacije na anteriornem robu hrbteničnega kanala. Rotacija glede na izbrani drugi prerez je bila nato določena z iskanjem največje korelacije slikovnih intenzitet v obeh prerezih (slika 1.12a, str. 40). Kouwenhoven in dr. (2006) so določali prečno rotacijo v' v v v v"v' v slikah normalnih hrbtenic s pomočjo ročno določenih prečnih prerezov skozi središča teles vretenc. Rotacija je bila določena s kotom med premico, kije povezovala središče hrbteničnega V • V V v v kanala s težiščem vretenca, določenega s postopkom razgradnje na osnovi rasti področja, ter med premico, ki je povezovala središče hrbteničnega kanala s prsnico na višini vretenca T540 (slika 1.12b, str. 40). Adam in Askin (2006) sta pravilne vrednosti rotacije v 3D poskušala določiti z uporabo poševnih prerezov, v katerih sta določala naklon premice, kije razpolavljala telo vretenca. Naklon premice je bil določen z iskanjem največje korelacije slikovnih intenzitet v razpolovljenih območjih vretenčnega telesa (slika 1.12c, str. 40). Vrednotenje prečne rotacije vretenc v MR slikah so predstavili Birchall in dr. (1997), ki so za merjenje uporabili tehniko, ki sta jo predlagala Aaro in Dahlborn (1981) za CT slike (slika 1.13a, str. 41). Podobno so Birchall in dr. (2005) določali rotacije v MR slikah z metodo po Hoju in dr. (1993), ki je bila prav tako razvita za CT slike. Metode, ki so jih predstavili Haughton in dr. (2002) ter Rogers in dr. (2002), so temeljile na ročnem določanju prečnega MR v v v v '•'" v prereza ter ročnem določanju središča rotacije ter krožnih področij, ki so zaobjemala vretence. Prečna rotacija vretenca glede na neko drugo vretence je bila izračunana na podlagi iskanja največje korelacije med krožnimi področji obeh vretenc (sliki 1.13b, str. 41 in 1.13c, str. 41). Metodo, ki je temeljila na simetriji vretenca v prečnih MR prerezih, sta predstavila Booth in Clausi (2001). Zasuk vsakega prereza okoli hrbtenjače, ki je torej predstavljala središče rotacije, je bil določen z iskanjem najmanjše povprečne kvadratne razlike slikovnih intenzitet v področjih, ki jih je z razpolavljanjem prereza določala navpična premica skozi hrbtenjačo. Reis-man in dr. (2006) so določali stranske rotacije medvretenčnih ploščic v stranskih MR prerezih, in sicer na podlagi iskanja podobnosti področij slike nad in pod vsako medvretenčno ploščico. Vrednotenje ukrivljenosti hrbtenice ter rotacije vretenc ima pomembno vlogo pri različnih postopkih obdelave slik ter medicinskih raziskavah (Doi in dr., 1997). Zaradi tega je sestavni del različnih raziskav v povezavi s hrbtenico, na primer pri merjenju ravnotežja telesa (Berthonnaud in dr., 2005b, Glassman in dr., 2005b, 2005a, Mac-Thiong in dr., 2003), na področju biomehanične analize hrbtenice (Cholewicki in dr., 1996, Huysmans in dr., 2004, Oda in dr., 2002, Orchowski in dr., 2000, Stokes, 1997, Teo in dr., 2007, Wever in dr., 1999), mor-fometrije vretenc in hrbtenice (Goh in dr., 2000b, Liljenqvist in dr., 2000, Masharawi in dr., 2004, Nojiri in dr., 2005, Parent in dr., 2002, Porter, 2000, Roberts in dr., 2003b, Smyth in dr., 1997, Tan in dr., 2002, 2004), pri združevanju rentgenskih, CT in MR slik hrbtenice (Chen in Wang, 2004, Hu in Haynor, 2004, Hu in dr., 2005, Panigrahy in dr., 2000), rekonstrukciji slik 40hrbtenico sestavlja sedem vratnih vretenc (od C1 ledvenih vretenc (od L1 do L5), krizˇnica ali sakralni do C7), dvanajst prsnih vretenc (od T1 do T12), pet predel ter trticˇne kosti (slika 1.6, str. 30) Povzetek 15 hrbtenice (Benameur in dr., 2005a, 2005b, Bifulco in dr., 2002, Chen in Wang, 2004, Gille in dr., 2007, Huynh in dr., 1997, Novosad in dr., 2004, Perdriolle in dr., 2001) ter pri razgradnji vretenc in hrbtenice (Carballido-Gamio in dr., 2004, Ghebreab in Smeulders, 2004, Herring in Dawant, 2001, Hoad in Martel, 2002, Hoad in dr., 2001, Muggleton in Allen, 1997, Peng in dr., 2005, Yao in dr., 2006, Zamora in dr., 2003, Zheng in dr., 2004). P.3 Motivacija Kljub vsem omenjenim tezˇavam in omejitvam sodobne slikovne tehnike omogocˇajo natancˇnejsˇo diagnostiko ter nacˇrtovanje ucˇinkovitejsˇih strategij zdravljenja hrbtenicˇnih obolenj. Narasˇcˇajocˇe sˇtevilo medicinskih slik ter klinicˇnih informacij spodbuja razvoj metod za racˇunalnisˇko podprto diagnostiko (CAD) (Giger, 2002). Povecˇanje ucˇinkovitosti v interpretaciji teh podatkov, zmanjsˇanje variabilnosti in napak zaradi rocˇnega vrednotenja ter premik od interpretacije proti kvantitativnemu vrednotenju predstavljajo najpomembnejsˇe razloge za razvoj CAD sistemov (Doi in dr., 1997). Racˇunalnisˇko podprto prikazovanje ter kvantitativno vrednotenje 3D slik hrbtenice predstavljata torej velik izziv na podrocˇju analize in obdelave medicinskih slik. P.4 Izvirni prispevki k znanosti Izvirni prispevki te doktorske disertacije zdruzˇujejo nacˇrtovanje, razvoj ter vrednotenje avtomatskih tehnik za izboljsˇanje prikazovanja 3D slik hrbtenice na podlagi dolocˇanja ukrivljenih prerezov ter avtomatskih tehnik za izboljsˇanje kvantitativnega vrednotenja najpomembnejsˇih parametrov hrbtenice v 3D, in sicer ukrivljenosti hrbtenice ter rotacije vretenc. P.4.1 Definicija hrbtenici lastnega koordinatnega sistema Poglavje 2: Avtomatsko prikazovanje 3D slik hrbtenice z ukrivljenimi prerezi Poglavje 3: Avtomatsko dolocˇanje ukrivljenih prerezov v MR slikah hrbtenice Uveljavljene tehnike 2D prikazovanja hrbtenice temeljijo na vecˇravninskih prerezih 3D slik. Vecˇravninski prerezi so ponavadi predstavljeni v kartezicˇnem koordinatnem sistemu (x, y, z), v katerem je vsaka koordinatna os usmerjena vzdolzˇ ali pravokotno na ravnino zajema slike. Z izbiranjem vrednosti na koordinatnih oseh x, y in z lahko prikazujemo pripadajocˇe stranske, cˇelne in precˇne ravninske prereze v koordinatnem sistemu slike. Orientacija koordinatnega sistema je torej odvisna od lege pacienta med zajemom slike ter popolnoma neodvisna od hrbtenice kot opazovane anatomske strukture. Za resˇitev tega problema predlagamo hrbtenici lasten koordinatni sistem (u, v, w), ki je neodvisen od lege pacienta med zajemom slike. Koordinatne osi 16 Povzetek hrbtenici lastnega sistema so usmerjene skladno z anatomijo hrbtenice ter tako hkrati opisujejo geometrijske in klinicˇno pomenljive lastnosti hrbtenice. Koordinatna os u je usmerjena v smeri precˇnih odrastkov vretenca, koordinatna os v v smeri trnastih odrastkov vretenca, koordinatna os w pa v smeri vzdolzˇne osi hrbtenice. P.4.2 Razvoj postopka za avtomatsko prikazovanje CT slik hrbtenice z ukrivljenimi prerezi Poglavje 2: Avtomatsko prikazovanje 3D slik hrbtenice z ukrivljenimi prerezi V tem poglavju je predstavljena avtomatska metoda za prikazovanje CT slik hrbtenice z ukrivljenimi prerezi. Postopek temelji na preslikavi slike iz kartezicˇnega koordinatnega sistema v hrbtenici lasten koordinatni sistem (poglavje P.4.1). Preslikava med koordinatnima sistemoma je dolocˇena na osnovi krivulje, ki poteka skozi sredisˇcˇa teles vretenc, ter na rotaciji vretenc okoli te krivulje. Pri dolocˇanju poteka hrbtenicˇne krivulje smo se oprli na anatomsko lastnost hrbtenice, da so telesa vretenc lokalno najvecˇje kostne strukture v hrbtenici ter da jih je mogocˇe v CT slikah uspesˇno razgraditi. Rotacija vretenc okoli hrbtenicˇne krivulje pa je dolocˇena na podlagi simetrije anatomske strukture vretenca v prerezih, ki so pravokotni na hrbtenicˇno krivuljo. Slednje omogocˇa, da je rotacija vretenc dejansko dolocˇena v 3D. Hrbtenicˇna krivulja ter rotacija vretenc okoli krivulje sta modelirani s polinomskimi funkcijami. Parametre, ki dolocˇajo polinomske funkcije, smo poiskali z optimizacijskimi postopki. Predlagano metodo smo kvalitativno ter kvantitativno vrednotili v petih CT slikah hrbtenice. Rezultati so pokazali, da je metoda ucˇinkovita v primeru normalnih kot tudi bolezenskih hrbtenicˇnih krivulj, ter da so rezultati metode skladni z rocˇno dolocˇenimi vrednostmi za hrbtenicˇno krivuljo in rotacijo vretenc. P.4.3 Razvoj postopka za avtomatsko prikazovanje MR slik hrbtenice z ukrivljenimi prerezi Poglavje 3: Avtomatsko dolocˇanje ukrivljenih prerezov v MR slikah hrbtenice V tem poglavju je predstavljena avtomatska metoda za prikazovanje MR slik hrbtenice z ukrivljenimi prerezi. Metoda temelji na preslikavi slike iz kartezicˇnega koordinatnega sistema v hrbtenici lasten koordinatni sistem (poglavje P.4.1). Preslikava med koordinatnima sistemoma je dolocˇena na osnovi krivulje, ki poteka skozi sredisˇcˇa teles vretenc, ter na rotaciji vretenc okoli te krivulje. Hrbtenicˇna krivulja ter rotacija vretenc okoli krivulje sta modelirani s polinom-skimi funkcijami. Parametri polinomskih funkcij so dolocˇeni z robustno regresijo zacˇetnih ocen polozˇajev sredisˇcˇ vretencˇnih teles ter precˇnih rotacij vretenc. Zacˇetne vrednosti smo dolocˇili z optimizacijski postopki, ki temeljijo na simetriji anatomske strukture vretenca ter homogenosti Povzetek 17 slikovnih intenzitet na področju telesa vretenca in medvretenčnih ploščic v prečnih prerezih MR slik. Predlagano metodo smo kvalitativno in kvantitativno vrednotili v 21 Ti- in T2-uteženih MR slikah. Rezultati so pokazali, da metoda učinkovito opisuje anatomijo hrbtenice. P.4.4 Razvoj postopka za kvantitativno vrednotenje ukrivljenosti hrbtenice v 3D Poglavje 4: Kvantitativna analiza ukrivljenosti hrbtenice v 3D: Uporaba v CT slikah normalne hrbtenice V tem poglavju je predstavljen postopek za kvantitativno vrednotenje ukrivljenosti hrbtenice v 3D. Obstoječe metode za vrednotenje ukrivljenosti hrbtenice so preveč zapletene za klinično uporabo, poleg tega pa deformacijo hrbtenice opisujejo le v 2D, medtem ko lahko s 3D opisovanjem pridobimo bolj celovito oceno o 3D ukrivljenosti hrbtenice. Ukrivljenosti hrbtenice smo vrednotili z geometrijsko ukrivljenostjo (GC, ang. geometric curvature) ter kotom ukrivljenosti (CA, ang. curvature angle) v 30 CT slikah normalne hrbtenice, in sicer na podlagi 3D hrbteničnih krivulj skozi središča teles vretenc, določenih s pomočjo dveh različnih metod. Prva metoda temelji na iskanju krivulje skozi ročno določena središča vretenčnih teles s postopkom najmanjših kvadratov. Pri drugi metodi pa se središča vretenčnih teles avtomatsko določijo s pomočjo optimizacijskega postopka, ki temelji na računalniško podprti analizi slik. V obeh primerih je normalna hrbtenična krivulja opisana s 3D polinomskimi funkcijami četrte stopnje. Bistvena prednost vrednotenja ukrivljenosti hrbtenice z GC in CA je v tem, da so meritve neodvisne od orientacije in velikosti hrbtenice ter tako omogočajo objektivno primerjavo med različnimi hrbteničnimi krivuljami. Poleg tega smo iz porazdelitve vrednosti GC in CA določili tudi položaje največje prsne kifoze (TK, ang. thoracic kyphosis), prsno-ledvenega spoja (TJ, ang. thoracolumbar junction) ter največje ledvene lordoze (LL, ang. lumbar lordosis). P.4.5 Razvoj postopka za avtomatsko določanje položaja in rotacije vretenc v CT in MR slikah hrbtenice Poglavje 5: Določanje 3D položaja in rotacije ledvenih vretenc v CT slikah z avto-poravnavo na osnovi simetrije Poglavje 6: Določanje položaja in rotacije vretenc v 3D neodvisno od tehnike slikanja V teh dveh poglavjih je predstavljena avtomatska metoda za določanje položaja ter rotacije vretenc v CT in MR slikah hrbtenice. Uveljavljene tehnike za določanje rotacije vretenc namreč nezadovoljivo izkoriščajo 3D slikovno informacijo, zaradi česar lahko nastopijo napake pri merjenju prečne rotacije, ki jih povzroči rotacija vretenc v stranski in čelni smeri. Poleg tega se meritve ponavadi opravljajo v ravninskih prerezih ter potrebujejo veliko ročnega poseganja. 18 Povzetek Predlagani pristop k avtomatskemu določanju položaja ter rotacije vretenc v 3D ne potrebuje predhodnega določanja za meritve najustreznejših prerezov ali znanja v obliki statističnih modelov. Različne dele opazovanega vretenca smo zaobjeli z maskami v obliki eliptičnih valjev v 3D. Položaj ter rotacija mask v 3D sta določena s šestimi parametri toge preslikave, in sicer s središčem rotacije (x, y, z) ter koti rotacije (ar,/5, y). Na osnovi razpolavljanja mask z njihovimi sredinskimi prečnimi, stranskimi ter čelnimi ravninami smo vrednotili naravno simetrijo telesa vretenca, hrbtenice ter hrbteničnega kanala, in sicer z robustno togo avto-poravnavo na tak način pridobljenih zrcalnih delov mask. V prvem eksperimentu smo metodo kvantitativno vrednotili na 50 ledvenih vretencih iz CT slik normalne ter skoliotične hrbtenice. V drugem eksperimentu smo metodo vrednotili na 52 vretencih, in sicer na 26 iz CT ter 26 iz MR slik hrbtenice. Rezultati so pokazali, da lahko s predlagano avto-poravnavo simetričnih delov vretenca uspešno določimo 3D položaj ter 3D rotacijo vretenc tako v CT kot tudi v MR slikah hrbtenice. And now, the end is near, and so I face the final curtain. My friend, I’ll say it clear, I’ll state my case, of which I’m certain. Frank Sinatra, 1915 - 1998 (My Way, 1968) CHAPTER 1 Introduction and Summary Medical images are of extreme importance for diagnosing and understanding of normal and pathological conditions of the human body. To some extent, the quality of image-assisted medical examinations depends on the acquisition of images, interpretation of the information present in images and on the research activity and clinical environment that stimulate image formation and its application. In the past decades, advances in medical imaging technology and computerized medical image processing led to the development of new three-dimensional (3D) image acquisition techniques that have become important clinical tools in modern diagnostic radiology and medical health care. Although two-dimensional (2D) images, especially radiographic (X-ray) images, are still widely present in clinical examination due to relatively low acquisition price and wide area of application, they are slowly being replaced by 3D images. The continuous increase in the number of acquired cross-sections, reduction in cross-sectional thickness and relatively short acquisition time (table 1.1, p. 20) led to the expansion of 3D imaging techniques (Sakas, 2002). Among the most important 3D techniques are computed tomography (CT) and magnetic resonance (MR) imaging, which provide qualitative data of the imaged structures. However, characteristic features of these techniques and variable positioning of the patient during image acquisition still represent a major source of variability that causes errors in the interpretation of image information. On the other hand, human capability of discovering and diagnosing diseases by proper interpretation of medical images is limited due to our non-systematic search patterns. 19 20 1 - Introduction and Summary Moreover, the presence of noise may conceal the natural anatomical background, such as actual geometrical relationship between anatomical structures, which may further hamper mental reconstruction of the 3D image information. Errors in interpretation may also be caused by similar characteristics of normal and pathological conditions and by the natural biological variability of human anatomy. Image interpretation therefore depends to a great extent on adequate presentation and measurement of the information about anatomical structures or physiological processes. As the information of interest is often associated with characteristic features of the selected structure or process, it is crucial to use specially designed image processing techniques for visualization and quantitative evaluation. Techniques for visualization and quantitative evaluation of medical images are therefore extremely valuable in the development of image-assisted diagnosis, planning of surgical interventions and assessment of medical treatment outcomes. Table 1.1. The evolution of the CT imaging technique. Tabela 1.1. Razvoj CT slikovne tehnike. Year Innovation Cross-sections Cross-sectional Time per per examination thickness [mm] cross-section [s] 1972 Prototype CT 1 10 240 1981 Clinical CT 20 5 15 1986 Dynamic CT 50 1 8 1989 Spiral CT 300 1 1 1997 Multislice (4) spiral CT 1000 1 0.5 2001 Multislice (16) spiral CT 1000 0.5 0.5 2004 Multislice (64) spiral CT 2000 0.4 0.33 Although current approaches to the treatment of spinal injuries and degenerative spinal disorders reach clinical expectations, the treatment methods are still not entirely adequate (Toyone et al., 2005). Most patients who experience spine-related pain or disability (e.g. low back pain, leg pain) are commonly treated with a combination of pain-relieving drugs and physical therapy, while surgical interventions are the preferred treatment in the case of acute disorders or traumatic spine injuries. However, the results of the treatment are unsatisfactory (e.g. persistent pain, disability) for a relatively large number of patients. The fact that current understanding of physical and biomechanical properties of the spine is inadequate to predict the exact outcomes of various treatment strategies greatly affects the management of spinal disorders. Moreover, the identification, visualization and quantitative evaluation of many spinal diseases by routine examinations is difficult because the spine is a complex and articulated anatomical structure. On the other hand, qualitative insight into the spine anatomy is possible by state-of-the-art im- 1 -Introduction and Summary 21 age acquisition techniques. The CT imaging technique is appropriate for observing the bones and other dense structures of the spine, while the MR imaging technique allows examination of soft tissues, such as intervertebral discs1, spinal cord2 and nerve roots3,4. Further development of spine visualization and quantitative evaluation techniques may therefore improve medical diagnosis and the design of more effective strategies for the treatment of spinal disorders. This thesis concentrates on the design, development and validation of automated techniques that aim to improve the visualization of 3D spine images, and techniques for an improved quantitative evaluation of the most important parameters of the spine in 3D, such as the spinal curvature and vertebral rotation. The fields of visualization and quantitative evaluation of spine images are closely related, as knowledge of spine parameters may provide a more effective spine visualization, and, on the other hand, proper spine visualization may allow a more effective measurement of spine parameters. 1.1 Visualization and quantitative evaluation of images Image formation is defined as the process of mapping selected properties of the imaged object into the image space. The image space represents the basis for visualization of the object and its properties, and may be further used for quantitative evaluation of its structure or function and interpretation of the information it contains. As quantitative evaluation and interpretation of images depend on the quality of the information of interest, the main purpose of image visualization is effective information extraction. In the field of medical image visualization, the extraction of clinically relevant information is therefore of significant importance for the development of accurate and non-invasive techniques for medical diagnosis and treatment. 