image guided respiratory motion analysis

151 Pages·2008·6.05 MB·Tagalog

IMAGE GUIDED RESPIRATORY MOTION
ANALYSIS:
TIME SERIES AND IMAGE REGISTRATION
by
DanRuan
Adissertationsubmittedinpartialfulfillment
oftherequirements forthedegreeof
DoctorofPhilosophy
(ElectricalEngineering: Systems)
inTheUniversityofMichigan
2008
DoctoralCommittee:
ProfessorJeffreyA.Fessler,Chair
ProfessorAlfredO.HeroIII
ProfessorCharlesR.Meyer
AssociateProfessorJamesM.Balter
AssistantProfessorSelimEsedog¯lu

DanRuan 2008
c
(cid:13) AllRightsReserved
ToMum,Dad,andmybestfriendHuaHe.
ii
ACKNOWLEDGEMENTS
I thank my previous advisor Professor David A. Castan˜on at Boston University, who
trustinglyledmetothedoorofappliedmathematics,andlet mewanderatwill. I enjoyed
thefreedomofexplorationandowemyconfidencetoperformindependentresearchtohis
encouragement.
ThisworkwouldnotbepossiblewithoutmyadvisorProfessorJeffreyA.Fessler. Jeffis
a natural; uncork the bottle and the charm flows. Working with him is fun and enjoyable.
I thank Professor James M. Balter for welcoming me to Michigan with open arms, and
generously showered me with support and friendship. I am grateful to Professor Alfred
O. Hero, whose intellectual power and enlightening guidance have always inspired me
to push for better. Much thanks goes to Professor Charles R. Meyer for his expertise,
valuable feedback, and patience with a humble graduate student like me. I am indebted
to ProfessorSelim Esedog¯lu, from whom I appreciated the professionalism, ambition and
passion for truth of a young scientist. I thank Professor Marc. L. Kessler for motivating
much of the research work, offering computational support and data access. I have also
benefited from discussions with ProfessorWilliam C. Karl (BU), ProfessorJeffrey Rauch
(UMich), Professor Susan Murphy (Umich), Professor Paul Keall (Stanford), Professor
Steve B. Jiang (UCSC), Dr. Gregory C. Sharp (Mass General Hospital) and many other
peopleovertheyears.
My colleagues and teammates have always been a source of wisdom for me, they
have made my time in Michigan a pleasant experience. I wish to acknowledge my lab-
iii
mates: MattJacobson,AnastasiaYendiki,YingyingZhang,RongpingZeng,EranBashan,
SomeshSrivastava,SeYoungChun,KimKhalsa,AmandaFunai,HugoShi,TedWayand
Yong Long. Special thanks goes to Drs. Derek Justice, Raviv Raich, Mark Kliger, with
whom I enjoyed many vivid discussions. Michigan Argentina Tango club has been the
ultimatefunplaceformylastyearofPh.Dwork,anditsactivitiesconstitutesmuchofmy
healthybreaksfrom work.
Finally, I am indebted to my family. I feel sorry for not being there at his bedside for
mylategrandfatherduringtheprocessoffinishingthisthesis. Ithankmyparentsfortheir
love, care, and nurtue with freedom and critical thinking. My appreciation goes to Dr.
HuaHe,whosegoodhumorandsensitivitynotonlybroughtmemuchhappiness,butalso
supported me through difficult times. Last but not least, I am grateful to my American
grandmother, Ms. Natalie Rammel, who has taught me to appreciate life, and to always
smile.
ThisworkwasfinanciallysupportedinpartbyNIH grantP01-CA59827,International
studentfellowshipandBarbourfellowshipattheUniversityofMichigan.
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TABLEOFCONTENTS
DEDICATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
LISTOFFIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
LISTOFTABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
LISTOFAPPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
ABSTRACT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
CHAPTER
I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
II. AdaptiveEllipseTrackinganditsApplicationinEstimatingRespiratoryDrifting1 . . 3
2.1 EllipseFittingModelforStaticData . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 AnIterativeAlgorithmforSolvingtheGeneralizedEigenProblem . . . . . . . . . 5
2.3 AdaptiveEllipseFitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.1 SlidingWindowAdaptation . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.2 DiscountingAdaptation . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 ApplicationtoTrackingRespiratoryMeanDrift . . . . . . . . . . . . . . . . . . . 10
2.4.1 ApplicationBackground . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4.2 ExperimentSetup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.5 GeneralizedFittingCostforRobustEstimation . . . . . . . . . . . . . . . . . . . . 19
2.6 Appendix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
III. RegularizedNonrigidImageRegistration. . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.1 GeneralOptimizationFormulationforRegularizedRegistration . . . . . . . . . . . 27
3.1.1 DataDissimilarity(Infidelity)Measure . . . . . . . . . . . . . . . . . . 27
3.2 Tissue-typeDependentRigidityRegularization . . . . . . . . . . . . . . . . . . . . 28
3.2.1 RegularizationDesign . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2.2 ExperimentandTestResults . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2.3 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3 Discontinuity-PreservingRegularization . . . . . . . . . . . . . . . . . . . . . . . 37
3.3.1 IndiscriminateDiscontinuityPreservingRegularization . . . . . . . . . 39
3.3.2 DiscriminativeShearPreservingRegularizer . . . . . . . . . . . . . . . 45
1Thischapterisbasedonmaterialsfrom[97,99].
v
3.3.3 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.4 EquivalenceBetweenTwoL Div-L CurlRegularizations⋆ . . . . . . . . . . . . . 60
2 1
