SPRINGER BRIEFS IN ELECTRICAL AND COMPUTER ENGINEERING Joseph Suresh Paul Subha Gouri Raveendran Understanding Phase Contrast MR Angiography A Practical Approach with MATLAB Examples 123 SpringerBriefs in Electrical and Computer Engineering More information about this series at http://www.springer.com/series/10059 Joseph Suresh Paul Subha Gouri Raveendran (cid:129) Understanding Phase Contrast MR Angiography A Practical Approach with MATLAB Examples 123 JosephSureshPaul SubhaGouri Raveendran Medical Image Computing Medical Image Computing andSignalProcessing Group andSignalProcessing Group Indian Institute of Information Technology Indian Institute of Information Technology andManagement-Kerala andManagement-Kerala Trivandrum Trivandrum India India Additional material tothis bookcanbedownloaded from http://extras.springer.com. ISSN 2191-8112 ISSN 2191-8120 (electronic) SpringerBriefs inElectrical andComputer Engineering ISBN978-3-319-25481-4 ISBN978-3-319-25483-8 (eBook) DOI 10.1007/978-3-319-25483-8 LibraryofCongressControlNumber:2015957051 ©TheAuthor(s)2016 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor foranyerrorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAGSwitzerland Preface This book discusses the basic concepts of MRI leading to PC-MRA. An intuitive understanding of PC-MRA concepts is provided through simulation techniques using the extended form of Bloch equation. For completeness, quantitative flow measuringtechniquesandpost-processingusingstatisticalmodelsarealsoincluded as separate chapters. Implementation details of important techniques discussed in this book are provided in the form of MATLAB codes. PC-MRA is one of the non-contrast MRA techniques using the idea that blood flowvelocitiescanbeencodedbyphase.ThiswasfirstdevelopedbyPaulR.Moran intheearly1980s.Morananalyzedthephaseeffectsonstationaryandmovingspins subjected to a pair of bipolar gradients. A stationary spin subjected to such a gradient pair will experience no net phase shift, but a moving spin will have a net phaseshiftproportionaltoitsvelocity.Twospinsflowingatthesamespeedbutin opposite directions will have equal but opposite phase shifts, and by measuring changes in phase, the velocity can be computed. PC-MRAisbasedonuseofbipolargradientsthatcreatephaseshiftsofmoving spins proportional to their velocities. The key applications include flow measure- ments,CineCSFflowstudies,andvenography.Thedegreeofsensitivitytoslowor fast flows is determined by the amplitude, duration, and spacing of bipolar gradi- ents, which is controlled by parameter VENC—velocity encoding. Simulation experiments outlined in this book provide a sound understanding of the encoding strategy and enable the reader to apply this knowledge in acquisition and post-processing methods. Acknowledgments Somesectionsofthisbookarebasedonpreviousarticles:“ComputerSimulationof Magnetic Resonance Angiography Imaging: Model Description and Validation,” Plosone9.(2014)and“InSilicoModelingofMagneticResonanceFlowImagingin ComplexVascularNetworks,”IEEEtransactionsonmedicalimaging,33:11(2014). v Contents 1 Introduction to MR Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Magnetic Resonance Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 MRI Physics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2.1 Spin Physics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2.2 RF Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.3 Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Signal Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3.1 Spatial Encoding of MR Signal. . . . . . . . . . . . . . . . . . . . 9 1.3.2 2D Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3.3 Small Tip Angle Approximation . . . . . . . . . . . . . . . . . . . 13 1.4 Phase Contrast Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2 Simulation Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.1 Bloch Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.1.1 Solution of Bloch Equation. . . . . . . . . . . . . . . . . . . . . . . 21 2.1.2 Time Update Form of Bloch Equation. . . . . . . . . . . . . . . 23 2.2 Working Principle of MR Simulator. . . . . . . . . . . . . . . . . . . . . . 24 2.2.1 Imaging Parameters and K-Space Generation . . . . . . . . . . 26 2.3 Incorporation of T * Effects in Gradient-Echo Imaging. . . . . . . . . 28 2 2.4 Incorporation of Susceptibility Effects . . . . . . . . . . . . . . . . . . . . 28 2.4.1 Susceptibility Artifacts. . . . . . . . . . . . . . . . . . . . . . . . . . 29 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3 Working Principle of PC-MRA with MATLAB Examples. . . . . . . . 33 3.1 Gradient Echo Imaging. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.2 Velocity Encoding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.3 Effects of Flow on the Image . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.4 Phase Contrast Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 vii viii Contents 3.5 Quantitative Flow Image Analysis . . . . . . . . . . . . . . . . . . . . . . . 42 3.5.1 Two-Point Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.5.2 Simple Four Point Method. . . . . . . . . . . . . . . . . . . . . . . 43 3.5.3 Balanced Four Point Method . . . . . . . . . . . . . . . . . . . . . 44 3.5.4 Processing of Multi-channel PC-MRA. . . . . . . . . . . . . . . 45 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4 Numerical Simulation of PC-MRA . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.1 Flow Phantom Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.1.1 Masking Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.2 Simulation of Magnetization Transport. . . . . . . . . . . . . . . . . . . . 54 4.2.1 Lattice Boltzmann Method (LBM). . . . . . . . . . . . . . . . . . 55 4.3 Simulation of MRI Signal Generation Using LBM and Bloch Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.3.1 Integration of LBM and Blochequation Simulation . . . . . . 59 4.4 MRA Simulation Using Particle Trajectory Models . . . . . . . . . . . 