Magnetic resonance elastography : physical background and medical applications

431 Pages·2017·12.794 MB·English

by  Braun, Jürgen, Hirsch, Sebastian, Sack, Ingolf

MagneticResonanceElastography
Magnetic Resonance Elastography
PhysicalBackgroundandMedicalApplications
SebastianHirsch,JürgenBraun,andIngolfSack
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v
Contents
AbouttheAuthors xiii
Foreword xv
Preface xvii
Acknowledgments xix
Notation xxi
ListofSymbols xxiii
Introduction 1
PartI MagneticResonanceImaging 7
1 NuclearMagneticResonance 9
1.1 ProtonsinaMagneticField 9
1.2 PrecessionofMagnetization 10
1.2.1 QuadratureDetection 11
1.3 Relaxation 13
1.4 BlochEquations 14
1.5 Echoes 15
1.5.1 SpinEchoes 15
1.5.2 GradientEchoes 17
1.6 MagneticResonanceImaging 17
1.6.1 SpatialEncoding 18
1.6.1.1 SliceSelection 19
1.6.1.2 PhaseEncoding 19
1.6.1.3 FrequencyEncoding 20
2 ImagingConcepts 23
2.1 k-Space 23
2.2 k-SpaceSamplingStrategies 26
2.2.1 SegmentedImageAcquisition 27
2.2.1.1 FastLow-AngleShot(FLASH) 27
2.2.1.2 BalancedSteady-StateFreePrecession(bSSFP) 28
2.2.2 Echo-PlanarImaging(EPI) 30
2.2.3 Non-CartesianImaging 32
vi Contents
2.3 FastImaging 33
2.3.1 FastImagingStrategies 33
2.3.2 PartialFourierImaging 34
2.3.3 ParallelImaging 35
2.3.3.1 GRAPPA 36
2.3.4 ImpactofFastImagingonSNRandScanTime 37
3 MotionEncodingandMRESequences 41
3.1 MotionEncoding 43
3.1.1 GradientMomentNulling 44
3.1.2 EncodingofTime-HarmonicMotion 46
3.1.3 FractionalEncoding 50
3.2 Intra-VoxelPhaseDispersion 51
3.3 Diffusion-WeightedMRE 52
3.4 MRESequences 53
3.4.1 FLASH-MRE 53
3.4.2 bSSFP-MRE 55
3.4.3 EPI-MRE 57
PartII Elasticity 61
4 ViscoelasticTheory 63
4.1 Strain 63
4.2 Stress 67
4.3 Invariants 68
4.4 Hooke’sLaw 69
4.5 Strain-EnergyFunction 70
4.6 Symmetries 71
4.7 EngineeringConstants 75
4.7.1 Young’sModulusandPoisson’sRatio 75
4.7.2 ShearModulusandLamé’sFirstParameter 76
4.7.3 CompressibilityandBulkModulus 77
4.7.4 ComplianceandElasticityTensorforaTransverselyIsotropicMaterial 79
4.8 ViscoelasticModels 80
4.8.1 ElasticModel:Spring 81
4.8.2 ViscousModel:Dashpot 82
4.8.3 CombinationsofElasticandViscousElements 83
4.8.4 OverviewofViscoelasticModels 89
4.9 DynamicDeformation 92
4.9.1 BalanceofMomentum 92
4.9.2 MechanicalWaves 96
4.9.2.1 ComplexModuliandWaveSpeed 98
4.9.3 Navier–StokesEquation 99
4.9.4 CompressionModulusandOscillatingVolumetricStrain 100
4.9.5 ElastodynamicGreen’sFunction 101
4.9.6 BoundaryConditions 103
Contents vii
4.10 WavesinAnisotropicMedia 104
4.10.1 TheChristoffelEquation 105
4.10.2 WavesinaTransverselyIsotropicMedium 106
4.11 EnergyDensityandFlux 110
4.11.1 GeometricAttenuation 113
4.12 ShearWaveScatteringfromInterfacesandInclusions 114
4.12.1 PlaneInterfaces 115
4.12.2 SpatialandTemporalInterfaces 118
4.12.3 WaveDiffusion 121
4.12.3.1 Green’sFunctionofWavesandDiffusionPhenomena 125
4.12.3.2 AmplitudesandIntensitiesofDiffusiveWaves 126
5 Poroelasticity 131
5.1 Navier’sEquationforBiphasicMedia 133
5.1.1 PressureWavesinPoroelasticMedia 136