1.1.1 Visualization of medical images Volumetric image visualization is defined as the transformation of image information from a 3D image space onto a 2D display device (Robb, 2000, Rubin et al., 1996, Udupa, 2000): • 2D image visualization is comprised of techniques that optimally display the selected property of the 3D image in 2D cross-sections: 1intervertebral disc: a disc between two adjacent vertebral bodies that consists of outer cartilage fibers and inner pulpous nucleus; intervertebral fibrocartilage (figure 1.4, p. 28) 2spinal cord: an extension of the central nervous system that consists of nerve cell bodies in the central region and neuronal white matter in peripheral regions, and is protected by the bony spinal canal 3anterior nerve root: the efferent motor root of a spinal nerve, which exits the frontal column of the medulla and joins the posterior nerve root at the inter-vertebral foramen to form a spinal nerve; ventral nerve root 4posterior nerve root: the afferent sensory root of a spinal nerve, which enters into the posterior part of the spinal cord; dorsal nerve root 22 1 - Introduction and Summary Original cross-sections display the primarily reconstructed images, composed of original picture elements (pixels) in image reconstruction planes. In CT imaging, the image planes are usually transversely oriented, while in MR imaging they are usually oriented parallel to the excited slab (figure 1.1a, p. 23). Multiplanar reformations (multiplanar cross-sections) display the originally reconstructed pixels along any arbitrary user-defined orientation that is orthogonal to image reconstruction planes. Depending on the orientation, axial5, sagittal6 and coro-nal7 reformations can be obtained (figures 1.1b, p. 23 and 1.3, p. 26). Oblique reformations (oblique cross-sections) display the originally reconstructed pixels along any arbitrary user-defined plane that is inclined against the image reconstruction plane (figure 1.1c, p. 23). Curved planar reformations (CPRs, curved cross-sections) display the originally reconstructed pixels along any user-defined curved surface that is flattened in order to appear as a plane (figure 1.1d, p. 23). • 3D image visualization is comprised of techniques that optimally display the selected structure in the 3D image in 2D projections: - Maximum intensity projections (MIPs) display the brightest volume element (voxel) intensities along parallel projection lines that are orthogonal to any arbitrary user-defined projection plane (figure 1.2a, p. 24). - Surface renderings display the surface of a structure by combining the projections of geometrical primitives (point, line, triangle, polygon) and visualization models (color effects, shading effects). The interior of the structure is not displayed, however, the structure needs to be pre-segmented (figure 1.2b, p. 24). - Volume renderings display the whole structure by combining the projections of voxel intensities along parallel projection lines and visualization models (color effects, shading effects, transparency effects). The interior of the structure is displayed, while the segmentation of the structure is not required (figure 1.2c, p. 24). The established techniques for 2D visualization of anatomical structures are based on planar (multiplanar and oblique) cross-sections that are obtained from 3D images of the structures. However, planar cross-sections do not always follow curved or tubular anatomical structures 5axial cross-section: a cross-section that is orthogo- p. 26) nal to the longitudinal axis of the body, organ or a struc- 7coronal cross-section: a cross-section that is paral-ture; transverse cross-section (figure 1.3, p. 26) lel to the plane that splits the body, organ or a structure 6sagittal cross-section: a cross-section that is paral- into anterior and posterior parts; frontal cross-section lel to the plane that splits the body, organ or a structure (figure 1.3, p. 26) into left and right parts; lateral cross-section (figure 1.3, 1 -Introduction and Summary 23 (a) (b) (c) (d) Figure 1.1. Examples of 2D volumetric visualization for a CT spine image. (a) Transversely oriented cross-sections. (b) Sagittal and coronal (multiplanar) cross-sections. (c) Oblique cross-sections. (d) Curved cross-sections. Slika 1.1. Primeri 2D prostorskega prikazovanja CT slike hrbtenice. (a) Prečni prerezi. (b) Stranski ter čelni (večravninski) prerezi. (c) Poševni prerezi. (d) Ukrivljeni prerezi. 24 1 - Introduction and Summary (a) (b) (d) (e) (c) (f) Figure 1.2. Examples of 3D volumetric visualization for a CT spine image and a single vertebra. (a),(d) Lateral MIP. (b),(e) Surface rendering. (c),(f) Volume rendering. Slika 1.2. Primeri 3D prostorskega prikazovanja CT slike hrbtenice ter vretenca. (a),(d) Stranska projekcija maskimalne intenzitete (MIP). (b),(e) Upodabljanje povrsˇine. (c),(f) Upodabljanje prostornine. 1 -Introduction and Summary 25 (e.g. spine, arteries, colon). As all of the important parts of the structure are not simultaneously visible in a single planar cross-section, the visualization of such structures is often unsatisfying, which may seriously affect the quality of the diagnostic information of the observed curved structures. The use of CPR visualization technique, which generates cross-sections that are orthogonal or tangent to the curve along the structure, represents a solution to this problem. The standard coordinate system, which is determined by the 3D image, is transformed to a coordinate system that is determined by the observed 3D anatomical structure. Manual determination of the curve that follows the structure represents the easiest way to obtain curved cross-sections. However, manual curve determination is a difficult and time consuming task as it requires complex 3D spatial navigation. As a visualization technique, CPRs are used in the field of angiography8 to display and evaluate blood vessels (He et al., 2001, Kanitsar et al., 2002, 2003, Maddah et al., 2003, Ochi et al., 1999, Raman et al., 2002, 2003, Saroul et al., 2003), in the field of pancreatography9 to display and evaluate pancreatic diseases (Gong and Xu, 2004, Prokesch et al., 2002a,b), for brain visualization (Leonardi et al., 1991), in the field of bronchoscopy10 (Law and Heng, 2000, Perchet et al., 2004) and in the field of colonoscopy11 (Ge et al., 1999, Samara et al., 1999, Wan et al., 2002). In all of the CPR visualization approaches, the determination of the curve that determines the central course of the visualized tubular structure is of utmost importance (Aylward and Bullitt, 2002, Bitter et al., 2000). Dedicated commercial software or software provided by CT and MR scanner manufacturers already allows generation of curved cross-sections, however, this requires manual determination of the curve that follows the anatomical structure. Although MR scanners allow arbitrary orientation of the image plane and can therefore simulate the generation of oblique cross-sections, such visualization is greatly influenced by the scanner operator that determines the orientation of the image plane and by the position of the patient in the scanner. Curved cross-sections can be also acquired directly from the MR scanner (Bo¨rnert, 2003, Bo¨rnert and Scha¨ffter, 1996, Jochimsen and Norris, 2002), however, the quality of the obtained images in not adequate due to low spatial resolution of images, presence of intensity modulation artefacts and the fact that the images can be curved only in one dimension (1D). The development of automated CPR visualization techniques may therefore represent a valuable support in the interpretation of 3D medical image information. 8angiography: radiographic visualization of blood vessels after injection of a radiocontrast material into the blood 9pancreatography: radiographic visualization of the pancreatic ducts after injection of a radiocontrast material into the collecting system 10bronchoscopy: visual examination of the bronchi through a bronchoscope, a slender tubular instrument for inspection of the interior of the bronchi 11colonoscopy: visual examination of the colon with a colonoscope, a long flexible endoscope; coloscopy 26 1 - Introduction and Summary Figure 1.3. Spine orientation. Labels: A - anterior, P - posterior, L - left, R - right, CR -cranial, CD - caudal, a - axial cross-section, s - sagittal cross-section, c - coronal cross-section. Slika 1.3. Orientacija hrbtenice. Oznake: A - spredaj, P - zadaj, L - levo, R - desno, CR -zgoraj, CD - spodaj, a - precˇni prerez, s - stranski prerez, c - cˇelni prerez. 1.1.2 Quantitative evaluation of medical images Quantitative evaluation of images is defined as the expression of selected measurable image properties with numerical values that are equipped with proper measurement units (Bankman et al., 2000, Brown and McNitt-Gray, 2000). Typical examples include the computation of length, area or volume in the image. In the case of medical images, quantitative evaluation represents the measurement of geometrical properties of selected anatomical structures (e.g. the diameter of a blood vessel) or properties that derive from the geometrical properties (e.g. blood flow through a vessel). Important fields of application include morphome-try12, computer-aided diagnosis (CAD), treatment planning, analysis of the treatment outcomes, image-guided surgical interventions and simulation of the structure and function of normal and 12morphometry: measurement of the form of organisms and their parts 1 -Introduction and Summary 27 pathological tissues. Quantitative evaluation techniques are most valuable when they are completely automated or require minimal manual intervention. However, to recognize the medical significance and potential use of (semi)automated techniques, methods for the verification of the accuracy and reliability of such techniques have to be provided. Quantitative evaluation techniques therefore need to be tested on real images and the results compared to reference measurements of the same property, performed in the same images by experts or adequately experienced individuals, or to other reference “gold standard” measurements. The reliability of the automated techniques has to be superior or at least comparable to the reliability of reference measurements, which can be confirmed by properly designed experiments and corresponding statistical tests. Quantitative evaluation is essential for objective comparison of the measured properties among patients. Nevertheless, it is extremely important to consider the relevance of the obtained results in clinical practice. 1.2 Visualization and quantitative evaluation of spine images 1.2.1 Visualization of spine images When visualizing 3D spine images with planar cross-sections, the spine may intersect with sagittal and coronal planes, while the axial plane may not always be located at the same level of the vertebral bodies13 or intervertebral discs. The important structural parts of the spine may therefore not be displayed simultaneously in any single cross-section. This is already the case when visualizing a normal spine due to its natural “S”-shaped curvature, and is even more present in pathological spinal curvatures, for example in case of scoliosis14 or increased kyphosis15 and lordosis16. Many approaches that aim to improve quantitative and qualitative evaluation of spinal deformities by an effective visualization of CT spine images have already been proposed. By generating oblique sagittal cross-sections, Rabassa et al. (1993) showed that visualization of vertebral facet joints17 improved, while oblique axial cross-sections allowed views that were parallel to inter-vertebral discs. Although the visualization was limited to oblique cross-sections, the authors concluded that in certain clinical situations, such as in evaluation of neural foraminal18 steno- 13vertebral body: the largest part of a vertebra from 16lordosis: deformity of the spine in the anterior di-which originate the vertebral processes (figure 1.4, rection (figure 1.6, p. 30) p. 28) 17vertebral facet joint: the vertebral joint between 14scoliosis: complex non-physiological deformity of the superior articular process of one vertebra and the the spine in the lateral direction due to muscular or bone inferior articular process of the adjacent vertebra (fig-anomalies ure 1.4,p.28) 15kyphosis: deformity of the spine in the posterior 18intervertebral foramen: the two apertures between direction (figure 1.6, p.30) every pair of vertebrae for the passage of spinal nerves and blood vessels (figure 1.4, p. 28) 28 1 - Introduction and Summary (a) (b) Figure 1.4. Vertebral anatomy. (a) Axial view from the top. (b) Sagittal view from the right. Labels: A - vertebral body, B - superior end-plate, C - inferior end-plate, D - intervertebral disc, E - transverse process, F - spinous process, G - superior articular process, H - inferior articular process, I - lamina of the vertebral arch, J - pedicle, K - spinal canal, L - intervertebral foramen. Slika 1.4. Anatomija vretenca. (a) Cˇelni pogled z vrha. (b) Stranski pogled z desne. Oznake: - telo vretenca, B - zgornja plosˇcˇica, C - spodnja plosˇcˇica, D - medvretencˇna plosˇcˇica, E -precˇni odrastek, F - trnasti odrastek, G - zgornji sklepni odrastek, H - spodnji sklepni odrastek, I - plosˇcˇa vretencˇnega loka, J - pedikel, K - hrbtenicˇni kanal, L - medvretencˇna odprtina. sis19 or localization of spinal injuries, the reformatted images could supplement the original CT images. Oblique cross-sections that were orthogonal to the long axis of both left and right neural foraminae of the cervical spine region were also generated by Roberts et al. (2003a). They improved the consistency in the interpretation of the neural foraminal stenosis between observers and suggested that oblique cross-sections should be considered in routine evaluation (figure 1.5a, p. 29). Rothman et al. (1984) demonstrated that curved cross-sections, obtained by connecting manually selected points into a continuous curve, were useful in evaluation of anatomical relationships in the coronal spine region. After reformation, structures such as nerve roots, vertebral facet joints and spinal cord could be observed in a single cross-section. Con-genital20 spinal deformities were examined by Newton et al. (2002), who manually outlined the boundaries of the spine in multiplanar cross-sections and created curved cross-sections that improved the identification and interpretation of abnormalities. The benefit of curved cross- 19spinal stenosis: the narrowing of the spinal canal birth (genetic or due to exposure to harmful substances and compression of the nerves due to spine degenera- during pregnancy) tion 21spinal canal: the canal formed by the vertebral bod- 20congenital: a medical condition that is present at ies and vertebral arches that contains the spinal cord; vertebral canal (figure 1.4, p. 28) 1 -Introduction and Summary 29 Source: Robertsetal. (2003a,p.168) Source: Newtonetal. (2002,p.846) (a) (b) Figure 1.5. Examples of oblique and curved planar reformation of CT spine images. (a) Oblique reformation after Roberts et al. (2003a). (b) CPR after Newton et al. (2002). Slika 1.5. Primeri prikazovanja CT slik hrbtenice s posˇevnimi in ukrivljenimi prerezi. (a) Posˇevni prerezi po Robertsu in dr. (2003a). (b) Ukrivljeni prerezi po Newtonu in dr. (2002). sections was, in comparison with multiplanar or oblique cross-sections, most valuable in the case of significant sagittal or coronal curvature of the spine (figure 1.5b, p. 29). Menten et al. (2005) presented a curved planospheric reformation method that was based on reconstruction from a cylindrical plane, defined around the approximate boundary of the spinal canal21 within an axial CT cross-section. As a result, the anterior22 and posterior23 elements of the spine were displayed simultaneously in the same plane, which improved the evaluation of congenital spinal deformities. Manual determination of points or curves that determined the curved cross-sections was required in all of the abovementioned studies. A semi-automated method was presented by Kaminsky et al. (2004), who segmented the spine on reformatted CT images in order to overcome the problems of orientation in the standard multiplanar reformation. The transformation axis was determined by a 3D spline24, obtained either manually by delineating centerlines in sagittal and coronal cross-sections or automatically by dropping spheres of maximum possible radius through the vertebral bodies or spinal canal. Over the past years, MR has become a more dominant modality in spine imaging, providing high-quality 3D images of soft tissues and bone structures of the spine by a correct selection of 22anterior: located in front of another structure or at 24spline: a mathematical function defined piecewise the frontal partofanorgan; ventral bypolynomials 23posterior: located behind another structure or at the rear part of an organ; dorsal 30 1 - Introduction and Summary Figure 1.6. Spine anatomy. Labels: C1. .. C7 - cervical vertebrae, T1.. . T12 - thoracic vertebrae, L1. .. L5 - lumbar vertebrae, S - sacrum, CY - coccyx (tailbone), CL - cervical lordosis, TK - thoracic kyphosis, TJ - thoracolumbar junction, LL - lumbar lordosis, SK - sacral kypho-sis. Slika 1.6. Anatomija hrbtenice. Oznake: C1. .. C7 - vratna vretenca, T1. . .T12 - prsna vretenca, L1.. . L5 - ledvena vretenca, S - krizˇnica, CY - trtica, CL - vratna lordoza, TK - prsna kifoza, TJ - prsno-ledveni spoj, LL - ledvena lordoza, SK - krizˇna kifoza. imaging parameters (Brown and Semelka, 1999, Grenier et al., 2005, 2006). The poor resolution of early MR scanners has been improved by dedicated multichannel spine coils with better signal-to-noise ratio (SNR). Visualization of spinal abnormalities, injuries and diseases is often superior in MR imaging than in other imaging methods, such as CT or the relatively invasive myelography25. Moreover, as the patient is not exposed to ionizing radiation, MR is considered to be the modality of choice for follow-up examinations and longitudinal studies. Image reformation has already been identified as a valuable visualization technique in MR imaging of the spine. Apicella and Mirowitz (1995) reported that multiplanar cross-sections could compensate for the apparent asymmetry of 3D anatomical structures, caused by improper patient positioning or patient motion during image acquisition, and that reformatting can be applied to different anatomical structures. In the case of spine images, they can be used to 25myelography: a radiographic examination of the spinal cord by injecting a radiocontrast material 1- Introduction and Summary 31 improve the visualization of the spinal canal and intervertebral foraminae. In order to avoid measurement errors, Birchall et al. (1997) and Adam and Askin (2006) computed the vertebral rotation from the position of landmarks that were manually placed in each oblique axial cross-section, defined in sagittal and coronal MR cross-sections through the superior and inferior vertebral end-plates26, or parallel to the end-plates through the centers of each vertebral body. Liljenqvist et al. (2002) focused their study on vertebral morphology27, which is of significant importance in the placement of pedicle28 screws as a part of the surgical intervention for the treatment of scoliosis (Kuklo et al., 2005a). The pedicle width, length and angle were measured in manually determined oblique MR cross-sections that were perpendicular to the vertebral bodies. Figure 1.7. Vertebral rotation. Labels: A - anterior, P - posterior, L - left, R - right, CR -cranial, CD - caudal, ?a - axial rotation, ?s - sagittal rotation, ?c - coronal rotation. Slika 1.7. Rotacija vretenca. Oznake: A - spredaj, P - zadaj, L - levo, R - desno, CR - zgoraj, CD - spodaj, ?a - precˇna rotacija, ?s - stranska rotacija, ?c - cˇelna rotacija. 