DonatiFabrizio_EMBC2014
64
Pressure Mapping from Flow Imaging: Enhancing Computation of the Viscous Term Through Velocity Reconstruction in Near-Wall Regions Fabrizio Donati, Nicolas P. Smith, David A. Nordsletten, Pablo Lamata [email protected] Department of Biomedical Engineering and Imaging Sciences King's College London Chicago, Illinois, 29 th August 2014
-
Upload
fabrizio-donati -
Category
Documents
-
view
29 -
download
0
Transcript of DonatiFabrizio_EMBC2014
PressureMappingfromFlowImaging:EnhancingComputationoftheViscousTermThroughVelocityReconstructioninNear-WallRegions
FabrizioDonati,NicolasP.Smith,DavidA.Nordsletten,[email protected]
DepartmentofBiomedicalEngineeringandImagingSciencesKing'sCollegeLondon
Chicago,Illinois,29thAugust2014
IntroductionandMotivation
IntroductionandMotivation Whatispressure?
IntroductionandMotivation Whatispressure?
• Pressureinafluidsystemisaforceoverunitareathatresiststhechangesinvolume• Pressuregradientisthevariationofpressureoverthevessels'length• DescribedbyNavier-Stokes'momentumconservationequation:
IntroductionandMotivation Whatispressure?
• Pressureinafluidsystemisaforceoverunitareathatresiststhechangesinvolume• Pressuregradientisthevariationofpressureoverthevessels'length• DescribedbyNavier-Stokes'momentumconservationequation:
Time-dependentAccelerationintimePulsatileflowFunctionofheartpump
IntroductionandMotivation Whatispressure?
• Pressureinafluidsystemisaforceoverunitareathatresiststhechangesinvolume• Pressuregradientisthevariationofpressureoverthevessels'length• DescribedbyNavier-Stokes'momentumconservationequation:
Time-dependentAccelerationintimePulsatileflowFunctionofheartpump
AdvectiveAccelerationinspaceFunctionofvesselmorphologyFunctionofvasculaturegeometry
IntroductionandMotivation Whatispressure?
• Pressureinafluidsystemisaforceoverunitareathatresiststhechangesinvolume• Pressuregradientisthevariationofpressureoverthevessels'length• DescribedbyNavier-Stokes'momentumconservationequation:
Time-dependentAccelerationintimePulsatileflowFunctionofheartpump
AdvectiveAccelerationinspaceFunctionofvesselmorphologyFunctionofvasculaturegeometry
ViscousDissipationDuetoneighbouringlaminaeoffluidmovingatdifferentvelocity
IntroductionandMotivation
IntroductionandMotivation Whydowecareaboutpressureinaclinicalarena?
Pressuregradientisacceptedbiomarkerinclinicalpre-andpost-operativeguidelines
IntroductionandMotivation Whydowecareaboutpressureinaclinicalarena?
Aorticcoarctation
Kellyetal.(2005)EHJCardiovImag,6:288-290
Pressuregradientisacceptedbiomarkerinclinicalpre-andpost-operativeguidelines
Valvularstenosis
Baumgardtneretal.(2009)EurJEcho,10:1-25
HypertrophicCardiomyopathy
Allenetal.(2014)JCMR,16
IntroductionandMotivation Whydowecareaboutpressureinaclinicalarena?
Aorticcoarctation
Kellyetal.(2005)EHJCardiovImag,6:288-290
Pressuregradientisacceptedbiomarkerinclinicalpre-andpost-operativeguidelines
Valvularstenosis
Baumgardtneretal.(2009)EurJEcho,10:1-25
HypertrophicCardiomyopathy
Allenetal.(2014)JCMR,16
IntroductionandMotivation Whydowecareaboutpressureinaclinicalarena?
Whyviscouspressuregradient?
• Inefficiencyoftheflow• Energylosses• RelatedtochangesinWallShearStress• Methodologicallychallenging:IIorderspatialderivatives
Aorticcoarctation
Kellyetal.(2005)EHJCardiovImag,6:288-290
Pressuregradientisacceptedbiomarkerinclinicalpre-andpost-operativeguidelines
Valvularstenosis
Baumgardtneretal.(2009)EurJEcho,10:1-25
HypertrophicCardiomyopathy
Allenetal.(2014)JCMR,16
IntroductionandMotivation Whydowecareaboutpressureinaclinicalarena?
Whyviscouspressuregradient?
• Inefficiencyoftheflow• Energylosses• RelatedtochangesinWallShearStress• Methodologicallychallenging:IIorderspatialderivatives
Aorticcoarctation
Kellyetal.(2005)EHJCardiovImag,6:288-290
Pressuregradientisacceptedbiomarkerinclinicalpre-andpost-operativeguidelines
Valvularstenosis
Baumgardtneretal.(2009)EurJEcho,10:1-25
HypertrophicCardiomyopathy
Allenetal.(2014)JCMR,16
IntroductionandMotivation Whydowecareaboutpressureinaclinicalarena?
Whyviscouspressuregradient?
Whylaminarpressuregradient?
• Inefficiencyoftheflow• Energylosses• RelatedtochangesinWallShearStress• Methodologicallychallenging:IIorderspatialderivatives
Aorticcoarctation
Kellyetal.(2005)EHJCardiovImag,6:288-290
Pressuregradientisacceptedbiomarkerinclinicalpre-andpost-operativeguidelines
Valvularstenosis
Baumgardtneretal.(2009)EurJEcho,10:1-25
HypertrophicCardiomyopathy
Allenetal.(2014)JCMR,16
IntroductionandMotivation Whydowecareaboutpressureinaclinicalarena?