IV. Fundamental Performance Analysis in Image Registration Problems: Crame´r-Rao
BoundanditsVariations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.1 Model-theIdealv.s. CommonlyUsed . . . . . . . . . . . . . . . . . . . . . . . . 64
4.2 Crame´r-RaoBoundanditsAsymptoticBehavior . . . . . . . . . . . . . . . . . . . 65
4.3 RelatingtoMCRB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.4 AnAlternatingMinimizationAlgorithm . . . . . . . . . . . . . . . . . . . . . . . 69
4.5 ComparisonwithConventionalMethods: CRBv.s. M-estimate . . . . . . . . . . . 70
4.6 ASimpleExample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
V. SummaryandFutureWork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.2 FutureWork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
APPENDIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
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LISTOFFIGURES
Figure
2.1 Effectofdriftcompensationforgatingsystem.. . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Illustrationofellipsefittingperformanceoftheproposedmethod. . . . . . . . . . . . . . 14
2.3 Comparisonofmovingaverage(MA)andellipsefittingestimatorformeanpositiontracking. 15
2.4 EffectofwindowlengthLontrackingperformance. . . . . . . . . . . . . . . . . . . . . . 16
2.5 Effectofdiscountfactorg ontrackingperformance. . . . . . . . . . . . . . . . . . . . . . 16
2.6 MeantrackingforRPMdatawithwindowsizedeterminedbyperiodestimator. . . . . . . 17
2.7 OverallRMSerror(acrossallpatients)asafunctionofsamplingrate. . . . . . . . . . . . 17
2.8 Evolutionofrobustfittedellipsewiththegradientprojectionmethod.. . . . . . . . . . . . 23
3.1 Illustrationofstiffnessfactors(). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
·
3.2 DifferentviewsoftheoriginalCTdataandtissueinformationinferredfromit. . . . . . . . 32
3.3 Deformedsourceimage(green)overlaidwithtargetimage(darkblue)forcomparisonof
intensitymatch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.4 Geometryextractedfromregistrationresults: target(blue)vs. deformedsource(white). . . 34
3.5 IllustrationoflandmarkdataonthoraxCT. . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.6 Registrationerrorfordifferentmethods: TPS,BSPandRegularizedBSP. . . . . . . . . . 36
3.7 Comparisonof3-dimensionalEuclideanlandmarkregistrationerror. . . . . . . . . . . . . 37
3.8 Truncatedquadraticregularizationwithvaryingscale. . . . . . . . . . . . . . . . . . . . . 42
3.9 Registration comparison between Tikhonov (Tik) and Truncated quadratic (TQ) regular-
izations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.10 Comparisonofdeformationfields. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.11 Regularizationresultsforacolliding/foldingflow. . . . . . . . . . . . . . . . . . . . . . . 47
3.12 Regularizationresultsforavacuumgeneratingflow. . . . . . . . . . . . . . . . . . . . . . 48
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3.13 Regularizationresultsforaslidingflow. . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.14 Regularizationresultsforaflowwithsimultaneouslysignificantdivergenceandcurlcom-
ponents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.15 Simulatedslidingblocksandthegroundtruthdeformation. . . . . . . . . . . . . . . . . . 50
3.16 Registrationperformancecomparison: registrationerrorv.s. intensitydiscrepancy. . . . . . 51
3.17 Bestestimationresults(relativetothegroundtruthdeformation)fromvariousregulariza-
tionmethods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.18 RegistrationresultsofCTdatawithvariousregularizations. . . . . . . . . . . . . . . . . . 54
3.19 VerticalcomponentofthedeformationfromCTregistration. . . . . . . . . . . . . . . . . 55
3.20 QuiverplotoverlainwithimageintensityforL regularizedimageregistration. . . . . . . 55
1
3.21 QuiverplotoverlainwithimageintensityforL regularizedimageregistration. . . . . . . 56
2
3.22 Quiverplotoverlainwithimageintensityfordiscriminatelyregularizedimageregistration. 56
3.23 Coronalviewfor3Ddiscriminateregistration. . . . . . . . . . . . . . . . . . . . . . . . . 57
3.24 Sagittalviewfor3Ddiscriminateregistration. . . . . . . . . . . . . . . . . . . . . . . . . 58
3.25 Illustrationforthethreecasesoffeasibleregion: strictlyconvexandeverywheredifferen-
tiable,nonstrictlyconvexandeverywheredifferentiable,nondifferentiable. . . . . . . . . . 61
3.26 Equivalencebetweenunconstrainedandconstrainedformulation. . . . . . . . . . . . . . . 62
4.1 BiasandvarianceapproximationobtainedfromexplicitsolutionforconventionalM-estimate. 77
4.2 BiasandvarianceapproximationforM-estimateobtainedfromexpansionabout(a¯,z¯). . . 79
4.3 BiasandvarianceapproximationofM-estimateobtainedfromexpansionabout(aˇ,zˇ). . . 83
4.4 BiasandvarianceapproximationofML-estimateobtainedfromexpansionabout(a¯,z¯).. . 89
A.1 Properinitializationhelpstoavoidsuboptimal(nonphysical)localminimum. . . . . . . . 99
A.2 Clinicalsignificantperformancemetricsv.s. RootMeanSquaredError(RMSE).. . . . . . 99
A.3 RMSE,Doseerror(%),PTVmargin(cm),95%dosecoverageofmodifiedcosinemodel
v.s. projectionmodel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
A.4 Trajectoryfittingwithprojectionmodelandmodifiedcosinemodel. . . . . . . . . . . . . 101
A.5 Predictionofbreathingtrajectorywithprojectionmodel. . . . . . . . . . . . . . . . . . . 102
B.1 State-spacedistanceandlocalregressionweightassignment. . . . . . . . . . . . . . . . . 105
B.2 Typicalbreathingtrajectories: (a)rapidyetregularbreath;(b)slowyetirregularbreath. . . 109
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