1.2.2 Quantitative evaluation of spine images Quantitative evaluation of spine parameters is important in planning of surgical procedures (Aronsson et al., 1996, Duke et al., 2005, Herring et al., 1998, Tamura et al., 2005), analysis of surgical results (Kuklo et al., 2005b, Lee et al., 2004, Petit et al., 2004), monitoring of the 26vertebral end-plate: a thin layer of cartilage be- 27morphology: the study of the structure of normal tween the surface of a vertebra and the intervertebral or pathological cells, tissues, organs and organisms disc on the superior and inferior part of the vertebral 28vertebral pedicle: the segment between the trans-body (figure 1.4,p.28) verse process and the vertebral body (figure 1.4,p.28) 32 1 - Introduction and Summary progression and treatment of spinal deformities (Asazuma et al., 2004, Stokes and Aronsson, 2001), and for the determination of reference values in normal and pathological conditions (Cyteval et al., 2002, Sevastik et al., 1995). Among the most significant spine parameters are the spinal curvature, the length of the spinal axis, the Cobb angle, the location of the centers of vertebral bodies, and vertebral axial, sagittal and coronal rotation angles (Stokes, 1994) (figure 1.7, p. 31). However, the spinal curvature and vertebral rotation are the most important in the evaluation of scoliotic deformations. As the origin and cause for the progression of both congenital and idiopathic29 scoliosis are still relatively unknown, it is not only important to assess the adequacy of the existing imaging techniques (Cassar-Pullicino and Eisenstein, 2002, Do et al., 2001, Schmitz et al., 2001, Wright, 2000), but also to develop classification systems for scoliotic deformities (Ajemba et al., 2005, King et al., 1983, Lenke et al., 2001, Poncet et al., 2001, Ramirez et al., 2006). Nevertheless, such classification systems have to be tested in order to prove their clinical value (Arlet et al., 2003, Coonrad et al., 1998, Edgar, 2002, Ogon et al., 2002, Richards et al., 2003). As coronal cross-sections display the most significant part of a scoliotic deformity, the methods for evaluation of spinal curvature were first developed for coronal radiographic images. One of the earliest methods, which is still in use nowadays, is the Ferguson method (Ferguson, 1930). The grade of a deformity is determined by the angle between two straight lines that connect the centers of end vertebrae30 with the center of the apical31 vertebra (figure 1.8a, p. 33). The Greenspan index (Greenspan et al., 1978) allows to measure the deformity at each individual vertebra and is therefore valuable in measuring short-segment or small spinal curvatures. The centers of the end vertebrae are connected to form a spinal line, orthogonally to which additional lines are drawn from the center of each vertebra in the spinal curve (figure 1.8b, p. 33). The sum of the lengths of these additional lines is then divided by the length of the spinal line. The obtained value represents the measure (index) of the deformity, which for a normal spine is equal to zero. The most commonly used method for the evaluation of spinal curvature on coronal radiographs is the Cobb method (Cobb, 1948). The Cobb angle is measured between two lines that are tangent to the superior end-plate of the superior end vertebra and to the inferior end-plate of the inferior end vertebra (figure 1.8c, p. 33). Curvatures that result in a Cobb angle greater than 10 degrees are diagnosed as scoliotic. Although the aforementioned methods are still widely in use, they are based on manual identification of the vertebrae and other properties of the spine. As a result, the variability and unreliability of the methods is relatively high (Beekman and Hall, 1979, Carman et al., 1990, Deacon et al., 1984, Diab et al., 1995, Morrissy et al., 1990, Shea et al., 1998, Stokes et al., 1993, Wills et al., 2007, Zmurko et al., 2003). On the other hand, the spinal curvature was due to its continuous course described by various mathematical functions, such as sinusoids (Drerup and Hierholzer, 29idiopathic: a medical condition that arises spontaneously or from an unknown cause 30end vertebrae: the superior (cranial) and inferior (caudal) vertebra without substantial rotation but with maximal tilt towards the concavity of the curve above and below its apex 31apical vertebra: the vertebra located in the apex of the deformity 1- Introduction and Summary 33 1996), splines (Kaminsky et al., 2004, Verdonck et al., 1998, Yang et al., 2007), polynomials (Patwardhan et al., 1996, Peng et al., 2005), and also statistical techniques, such as kriging32 (Poncet et al., 1999). (a) (b) (c) Figure 1.8. Measurement of spinal curvature in frontal radiographic images. (a) Method of Ferguson (1930). (b) Method of Greenspan et al. (1978). (c) Method of Cobb (1948). Slika 1.8. Dolocˇanje ukrivljenosti hrbtenice v cˇelnih rentgenskih slikah. (a) Metoda po Fergu-sonu (1930). (b) Metoda po Greenspanu in dr. (1978). (c) Metoda po Cobbu (1948). Approaches that were supported by computer alogrithms tried to improve the reliability and accuracy of the Cobb angle measurement and classification of scoliotic deformities (Chockalingam et al., 2002, Goh et al., 2000a, Stokes and Aronsson, 2006). However, the inaccuracy of the Cobb method originates from the fact that a relatively complex 3D spinal deformity is evaluated by a relatively simple measurement in a single 2D cross-section, i.e. in a coronal radiographic image. Cheung et al. (2002) proposed to improve the measurements by combining coronal and sagittal radiographs for the estimation of the spinal centerline. The spinal curvature was also estimated in images, acquired by other imaging techniques, for example in stereoradiographic33 images and stereophotographies34 of the back (Asamoah et al., 2000, 32kriging: a group of geostatistical techniques to reconstruction of the properties of an object in 3D interpolate the value of a random field at an unob- 34stereophotography: an imaging technique, where served location from observations of the random field images of a grid projected to the observed object are at nearby locations acquired at different angles, allowing the observation 33stereoradiography: the method of acquiring radio- of the depth of the object; rasterstereography graphs from two slightly different positions that allows 34 1 - Introduction and Summary Bendels et al., 2005, Bergeron et al., 2005, Drerup and Hierholzer, 1994, Gille et al., 2007, Liljenqvist et al., 1998, Stokes et al., 1988, Tredwell et al., 1999, Zubairi, 2002), stereoradio-graphic images of the chest (Aykroyd and Mardia, 2003, Boisvert et al., 2006, Jaremko et al., 2001), or moire´35 and other topographic images of the back (Kim et al., 2001, Knott et al., 2006), and even by various non-invasive instruments, such as the electrogoniometer36 (Campbell-Kyureghyan et al., 2005) or scoliometer37 (Amendt et al., 1990). The evaluation of spinal curvature was also performed in coronal cross-sections that were obtained from CT spine images (Adam et al., 2005, Verdonck et al., 1998), which provide qualitative views of the 3D spine geometry. However, for acquiring whole-length spine images, CT imaging is considered to be an invasive approach due to exposure of a patient to a relatively high dose of ionizing radiation (Brant-Zawadzki, 2002). Therefore, CT imaging is not recommended when multiple image acquisition is required (e.g. in monitoring of the progression of the deformity or treatment). The MR technique was, as a non-radiating alternative for imaging of spinal curvature, studied by Wessberg et al. (2006). The evaluation of vertebral rotation was mostly limited to axial rotation, i.e. the rotation of the vertebrae around the longitudinal spinal axis. As a consequence, axial rotation is often referred to as “rotation”. Depending on the image acquisition technology, various approaches to the measurement of axial vertebral rotation were developed for coronal, sagittal and axial cross-sections. One of the earliest methods for coronal radiographic images was presented by Cobb (1948). The method was based on the determination of the position of the vertebral spinous process38, which is normally located in the middle of the vertebral body. With increasing rotation, the spinous process rotates towards the concave side of the spine curve. The grade of axial vertebral rotation was determined by dividing the vertebral body into six equal segments and identifying the segment that contained the spinous process (figure 1.9a, p. 35). A similar method was proposed by Nash and Moe (1969), where the rotation is quantified on the basis of the position of the vertebral pedicles. The pedicles are normally located in the outer parts of the vertebral body, however, with increasing rotation, they move towards the convex side of the spine curve (figure 1.9b, p. 35). The abovementioned methods stimulated the development of various methods that attempted to improve the description of vertebral anatomy in coronal radiographs by introducing different geometrical principles and various semi-automated computer techniques that attempted to improve the accuracy of axial vertebral rotation measurement (Benson et al., 1976, Chi et al., 2006, Coetsier et al., 1977, Deacon et al., 1984, Drerup, 1984, 1985, 1992, Mehta, 1973, Perdriolle and Vidal, 1985, Stokes et al., 1986). The analysis of the performance of the pro- 35moire´ topographic images: light is projected on the object and observed by a special camera; the shape of a 3D object is described with interference optical patterns, the intensity of which determines areas that are equidistant from the camera 36electrogoniometer: an instrument that measures the axis and range of motion of a joint 37scoliometer: a tool for measuring the angle of trunk asymmetry; inclinometer 38vertebral spinous process: the vertebral process that is directed backward and downward from the junction of the vertebral laminae and serves for the attachment of muscles and ligaments (figure 1.4, p. 28) 1- Introduction and Summary 35 (a) (b) Figure 1.9. Measurement of axial vertebral rotation in coronal radiographic images. Labels: cv - concave side of the spine curve, cx - convex side of the spine curve. (a) Method of Cobb (1948). Grade of vertebral rotation: 0 - normal, 1 - mild, 2 - moderate, 3 - severe. (b) Method of Nash and Moe (1969). Grade of vertebral rotation: 0 - normal, 1 - mild, 2 - moderate, 3 - severe, 4 - marked. Slika 1.9. Dolocˇanje precˇne rotacije vretenc v cˇelnih rentgenskih slikah. Oznake: cv -konkavna stran hrbtenicˇne krivulje, cx - konveksna stran hrbtenicˇne krivulje. (a) Metoda po Cobbu (1948). Stopnja rotacije vretenca: 0 - normalna, 1 - blaga, 2 - zmerna, 3 - mocˇna. (b) Metoda po Nashu in Moeju (1969). Stopnja rotacije vretenca: 0 - normalna, 1 - blaga, 2 - zmerna, 3 - mocˇna, 4 - izrazita. posed techniques (Drerup and Hierholzer, 1992a,b, Ho et al., 1993, Omerogˇlu et al., 1996, Russell et al., 1990, Skalli et al., 1995, Weiss, 1995) proved that the evaluation of axial vertebral rotation in coronal radiographic images is unreliable, which is mostly because the radio-graphic projections do not provide sufficient or qualitative enough information of the observed anatomical structures. Although sagittal radiographic images are not adequate for the measurement of axial vertebral rotation, they can be used to measure sagittal vertebral rotation, i.e. the rotation of the vertebrae around the latitudinal spinal axis, which is the axis from the left to the right part of the body. By measuring sagittal vertebral rotation, maximal values of kyphosis and lordosis, inclination of the sacral spine region and segmental vertebral inclinations can be obtained. The measurements were first performed by the Cobb method (Bernhardt and Bridwell, 1989, Co^te´ et al., 1997, Korovessis et al., 1998, Stagnara et al., 1982) (figure 1.10a, p. 36), however, alternative approaches were proposed due to the already described problems. In the works of De Smet et al. (1980), Stokes (1989), Dumas et al. (2004) and Poncet et al. (2001), the Cobb angle was measured in stereoradiographic images. Harrison et al. (2000) determined the sagittal rotation as 36 1 - Introduction and Summary (a) (b) (c) (d) (e) Figure 1.10. Measurement of sagittal vertebral rotation in sagittal radiographic images. (a) Method of Cobb (1948). (b) Posterior tangent method of Harrison et al. (2000). (c) Mean radius of curvature method of Goh et al. (2000a). (d) Tangent circles method of Pinel-Giroux et al. (2006). (e) Best-fit ellipses of Janik et al. (1998) and Harrison et al. (1998). Slika 1.10. Dolocˇanje stranske rotacije vretenc v stranskih rentgenskih slikah. (a) Metoda po Cobbu (1948). (b) Metoda posteriornih tangent po Harrisonu in dr. (2000). (c) Povprecˇni polmer ukrivljenosti po Gohu in dr. (2000a). (d) Metoda tangentnih krozˇnic po Pinel-Girouxu in dr. (2006). (e) Metoda prilegajocˇih elips po Janiku in dr. (1998) ter Harrisonu in dr. (1998). 1 -Introduction and Summary 37 the angle between the two lines that were manually drawn tangently to the posterior wall of the selected vertebral bodies (figure 1.10b, p. 36). In the work presented by Goh et al. (2000a), the measure for the sagittal rotation was represented by the mean radius of curvature of the two circular arcs through the manually identified points at the corners of vertebral bodies (figure 1.10c, p. 36). Pinel-Giroux et al. (2006) constructed the spine curve from four circular arcs that were tangent to the centers of the selected vertebral bodies. The measured rotation was defined as the angle between the lines that connected the centers of the circular arcs with the centers of vertebral bodies and the reference horizontal line (figure 1.10d, p. 36). A similar approach was proposed by Janik et al. (1998) for lumbar lordosis and Harrison et al. (1998, 2002, 2004) for thoracic kyphosis, who defined ellipses that represented the best-fit to the points at the corners of vertebral bodies (figure 1.10e, p. 36). Prince et al. (2007) evaluated the sagittal vertebral rotation by measuring the kyphosis index, which was determined as the ratio between the maximal distance of the spine to the reference coronal plane and the length of the straight line that connected the measured points on the spine. The measurement of axial vertebral rotation on axial cross-sections is the most intuitive measurement approach (Heithoff and Herzog, 1991), however, it only became possible with the development of 3D imaging techniques. CT proved to be the most accurate imaging technique for the determination of axial vertebral rotation (Krismer et al., 1996, Kuklo et al., 2005b). One of the first attempts for measuring axial vertebral rotation in axial CT cross-sections was proposed by Aaro and Dahlborn (1981). The rotation was determined by the angle between the line that connected the points at the two laminae39 of the vertebral arch40 with the center of the vertebral body and the reference sagittal plane (figure 1.11a, p. 38). A similar method was presented by Ho et al. (1993). The angle, defined between the two lines that connected the junction of each lamina and the pedicle with the junction of the two laminae, was first bisected by a third line. Axial rotation was then measured as the angle between the obtained line and the reference sagittal plane (figure 1.11b, p. 38). Krismer et al. (1996) proposed a more complex method that was based on the determination of five distinctive points, namely the points at the center of the vertebral body, at the tip of the spinous process, at the center of the spinal canal between both laminae and at the most anterior and posterior parts of the spinal canal. The points served to form lines that determined different axial rotation angles, measured against the reference sagittal plane (figure 1.11c, p. 38). Go¨c¸en et al. (1999) defined the axial rotation by the angle between the line that connected the most posterior points of the two pedicles and the reference sagittal plane of the CT image (figure 1.11d, p. 38). Although the axial vertebral rotation was defined by precise procedures, the abovementioned methods ignored the fact that, due to spinal deformities, the vertebrae may be rotated also in sagittal and coronal direction, which may result in measurement errors in the form of an induced “virtual” axial rotation. Skalli et al. (1995) compared the measurements, performed in 39lamina of the vertebral arch: either of the pair of broad plates at the posterior part of the vertebral arch that provide a base for the spinous process (figure 1.4, p. 28) 40vertebral arch: the bony arch at the posterior aspect of a vertebra that supports the vertebral processes 38 1 - Introduction and Summary (a) (c) (b) (d) Figure 1.11. Measurement of axial vertebral rotation in axial CT cross-sections. (a) Method of Aaro and Dahlborn (1981). (b) Method of Ho et al. (1993). (c) Method of Krismer et al. (1996). (d) Method of Go¨c¸en et al. (1999). Slika 1.11. Določanje prečne rotacije vretenc v prečnih CT prerezih. (a) Metoda po Aaroju in Dahlbornu (1981). (b) Metoda po Hoju in dr. (1993). (c) Metoda po Krismerju in dr. (1996). (d) Metoda po Gogenu in dr. (1999). 1 -Introduction and Summary 39 3D, with the measurements, performed in 2D, and concluded that the determination of axial vertebral rotation in axial cross-sections can be inaccurate, especially in the case of strong sagittal or coronal vertebral rotation. Krismer et al. (1996) reported that the measurement errors can also occur when the vertebrae are completely symmetrical and when the measurements in axial cross-sections are replaced with measurements in oblique cross-sections. Yazici et al. (2001) compared the measurements in axial CT cross-sections with the measurements in coronal ra-diographic images, which were acquired in patient’s standing and supine positions. They concluded that patient positioning influences the measurements in both axial and coronal images, which can be considered as an additional rotation in 3D. Computer-assisted methods for the evaluation of axial vertebral rotation in CT images were also proposed, however, they are considered to be semi-automatic as their initialization is based on manual interaction. Besides manual selection of the axial cross-section that was most appropriate for the measurements, the method proposed by Rogers et al. (2005) also required manual determination of the center of rotation at the anterior edge of the spinal canal. After initialization, the method automatically measured the rotation relative to a second cross-section by searching for the maximal correlation of the image intensities between the cross-sections (figure 1.12a, p. 40). Kouwenhoven et al. (2006) determined the axial vertebral rotation in manually selected axial cross-sections through the centers of the vertebral bodies in images of normal spines. The rotation was defined by the angle between the line that connected the center of the spinal canal with the center of vertebral mass, obtained by region growing segementation, and the line that connected the center of the spinal canal with the sternum at the T5 vertebra41 (figure 1.12b, p. 40). Oblique cross-sections were used by Adam and Askin (2006), who measured the axial rotation in 3D by determining the orientation of the line that bisected the vertebral body. The orientation of the line was obtained by the maximal correlation of the image intensities between the bisected areas of the vertebral body (figure 1.12c, p. 40). The evaluation of vertebral rotation in MR spine images was presented by Birchall et al. (1997), who used the technique proposed by Aaro and Dahlborn (1981) for the CT images (figure 1.13a, p. 41). Similarly have Birchall et al. (2005) evaluated the rotation on MR images with the method proposed by Ho et al. (1993), again developed for the CT spine images. The methods proposed by Haughton et al. (2002) and Rogers et al. (2002) required manual selection of the axial MR cross-section and manual determination of the center of rotation and circular areas that encompassed the vertebra. The axial rotation relative to a second vertebra was computed by searching for the maximal correlation of image intensities between circular areas that encompassed the two vertebrae (figures 1.13b, p. 41 and 1.13c, p. 41). A symmetry-based approach to the determination of the position and rotation of vertebrae in each axial MR cross-section was presented by Booth and Clausi (2001). After identifying the spinal cord as the center of rotation in each axial cross-section, the cross-sections were rotated around the spinal cord until 41the vertebral column consists of seven cervical ver- T1 to T12), five lumbar vertebrae (from L1 to L5), the tebrae (from C1 to C7), twelve thoracic vertebrae (from sacrum and the coccyx or the tailbone (figure 1.6, p. 30) 40 1 - Introduction and Summary Source: Rogers et al. (2005, p. 695) Source: Kouwenhoven et al. (2006, p. 1468) (a) (b) Source: Adam and Askin (2006, p. E81) (c) Figure 1.12. Automated measurement of axial vertebral rotation in CT spine images. (a) Method of Rogers et al. (2005). (b) Method of Kouwenhoven et al. (2006). (c) Method of Adam and Askin (2006). Slika 1.12. Avtomatsko dolocˇanje precˇne rotacije vretenc v CT slikah hrbtenice. (a) Metoda po Rogersu in dr. (2005). (b) Metoda po Kouwenhovenu in dr. (2006). (c) Metoda po Adamu in Askinu (2006). obtaining the minimal mean square difference of image intensities in areas that were split by a vertical line through the spinal cord. Reisman et al. (2006) estimated the sagittal rotation of in-tervertebral discs in sagittal MR cross-sections by evaluating the similarity of the regions above and below each intervertebral disc. Quantitative evaluation of spinal curvature and vertebral rotation is important in providing support to various image processing techniques and clinical measurements (Doi et al., 1997), and was therefore part of various spine-related studies, for example in measuring of the trunk balance (Berthonnaud et al., 2005b, Glassman et al., 2005a,b, Mac-Thiong et al., 2003), in the field of spine biomechanics (Cholewicki et al., 1996, Huysmans et al., 2004, Oda et al., 2002, Orchowski et al., 2000, Stokes, 1997, Teo et al., 2007, Wever et al., 1999), 1 -Introduction and Summary 41 Source: Birchall et al. (2005, pp. 124–125) (a) Source: Haughton et al. (2002, p. 1111) (b) Source: Rogers et al. (2002, p. 1073) (c) Figure 1.13. Measurement of axial vertebral rotation in MR spine images. (a) Method of Birchall et al. (2005). (b) Method of Haughton et al. (2002). (c) Method of Rogers et al. (2002). Slika 1.13. Dolocˇanje precˇne rotacije vretenc v MR slikah hrbtenice. (a) Metoda po Birchallu in dr. (2005). (b) Metoda po Haughtonu in dr. (2002). (c) Metoda po Rogersu in dr. (2002). 