Automated Detection and Classification of Intracranial Aneurysms based on 3D Surface Analysis

147 Pages·2010·4.69 MB·English

Automated Detection and Classification of
Intracranial Aneurysms based on 3D Surface
Analysis
Adissertationsubmittedby
Alexandra Lauric
Inpartialfulfillmentoftherequirements
forthedegreeofDoctorofPhilosophyin
Computer Science
TUFTS UNIVERSITY
August2010
ADVISER:EricL.Miller
ii
Abstract
Intracranial aneurysms are localized, abnormal arterial dilations with a variable risk of rupture,
whichcanleadtosubarachnoidhemorrhage(SAH),aconditionassociatedwithhighmorbidityand
mortality. Themajorityofnon-traumaticSAHcasesarecausedbyrupturedintracranialaneurysms.
Accurate detection can decrease a significant proportion of misdiagnosed cases. However, only a
smallpercentofalldetectedincidentalaneurysmsproceedtoruptureandpreventivetreatmentcar-
riesrisksofcomplications,thuscreatinganeedforaneurysmruptureriskstratificationtoolstohelp
guidethetreatmentoftheseasymptomaticlesions. Thisresearchinvestigatesthetwomajorareasof
intracranialaneurysmanalysis-aneurysmdetectionandruptureriskclassification. Firstamethod
for automatic detection of intracranial aneurysms is proposed. Applied to the segmented cerebral
vasculature,themethoddetectsaneurysmsassuspectregionsonthevasculartree,andisdesigned
toassistdiagnosticianswiththeirinterpretations. Themethodisimagingmodalityindependentand
wastestedonmagneticresonanceimaging,computedtomographyand3Dangiographydata. Sec-
ond, a new approach to morphological analysis of the 3D shape of an aneurysm is presented as a
differentiator of rupture risk status in cerebral aneurysms. The writhe number is introduced as a
novelsurfacedescriptorwhichprovesusefulinbothdetectionandclassificationstudies. Inaddition
tothewrithenumber,3Dshapedescriptorsbasedonsurfacecurvatureandcentroid-radiimodelare
proposedandinvestigatedforruptureriskclassification. Thecombineduseofallthesenewfeatures
yieldsverypromisingresultsforpredictingruptureriskinintracranialaneurysms. Inexperiments,
theaneurysmdetectionmethodachieved100%sensitivity,independentofmodality. Dependingon
theimagingmodality,therearebetween0.66and5.7falsepositivesperstudy; theworstcaseper-
formanceiscomparabletothatofexistingdetectionresearch. Theclassificationmethodresultedin
a∼20%increaseinpredictionaccuracy, comparedtoothercommonlyusedshapeindexes. These
resultssupporttheutilityofwrithenumberaneurysmshapeanalysisasahighorderdescriptorwith
potentialclinicaluseinintracranialaneurysmdetectionandruptureriskstratification.
Acknowledgements
IwouldliketothanktheTuftsUniversityDepartmentofComputerScienceforpro-
viding an academic atmosphere that is stimulating, challenging, and supportive of
its students. I am particularly grateful to my advisor, Eric Miller, for his guidance
over the period we worked together. Prof. Miller achieved the perfect balance be-
tween offering all his support, while at the same time allowing me to grow into an
independent researcher. His high research standards inspired me to push my limits
and thrive for excellence. I would like to thank the members of my dissertation
committee, not only for their helpful suggestions in the final writing of this the-
sis, but also for the constant inspiration they provided as researchers, teachers and
mentors during my graduate years: Prof. Diane Souvaine for encouraging me to
pursueaPhDdegree,Dr. SarahFriskenforintroducingmetotheworldofmedical
imaging, Dr. Adel Malek for providing great research problems and acting as my
medical research advisor, and Prof. Lenore Cowen for her advice and support at
keytimesinmydoctoralstudies.