5.1.2 ShearWavesinPoroelasticMedia 140
5.2 PoroelasticSignalEquation 142
PartIII TechnicalAspectsandDataProcessing 145
6 MREHardware 147
6.1 MRISystems 147
6.2 Actuators 153
6.2.1 TechnicalRequirements 153
6.2.2 Practicality 153
6.2.3 TypesofMechanicalTransducers 154
7 MREProtocols 161
8 NumericalMethodsandPostprocessing 165
8.1 NoiseandDenoisinginMRE 165
8.1.1 Denoising:AnOverview 165
8.1.2 LeastSquaresandPolynomialFitting 167
8.1.3 FrequencyDomain(k-Space)Filtering 168
8.1.3.1 Averaging 168
8.1.3.2 LTIFiltersintheFourierDomain 170
8.1.3.3 Band-PassFiltering 172
8.1.4 WaveletsandMulti-ResolutionAnalysis(MRA) 172
8.1.5 FFTversusMRAinvivo 174
8.1.6 SparserApproximationsandPerformanceTimes 175
8.2 DirectionalFilters 176
8.3 NumericalDerivatives 179
8.3.1 MatrixRepresentationofDerivativeOperators 182
8.3.2 AnderssenGradients 183
8.3.3 FrequencyResponseofDerivativeOperators 186
8.4 FiniteDifferences 187
viii Contents
9 PhaseUnwrapping 191
9.1 Flynn’sMinimumDiscontinuityAlgorithm 193
9.2 GradientUnwrapping 195
9.3 LaplacianUnwrapping 196
10 ViscoelasticParameterReconstructionMethods 199
10.1 DiscretizationandNoise 201
10.2 PhaseGradient 204
10.3 AlgebraicHelmholtzInversion 205
10.3.1 MultiparameterInversion 207
10.3.2 HelmholtzDecomposition 207
10.4 LocalFrequencyEstimation 208
10.5 MultifrequencyInversion 210
10.5.1 Reconstructionof𝜑 211
10.5.2 Reconstructionof|G∗| 213
10.6 k-MDEV 214
10.7 FiniteElementMethod 217
10.7.1 WeakFormulationoftheOne-DimensionalWaveEquation 218
10.7.2 DiscretizationoftheProblemDomain 219
10.7.3 BasisFunctionintheDiscretizedDomain 220
10.7.4 FEFormulationoftheWaveEquation 221
10.8 DirectInversionforaTransverseIsotropicMedium 224
10.9 WaveguideElastography 225
11 MulticomponentAcquisition 229
12 UltrasoundElastography 233
12.1 StrainImaging(SI) 235
12.2 StrainRateImaging(SRI) 235
12.3 AcousticRadiationForceImpulse(ARFI)Imaging 235
12.4 Vibro-Acoustography(VA) 237
12.5 Vibration-AmplitudeSonoelastography(VASono) 237
12.6 CardiacTime-HarmonicElastography(CardiacTHE) 237
12.7 VibrationPhaseGradient(PG)Sonoelastography 238
12.8 Time-HarmonicElastography(1D/2DTHE) 238
12.9 CrawlingWaves(CW)Sonoelastography 238
12.10 ElectromechanicalWaveImaging(EWI) 239
12.11 PulseWaveImaging(PWI) 239
12.12 TransientElastography(TE) 240
12.13 PointShearWaveElastography(pSWE) 240
12.14 ShearWaveElasticityImaging(SWEI) 240
12.15 Comb-PushUltrasoundShearElastography(CUSE) 241
12.16 SupersonicShearImaging(SSI) 241
12.17 SpatiallyModulatedUltrasoundRadiationForce(SMURF) 241
12.18 ShearWaveDispersionUltrasoundVibrometry(SDUV) 241
12.19 HarmonicMotionImaging(HMI) 242
Contents ix
PartIV ClinicalApplications 243
13 MREoftheHeart 245
13.1 NormalHeartPhysiology 245
13.1.1 CardiacFiberAnatomy 247
13.1.2 WallShearModulusversusCavityPressure 249
13.2 ClinicalMotivationforCardiacMRE 250
13.2.1 SystolicDysfunctionversusDiastolicDysfunction 250
13.3 CardiacElastography 252
13.3.1 ExvivoSWI 253
13.3.2 InvivoSDUV 253