42 1 - Introduction and Summary spine and vertebral morphometry (Goh et al., 2000b, Liljenqvist et al., 2000, Masharawi et al., 2004, Nojiri et al., 2005, Parent et al., 2002, Porter, 2000, Roberts et al., 2003b, Smyth et al., 1997, Tan et al., 2002, 2004), fusion of radiographic, CT and MR spine images (Chen and Wang, 2004, Hu and Haynor, 2004, Hu et al., 2005, Panigrahy et al., 2000), reconstruction of spine images (Benameur et al., 2005a,b, Bifulco et al., 2002, Chen and Wang, 2004, Gille et al., 2007, Huynh et al., 1997, Novosad et al., 2004, Perdriolle et al., 2001), and spine and vertebral segmentation (Carballido-Gamio et al., 2004, Ghebreab and Smeulders, 2004, Herring and Dawant, 2001, Hoad and Martel, 2002, Hoad et al., 2001, Muggleton and Allen, 1997, Peng et al., 2005, Yao et al., 2006, Zamora et al., 2003, Zheng et al., 2004). 1.3 Motivation Despite all the reported limitations and difficulties, modern imaging techniques help clinicians in making more accurate diagnosis and planning more effective treatment strategies for spinal disorders. Methods of CAD are constantly developed to aid in the interpretation of the increasing amount of medical image data and clinical information (Giger, 2002). Increased efficiency in the interpretation, reduced human variability and error, and making the interpretation more quantitative are among the most important motivations for developing CAD systems (Doi et al., 1997). Computer-assisted visualization and quantitative evaluation of 3D spine images therefore remain challenging tasks in the field of medical image analysis and processing. 1.4 Contributions The main contributions of this thesis are united under the design, development and validation of automated techniques that aim to improve the visualization of 3D spine images by generating curved cross-sections, and automated techniques for an improved quantitative evaluation of the most important parameters of the spine in 3D, namely the spinal curvature and vertebral rotation. 1.4.1 Definition of the spine-based coordinate system Chapter 2: Automated curved planar reformation of 3D spine images Chapter 3: Automated generation of curved planar reformations from MR images of the spine The established techniques for 2D visualization of the spine are based on multiplanar cross-sections, obtained from 3D images. Multiplanar cross-sections are usually displayed in the 1 -Introduction and Summary 43 image-based (Cartesian) coordinate system (x, y, z), where the direction of each axis is determined along or orthogonal to the image acquisition plane. By navigating through the values on the x, y and z axis, corresponding image-based sagittal, coronal and axial planar cross-sections are displayed, respectively. The orientation of the coordinate system therefore depends on the position of the patient during image acquisition and is completely independent of the spine, which is the observed anatomical structure. To overcome these shortcomings, we propose a spine-based coordinate system (u, v, w) that is independent of patient positioning. The coordinate axes are oriented according to the spine and therefore can simultaneously describe geometrical and clinically relevant properties of the spine. The coordinate axis u is oriented in the direction of vertebral transverse processes, the coordinate axis v is oriented in the direction of vertebral spinous processes and the coordinate axis w is oriented along the longitudinal spine axis. 1.4.2 Development of an automated technique for curved planar reformation of CT spine images Chapter 2: Automated curved planar reformation of 3D spine images A method for automated CPR visualization of CT spine images, which is based on the transformation from the standard image-based to the spine-based coordinate system (section 1.4.1), is presented in this chapter. The transformation between the coordinate systems is determined on the curve that passes through the centers of vertebral bodies and on the rotation of the vertebrae around the spine curve, both of which are described by polynomial models. The parametrized spine curve is obtained by exploiting the anatomical property that vertebral bodies are locally the largest bone structures in the spine, which can be successfully segmented in CT images. The rotation of the vertebra around the spine curve is determined by the symmetry of the vertebra in cross-sections which are orthogonal to the spine curve in order to measure the rotation angle in 3D. The optimal polynomial parameters are obtained in an optimization framework. The proposed method was qualitatively and quantitatively evaluated on five CT spine images. The method performed well on both normal and pathological cases and was consistent with the manually obtained ground truth data. 1.4.3 Development of an automated technique for curved planar reformation of MR spine images Chapter 3: Automated generation of curved planar reformations from MR images of the spine A method for automated CPR visualization of MR spine images, which is based on the transformation from the standard image-based to the spine-based coordinate system (section 1.4.1), is 44 1 - Introduction and Summary presented in this chapter. The 3D spine curve and the axial vertebral rotation, which determine the transformation, are described by polynomial functions. The 3D spine curve passes through the centers of vertebral bodies, while the axial vertebral rotation determines the rotation of vertebrae around the axis of the spinal column. The optimal polynomial parameters are obtained by a robust refinement of the initial estimates of the centers of vertebral bodies and axial vertebral rotation. The optimization framework is based on the automatic image analysis of MR spine images that exploits some basic anatomical properties of the spine. The centers of vertebral bodies and the vertebral rotation of vertebrae are determined by evaluating the symmetry of the vertebra and the fact that the vertebral body and intervertebral discs are homogeneous in image intensity when observed in axial cross-sections. The method was evaluated on 21 T1-and T2-weighted MR images from 12 patients and the results provided a good description of spine anatomy. 1.4.4 Development of a framework for quantitative evaluation of spinal curvature in 3D Chapter 4: Quantitative analysis of spinal curvature in 3D: Application to CT images of normal spine A framework for quantitative analysis of spinal curvature in 3D is presented in this chapter. Existing methods for measuring spinal curvature proved to be too complex for clinical environment and provide only 2D description of spinal deformity, while 3D descriptors may yield a more complete assessment of 3D spinal curvature. The 3D descriptors of spinal curvature, namely the geometric curvature (GC) and the curvature angle (CA), were measured on 30 CT images of normal spine in order to observe the characteristics of spine anatomy in 3D. The measurements were determined from 3D vertebral body lines, obtained by two different methods. The first method was based on the least squares techniques that approximated the manually identified vertebra centroids. The second method searched for vertebra centroids in an automated optimization scheme, based on computer-assisted image analysis. Polynomial functions of the fourth degree were used for describing normal spinal curvature in 3D. The main advantage of GC and CA features is that the measurements are independent of the orientation and size of the spine, thus allowing objective intra-subject and inter-subject comparisons. From the distributions of GC and CA, the locations of maximal thoracic kyphosis (TK), thoracolumbar junction (TJ) and maximal lumbar lordosis (LL) were also determined. 1 -Introduction and Summary 45 1.4.5 Development of an automated technique for the determination of the position and rotation of vertebra in CT and MR spine images Chapter 5: Determination of 3D location and rotation of lumbar vertebrae in CT images by symmetry-based auto-registration Chapter 6: Modality-independent determination of vertebral position and rotation in 3D An automated method for the determination of position and rotation of vertebra in 3D from CT and MR spine images is presented in these two chapters. Many established techniques for measuring vertebral rotation do not exploit 3D image information, which may result in virtual axial rotation because of the sagittal and coronal rotations of vertebrae. Moreover, the measured parameters are estimated from planar cross-sections and the methods require a lot of manual interaction. The proposed automated approach to the measurement of the position and rotation of vertebrae in 3D does not require prior volume reformation, identification of appropriate cross-sections or knowledge in the form of statistical models. Different parts of the vertebra under investigation are encompassed by masks in the form of 3D elliptical cylinders. Their position and rotation in 3D is defined by six rigid parameters, namely the center of rotation (x,y,z) and rotation angles (a,J3,y). The natural symmetry of the vertebral body, vertebral column and vertebral canal is obtained by dividing the vertebral masks by their mid-axial, mid-sagittal and mid-coronal planes. The obtained mirror volume pairs are then simultaneously registered to each other by robust rigid auto-registration. In the first experiment, the method was quantitatively evaluated on 50 lumbar vertebrae from normal and scoliotic spine CT images. In the second experiment, the method was tested on 52 vertebrae; 26 were acquired by CT and 26 by MR imaging technique. The results show that by the proposed auto-registration of symmetrical vertebral parts, the 3D position and 3D rotation of vertebrae can be successfully determined in both CT and MR spine images. One man’s “magic” is another man’s engineering. “Supernatural” is a null word. Robert A. Heinlein, 1907 - 1988 (Time Enough for Love, 1973) CHAPTER 2 Automated curved planar reformation of 3D spine images Tomaž Vrtovec, Boštjan Likar and Franjo Perntjs Physics in Medicine and Biology, 50(19):4257-4540, 2005 47 48 2 - Automated curved planar reformation of 3D spine images Abstract Traditional techniques for visualizing anatomical structures are based on planar cross-sections from volume images, such as images obtained by computed tomography (CT) or magnetic resonance (MR) imaging. However, planar cross-sections taken in the coordinate system of the three-dimensional (3D) image often do not provide sufficient or qualitative enough diagnostic information, because planar cross-sections cannot follow curved anatomical structures (e.g. arteries, colon, spine, etc.). Therefore, not all of the important details can be shown simultaneously in any planar cross-section. To overcome this problem, reformatted images in the coordinate system of the inspected structure must be created. This operation is usually referred to as curved planar reformation (CPR). In this paper we propose an automated method for CPR of 3D spine images, which is based on the image transformation from the standard image-based to a novel spine-based coordinate system. The axes of the proposed spine-based coordinate system are determined on the curve that represents the vertebral column, and the rotation of the vertebrae around the spine curve, both of which are described by polynomial models. The optimal polynomial parameters are obtained in an image analysis based optimization framework. The proposed method was qualitatively and quantitatively evaluated on five CT spine images. The method performed well on both normal and pathological cases and was consistent with manually obtained ground truth data. The proposed spine-based CPR benefits from reduced structural complexity in favour of improved feature perception of the spine. The reformatted images are diagnostically valuable and enable easier navigation, manipulation and orientation in 3D space. Moreover, reformatted images may prove useful for segmentation and other image analysis tasks. 2.1 Introduction Traditional techniques for visualizing anatomical structures are based on planar cross-sections from volume images, such as images obtained by computed tomography (CT) or magnetic resonance (MR) imaging. Modern scanners enable acquisition of high-resolution image data for visualization of bony anatomy and soft tissue. However, visualization of a structure of interest is difficult in the standard reformation (axial, sagittal and coronal), and thus planar cross-sections taken in the coordinate system of the three-dimensional (3D) image often do not provide sufficient or qualitative enough diagnostic information. The reason is that because planar cross-sections generally do not follow curved or tubular anatomical structures (e.g. arteries, colon, spine, etc.), not all of the important details can be shown simultaneously in any planar cross-section. For a better visualization of curved structures, reformatted images orthogonal or tangent to a curve along a tortuous 3D structure, i.e. images in the coordinate system of the structure, must be created. This operation is called curved planar reformation (CPR) and can be used to overcome the shortcomings of standard reformation. 2 -Automated curved planar reformation of 3D spine images 49 In CT angiography, curved planar reformation has been widely used for visualization of blood vessels and evaluation of vascular abnormalities. Different CPR methods for visualization of blood vessels, such as projected, stretched and straightened CPR, were described and evaluated by Kanitsar et al. (2002). The authors also proposed a number of enhancements to the existing methods in order to overcome some of their limitations, and continued their work by introducing two advanced CPR methods (Kanitsar et al., 2003). The helical CPR was used to visualize the interior of a blood vessel within a single image, whereas the untangled CPR produced an un-obscured display of a vascular tree regardless of the viewing direction. In Raman et al. (2002), a method capable of automatically producing and interactively displaying curved planar reformations from volumetric image data of blood vessels has been presented. The boundaries of the arteries and branches, found by simple thresholding, were morphologically thinned to obtain the medial centreline between user-specified start and end points. Saroul et al. (2003) extended the notion of CPR to extraction of free form surfaces, defined by user-placed surface boundary curves. While focusing on the visualization of blood vessels, they also mentioned the possibility of using free form surfaces for following non-tubular structures, such as the sternum and the costal cartilage, and irregular anatomical structures, such as the pelvis and the jaw. Their results were, however, limited to the Visible Human data. Recently, these new CPR techniques have been applied to other structures of interest than blood vessels. Gong and Xu (2004) showed that the generation of curved planar reformations could be used for evaluating pancreatic and peri-pancreatic diseases. However, the curved lines that follow the course of the bile–duct system and peripancreatic vessels were drawn manually on stacks of transverse cross-sections. Common to all of the reported methodologies is that the most important issue for CPR visualization is the appropriate and accurate estimation of the centreline of a tubular structure. Besides in an-giography (He et al., 2001, Maddah et al., 2003, Raman et al., 2003), centreline extraction is an important issue in virtual colonoscopy (Ge et al., 1999, Samara et al., 1999, Wan et al., 2002), bronchoscopy (Law and Heng, 2000, Perchet et al., 2004), and can be considered as a common problem (Bitter et al., 2000). General issues were presented by Aylward and Bullitt (2002), who evaluated the effects of initialization, noise and singularities on centreline extraction of tubular objects. In the analysis of spinal structures, a model of the curvature of the vertebral column which describes the spatial relationship between vertebrae may assist high level image analysis, such as segmentation. Ghebreab and Smeulders (2004) stacked models of single vertebrae to construct a model of the spine, which was used to assist segmentation. Determination of the spinal curvature was based on the assumption that surface landmarks occur at approximately the same position on each vertebra and can be therefore connected by a curve. In Benameur et al. (2003b), an a priori geometric model of the whole spine was presented. The model, based on a set of simple cubic templates, whose parameters were given by statistical knowledge on deformations in a scoliotic population, provided an estimation of position and orientation of each vertebra, from which the spine curve could be defined. Different approaches to reformation of CT spine data have been introduced and reported to be useful in assisting the evaluation of spine defor- 50 2 - Automated curved planar reformation of 3D spine images mities. Roberts et al. (2003a) reformatted the image data perpendicular to the long axis of both the left and right neural foramina of the cervical spine segment. They showed that by oblique reformation, consistency in the interpretation of neural foraminal stenosis between observers was improved and suggested that such an approach should be considered in routine evaluation. Congenital spine abnormalities were examined by Newton et al. (2002), who showed that advanced visualization improved the identification of deformities that were inherently difficult to interpret and understand by conventional visualization. By manually outlining the boundaries of the spine curve, they generated curved multiplanar reformatted images that showed the whole spine. The benefit of these images, in comparison with multiplanar (oblique) images, is most valuable in the case of significant sagittal or coronal bending of the spine, as they may help spine surgeons to achieve a more complete understanding and evaluation of spine deformity. Kaminsky et al. (2004) proposed a protocol for spine segmentation composed of standard and novel interactive segmentation tools that were applied on reformatted data. A 3D spline, placed through vertebrae centres, was defined either manually by determining centrelines on sagittal and coronal planes, or automatically by dropping spheres of maximum possible radius through the vertebral bodies or the spinal canal. In order to overcome the problems of orientation in standard reformation, the initial image was reformatted in such a way that the centre spline formed the centre axis of the rotated images. The motivation for the present work was to design, develop and test an automated CPR method for CT spine images with minimal human intervention. We introduce a transformation that converts the standard image-based to a novel spine-based coordinate system. The proposed algorithm automatically extracts the vertebral column curve and the rotation of individual vertebrae around this curve. The algorithm works well on both normal and deformed (e.g. scoliotic) spines. The information gained from the spine curve is then used to reformat the images. The spine curve and the rotation of vertebrae around the curve are not only important for extracting diagnostically important images, but also for easier navigation, manipulation and orientation in 3D space, and for easier identification of the marginal structures of the spine. 