IwouldliketothankmyfriendElenaforherhelpeditingthisthesis,butmostly
for her support and friendship during our graduate years and beyond. I must thank
my parents for compelling me to study Computer Science. As it turns out, they
wereright! Finally,thisthesisisdedicatedtomyhusband,Petru. Hisnever-ending
patience,encouragementandsupportmadethisworkpossible.
ii
Contents
1 Introduction 1
1.1 OverviewofAutomaticDetection . . . . . . . . . . . . . . . . . . 3
1.2 OverviewofRuptureStatusClassification . . . . . . . . . . . . . . 5
1.3 OutlineoftheThesis . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 BackgroundandRelatedWork 10
2.1 GeometryofCurvesandSurfaces . . . . . . . . . . . . . . . . . . 10
2.1.1 CurvesinthePlane . . . . . . . . . . . . . . . . . . . . . . 10
2.1.2 Surfacesin3-DimensionalSpace . . . . . . . . . . . . . . 11
2.1.3 Curvature . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.4 WritheNumber . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 ProbabilityandStatistics . . . . . . . . . . . . . . . . . . . . . . . 23
2.3 AneurysmDetectionandCharacterization . . . . . . . . . . . . . . 25
2.3.1 AneurysmDetection . . . . . . . . . . . . . . . . . . . . . 25
2.3.2 RuptureAnalysis . . . . . . . . . . . . . . . . . . . . . . . 27
3 TheWritheNumber 34
3.1 TheWritheNumberofSurfaces . . . . . . . . . . . . . . . . . . . 34
3.2 WritheNumberforAneurysmDetection . . . . . . . . . . . . . . . 36
3.2.1 TheWritheofaCylinder . . . . . . . . . . . . . . . . . . . 36
3.2.2 TheWritheofanExtrudedSurfaceAlongaParabola . . . . 37
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3.2.3 GeneralizationofWritheNumber . . . . . . . . . . . . . . 37
3.3 WritheNumberforRuptureStatusPrediction . . . . . . . . . . . . 38
3.3.1 Aphysicalinterpretationofsurfacewrithe . . . . . . . . . . 38
4 AutomatedDetectionofIntracranialAneurysmsusingtheWrithe
NumberofSurfaces 41
4.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.1.1 OverviewoftheDetectionAlgorithm . . . . . . . . . . . . 41
4.1.2 Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.1.3 MedialAxisDetection . . . . . . . . . . . . . . . . . . . . 42
4.1.4 ShortBranchesSelection . . . . . . . . . . . . . . . . . . . 42
4.1.5 LocalNeighborhoodModel . . . . . . . . . . . . . . . . . 43
4.1.6 WritheNumberComputation . . . . . . . . . . . . . . . . 45
4.1.7 FalsePositiveReduction . . . . . . . . . . . . . . . . . . . 45
4.2 ClinicalData . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2.1 3D-RA,MRAandCTA . . . . . . . . . . . . . . . . . . . 46
4.2.2 Preprocessing . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2.3 ExperimentalValidationofLocalNeighborhoods . . . . . . 49
4.3 AneurysmDetectionResults . . . . . . . . . . . . . . . . . . . . . 52
4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5 RuptureStatusClassificationofIntracranialAneurysmsusing
theWritheNumberofSurfaces 61
5.1 ClinicalData . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.2.1 OverviewoftheClassificationAlgorithm . . . . . . . . . . 64
5.2.2 Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.2.3 IsolationofAneurysms . . . . . . . . . . . . . . . . . . . . 65
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5.2.4 WritheNumberComputation . . . . . . . . . . . . . . . . 67
5.2.5 HistogramStatistics . . . . . . . . . . . . . . . . . . . . . 67
5.2.6 Classification . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.3 ClassificationResults . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.3.1 RuptureStatusPrediction . . . . . . . . . . . . . . . . . . 68
5.3.2 SensitivitytoSegmentation . . . . . . . . . . . . . . . . . 73
5.3.3 SensitivitytoCuttingPlanesDefinition . . . . . . . . . . . 74
5.3.4 SyntheticDataAnalysis . . . . . . . . . . . . . . . . . . . 76
5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
6 RuptureStatusClassificationofIntracranialAneurysmsusing
SurfaceCurvatureandtheCentroid-RadiiModel 89