13.3.3 InvivoCardiacMREinPigs 254
13.3.4 InvivoCardiacMREinHumans 256
13.3.4.1 Steady-StateMRE(WAV-MRE) 256
13.3.4.2 WaveInversionCardiacMRE 259
13.3.5 MREoftheAorta 260
14 MREoftheBrain 263
14.1 GeneralAspectsofBrainMRE 264
14.1.1 Objectives 264
14.1.2 DeterminantsofBrainStiffness 264
14.1.3 ChallengesforCerebralMRE 264
14.2 TechnicalAspectsofBrainMRE 265
14.2.1 ClinicalSetupforCerebralMRE 265
14.2.2 ChoiceofVibrationFrequency 266
14.2.3 Driver-FreeCerebralMRE 269
14.2.4 MREintheMouseBrain 270
14.3 Findings 271
14.3.1 BrainStiffnessChangeswithAge 272
14.3.2 MaleBrainsAreSofterthanFemaleBrains 273
14.3.3 RegionalVariationinBrainStiffness 274
14.3.4 AnisotropicPropertiesofBrainTissue 274
14.3.5 TheinvivoBrainIsCompressible 276
14.3.6 PreliminaryFindingsofMREwithFunctionalActivation 277
14.3.7 DemyelinationandInflammationReduceBrainStiffness 277
14.3.8 NeurodegenerationReducesBrainStiffness 279
14.3.9 TheNumberofNeuronsCorrelateswithBrainStiffness 280
14.3.10 PreliminaryConclusionsonMREoftheBrain 280
15 MREofAbdomen,Pelvis,andIntervertebralDisc 283
15.1 Liver 283
15.1.1 EpidemiologyofChronicLiverDiseases 286
15.1.2 LiverFibrosis 287
15.1.2.1 PathogenesisofLiverFibrosis 289
15.1.2.2 StagingofLiverFibrosis 291
15.1.2.3 NoninvasiveScreeningMethodsforLiverFibrosis 292
15.1.2.4 ReversibilityofLiverFibrosis 293
x Contents
15.1.2.5 BiophysicalSignsofLiverFibrosis 293
15.1.3 MREoftheLiver 294
15.1.3.1 MREinAnimalModelsofHepaticFibrosisandLiverTissueSamples 294
15.1.3.2 EarlyClinicalStudiesandFurtherDevelopments 295
15.1.3.3 MREofNonalcoholicFattyLiverDisease 303
15.1.3.4 ComparisonwithotherNoninvasiveImagingandSerumBiomarkers 304
15.1.3.5 MREoftheLiverforAssessingPortalHypertension 307
15.1.3.6 MREinLiverGrafts 309
15.1.3.7 Confounders 310
15.2 Spleen 311
15.2.1 MREoftheSpleen 311
15.3 Pancreas 314
15.3.1 MREofthePancreas 315
15.4 Kidneys 315
15.4.1 MREoftheKidneys 316
15.5 Uterus 318
15.5.1 MREoftheUterus 318
15.6 Prostate 319
15.6.1 MREoftheProstate 320
15.7 IntervertebralDisc 321
15.7.1 MREoftheIntervertebralDisc 322
16 MREofSkeletalMuscle 325
16.1 InvivoMREofHealthyMuscles 326
16.2 MREinMuscleDiseases 330
17 ElastographyofTumors 333
17.1 MicromechanicalPropertiesofTumors 333
17.2 UltrasoundElastographyofTumors 336
17.2.1 UltrasoundElastographyinBreastTumors 337
17.2.2 UltrasoundElastographyinProstateCancer 338
17.3 MREofTumors 339
17.3.1 MREofTumorsintheMouse 340
17.3.2 MREinLiverTumors 342
17.3.3 MREofProstateCancer 344
17.3.3.1 ExVivoStudies 344
17.3.3.2 InVivoStudies 345
17.3.4 MREofBreastTumors 345
17.3.4.1 InVivoMREofBreastTumors 346
17.3.5 MREofIntracranialTumors 347
PartV Outlook 351
Dimensionality 351
Sparsity 352
Heterogeneity 353
Reproducibility 353
Contents xi
A SimulatingtheBlochEquations 355
B ProofthatEq.(3.8)IsSinusoidal 357
C ProofforEq.(4.1) 359
D WaveIntensityDistributions 361
D.1 CalculationofIntensityProbabilities 361
D.2 PointSourcein3D 362
D.3 ClassicalDiffusion 363
D.4 DampedPlaneWave 365
References 367
Index 417