2.2 Method 2.2.1 Spine-based coordinate system Usually, 3D images of the spine are inspected and analysed in the standard image-based reformation, represented by the Cartesian coordinate system, where the x, y, and z axes determine the standard sagittal, coronal and axial view, respectively. To inspect the structures in the coordinate system of the spine and to create CPR images, a new spine-based (i.e. spine-specific) coordinate system must be introduced. To render a complete 3D representation of the space, the new coordinate system requires three directional variables, i.e. axes, say u, v and w. The axes 2-Automated curved planar reformationof3Dspine images 51 (a) (b) Figure 2.1. Spine-based coordinate system (u, v, w) (a), determined by the course c(n) and orientation (p(n) of the spine curve, and the corresponding discretization of the spine domain (b). are defined by a continuous curve c(n) = (x(n), y(n), z(n)) that goes through the same anatomical landmarks on individual vertebrae and represents the spine (vertebral column) curve. The continuous independent variable n parametrizes the curve. The coordinate axis w of the spine-based coordinate system (figure 2.1, p. 51) is tangent to the spine curve. The axis v is orthogonal to w, i.e. to the spine curve, and oriented in the direction of vertebral spinous processes. The rotation of the axis v around the curve is determined by the angle (p(n) = (p(v(n),y'(n)) between v and the corresponding projection y' of the Cartesian coordinate y onto the plane P(n), i.e. the plane orthogonal to the spine curve, which is determined by the tangent to the curve (figure 2.1, p. 51). The u axis is orthogonal to v and therefore extends in the direction parallel to the vertebral transverse processes. Both u and v axes lie in the normal plane P(n); hence the axis u is also orthogonal to the axis w. As a result, the direction of the spine-based coordinates (u, v, w), when observed in the Cartesian coordinate system (x,y, z), depends on the spine curve and the vertebrae rotation around the spine curve. To inspect the structures in the spine-based coordinate system we define three spine-based views, which are analogous to the standard sagittal, coronal and axial views in the imagebased Cartesian coordinate system. A spine-based view is a curved two-dimensional (2D) cross-section of the 3D original image, defined by any two of the (u, v, w) axes for a chosen value on the third axis: 52 2 - Automated curved planar reformation of 3D spine images • The spine-based sagittal view is defined by the v and w axes for a chosen value on the u axis. • The spine-based coronal view is defined by the u and w axes for a chosen value on the v axis. • The spine-based axial view is defined by the u and v axes for a chosen value on the w axis. Using any of these views, we can create a 3D spine-based reformatted image by stacking the corresponding 2D cross-sections. For example, if we stack spine-based axial 2D cross-sections, obtained for a selected set of values on the w axis, we obtain the 3D spine-based reformatted image. 2.2.2 Coordinate system parametrization Since the spine curve c(ri) and the rotation ?(ri) of the vertebrae around the spine curve are expected to be smooth functions of n, we parametrize them by the following polynomial functions: K* k Ky k Kz k x(n) = / bxk ^ y(n) = > byk ^ z(n) = > bzk ^ ?(n) = 2, b?,k nk (2.1) k=0 where Kx,Ky,Kz and K?. are the degrees and bx = {bx,k;k = 0, 1,...,Kx}, by = {by,k;k = 0,1,..., Ky], bz = {bz, k; k = 0,1,..., Kz] and b? = {b?, k; k = 0,1,..., K?} are the parameters of polynomials x(n), y(n), z(n) and ?(n), respectively. The polynomial parameters are normalized over the spine domain Q.n, so that a modification of each parameter has the same impact on the absolute variation of the corresponding polynomial term: Q.n \nk\dn. (2.2) The crucial part of the proposed automated spine-based CPR is estimation of the spine-specific parameters b = bx U by U bz U b?, which by equation 2.1 (p. 52) define the parametrized spine curve and the vertebrae rotation. We address this issue in the following sections. For the purpose of implementation, the continuous variable n is discretized. The discrete spine domain consists of jV samples, rii,i = 1,2,. ..,N (figure 2.1, p. 51), which can be transformed 2 -Automated curved planar reformation of 3D spine images 53 to the Cartesian coordinate system by using the discrete form of equation 2.1 (p. 52). After discretization, a discrete spine curve c(n,) = c(xi,yi, z), i = 1,2,...,N and a discrete rotation of vertebrae yj(x) (3.2) SAGITTAL CORONAL SAGITTAL CORONAL 3 -Automated generation of CPRs from MR images of the spine 69 CERVICAL REGION THORACIC REGION LUMBAR REGION 1-" l0'8 f 0-6 «¦ 0-4 (xj,yj) = (239.9,144.3) pixel T; = _2.4° (M, Am) = (18,2 pixel/ring) (xj,yj) = (241.1,323.6) pixel jj = -0.6° (M, Am) = (29,2 pixel/ring) (xj, yj) = (237.5,235.9) pixel jj = -3.9° (M, Am) = (38,2 pixel/ring) (a) (b) (c) Figure 3.2. Detection of the centres of vertebral bodies in cross-sections of the cervical (a), thoracic (b) and lumbar (c) spinal region. The response of the operator ? has a (local) minimum in the centre of the vertebral body. where tan(90c'—yj) is the slope and ^,- is the intersection of the optimal in-plane line of symmetry yj(x) = tan(90° - jj) (x - Xj) with the axis x. Next, the centre of the vertebral body is searched for along the obtained optimal in-plane line of symmetry yj(x) by an operator, sensitive to the circular structure of the vertebral body in the axial cross-section. For a circular structure, a certain intensity variation along any radial direction is always present, while the intensity variation in the direction perpendicular to the radial direction should be relatively small. To estimate these properties of a circular structure, the proposed operator is made of concentric rings. Intensity variation in the direction perpendicular to the radial direction is estimated by the sum of entropies of pixel intensities in individual concentric rings. On the other hand, to estimate the intensity variation along radial directions and to penalize the homogeneous regions, the entropy of the entire operator is also computed. The operator Y, which consists of M concentric rings of radii rm; rm < rm+1; m = 0,1,..., M - 1, is 70 3-Automated generation of CPRs from MR images of the spine defined as: EAf-1 „ 1 = —m= M-1; Wm = ^~12 (V' ) , (3.3) where Hm; Hm = - Y2q=1 Pq,mlogpq,m is the entropy defined by the probability distribution pq>m of intensities in the mth ring, H; H = - Ylq=1 Pq log Pq is the entropy defined by the probability distribution pq of intensities within the entire operator, and Q is the number of bins used for probability estimation. The ring weights wm are chosen to be within S standard deviations of the Gaussian distribution (equation 3.3, p. 70), so that the inner rings have a relatively larger impact to the operator response than the outer ones. The centre (%j, yj(Xj)) = (Xj, 9j) of the vertebral body is found by minimizing the response of the entropy-based operator Y along the line of symmetry yj(x) in plane Pax(Zj): Xj = argmin ^/(Zj)!! (x,yj(x),Zj)). (3.4) Initial estimates of the centres of vertebral bodies {c} = {cj = (Xj,yj,Zj); j = 1,2,... ,Z} and axial vertebral rotations {y} = {yf; j = 1,2,... ,Z} along the spine are obtained by applying the above procedure (equations 3.2, p. 68 and 3.4, p. 70) to all axial cross-sections Pax(z = Zj); j = 1,2,..., Z of the original 3D spine image. 3.3.2 Robust refinement of centres and rotations of vertebrae The initial estimates of the centres of vertebral bodies and axial vertebral rotations, obtained by procedure above, are refined in 3D by robust nonlinear regression. For this purpose, we introduce the continuous 3D spine curve c(n) = (x(ri),y(ri),z(ri)) and axial vertebral rotation ^ where K is the number of voxels in each volume, i1 and i2 are the corresponding voxel intensities in a volume and in its mirror pair, respectively, T = 30 represents the intensity threshold and S w denotes the chosen S [axial], S [sagittal] or S [coronal] symmetry. The maximal joint symmetry, which determines the optimal vertebral parameters popt, was obtained by rigid registration of the mirror volume pairs (equation 5.3, p. 100). Simulated annealing (Press et al., 2002) combined with the simplex method in multidimensions (Press et al., 2002) was used as the registration optimization method (T0 = 3, K = 500, a = 2, Niter = 4). Quantitative evaluation of registration results was achieved by mapping the vertebral parameters p from the 3D image space I into normalized vertebral parameters pn in a six-dimensional (6D) parameter space ln. After normalization, the (x,y,z) = (1,1,1) mm translation and (a,J3,y) = (2,2,2) degrees rotation in I (equation 5.1, p. 98) were represented as a pn = (1,1,1,1,1,1) mm translation in ln. 5.3.3 Experiments Manual determination of vertebral parameters in 3D is a difficult and error-prone task, affected by many factors, such as the mechanical vertebral torsion, asymmetrical vertebral transverse and spinous processes, low resolution in axial image direction and subjective interpretation of each observer. Moreover, a relatively high variability can be induced by interparameter dependency, since the relatively small Ax = 1 mm translation of the center of rotation causes an average 102 5- Determination of 3D location and rotation of vertebrae by symmetry-based auto-registration difference of Ay « 2 degrees in the rotation angle (mask size 2b 1 = 49 mm is taken into account). The manually determined vertebral parameters p1[m] and P2[m] can therefore not be directly used as the reference for quantitative evaluation of the proposed method. In order to obtain the reference vertebral parameters, an initial experiment of N1 = 100 symmetry-based auto-registrations was first performed on each of the 50 lumbar vertebrae. The registration starting positions were defined by uniformly distributed displacements with maximal length of 5 mm in the normalized parameter space In that were randomly generated from the mean P12[m] of the manually determined vertebral parameters. The median vertebral parameters of the displacements that resulted from the registration were then presented to the observers for final verification. If the observers identified that a parameter did not provide a good description of the center of rotation and/or rotation of the vertebrae, the parameter was replaced by the mean of the manually determined parameters. The resulting configuration represented the reference vertebral parameters p[r] that were used for quantitative evaluation of the proposed method in the main registration experiment. The main registration experiment was performed similarly, however, in this case N2 = 1000 uniformly distributed displacements with maximal length of 25 mm in the normalized parameter space ln were randomly generated from the reference vertebral parameters p[r]. The displacements were used as starting positions for the proposed symmetry-based auto-registration of the mirror volume pairs, which were obtained from 3D vertebral masks and contained symmetrical parts of vertebral anatomy. The vertebral parameters that corresponded to the median resulting displacements after registration were quantitatively and qualitatively assessed by comparison to the reference parameters and by the verification by the observers, respectively. In order to simulate manual initialization of the registration starting positions, an additional registration experiment was performed on the scoliotic vertebra L1. The translation parameters t that represent the position of the vertebral center of rotation (equation 5.1, p. 98) were initialized in the vertebral canal, which was simulated by displacing each of the translation parameter independently for +2.5 mm. The rotation parameters (f that represent the vertebral rotation angles (equation 5.1, p. 98) were, on the other hand, always initialized as zero, which corresponds to the manual determination of a point in the 3D image (i.e. pinpointing) approximately at the vertebral center of rotation. The experiment was applied to the scoliotic vertebra because the rotation angles are relatively high when compared to those in normal spines. 5.3.4 Results The differences between the manually determined vertebral parameters p1[m] and P2[m] are presented in table 5.1 (p. 106) as distances in the normalized parameter space ln. The mean difference between observers along all 50 vertebrae is approximately 2.2 mm, which can be considered as an estimate of the uncertainty. This means that the manually determined parameters on average differ for a 2.2 mm translation in a single direction or for a 4.4 degrees 5 - Determination of 3D location and rotation of vertebrae by symmetry-based auto-registration 103 Figure 5.2. Courses of the symmetry-based similarity measure S for lumbar vertebrae in image 8, evaluated by displacing each of the vertebral parameters p = (x, y, z, a,P, y) from the manually determined parameters p1[m]. rotation around a single axis in the 3D image space I. However, by observing the courses of the similarity measure (figure 5.2, p. 103), it can be concluded that the manually determined parameters can nevertheless be used to roughly determine the reference vertebral parameters p^. Most courses have relatively large capture ranges and distinctive maxima in the proximity of the manually determined center of rotation and rotation angles of the vertebrae, which indicates that the proposed symmetry-based similarity measure (equations 5.2, p. 100 and 5.4, p. 101) is feasible for the determination of the 3D location and rotation of vertebrae in CT images. The reference rotation parameters p^ were obtained from the results of N1 = 100 symmetry-based auto-registrations, where the starting positions were defined by the displacements from the mean p12[m] of the manually determined parameters, and are presented in table 5.1 (p. 106) for all 50 vertebrae. The parameters that did not provide a good description of the center of rotation and/or rotation angles of the vertebrae (10 out of 50) and were therefore replaced by the mean of the manually determined parameters, were the translation parameters y or z. This can be explained by the fact that, besides in the center of the vertebral body, the symmetry S [axial] may reach local maxima in adjacent intervertebral discs or even in the adjacent vertebral bodies, which affects directly the translation parameter z. For the parameter y, the symmetry S [coronal] may reach a local maximum when the mask that encompasses the area around the vertebral canal is positioned on the vertebral body (figure 5.2, p. 103). Visual assessment of the results confirmed this explanation. However, this problem could be solved by isolating each vertebra 104 5 - Determination of 3D location and rotation of vertebrae by symmetry-based auto-registration Figure 5.3. Scatter plots of the vertebral parameters before and after registration of N1 = 100 displacements from the mean p12[m] of the manually determined vertebral parameters, presented as distances in the normalized parameter space In for vertebrae in images 8 (left) and 9 (right). Figure 5.4. Scatter plots of the vertebral parameters before and after regsitration of N2 = 1000 displacements from the reference vertebral parameters p[r], presented as distances in the normalized parameter space In for vertebrae in image 8 (top row). The corresponding convergence curves (bottom row) represent the ratio of the successful registration results, defined by the threshold distance dc = V6 ~ 2.45 mm. in the 3D image or by initializing additional 3D vertebral masks that would contribute to the distinctiveness of the correct symmetry maxima. Nevertheless, most of the resulting reference vertebral parameters passed the verification by the observers (40 out of 50) and their normalized values were comparable to the uncertainty of the manually determined parameters. For all 50 vertebrae, the mean of the median displacements d~[1] of the parameters that provided a good description of the vertebrae after registration was 2.3 mm. Figure 5.3 (p. 104) shows the results of this initial registration experiment in the normalized parameter space In for the CT scans 8 and 9. Although the results for the vertebrae in CT image 9 are more dispersed, especially for vertebrae L4 and L5, the resulting median parameters provided a good description of the vertebral location and rotation, which confirms that a relatively high variability may be induced in the manual determination of vertebral parameters. 