6.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.1.1 OverviewoftheClassificationAlgorithm . . . . . . . . . . 89
6.1.2 Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . 90
6.1.3 IsolationofAneurysms . . . . . . . . . . . . . . . . . . . . 90
6.1.4 SurfaceCurvatureandCentroid-RadiiComputation . . . . . 90
6.1.5 HistogramStatistics . . . . . . . . . . . . . . . . . . . . . 91
6.1.6 Classification . . . . . . . . . . . . . . . . . . . . . . . . . 91
6.2 ClassificationResults . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.2.1 RuptureStatusPrediction . . . . . . . . . . . . . . . . . . 92
6.2.2 SensitivitytoSegmentation . . . . . . . . . . . . . . . . . 96
6.2.3 SensitivitytoCuttingPlanesDefinition . . . . . . . . . . . 97
6.2.4 SyntheticDataAnalysis . . . . . . . . . . . . . . . . . . . 99
6.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
7 ConclusionsandFutureWork 107
7.1 OngoingResearch . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
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7.2 FutureWork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Appendices 111
A WritheNumberAnalysis . . . . . . . . . . . . . . . . . . . . . . . 111
A.1 WritheNumberofaCylinder . . . . . . . . . . . . . . . . 111
A.2 WritheNumberofanExtrudedSurfaceAlongaParabola . . 112
Bibliography 115
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List of Figures
2.1 Illustration of the curvature of elliptical surfaces. (a) The Gaussian
curvatureofanellipticalsurfaceispositive. (b)Themeancurvature
ofanellipticalsurfaceispositiveifthesurfaceislocallyconvexand
negativeifthesurfaceislocallyconcave. . . . . . . . . . . . . . . . 15
2.2 Illustration of the curvature of hyperbolic surfaces. (a) The Gaus-
sian curvature of a hyperbolic surface is negative. (b) The mean
curvature of a hyperbolic surface can take both zero and non-zero
values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3 Gaussianandmeancurvatureofamorecomplexsurface. (a)Gaus-
sian curvature capture intrinsic geometric properties - elliptical or
hyperbolic patches. (b) mean curvature captures extrinsic geomet-
ricproperties-convexorconcaveregions. . . . . . . . . . . . . . . 16
2.4 A tubular neighborhood of a polygon 𝑃, represented as an offset
manifold in the direction of the unit normal field of 𝑃. The offset
distanceisboundedbyconstant 𝜖. . . . . . . . . . . . . . . . . . . 17
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2.5 Computingthecurvatureontriangularmeshes. (a)Completemodel
of an aneurysm represented as a triangular mesh. (b) Detail on the
mesh. The yellow disk surrounding vertex 𝑣 represents the neigh-
borhood𝐵 overwhichthecurvatureat𝑣iscomputed. (c)Theangle
between a pair of adjacent faces sharing an edge 𝑒 is computed as
the angle between the normals at the two triangles. ∣𝑒 ∩ 𝐵∣ is the
lengthof 𝑒∩𝐵 (between0and∣𝑒∣). . . . . . . . . . . . . . . . . . 19
2.6 (a) A curve crossing is considered positive if, in order to align two
curve intervals, the upper interval is rotated counterclockwise with
an angle between 0 and 𝜋. (b) A curve crossing is considered neg-
ative if, in order to align two curve intervals, the upper interval is
rotatedclockwisewithananglebetween0and 𝜋. . . . . . . . . . . 22
2.7 Thetrefoilknotcurvehas3crossingsandawrithenumberof3. (a)
3D view along x axis. (b) 3D view along the y axis. (c) 3D view
alongthezaxis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.8 Interpretation of third and fourth central moments. (a) Normal dis-
tributionwithmean𝜇. (b)Distributionwithpositiveskewness. The
asymmetric tail extend out toward positive 𝑥 values. (c) Distribu-
tion with negative skewness. The asymmetric tail extend toward
negative 𝑥 values. (d) Flat distribution with large kurtosis is called
platykurtic. (e) Sharp distribution with small kurtosis is called lap-
tokurtic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
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