X-Ray Computed Tomography in Biomedical Engineering Robert Cierniak X-Ray Computed Tomography in Biomedical Engineering 123 Dr. RobertCierniak Department of Computer Engineering Technical University ofCze˛stochowa Al.Armii Krajowej36 42-200 Cze˛stochowa Poland e-mail: [email protected] ISBN 978-0-85729-026-7 e-ISBN978-0-85729-027-4 DOI 10.1007/978-0-85729-027-4 SpringerLondonDordrechtHeidelbergNewYork BritishLibraryCataloguinginPublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary LibraryofCongressControlNumber:2010936694 (cid:2)Springer-VerlagLondonLimited2011 Translation:MikeButynski Apart from anyfair dealing for the purposes of researchor privatestudy, or criticismor review,as permittedundertheCopyright,DesignsandPatentsAct1988,thispublicationmayonlybereproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers,orinthecaseofreprographicreproductioninaccordancewiththetermsoflicensesissued bytheCopyrightLicensingAgency.Enquiriesconcerningreproductionoutsidethosetermsshouldbe senttothepublishers. Theuseofregisterednames,trademarks,etc.,inthispublicationdoesnotimply,evenintheabsenceof aspecificstatement,thatsuchnamesareexemptfromtherelevantlawsandregulationsandtherefore freeforgeneraluse. The publisher makes no representation, express or implied, with regard to the accuracy of the informationcontainedinthisbookandcannotacceptanylegalresponsibilityorliabilityforanyerrors oromissionsthatmaybemade. Coverdesign: eStudioCalamarS.L. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) To my Parents Preface This book is an attempt at a comprehensive treatment of those medical imaging techniques commonly referred to as Computed Tomography (CT) and sometimes known as Computerised Tomography, which rely on X-rays for their action. As thisisaplacetoexplainmyreasonsforwritingthebook,Iwouldliketobeginby assuring the reader of my passion for the medical technology discussed here. My main motivation in publishing this work was a desire to share with the widest possible readership my fascination with the topic. I would expect the target audience for this account to be primarily academics, students and technicians involved withbiomedical engineering, aswell asdoctors andmedical technicians concerned with medical imaging. The structure and content of the book place particular emphasis on issues related to the reconstruction of images from pro- jections,akeyproblemintomography.Thisreflectsmyareaofinterestinthefield. Other problems will be treated as technical and physical background to the reconstruction algorithms, in so far as is necessary for an understanding of how theywork(andperhapsalittlemore).Thereconstructionalgorithmscoveredrelate to all the basic designs of tomographic equipment, from the first Hounsfield scanner to the most recent spiral CT devices for reconstructing images in three dimensions.Ihopethatthesummariesofvariouspracticalimplementationsofthe algorithms will help people to test the individual reconstruction methods for themselves.Thefinalchaptercontainsanaccount ofavirtualtestenvironmentso that those without access to physical measurement data from a real scanner can carry out these tests. Perhaps it is a good point here to wish you the best of luck. There is another reason for engaging the reader at this point, in addition to spreading enthusiasm for the subject. It is to thank those particularly who have made significant contributions to the conception of ‘‘the work’’. I would like to start with mylecturer Professor Ryszard Tadeusiewicz. It was at his lecture thatI first heard about the reconstruction problem. It was then, perhaps thanks to his eloquence, that I was quite simply struck by the ‘‘beauty’’ of the problem. The secondpersonwho,inmyacademiclife,hadadecisiveinfluenceonthedirection ofmyresearchwas Professor Leszek Rutkowski.He, asmyacademic supervisor, always gave me enough freedom to choose the direction of my own interests. vii viii Preface However, I also cannot forget those individuals and institutions that, during the writing of this monograph, enabled me to bring the project to fruition. Amongst these I would like to stress the contribution of Dr. Marek Waligóra from the PrivateHealthCareGroup‘‘Unimed’’inCzestochowa,whoprovidedmewiththe tomographic images contained in the book, and offered advice on all contentious medical issues. I would like to thank Mr Marcin Gabryel for his assistance in preparing the program listings included in the book. These should prove very useful to those wishing to test the reconstruction algorithms described here. I would also like to offer my special thanks to Japan Industries Association of Radiological Systems (JIRA) and Sumio Makino for allowing the publication of historical photographs related to the development of computed tomography techniques. A significant role was also played by Ms. Claire Protherough, on behalf of Springer Publishing. She showed great patience with such an ill-disci- plined author as myself and took such care during the editorial work on the publication. This book would probably not have arisen at all without Mike Bu- tynski, who not only translated the text from the Polish language but also, thanks tohis physics background, helpedme with many ofthe basicproblems that arose duringthewritingofthismonograph.Thankyou,Mike,fortheheartthatyouput into the book. To others not mentioned here by name, but who helped with this work, I apologise and ask for understanding. Inconclusion,Iwouldliketohope,dearreader,thatyouarewillingtosparethe book a moment of your attention and not regard it as time ill spent. Cze˛stochowa, March 2010 Robert Cierniak Contents 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Some Words About the History of Computed Tomography . . . . . 7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3 Technical Concepts of X-ray Computed Tomography Scanners . . 21 3.1 Data Acquisition Systems . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.1.1 First-Generation Scanners . . . . . . . . . . . . . . . . . . . . . 24 3.1.2 Second-Generation Scanners . . . . . . . . . . . . . . . . . . . 25 3.1.3 Third-Generation Scanners . . . . . . . . . . . . . . . . . . . . 25 3.1.4 Fourth-Generation Scanners. . . . . . . . . . . . . . . . . . . . 27 3.1.5 Spiral Scanners . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2 X-ray Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.2.1 The Physics of X-ray Sources . . . . . . . . . . . . . . . . . . 33 3.2.2 X-ray Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.2.3 Electrical Aspects of X-ray Tubes . . . . . . . . . . . . . . . 43 3.3 X-ray Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.3.1 Detector Matrices. . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.3.2 Detector Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.4 Imaging in Computed Tomography Devices . . . . . . . . . . . . . 52 3.4.1 Luminance of the Image. . . . . . . . . . . . . . . . . . . . . . 52 3.4.2 Discretisation and Quantisation of the Image. . . . . . . . 53 3.4.3 The Display of Reconstructed Images. . . . . . . . . . . . . 56 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4 The Physics of Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.1 X-ray Propagation Through Matters . . . . . . . . . . . . . . . . . . . 63 4.2 The Radon Transform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.3 X-ray Collimators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 4.4 Physical Causes of Artefacts in the Reconstructed Image . . . . 73 4.4.1 Spectral Nonlinearities . . . . . . . . . . . . . . . . . . . . . . . 74 ix