5 -Determination of 3D location and rotation of vertebrae by symmetry-based auto-registration 105 The results of the main registration experiment, which consisted of symmetry-based auto-registrations of A^2 = 1000 displacements from the reference vertebral parameters p[r], are presented in table 5.1 (p. 106) and shown in figures 5.4 (p. 104) and 5.5 (p. 108) as distances in the normalized parameter space ln. The parameters that did not provide a good description of the center of rotation and/or rotation angles of the vertebrae in the initial experiment also failed do provide such a description in the main experiment. For all 50 vertebrae, the mean of the median displacements d~[2] of the parameters that provided the correct description of the vertebrae after registration was 0.4 mm. Convergence curves (figures 5.4, p. 104 and 5.5, p. 108) represent the cumulative ratio of successful registrations against the number of all registrations. We considered a registration successful when the displacement after registration was less than the threshold distance dc = V6 « 2.45 mm, which represents a 1 mm unit translation of each vertebral parameter in the 6D normalized parameter space In and corresponds to (x,y,z) = (1,1,1) mm translation and (a,J3, y) = (2,2,2) degrees rotation in the 3D image space I. It can be observed that displacements result in successful registrations if they are approximately inside the 5 mm radius of a sphere in the normalized parameter space, centered in the reference vertebral parameters p[r]. Therefore, if manual initialization of the parameters is performed in the 3D image space, the registration will most likely converge when a vertebral parameter is 5 mm translated in a single direction or 10 degrees rotated around a single axis from the reference 3D location and rotation of the vertebra. However, the results show that the registration tends to converge to incorrect optima even when the starting position is less than 5 mm from the reference parameters, e.g. in case of vertebrae L2 and L4 in image 9 as shown in figure 5.5 (p. 108). The inspection of the resulting parameters showed that the registration error was caused by the same reason as in the initial registration experiment. Namely, the error occurred because the translation parameter z converged to the adjacent intervertebral discs, where a relatively high symmetry S [axial] was obtained, and not to the center of the vertebral body. The results of the experiment that simulates manual determination of the vertebral parameters in the vertebral canal on the scoliotic vertebra L1 are presented in table 5.2 (p. 107). The registration results were compared to the mean p12[m] of the manually determined vertebral parameters and show that the largest error occurs in the estimation of vertebral parameters z and y, however, the mean distance d = 2.6 mm in the normalized parameter space ln indicates that the results are within the uncertainty of the manually determined parameters. The purpose of this experiment was to show that by using the proposed symmetry-based auto-registration, vertebral parameters can be obtained when the initialization is represented by pinpointing the approximate position of the vertebral center of rotation in the 3D image (figure 5.6, p. 108). Moreover, the results show that also relatively high vertebral rotation angles, which are in general present in scoliotic vertebrae, can be measured. Table 5.1. Difference d\[m] between the manually determined vertebral parameters, the median displacement d\\\ after registration of N\ = 100 displacements from the mean Pf2[m] °f me manually determined vertebral parameters and the median displacement d[2\ after registration of N2 = 1000 displacements from the reference vertebral parameters p[r], presented as distances in the normalized parameter space In- The parameters that did not provide a good description of the center of rotation and/or rotation angles of the vertebrae are displayed in square brackets below the corresponding values. (Note*: The mean values are computed from the results that provided a good description.) image dA[m] [mm] d[\] [mm] dm [mm] LI L2 L3 L4 L5 LI L2 L3 L4 L5 LI L2 L3 L4 L5 1 2.8 2.2 2.5 1.8 2.4 1.5 1.8 6.9 8.1 5.3 0.3 0.2 6.2 8.0 4.1 [y] [y,z] [y,z] [y,z] 2 2.2 2.7 2.2 2.3 3.9 1.0 1.8 7.6 9.0 5.7 0.2 0.3 6.9 8.1 0.4 3 2.3 1.1 2.0 2.0 2.4 2.1 2.4 1.2 0.9 29.9 0.2 0.3 0.5 0.1 25.1 [y,z] [y,z] 4 3.3 2.6 2.5 2.2 3.0 2.3 1.5 2.4 1.9 2.5 0.4 0.2 0.2 0.2 0.3 5 1.2 2.3 2.4 2.4 2.3 6.2 0.7 1.4 25.3 3.5 5.9 0.2 0.2 40.0 0.5 h b] w bi 6 2.8 0.9 1.5 2.3 3.4 16.8 0.9 1.1 2.2 3.0 14.3 0.3 0.3 0.4 0.4 Iz] [z] 7 2.4 4.1 2.5 3.0 4.1 1.9 2.1 0.7 25.0 30.3 0.2 0.5 0.3 24.8 18.5 [y,z] [y,z] [y,z] [y,z] 8 1.4 2.2 1.1 2.0 5.4 1.7 2.0 1.6 1.7 1.6 0.4 0.2 0.2 0.2 0.4 9 0.9 1.1 2.3 1.1 2.1 10 0.7 1.2 1.1 0.9 2.4 0.8 2.1 2.6 3.2 3.0 0.2 0.5 0.4 1.1 0.3 3.0 1.3 1.6 6.2 6.7 0.3 0.2 0.2 0.4 1.0 mean* 2.0 2.0 2.0 2.0 3.1 1.8 1.7 1.6 2.7 3.9 0.3 0.3 0.3 0.4 0.9 5 -Determination of 3D location and rotation of vertebrae by symmetry-based auto-registration 107 Table 5.2. Results of applying the symmetry-based auto-registration to the scoliotic vertebra L1. The vertebral parameters p[i] before registration, the vertebral parameters p[r] after registration and the corresponding distances d in the normalized parameter space In are relative to the the mean p12[m] of the manually determined parameters. parameters x [mm] y [mm] z [mm] a [deg] jS [deg] 7[deg] d [mm] P12[m] 65.8 52.9 356.5 4.5 -22.5 -8.0 0.0 × Ap[i] 0.0 0.0 0.0 -4.5 +22.5 +8.0 12.2 Ap[r] +0.2 -0.5 -0.5 -0.1 +2.0 - 1.8 1.5 +X Ap[i] Ap[r] +2.5 -1.2 0.0 -0.4 0.0 -3.7 -4.5 +0.6 +22.5 +2.7 +8.0 -2.0 12.4 4.3 -x Ap[i] Ap[r] -2.5 -0.5 0.0 -0.6 0.0 -2.7 -4.5 + 1.2 +22.5 -0.9 +8.0 -3.7 12.4 3.4 +y Ap[i] Ap[r] 0.0 +0.8 +2.5 -0.6 0.0 +0.4 -4.5 +0.1 +22.5 +0.6 +8.0 -0.5 12.4 1.1 Ap[i] 0.0 -2.5 0.0 -4.5 +22.5 +8.0 12.4 y Ap[r] -0.5 -0.5 -2.8 0.0 +0.9 - 1.0 3.0 +z Ap[i] Ap[r] 0.0 +0.9 0.0 -0.9 +2.5 - 1.6 -4.5 +0.7 +22.5 +1.3 +8.0 - 1.4 12.4 2.3 -z Ap[i] Ap[r] 0.0 0.0 0.0 -0.1 -2.5 -2.1 -4.5 -0.1 +22.5 +1.6 +8.0 -3.7 12.4 2.9 Ap[r] 0.0 -0.5 - 1.9 +0.4 1.2 -2.0 mean 2.6 \AP[r]\ 0.6 0.5 2.0 0.5 1.4 2.0 5.4 Conclusions A novel approach to the determination of the 3D location and rotation of vertebrae in CT images was presented. The proposed method does not require prior volume reformation, identification of the most appropriate axial cross-section or aid by high-level prior information, such as statistical shape and/or appearance models. Instead, the method benefits from the natural symmetry of the vertebral anatomy, namely from the symmetry of the vertebra as a whole structure and the symmetry of the vertebral body, vertebral column and vertebral canal. The flexibility in the determination of the 3D vertebral masks that encompass the vertebra or parts of the vertebra under investigation allows that an arbitrary number of masks of different shape, size and 108 5 - Determination of 3D location and rotation of vertebrae by symmetry-based auto-registration displacement before registration [mm] Figure 5.5. Scatter plots of the vertebral parameters before and after registration of N2 = 1000 displacements from the reference vertebral parameters p[r], presented as distances in the normalized parameter space In for vertebrae in image 9 (top row). The corresponding convergence curves (bottom row) represent the ratio of the successful registration results, defined by the threshold distance dc = y6 « 2.45 mm. Figure 5.6. Example of the symmetry-based auto-registration of the scoliotic vertebra L1 in an axial (left), sagittal (middle) and coronal (right) cross-section. The vertebral parameters before (initialization with zero rotation angles) and after registration are shown with vertebral masks in black and white, respectively. 5 -Determination of 3D location and rotation of vertebrae by symmetry-based auto-registration 109 position according to the center of rotation and rotation angles of the vertebra can be determined for evaluation of symmetry. Although the size of the 3D vertebral masks was determined manually, reliable values can be obtained from a large set of vertebrae by statistical analysis of their size (the field of vertebral morphometry). However, it is important to note that a compromise between the number, size and sampling of the vertebral masks regulates the complexity of the computation, as a larger mask size or finer sampling increase the time needed for the computation of the corresponding symmetry. The main drawback of the proposed method is that the reference vertebral parameters, i.e. the reference location and rotation of vertebrae in 3D, used to quantitatively evaluate the performance of the proposed method, can not uniquely defined and therefore may not be treated as a “gold standard”. The same problem is present in existing methods for measuring vertebral rotation, where only local geometrical properties of the vertebral anatomy are usually taken into account, such as the posterior central aspect of the vertebral foramen (Aaro and Dahlborn, 1981), the junction of the inner surfaces of the two laminae (Ho et al., 1993), or the most posterior points of the pedicles (Go¨c¸en et al., 1999). Moreover, even if anatomical landmarks are identified on vertebrae before image acquisition (e.g. markers on cadaveric spines), the selection of landmarks can considerably influence the measured parameter values, as different landmarks result in different centers of rotation and rotation angles. The determination of the reference vertebral parameters therefore represents a difficult and poorly defined problem. On the other hand, we have approached this problem by exploiting global characteristics of the vertebrae, i.e. the natural symmetry that is present in vertebral anatomy. The main purpose of this study was to verify if the natural symmetry of the vertebral anatomy is feasible for determining the 3D location and rotation of vertebrae. The results show that the vertebral parameters can be successfully determined in CT scans of both normal and scoliotic spines, however, determination of some of the parameters (e.g. translation parameters y and z) may need additional attention. The implementation of a more robust symmetry-based similarity measure may represent a solution to this problem and therefore improve the performance of the proposed method. Nevertheless, the possibility of deforming the 3D vertebral masks may be exploited to model more detailed properties of the vertebral anatomy, for example, mask shear and/or twist may provide a good description of mechanical vertebral torsion. Although the method is designed for 3D images of arbitrary modality and for vertebrae of arbitrary spinal sections, an estimation of the performance on other imaging modalities (e.g. MR spine images) and other spinal sections (e.g. on thoracic vertebrae) is needed to confirm such conclusions. The location of vertebrae and vertebral rotation angles are among the most important parameters for the evaluation of spinal deformities and may assist other image analysis methods. The proposed method may therefore aid the measurement of the dimensions of vertebral pedicles, foraminae and canal, and may be a valuable tool for clinical evaluation of the spinal deformities in 3D. 110 5- Determination of 3D location and rotation of vertebrae by symmetry-based auto-registration Acknowledgments This work has been supported by the Ministry of Higher Education, Science and Technology, Slovenia, under grant P2-0232. The authors would like to thank P. Markelj from the University of Ljubljana, Faculty of Electrical Engineering, Slovenia, for the manual determination of vertebral rotation parameters. “I think that one of these days,” he said, “you’re going to have to find out where you want to go. And then you’ve got to start going there. But immediately. You can’t afford to lose a minute. Not you.” Jerome D. Salinger, 1919 – (The Catcher in the Rye, 1951) CHAPTER 6 Modality-independent determination of vertebral position and rotation in 3D Tomaž Vrtovec, Sebastien Ourselin, Boštjan Likar and Franjo Pernuš Submitted for conference presentation. 111 112 6 - Modality-independent determination of vertebral position and rotation in 3D Abstract The determination of position and rotation parameters of vertebrae is important for the understanding of normal and pathological spine anatomy. Existing techniques estimate the parameters from planar cross-sections, are relatively complex or require a lot of manual interaction. We have developed an automated and modality-independent method for the determination of position and rotation of vertebrae in three dimensions (3D) that is based on registration of image intensity gradients, extracted in 3D from symmetrical vertebral parts. The method was evaluated on 52 vertebrae; 26 were acquired by computed tomography (CT) and 26 by magnetic resonance (MR). The results show that by the proposed gradient-based registration of symmetrical vertebral parts, the position and rotation of vertebrae in 3D can be successfully determined in both CT and MR spine images. 6.1 Introduction The determination of position and rotation of individual vertebrae is important for the understanding of the nature of normal and pathological spine anatomy. The Cobb technique (Cobb, 1948) is the most established method for measuring vertebral rotation from radio-graphic images of the spine in cases of scoliotic (Chockalingam et al., 2002, Shea et al., 1998) and kyphotic or lordotic deformities (Bernhardt and Bridwell, 1989, Pinel-Giroux et al., 2006). Techniques that exploit the information in three-dimensional (3D) imaging modalities, such as computed tomography (CT) and magnetic resonance (MR), were proposed in (Birchall et al., 1997, Hecquet et al., 1998, Krismer et al., 1996, Skalli et al., 1995) and further combined with low level image analysis methods (Chockalingam et al., 2002, Kouwenhoven et al., 2006, Pinel-Giroux et al., 2006, Shea et al., 1998). More sophisticated techniques were presented by Rogers et al. (2002), who measured axial vertebral rotation by registering circular areas in two MR axial cross-sections, Benameur et al. (2005b), who determined the vertebral pose by registering statistical shape models of vertebrae to pre-segmented vertebral bodies in stereoradio-graphic images, and Adam and Askin (2006), who defined axial vertebral rotation as the axis of maximum symmetry in axial CT cross-sections. The vertebral center of rotation, located in the mid-sagittal plane at the anterior wall of the vertebral canal (Molna´r et al., 2006) and at the superior vertebral end-plate (Petit et al., 2004), was inherently included in the estimation of vertebral rotation. Although the aforementioned methods aim to exploit the information in 3D, the measurements are still performed in two-dimensional (2D) cross-sections and require a relatively high number of parameters or a lot of manual interaction. Besides manual determination of the center of rotation, the cross-sections are manually selected either from the original images or, in order to reduce the effect of virtual rotation (Hecquet et al., 1998, Skalli et al., 1995) and vertebral torsion (Kouwenhoven et al., 2006, Krismer et al., 1996), from manually reformatted images where cross-sections are perpendicular or tangent to the spine. Moreover, 6 -Modality-independent determination of vertebral position and rotation in 3D 113 the measurements are based on manually identified reference points (e.g. center of the vertebral body and the vertebral canal, extreme points of pedicles and processes), which reflect only local characteristics of vertebral anatomy. The purpose of this study is to develop a method for the determination of position and rotation of vertebrae (i.e. vertebral parameters) that exploits the information available in 3D images, does not require manual interaction and takes into account the global characteristics of vertebral anatomy. We propose and test the performance of an automated, modality-independent method that is based on registration of image intensity gradients that are extracted in 3D from symmetrical vertebral parts. Automated determination of vertebral parameters in 3D may improve clinical diagnosis (e.g. diagnostics of spinal deformities) and support high-level image analysis techniques (e.g. segmentation of vertebrae). 6.2 Method 6.2.1 Vertebral parameters and natural vertebral symmetry The position and rotation of a vertebra in a 3D image can be represented by vertebral parameters p, i.e. by translation parameters t (coordinates x, y and z represent the sagittal, coronal and axial position of the center of rotation, respectively) and rotation parameters (f (angles a, /5 and y represent the rotation around coordinate axes x, y and z, respectively): p = (t,ip) = (x,y,z,Q!,j3,y) . (6.1) Symmetrical volume pairs of vertebral anatomy can be obtained by dividing the vertebral body by the following planes (figure 6.1, p. 114): • The mid-sagittal plane of the vertebral body splits the whole vertebra into symmetrical left and right parts Ix and I'x. • The mid-coronal plane of the vertebral body splits the vertebral body into symmetrical anterior and posterior parts Iy and /'. • The mid-axial plane of the vertebral body splits the vertebral body (and intervertebral discs) into symmetrical cranial and caudal parts Iz and I'. The proposed method is based on the assumption that, if the translation parameters t are defined by the center of vertebral body and the rotation parameters (p are defined by the rotation of vertebra, the vertebral parameters p can be obtained by exploiting the natural symmetry of vertebral anatomy. 114 6 - Modality-independent determination of vertebral position and rotation in 3D axial view sagittal view coronal view Figure 6.1. Division of the vertebral body by mid-sagittal, mid-coronal and mid-axial planes, yielding symmetrical volume pairs Ix-I'x, Iy-Iy and Iz-Iz , respectively. The symmetry captured within two vertebral masks, M1 and M2, is used to determine the vertebral parameters p = (x,y,z, a,/3,y). 6.2.2 Registration of symmetrical vertebral parts For each vertebra, two 3D vertebral masks, defined as elliptical cylinders, are created. The first mask M1 roughly encompasses the whole vertebra and the second mask M2 encompasses the vertebral body. The mid-axial, mid-sagittal and mid-coronal planes of the two masks determine mirror volume pairs that, when the vertebral masks are perfectly aligned with the vertebra (figure 6.1, p. 114), contain symmetrical parts of vertebral anatomy. Therefore, the vertebral masks most correctly estimate the parameters p (equation 6.1, p. 113) when the symmetry within the two masks is maximal. The sagittal (d = x), coronal (d = y) and axial (d = z) symmetry S of the mirror volume pairs Id and Id in the vertebral mask M is estimated by comparing the corresponding intensity gradients of Id and Id (figure 6.2a, p. 115): K K 1 ^ 1 ^ S (Id I'd) =------ (vk • md) (v^ k • md) = — Ivkl v k cos9kcos0fk k=1 (6.2) k=1 where K is the number of voxels in each volume, and 9 and 9' are the angles of the gradient vector v and its corresponding pair v (v' denotes the mirrored vector), respectively, against the directional unit vector md; d = {x,y, z] in the coordinate system of the mask M. The computed symmetry is a measure of similarity of gradient vectors v and v', projected in the selected direction d. The larger are the vectors and the more similar are their directions, the higher is the computed symmetry. 6 - Modality-independent determination of vertebral position and rotation in 3D 115 axial view sagittal view coronal view (a) (b) Figure 6.2. (a) An illustrative example of the computation of the axial symmetry Sz (lz,I'z) for a single point inside the vertebral mask M2. (b) Example of the initialization of vertebral masks for the T7 vertebra in their mid-plane cross-sections. The sum of symmetries over the mid-sagittal (d = x) plane in mask M1, and over the mid-coronal (d - y) and mid-axial (d - z) planes in mask M2, represents the joint symmetry. The joint symmetry is therefore used as a criterion function CF = CF (p) for the rigid registration of the corresponding mirror volume pairs: CF = S (lx,K)\*, + S (lv,I,)\ + S (l7,lC)\ • (6.3) A x \ M1 y y IM2 *¦ z IM2 The criterion function reaches its maximum (figure 6.3, p. 116) at vertebral parameters popt that maximize the joint symmetry of the mirror volume pairs, obtained from the 3D vertebral masks. 6.3 Experiments and results 6.3.1 Data and experiments The proposed method was evaluated on 26 vertebrae from two CT (voxel size 0.7 × 0.7 × 1.0 mm) and 26 vertebrae from two T2-weighted MR (voxel size 0.4 × 0.4 × 3.0 mm) spine images (table 6.1, p. 119). The images were filtered with a Gaussian kernel (? = 2 mm) and the gradients were computed for each voxel. For the purpose of quantitative evaluation of the method, the position and rotation of each vertebra were determined manually (manually determined vertebral parameters pman). The vertebral parameters were normalized, so that the 116 6 - Modality-independent determination of vertebral position and rotation in 3D (a) (b) Figure 6.3. Criterion function CF = CF (p) (joint symmetry), evaluated by displacing each reference vertebral parameter independently, shown for the T7 vertebra from (a) a CT and (b) an MR spine image. The criterion function has rather large capture ranges and distinctive maxima. translation of t = (1, 1, 1) mm and rotation of ? = (2, 2, 2) degrees were represented as a translation of pN = (1, 1, 1, 1, 1, 1) mm in the normalized parameter space (displacement D = ?6 mm). The direction set (Powell’s) method in multidimensions (Niter = 4, ftol = 10-5) was used as the optimization technique in the registration procedure. The sizes of the 3D vertebral masks (figure 6.2b, p. 115) were M1 = (30, 50, 25) mm and M2 = (25, 25, 25) mm (M = (a,b, c), where a and b are the ellipse half-axes and c is the cylinder half-height). Manual determination of vertebral parameters is a difficult and error-prone task, affected by the subjective interpretation of the observer, low image resolution, vertebral torsion, imperfect symmetry of vertebral structures and interdependence of parameters (i.e. the center of rotation affects the rotation angles). An initial experiment of N1 = 50 registrations was therefore performed on each vertebra to obtain the reference vertebral parameters. The registrations were initialized in the manually determined parameters pman, and the starting positions were defined by randomly generated displacements (D1,max = 5 mm), uniformly distributed in the normalized parameter space. The median of the obtained results represented the reference vertebral parameters pre f , which were used for initialization in the main experiment of N2 = 500 registrations on each vertebra (D2,max = 10 mm). The results of the main experiment represented the basis for the quantitative evaluation of the proposed method. 