61 4.5 Bloch Flow Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5 Modeling of PC-MRA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 5.1 An Overview of PC-MRA Modeling . . . . . . . . . . . . . . . . . . . . . 71 5.1.1 Partial Volume Effect. . . . . . . . . . . . . . . . . . . . . . . . . . . 72 5.2 Global Segmentation of Speed Images . . . . . . . . . . . . . . . . . . . . 75 5.3 Initial Estimation of Mixture Parameters. . . . . . . . . . . . . . . . . . . 80 5.3.1 Iterated EM Algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.3.2 Segmentation Using Local Phase Coherence. . . . . . . . . . . 83 5.3.3 Segmentation Using MRF Formulation . . . . . . . . . . . . . . 83 5.4 Vascular Tree Construction. . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.4.1 Skeletonization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Chapter 1 Introduction to MR Imaging Abstract This chapter provides a quick introduction to the basics of MRI, adequateforunderstandingoftheterminologyandconceptsusedinPhase-Contrast MR Angiography (PC-MRA). Chapter begins with a description of signal gener- ation, followed by an explanation for the need of spatial encoding necessary for derivation of the Fourier imaging approximation. A brief introduction to the magnetization dynamics using Bloch equation, with extension to small tip angle approximation is also provided. The chapter concludes with an introduction to the basic principle of flow measurement using PC-MRA, and the need for additional flow encoding gradients. (cid:1) (cid:1) (cid:1) (cid:1) Keywords Spin physics RF excitation Bloch equation Spatial encoding PC-MRA 1.1 Magnetic Resonance Imaging Magnetic Resonance Imaging (MRI) is a non-invasive method of mapping the tissueintermsofitsspatialdensityofprotons.Sincetheprotondensityvarieswith thetypeoftissue,imagingcontrastisachievedtodifferentiatetissuetypesbasedon variations in their proton density. The imaging contrast can be easily maneuvered byutilizingthedependenceofreceivedsignalintensity onthephysical parameters of proton density, longitudinal relaxation time (T ), and transverse relaxation time 1 (T ). For example, chemical and structural changes of tumors over time directly 2 affect the signal intensity on MR images, providing information about their age. Unlike many other medical imaging modalities, the contrast in an MR image is strongly dependent upon the way the image is acquired. By adding Radio Frequency (RF), or gradient pulses, and by careful choice of timings,it ispossible to highlight different components in the object being imaged. TheMRImageisconstructedbyplacingthepatientinsidealargemagnet,which induces a relatively strong external magnetic field (B ). This causes the nuclei of 0 ©TheAuthor(s)2016 1 J.SureshPaulandS.GouriRaveendran,UnderstandingPhaseContrast MRAngiography,SpringerBriefsinElectricalandComputerEngineering, DOI10.1007/978-3-319-25483-8_1 2 1 IntroductiontoMRImaging manyatomsinthebody,includingHydrogen,toalignthemwiththemagneticfield. WithapplicationofRFsignal,energyisreleasedfromtheareabeingimaged,inthe formofatime-varyingvoltage.ThedetectordemodulatestheRFcomponents,and storesthediscretesamplesinaFourierspace,knownask-space.TheMRimageis then obtained byperforminganinverse Fouriertransformontheacquired k-space. Using slice-selection gradients, the imaging plane can be optimized for the anatomicareabeingstudied.Flow-sensitivepulsesequencesandMRAngiography (MRA)yielddataaboutbloodflow,aswellasdisplayingthevascularanatomy.In conventionalMRimaging,thespinsareconsideredtobestationarythroughoutthe imaging process.However,thisdoesnothold trueinthecase offlow andvascular imaging.Thisisparticularlyapplicabletothesituationofimagingaslicecontaining blood vessels. A critical problem with flow imaging is that the excited spins in a vessel can flow out of the slice by the time readout is performed. Since the unexcited spins have flown in during readout, the image formed will not have contributions from MR signals originated from the vessel. Consequently, mea- surements of flow would require some form of spatial encoding that is flow sen- sitive. This is done by applying a magnetic field gradient along the direction in which flow is to be measured. A large enough gradient amplitude can dephase the stationary as well as moving spins depending on their position along the gradient. The gradient when reversed, will completely rephase only the stationary spins. Spins that have moved will not be completely rephased. For uniform flow, the phasedifferenceandflowaredirectlyrelatedtothetimedelaybetweentheforward and reverse gradients. Spinsthataremovinginthesamedirectionasamagneticfieldgradientdevelop a phase shift that is proportional to the spin velocity. This is the basis of Phase-Contrast MRA (PC-MRA). In PC-MRA pulse sequence, the spin velocities are encoded using bipolar gradients (two gradients with equal magnitude but opposite direction). Following the gradient application, stationary spins do not undergo a net change in phase. Due to varying spatial position, the moving spins will experience a different magnitude of the second gradient compared to the first. As a result, the moving spins attain a net phase shift during readout. The resultant phase information can be used directly to determine the spin velocity. Understanding the key physical concepts in MRI is a prerequisite for analyzing thetheoryandpostprocessingmethodsusedinPC-MRA.Thesuccessivechapters in this book are organized to orient the reader towards systematically building up the knowledge base needed to understand the technical aspects through a series of methods which outline the interface between flow and image formation process. This chapter provides the theoretical prelude to understand the key MRI concepts from a technical perspective. Chapter 2 highlights the fundamental approach to generatesyntheticMRimagesfromdataconsistingofrelevantphysicalparameters, and geometry using known MR sequences. Chapter 3 describes the theory of PC-MRA together with details of methods used to derive flow information from raw data. Chapter 4 enables the reader to extend the image generation ideas