6.3.2 Results The results, presented in table 6.1 (p. 119) for all vertebrae, show that the method was successful on 23 out of 26 vertebrae from CT and on 20 out of 26 vertebrae from MR spine images. The cases of failure were detected by the large median displacement after the initial or main 6 - Modality-independent determination of vertebral position and rotation in 3D 117 (a) (b) (c) (d) Figure 6.4. Scatter plots of the displacements of vertebral parameters from the reference vertebral parameters pre f in the normalized parameter space before and after the main registration ? experiment (N2 = 500), and the corresponding success rates (Dth = 6 ? 2.45 mm), shown for the T7 vertebrae in (a) CT and (b) MR spine images and for the T9 vertebrae in (c) CT and (d) MR spine images. 118 6 - Modality-independent determination of vertebral position and rotation in 3D experiment (D > 10 mm). Visual verification indicated that failures probably occurred due to non-vertebral anatomical structures such as ribs and arteries, which are less or non-symmetrical. Nevertheless, the method was successful for most vertebrae (43 out of 52; 83%), for which the mean of the median displacements after registration from the manually determined vertebral parameters Pman was 2.8 mm (initial experiment N1 = 50) and from the reference vertebral parameters pref 1.3 mm (main experiment N2 = 500). The results also show that the method is more accurate on CT spine images, which may be due to more distinctive intensity edges and higher image resolution in CT than in MR images used in the experiments. Success rates, which are the cumulative ratios of successful registrations against all registrations, were obtained from the scatter plots of the main registration experiment results (figure 6.4, p. 117). A registration was considered successful when the displacement after registration was less than the threshold Dth = V6 ~ 2.45 mm in the normalized parameter space, which corresponds to the translation of t = (1,1,1) mm and rotation of ? = (2,2,2) degrees. The obtained success rates indicated that an arbitrary registration converges if the displacement is lower than Dconv « 2.5 mm, which corresponds to a translation of 2.5 mm in a single direction or a rotation of 5.0 degrees around a single axis from the reference vertebral parameters. 6.4 Discussion We proposed a method for the automated determination of position and rotation of vertebrae in 3D, which are among the most important parameters in the evaluation of spinal deformities. The method is applicable to both CT and MR spine images (i.e. modality-independent method) and exploits global characteristics of vertebral anatomy (i.e. natural symmetry of the vertebra). Moreover, image reformation, manual selection of cross-sections or a priori knowledge in the form of statistical shape models is not required. The size of the vertebral masks can be obtained by statistical analysis of the population. The results show that the position and rotation of vertebrae in 3D can be successfully determined by the proposed gradient-based evaluation of vertebral symmetry. We have recently presented an intensity-based method for evaluation of symmetry on lumbar vertebrae in CT spine images (Vrtovec et al., 2007), where we reported low convergence of y and z translation parameters and, on the other hand, high precision of the method (Dconv « 5.0 mm). Although the proposed gradient-based method improves the distinctiveness of the maxima of the criterion function (figure 6.3, p. 116), a combination of the intensity and gradient-based approaches may result in a method of relatively high success rate and precision, which is the topic of ongoing research. Table 6.1. Median displacements D\ and D% after registration from the manually determined (pman) and reference (Pre/) vertebral parameters, respectively, in the normalized parameter space for the vertebrae in CT and MR spine images (the mark x denotes the unsuccessful parameter estimations). CT MR man )[mm] i>2 (pref) [mm] 1 2 1 2 (Nt = 50) (N2 = 500) Tl Tl 3.1 3.3 0.8 0.9 T2 T2 3.6 2.3 0.9 0.7 T3 T3 2.5 5.0 1.0 1.6 T4 T4 X 1.5 X 1.5 T5 T5 T5 T5 3.5 2.5 3.2 3.0 0.7 X X 1.3 T6 T6 T6 T6 4.6 2.0 4.4 X 0.7 1.1 X X T7 T7 T7 T7 2.0 3.0 3.0 1.9 0.9 1.0 1.2 0.9 T8 T8 T8 T8 2.2 3.7 1.9 1.9 1.0 2.5 1.1 0.7 T9 T9 T9 T9 2.2 1.9 3.0 2.7 1.2 1.6 2.3 1.4 T10 T10 T10 T10 1.7 2.6 2.7 4.2 1.0 2.4 1.7 X Til Til Til Til 2.3 3.9 2.4 3.3 0.7 X 1.2 X T12 T12 T12 T12 1.1 1.1 1.4 3.9 0.7 0.8 0.8 X LI LI LI 2.4 4.9 3.3 0.4 0.7 2.5 L2 L2 L2 1.6 1.9 2.4 0.7 2.3 2.4 L3 L3 2.6 2.1 1.6 2.4 L4 L4 3.8 2.8 0.9 1.9 L5 L5 3.0 5.7 1.7 1.3 mean 2.6 3.0 1.1 1.5 When shall we three meet again, in thunder, lightning, or in rain? When the hurly-burly’s done, when the battle’s lost and won. William Shakespeare, 1564 - 1616 (Macbeth, 1606) CHAPTER 7 Conclusion Automatic analysis of medical images is a wide area of scientific research that aims to develop new clinical tools for modern diagnostic radiology and medical health care. The focus of this thesis was on automatic analysis of three-dimensional (3D) spine images, a relatively specific field in medical image analysis with its own characteristics and requirements. The increasing number of scientific publications over the past years indicates that automatic analysis of spine images is becoming of particular interest. Although current methods for the treatment of spinal injuries and degenerative spinal disorders reach clinical expectations, the methods are still not widely accepted. However, present-day sedentary lifestyle reflects in spine and spine-related diseases affecting more and more people. This is why modern imaging techniques and automated image analysis methods play an important role in diagnosis and treatment planning for spinal disorders. The methods for automated curved planar reformation (CPR) of computed tomography (CT) and magnetic resonance (MR) spine images were presented in chapter 2 and chapter 3, respectively. The main purpose of the proposed automated CPR methods is to reduce the structural complexity in favour of an improved feature perception of the spine, and to provide clinically relevant quantitative analysis of the 3D spine anatomy. Displaying the whole length of the spine within a single two-dimensional (2D) image makes the inspection of images quicker and more precise, while the probability of overlooking certain important features of the spine is reduced. The curvature of the spine and the rotation of vertebrae around the spine curve were obtained 121 122 7 - Conclusion automatically and used to transform the 3D spine images from the image-based to the spine-based coordinate system. The spinal curvature and vertebral rotation are inherent properties of the spine and therefore not affected by rigid body transformations. The generated CPR images are therefore independent of the position of the patient in the scanner and of the orientation of the image acquisition plane. Moreover, when visualizing and inspecting 3D images in the spine-based coordinate system, pathological anatomy is oriented comparable to healthy anatomy, thus facilitating image interpretation and allowing a more objective evaluation and diagnosis of the abnormalities, especially in the case of significant coronal (i.e. scoliosis) or sagittal (i.e. kypho-sis or lordosis) spinal curvatures. CT is a standard orthopaedic modality that provides a good bone contrast but a relatively large radiation dose. On the other hand, MR is a non-invasive alternative that is especially adequate for frequent and whole-body scanning. The proposed spine-based coordinate system is modality-independent and therefore it may be used to join the advantages of both modalities by data fusion, i.e. by merging the CT and MR images of the same patient. Among the most significant parameters that may assist an orthopaedic surgeon in evaluating spinal deformities, is the length of the spinal axis, the Cobb angle, the locations of the centers of vertebral bodies, and vertebral rotation angles, i.e. axial rotation, sagittal and coronal inclination. Besides direct automated localization of the centers of vertebral bodies (i.e. the 3D spine curve) and measurement of axial vertebral rotation, the proposed methods implicitly allow automated measurement of the remaining parameters. The length of the spinal axis can be computed from the arc length, which is a geometrical property of the parameterized 3D spine curve. In case of a scoliotic spinal deformity, the location of the end vertebrae could be extracted from the course of curvature and axial vertebral rotation, allowing the measurement of the Cobb angle. The sagittal and coronal vertebral inclinations can be associated with the inclination of the planes, orthogonal to the 3D spine curve. Furthermore, the knowledge on the location and orientation of the spine in 3D can be exploited by other image analysis techniques and applied in a clinical environment. For example, for the identification and measurement of the dimensions of the spinal canal and the spinal cord, for segmentation methods that model the spinal curvature by taking into account spatial relationships between vertebrae, for statistical shape analysis of vertebrae and/or for the determination of inter- and intra-vertebral rotations. Automated measurement of the spine-specific parameters may therefore provide a complete quantitative representation of the spine in 3D. A framework for quantitative analysis of spinal curvature in 3D was presented in chapter 4. The established methods for quantifying spinal deformities depend on various factors that induce high variability in the measurements (e.g. correct identification of the end vertebrae, determination of vertebral end-plate inclination). Besides, the methods are associated with a large number of clinically unintuitive parameters and/or require a relatively high degree of user interaction (e.g. precise outlining or drawing tangent lines to vertebral bodies). Moreover, although spinal curvatures can occur in an arbitrary plane, they are usually evaluated separately in either coronal or sagittal image plane, therefore in 2D. This requires the images to be uniform in orientation and size, which can be achieved by a standardized image acquisition process. On the 7 -Conclusion 123 other hand, descriptors that measure the spinal curvature in 3D and are independent of the orientation and size of the spine may allow a more general (e.g. using images of different modality) and more objective (e.g. measuring the curvature in multiple image planes) evaluation of spinal deformities. The main advantage of the presented 3D descriptors of geometric curvature (GC) and curvature angle (CA) is that the measurements are independent of the orientation and size of the spine. The acquisition of images is therefore not required to be standardized, thus allowing a comparison between images with different properties (e.g. different scanners, acquisition parameters, patient orientation, spinal deformities, clinical environments). The measures also do not depend on vertebral body or intervertebral disc shape, or vertebral end-plate inclination, but solely on the global properties of the 3D vertebral body lines, which were obtained by two different methods. The least squares fitting (LSF) method is based on spatial coordinates of vertebra centroids, which are clinically intuitive and can be unambiguously defined on images of different size, dimensionality (e.g. 2D or 3D images) and modality (e.g. radiographs, CT or MR images). However, the identification of vertebra centroids is a process that requires clinical experience and a relatively high amount of user interaction. The proposed automated edge distance optimization (EDO) method is an example of how computer-assisted image analysis techniques can be used to overcome these problems. The parametric description of the 3D vertebral body line may be useful in different applications and studies. Moreover, the analysis can be reduced to 2D without losing the independence of the orientation and size by observing the 3D vertebral body line separately in sagittal and coronal image planes. If the exact location of the thoracolumbar junction (TJ) was automatically identified, automated evaluation of total thoracic kyphosis (TK) and total lumbar lordosis (LL) may be possible. By comparing an arbitrary spine anatomy to the mean GC and CA values over a healthy population, the presence and exact location of hyperkyphosis and/or hyperlordosis may be easily identified and more objectively evaluated. The automated detection of all characteristic spine regions (i.e. flexion points of the 3D vertebral body line) may be further used to classify spinal deformities. The methods for automated determination of position and rotation of vertebrae in 3D, which are among the most important parameters in the evaluation of spinal deformities, were proposed in chapters 5 and 6. The method in chapter 5 is intensity-based and applicable to CT spine images, while the method in chapter 6 is gradient-based an therefore modality-independent, i.e. applicable to both CT and MR spine images. In order do determine the vertebral position and rotation in 3D, the proposed methods do not require prior image reformation, identification of the most appropriate axial cross-section or aid by high-level a priori information, such as statistical shape and/or appearance models. Instead, the methods exploit global characteristics of the vertebral anatomy, i.e. the natural symmetry of the vertebra, the vertebral body, the vertebral column and the vertebral canal. The position and rotation of each vertebra (i.e. the vertebral parameters) were obtained by simultaneously matching mirror vertebra subvolumes by robust rigid auto-registration, where the natural symmetry of the vertebral anatomy was used as the similarity 124 7 - Conclusion measure. The results showed that the vertebral parameters can be successfully determined in CT and MR spine images, however, the determination of some of the parameters may need further improvement. When compared to the intensity-based method, the proposed modality-independent gradient-based method improved the distinctiveness of the similarity measure optima. Therefore, a combination of the intensity- and gradient-based approaches may result in a robust method with a relatively high success rate and precision. The natural symmetry of the vertebral anatomy may be exploited to model more detailed properties of the vertebral anatomy, for example, shear and/or twist of the subvolumes in the registration procedure may provide a good description of the mechanical vertebral torsion. The proposed method may also aid the measurement of the dimensions of vertebral pedicles, foraminae and canal, and may be a valuable tool for clinical evaluation of the spinal deformities in 3D. In general, automated image analysis techniques highly depend on the resolution of images and time required to complete a series of computationally demanding tasks. Namely, the higher is the resolution of images, the better is the performance of the techniques and the more computationally demanding the tasks are. Modern CT and MR scanners already enable high resolution images that are acquired at a relatively high speed, yet the imaging technology is continuously advancing. Shorter acquisition times, greater numbers of cross-sections and increased power are the main characteristics of the next generation of CT and MR scanners, which will reflect in an even higher image resolution and reduction of the delivered ionizing radiation. The same holds true for the computational methods, as the next generation of computers will deliver computational speeds that will make present computationally demanding and therefore time-consuming tasks feasible for clinical practice. Techniques for visualization and quantitative evaluation of medical images in general are extremely valuable in the development of image-assisted diagnosis, planning of surgical interventions and assessment of medical treatment outcomes. In the field of spine image analysis, quantitative assessment of spinal curvature and axial vertebral rotation is important not only for planning of orthopaedic surgical procedures and analysis of surgical results, but also for diagnosing and monitoring of the progression of spinal deformities. Computer-assisted visualization and quantitative evaluation of 3D spine images therefore remain challenging tasks in the field of medical image analysis. I have always imagined that paradise will be a kind of library. Jorge Luis Borges, 1899 - 1986 (Dreamtigers, 1960) Appendix A Reprint permissions Reprint permission in written form was obtained for the following material: Figure 1.5a (p. 29): Roberts C, McDaniel N, Krupinski E, and Erly W. Oblique reformation in cervical spine computed tomography: A new look at an old friend. Spine, 28(2):167-170, 2003, © by Lippincott Williams & Wilkins. Figure 1.5b (p. 29): Newton P, Hahn G, Fricka K, and Wenger D. Utility of three-dimensional and multiplanar reformatted computed tomography for evaluation of pediatric congenital spine abnormalities. Spine, 27(8):844-850, 2002, © by Lippincott Williams & Wilkins. Figure 1.12a (p. 40): Rogers B, Wiese S, Blankenbaker D, Meyerand E, and Haughton V. Accuracy of an automated method to measure rotations of vertebrae from computerized tomography data. Spine, 30(6):694—696, 2005, © by Lippincott Williams & Wilkins. Figure 1.12b (p. 40): Kouwenhoven J-WM, Vincken KL, Bartels LW, and Castelein RM. Analysis of preexistent vertebral rotation in the normal spine. Spine, 31(13):1467—1472, 2006, © by Lippincott Williams & Wilkins. 125 126 Appendix Figure 1.12c (p. 40): Adam CJ and Askin GN. Automatic measurement of vertebral rotation in idiopathic scoliosis. Spine, 31(3):E80—E83, 2006, © by Lippincott Williams & Wilkins. Figure 1.13a (p. 41): Birchall D, Hughes D, Gregson V, and Williamson B. Demonstration of vertebral and disc mechanical torsion in adolescent idiopathic scoliosis using three-dimensional MR imaging. European Spine Journal, 14(2):123—129, 2005, © with kind permission from Springer Science and Business Media. Figure 1.13b (p. 41): Haughton VM, Rogers B, Meyerand E, and Resnick DK. Measuring the axial rotation of lumbar vertebrae in vivo with MR imaging. American Journal of Neuroradiology, 23(7):1110—1116, 2002, © by American Society of Neuroradiology. Figure 1.13c (p. 41): Rogers B, Haughton V, Arfanakis K, and Meyerand E. Application of image registration to measurement of intervertebral rotation in the lumbar spine. 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Tomazˇ Vrtovec, Sebastien Ourselin, Lavier Gomes, Bosˇtjan Likar, and Franjo Pernusˇ. Automated generation of curved planar reformations from MR images of the spine. Physics in Medicine and Biology, 52(10):2865-2878, 2007. 2. Tomazˇ Vrtovec, Bosˇtjan Likar, and Franjo Pernusˇ. Automated curved planar reformation of 3D spine images. Physics in Medicine and Biology, 50(19):4527-4540, 2005. 3. Tomazˇ Vrtovec. Curved planar reformation of CT spine images. Elektrotehnisˇki vestnik (Electrotechnical Review), 72(5):285-290, 2005. ˇ ˇ ˇ sˇ sˇ 4. Tomaz Vrtovec, Dejan Tomazevic, Botjan Likar, Ludvik Travnik, and Franjo Pernu. Automated construction of 3D statistical shape models. Image Analysis & Stereology, 23(2):111-120, 2004. • Tomazˇ Vrtovec, Bosˇtjan Likar, and Franjo Pernusˇ. Quantitative analysis of spinal curvature in 3D: Application to CT images of normal spine. Submitted for journal publication. source of bibliographic records: shared bib- (http://www.cobiss.si) liographic/catalogue database COBISS.SI/COBIB.SI xix xx Publications Papers in conference proceedings 1. Tomazˇ Vrtovec, Bosˇtjan Likar, and Franjo Pernusˇ. Determination of 3D location and rotation of lumbar vertebrae in CT images by symmetry-based auto-registration. In: Proceedings of the SPIE Medical Imaging 2007: Image Processing Conference (J. Pluim and J. Reinhardt, eds.), vol. 6512, pp. 65121Q–1 (SPIE, San Diego, CA, USA, Feb 17-22), 2007. 2. Tomazˇ Vrtovec, Se´bastien Ourselin, Lavier Gomes, Bosˇtjan Likar, and Franjo Pernusˇ. Generation of curved planar reformations from magnetic resonance images of the spine. In: Lecture Notes in Computer Science (LNCS): Proceedings of the 9th International Conference on Medical Image Computing and Computer-Assisted Intervention - MICCAI 2006 (R. Larsen, M. Nielsen, and J. Sporring, eds.), vol. 4191, pp. 135–143 (Springer-Verlag, Copenhagen, Denmark, Oct 1-6), 2006. 3. Tomazˇ Vrtovec, Bosˇtjan Likar, and Franjo Pernusˇ. Curved planar reformation of CT spine data. In: Proceedings of the SPIE Medical Imaging 2005: Image Processing Conference (J.M. Fitzpatrick and J.M. Reinhardt, eds.), vol. 5747, pp. 1446–1456 (SPIE, San Diego, CA, USA, Feb 12-17), 2005. 4. Tomazˇ Vrtovec, Bosˇtjan Likar, and Franjo Pernusˇ. Spine-based coordinate system. In: Proceedings of the 27th IEEE Annual International Conference of the Engineering in Medicine and Biology Society (EMBS) - EMBC 2005 (Y.T. Zhang, L.X. Xu, C. Roux, T.G. Zhuang, T. Tamura, and H. Galiana, eds.), pp. 5120–5123 (IEEE, Shanghai, China, Sep 1-4), 2005. 5. Tomazˇ Vrtovec, Bosˇtjan Likar, Dejan Tomazˇevicˇ, and Franjo Pernusˇ. Automated robust generation of compact 3D statistical shape models. In: Proceedings of the SPIE Medical Imaging 2004: Image Processing Conference (J.M. Fitzpatrick and M. Sonka, eds.), vol. 5370 pp. 1312–1323 (SPIE, San Diego, CA, USA, Feb 14-19), 2004. 6. Tomazˇ Vrtovec, Dejan Tomazˇevicˇ, Bosˇtjan Likar, and Franjo Pernusˇ. Statistical shape deformable model of a lumbar vertebra. In: Proceedings of the 8th Computer Vision Winter Workshop - CVWW 2003 (O. Drbohlav, ed.), pp. 91–96 (Valtice, Czech Republic, Feb 3-6), 2003. • Tomazˇ Vrtovec, Se´bastien Ourselin, Bosˇtjan Likar, and Franjo Pernusˇ. Modality-independent determination of vertebral parameters in 3D. Submitted for conference presentation. Publications xxi Monographs and other completed works 1. Tomazˇ Vrtovec. Statisticˇni deformabilni model oblike ledvenega vretenca (Translation of the title: Statistical shape deformable model of the lumbar vertebra). BSc thesis (F Pernusˇ, supervisor), University of Ljubljana, Faculty of Electrical Engineering (Ljubljana, Slovenia), 2002. Nothing shocks me. I’m a scientist. Indiana Jones (Indiana Jones and the Temple of Doom, 1984) About the author ˇ Tomazˇ Vrtovec was born on March 6th 1978 in Sempeter pri Novi Gorici, Slovenia. After spending a lively childhood in his home village of Bukovica and nearby Rencˇe, he finished secondary school in Nova Gorica in 1997. In the same year he began the undergraduate studies at the University of Ljubljana, Faculty of Electrical Engineering, Slovenia. After specializing in telecommunications, he successfully defended his BSc thesis in 2002. As a PhD student he joined the Laboratory of Imaging Technologies at the University of Ljubljana, Faculty of Electrical Engineering, Slovenia, where he has been employed as a researcher since 2003. In 2006, he spent six months in Australia with the CSIRO ICT Centre as a visiting researcher. His research interests are concentrated around biomedical image analysis and development of computer vision systems. In his free time he cultivates various hobbies, among the most favorite are visiting new places home and around the world, when possible in the saddle of a bicycle, taking and developing black & white photographies, and examining his continuously growing collection of coins. xxiii Nič me ne preseneti. Sem znanstvenik. Indiana Jones (Indiana Jones in tempelj usode, 1984) O avtorju Tomaž Vrtovec se je rodil 6. 3.1978 v Šempetru pri Novi Gorici. Po živahnem otroštvu v domači vasi Bukovica in sosednjih Renčah je leta 1997 opravil maturo na gimnazijskem programu Srednjega šolskega centra v Novi Gorici. V istem letu seje vpisal na dodiplomski študijski program elektrotehnike na Fakulteti za elektrotehniko, Univerza v Ljubljani, ter po študiju na smeri telekomunikacije leta 2002 uspešno zagovarjal diplomsko nalogo. Kot podiplomski študent se je pridružil Laboratoriju za slikovne tehnologije na Fakulteti za elektrotehniko, Univerza v Ljubljani, kjer je od leta 2003 tudi zaposlen kot mladi raziskovalec. Leta 2006 je v sklopu doktorskega študija preživel šest mesecev v Avstraliji kot gostujoči raziskovalec na inštitutu CSIRO ICT Centre. Njegovo področje raziskovanja obsega obdelavo in analizo biomedicinskih slik ter razvoj sistemov z računalniškim vidom. V prostem času se ukvarja z različnimi konjički, najljubši izmed njih so obiskovanje krajev doma in po svetu, če je mogoče v sedlu kolesa, razvijanje fotografij v črno-beli tehniki ter preučevanje njegove nenehno rastoče zbirke kovancev. XXV To see a World in a Grain of Sand And a Heaven in a Wild Flower, Hold Infinity in the palm of your hand And Eternity in an hour. William Blake, 1757 - 1827 (Auguries of Innocence, 1805) Acknowledgments During the past years I have been supported by many people, and it is a pleasure to use this opportunity and express my gratitude to them. Prof. Dr. Franjo Pernusˇ introduced me to the field of medical imaging and provided the valuable guidance to reach the end of my studies. I consider it a privilege to have been working in his group. I have benefited immensely from Prof. Dr. Bosˇtjan Likar, who supported my work with continuous interest, advice and discussion. Without him, my work would not be as it is. The present and former members of the Laboratory of Imaging Technologies – Dr. Darko Sˇkerl, Dr. Urosˇ Vovk, Marko Bukovec, Mario Medved, Dejan Stojakovic´, Dr. Dejan Tomazˇevicˇ, Miran Bu¨rmen, Primozˇ Markelj and Zˇiga Sˇpiclin – created a relaxing atmosphere along very frequent coffee breaks, which sometimes went on until the early hours. Spending six months with the CSIRO ICT Centre in Australia was a wonderful and fruitful experience that was made possible by Prof. Dr. Se´bastien Ourselin. I also appreciate the financial support provided by the Ministry of Higher Education, Science and Technology, Slovenia, according to the “Junior Researchers” program. Last, but certainly far from least, I want to express my gratitude to my parents, Anka and Vojko, and my sister, Jana, for their continuous encouragement, support and especially patience. I can only but hope that some things will never change. Thank You Tomazˇ xxvii V zrnu peska videti cel Svet in Nebo v Roži na poljani, Večni čas imeti v hip ujet in Neskončnost obdržati v dlani. William Blake, 1757 - 1827 (Slutnja nedolžnosti, 1805) Zahvala V veliko zadovoljstvo mi je, da lahko izrabim to priložnost za zahvalo vsem, ki so me v teh letih podpirali. Prof. dr. Franjo Pernuš meje vpeljal v področje obdelave biomedicinskih slik ter mi priskrbel dragoceno vodstvo, ki me je pripeljalo do zaključka mojega študija. Delo v njegovi skupini je bilo zame privilegij. Ogromno znanja in izkušenj sem pridobil od prof. dr. Boštjana Likarja, ki je podpiral moje delo z neprestanim zanimanjem, nasveti ter razpravami. Brez njega moje delo ne bi bilo takšno, kot je. Sedanji ter bivši člani Laboratorija za slikovne tehnologije - dr. Darko Skerl, dr. Uroš Vovk, mag. Marko Bukovec, Mario Medved, mag. Dejan Sto-jakovič, dr. Dejan Tomaževič, Miran Burmen, Primož Markelj in Žiga Špiclin - so ustvarili sproščeno vzdušje ter zelo pogoste odmore za kavo, ki so se včasih zavlekli tudi v jutranje ure. Šestmesečno delo na inštitutu CSIRO ICT Centre v Avstraliji mi bo ostalo v spominu kot čudovita ter uspešna izkušnja, za kar ima zasluge predvsem prof. dr. Sebastien Ourselin. Zelo cenim tudi štiri in pol leta trajajočo finančno podporo Ministrstva za visoko šolstvo, znanost in tehnologijo v okviru programa “mladih raziskovalcev”. Posebne zahvale so deležni moji starši Anka in Vojko ter sestra Jana, ki so me v teh letih spremljali z neprestanim spodbujanjem, podporo in še posebej potrpežljivostjo. Ob tem lahko samo upam, da se nekatere stvari ne bodo nikoli spremenile. Hvala Tomaž xxix The most merciful thing in the world is the inability of the human mind to correlate all its contents. Howard P. Lovecraft, 1890 - 1937 (The Call of Cthulhu, 1926) Index 0–9 1D .................... see dimensional, one 2D .................... see dimensional, two 3D ................... see dimensional, three 6D ..................... see dimensional, six 2D visualization ........ see visualization, 2D 3D visualization ........ see viusalization, 3D apical vertebra arch, vertebral auto-registration . . axial cross-section axial rotation ..... see vertebra, apical 37 ..... see registration, auto. . . see cross-section, axial see rotation, axial vertebral axial symmetry .......... see symmetry, axial A anatomy spine ............................. 30, 83 vertebral ..................... 28, 98, 113 angiography ......................... 25, 49 angle Cobb ........... curvature ....... rotation ......... anterior . . . see method, Cobb ................. 85 see rotation, vertebral 29 anterior nerve root see nerve root, anterior B body, vertebral .......................... 27 bronchoscopy ....................... 25, 49 C CA ..................... see angle, curvature CAD .......... see diagnosis, computer-aided canal, spinal ............................ 29 Cartesian coordinate system ........ . . . . see coordinate system, image-based center of rotation .................. xxxi xxxii Index ........ see rotation, center of vertebral cervical lordosis ........ see lordosis, cervical Cobb angle ............... see method, Cobb Cobb method ............. see method, Cobb computed tomography . . . . 19, 48, 83, 96, 112 computer-aided diagnosis .......... ......... see diagnosis, computer-aided colonoscopy ......................... 25, 49 congenital .............................. 28 convergence curve .......... see rate, success coordinate system Cartesian ................ see image-based image-based ................... 43, 50, 67 spine-based ....................... 50, 67 cord, spinal ............................. 21 coronal cross-section ............... ............. see cross-section, coronal coronal rotation ................... ......... see rotation, coronal vertebral coronal symmetry ..... see symmetry, coronal correlation coefficient .................... 54 criterion function ...... see function, criterion cross-section axial ................................. 22 coronal .............................. 22 curved ............................... 22 frontal .......... see cross-section, coronal lateral ........... see cross-section, sagittal oblique .............................. 22 original .............................. 22 sagittal .............................. 22 transverse ......... see cross-section, axial CT ............... see computed tomography curvature geometric ............................ 85 spinal ..................... 27, 49, 64, 82 curvature angle .......... see angle, curvature curve parameters ....... see parameters, curve curve convergence ............. see rate, success spine ......................... 34, 49, 66 curved cross-section ............... ............. see cross-section, curved curved planar reformation .......... ........ see reformation, curved planar D diagnosis, computer-aided ................ 26 direction set optimization ........... ......... see optimization, direction set disc, intervertebral ................... 21, 67 dimensional one .................................. 25 six ................................. 101 three .............. 19, 48, 64, 82, 98, 112 two ....................... 19, 51, 64, 82 dorsal nerve root . . . . see nerve root, posterior downhill simplex optimization ...... . . . . see optimization, downhill simplex E edge distance optimization ......... ........ see optimization, edge distance EDO ......... see optimization, edge distance electrogoniometer ....................... 34 end-plate, vertebral ............ 31, 62, 78, 88 end vertebra ............... see vertebra, end evaluation qualitative ..................... 27, 57, 76 quantitative ................ 26, 57, 72, 83 F facet joint, vertebral ..................... 27 foramen, intervertebral ................... 27 frontal cross-section ............... ............. see cross-section, coronal function criterion ............................ 115 polynomial ................ 33, 52, 70, 82 Index similarity ......................... 54, 68 G GC ................ see curvature, geometric geometric curvature ................ .............. see curvature, geometric gradient ............................... 114 H hierarchical optimization ........... ......... see optimization, hierarchical I idiopathic .............................. 32 image-based coordinate system ..... . . . . see coordinate system, image-based image space ............... see space, image intervertebral disc ..... see disc, intervertebral intervertebral fibrocartilage ......... ................ see disc, intervertebral intervertebral foramen ............. ............ see foramen, intervertebral inter-segmental rotation ............ ........... see rotation, inter-vertebral intra-segmental rotation ............ ........... see rotation, intra-vertebral inter-vertebral rotation ............. ........... see rotation, inter-vertebral intra-vertebral rotation ............. ........... see rotation, intra-vertebral J joint symmetry .......... see symmetry, joint junction, thoracolumbar .............. 30, 84 xxxiii K kyphosis sacral ......................... 27, 79, 82 thoracic ....................... 27, 79, 82 L lamina of the vertebral arch .............. 37 lateral cross-section ................ ............. see cross-section, sagittal least squares fitting ...................... 84 least trimmed squares .................... 71 LL ..................... see lordosis, lumbar lordosis cervical ....................... 27, 79, 82 lumbar ........................ 27, 79, 82 LSF ................. see least squares fitting LTS ............... see least trimmed squares lumbar lordosis ......... see lordosis, lumbar M magnetic resonance .............. 19, 65, 115 mask, vertebral ..................... 99, 114 maximum intensity projection ...... ................ see visualization, MIP method, Cobb ........ 32, 61, 79, 82, 97, 112 MIP ................. see visualization, MIP moire´ topographic images ................ 34 morphology ............................ 31 morphometry ........................... 26 MR ................. see magnetic resonance multiplanar reformation ............ .......... see reformation, multiplanar mutual information ...................... 72 myelography ............................ 30 N nerve root anterior .............................. 29 xxxiv dorsal ............ see nerve root, posterior posterior ............................. 29 ventral ............ see nerve root, anterior O oblique reformation . . see reformation, oblique one-dimensional ........ see dimensional, one optimization direction set ......................... 116 downhill simplex ............. 57, 72, 101 edge distance ......................... 84 hierarchical .......................... 53 Powell ...... see optimization, direction set simulated annealing .................. 101 P pancreatography ........................ 25 parameter space ........ see space, parameter parameters curve ............................. 53, 71 rotation ........................... 53, 71 translation ....................... 98, 113 vertebral ........................ 98, 113 pedicle, vertebral ........................ 31 polynomial function ............... .............. see function, polynomial position, vertebral .................. 95, 111 posterior ............................... 29 posterior nerve root . . see nerve root, posterior Powell ........ see optimization, direction set process vertebral spinous ............... 34, 51, 67 vertebral transverse ................ 31, 51 Q qualitative evaluation .............. ............. see evaluation, qualitative quantitative evaluation ............. Index ........... see evaluation, quantitative R radiography ............................. 19 rate, success ...................... 105, 118 reformation curved planar .................. 22, 48, 64 multiplanar ........................... 22 oblique .............................. 22 registration auto- ............................ 99, 115 rigid ............................ 99, 115 rendering surface .............................. 22 volume .............................. 22 rigid registration ....... see registration, rigid rotation parameters . . . see parameters, rotation rotation axial vertebral ............. 34, 74, 96, 112 center of vertebral ............ 39, 98, 113 coronal vertebral ...................... 39 inter-vertebral ..................... 61, 79 intra-vertebral ..................... 62, 79 sagittal vertebral .................. 35, 97 vertebral .......................... 34, 98 S sacral kyphosis .......... see kyphosis, sacral sagittal cross-section ............... ............. see cross-section, sagittal sagittal rotation .................... ......... see rotation, sagittal vertebral sagittal symmetry ..... see symmetry, sagittal scoliometer ............................. 34 scoliosis ........................ 27, 57, 100 signal-to-noise ratio .................. 30, 65 similarity function . . . . see function, similarity similarity measure . . . . see function, similarity simplex optimization ............... Index xxxv . . . . see optimization, downhill simplex simulated annealing ................ . . see optimization, simulated annealing six-dimensional ......... see dimensional, six SNR ................ see signal-to-noise ratio space image parameter ........ spinal canal ......... spinal cord .......... spinal curvature ..... spinal stenosis ...... spine anatomy ...... spine-based coordinate system 98 .......... 101, 101 . . . . see canal, spinal ..... see cord, spinal see curvature, spinal . see stenosis, spinal . see anatomy, spine . . . . see coordinate system, spine-based spine curve ....... spine visualization spinous process ...... see curve, spine see visualization, spine ......... see process, vertebral spinous spline .................................. 29 stenosis, spinal .......................... 28 stereophotography stereoradiography success rate ...... surface rendering . symmetry .................. 33 ................. 33 ..... see rate, success see rendering, surface axial ............................ 99, 113 coronal .......................... 99, 113 joint ........................... 100, 115 ..................... 99, 113 ..................... 98, 113 sagittal . vertebral T thoracic kyphosis......see kyphosis, thoracic TJ .............. see junction, thoracolumbar TK...................see kyphosis, thoracic thoracolumbar junction............. ...........see junction, thoracolumbar three-dimensional.....see dimensional, three two-dimensional ....... see dimensional, two translation parameters.............. ............see parameters, translation transverse cross-section ............ ............... see cross-section, axial transverse process ................. .......see process, vertebral transverse V ventral nerve root vertebra apical ........ end ........... see nerve root, anterior ................... 32 ......... 32, 79, 88, 97 vertebral anatomy ..... see anatomy, vertebral vertebral arch see arch, vertebral vertebral body ............ see body, vertebral vertebral canal ..... vertebral end-plate . . vertebral facet joint . vertebral location . . . vertebral mask ..... vertebral parameters ............ vertebral pedicle . . . vertebral position . . . vertebral rotation . . . ....... see canal, spinal . see end-plate, vertebral see facet joint, vertebral . . see position, vertebral . . . . see mask, vertebral see parameters, vertebral . . . see pedicle, vertebral . . . see position, vertebral . . . see rotation, vertebral vertebral symmetry . . see symmetry, vertebral VH ...................... see visible human Visible Human .......................... 49 visualization 2D .................................. 21 3D .................................. 22 MIP . spine 22 27 surface rendering . . . . see rendering, surface volume rendering . . . see rendering, volume volume rendering ...... see rendering, volume X X-ray see radiography