Whyviscouspressuregradient?
Whylaminarpressuregradient?• Turbulencedoesneedtimetodevelop• Pulsatileregimeisnotsoproneforit
IntroductionandMotivation
IntroductionandMotivation Howcanpressuregradientbemeasured?
IntroductionandMotivation
Cardiaccatheterization
Schlantetal.(1984),JAmCollCardiol,3(4):1096-8
Howcanpressuregradientbemeasured?
IntroductionandMotivation
Cardiaccatheterization EchoDopplerUltrasoundB-modeorM-mode
Imageacquisition
Velocitytracedetection
PGestimation
Bernoulli'sprinciple
Eulerequation
Yottietal.(2005),JAmCollCardiol,122:1771-1779Schlantetal.(1984),JAmCollCardiol,3(4):1096-8
Howcanpressuregradientbemeasured?
IntroductionandMotivation
Imageacquisition
Computermodel
Boundaryconditions
Pressuresolution
Cardiaccatheterization EchoDopplerUltrasoundB-modeorM-mode
Navier-StokessimulationsModeldriven
Figueroaetal.(2009),AnnuRevBiomedEng,11:109-134
Imageacquisition
Velocitytracedetection
PGestimation
Bernoulli'sprinciple
Eulerequation
Yottietal.(2005),JAmCollCardiol,122:1771-1779Schlantetal.(1984),JAmCollCardiol,3(4):1096-8
Howcanpressuregradientbemeasured?
IntroductionandMotivation
Imageacquisition
Computermodel
Boundaryconditions
Pressuresolution
Cardiaccatheterization EchoDopplerUltrasoundB-modeorM-mode
Navier-StokessimulationsModeldriven
PoissonPressureEquation(PPE)Datadriven
Figueroaetal.(2009),AnnuRevBiomedEng,11:109-134
4DflowPC-MRIacquisition
Quadratichexahedrals
Maskingoperator:nodalintensityvalues FiniteElements
Method
Imageacquisition
FEMmeshMaskedfield+velocity
fieldPGmapping
Krittianetal.(2011),MedImageAnal,16:1029-1037
Imageacquisition
Velocitytracedetection
PGestimation
Bernoulli'sprinciple
Eulerequation
Yottietal.(2005),JAmCollCardiol,122:1771-1779Schlantetal.(1984),JAmCollCardiol,3(4):1096-8
Howcanpressuregradientbemeasured?
IntroductionandMotivation Whichisthebesttechnique?
Imageacquisition
Computermodel
Boundaryconditions
Pressuresolution
Cardiaccatheterization EchoDopplerUltrasoundB-modeorM-mode
Navier-StokessimulationsModeldriven
PoissonPressureEquation(PPE)Datadriven
Figueroaetal.(2009),AnnuRevBiomedEng,11:109-134
4DflowPC-MRIacquisition
Quadratichexahedrals
Maskingoperator:nodalintensityvalues FiniteElements
Method
Imageacquisition
FEMmeshMaskedfield+velocity
fieldPGmapping
Krittianetal.(2011),MedImageAnal,16:1029-1037
Imageacquisition
Velocitytracedetection
PGestimation
Bernoulli'sprinciple
Eulerequation
Yottietal.(2005),JAmCollCardiol,122:1771-1779Schlantetal.(1984),JAmCollCardiol,3(4):1096-8
IntroductionandMotivation Whichisthebesttechnique?
Imageacquisition
Computermodel
Boundaryconditions
Pressuresolution
Cardiaccatheterization EchoDopplerUltrasoundB-modeorM-mode
Navier-StokessimulationsModeldriven
PoissonPressureEquation(PPE)Datadriven
Figueroaetal.(2009),AnnuRevBiomedEng,11:109-134
4DflowPC-MRIacquisition
Quadratichexahedrals
Maskingoperator:nodalintensityvalues FiniteElements
Method
Imageacquisition
FEMmeshMaskedfield+velocity
fieldPGmapping
Krittianetal.(2011),MedImageAnal,16:1029-1037
Imageacquisition
Velocitytracedetection
PGestimation
Bernoulli'sprinciple
Eulerequation
Yottietal.(2005),JAmCollCardiol,122:1771-1779Schlantetal.(1984),JAmCollCardiol,3(4):1096-8
Noninvasive
IntroductionandMotivation Whichisthebesttechnique?
Imageacquisition
Computermodel
Boundaryconditions
Pressuresolution
EchoDopplerUltrasoundB-modeorM-mode
Navier-StokessimulationsModeldriven
PoissonPressureEquation(PPE)Datadriven
Figueroaetal.(2009),AnnuRevBiomedEng,11:109-134
4DflowPC-MRIacquisition
Quadratichexahedrals
Maskingoperator:nodalintensityvalues FiniteElements
Method
Imageacquisition
FEMmeshMaskedfield+velocity
fieldPGmapping
Krittianetal.(2011),MedImageAnal,16:1029-1037
Imageacquisition
Velocitytracedetection
PGestimation
Bernoulli'sprinciple
Eulerequation
Yottietal.(2005),JAmCollCardiol,122:1771-1779
Noninvasive
IntroductionandMotivation Whichisthebesttechnique?
Imageacquisition
Computermodel
Boundaryconditions
Pressuresolution
EchoDopplerUltrasoundB-modeorM-mode
Navier-StokessimulationsModeldriven
PoissonPressureEquation(PPE)Datadriven
Figueroaetal.(2009),AnnuRevBiomedEng,11:109-134
4DflowPC-MRIacquisition
Quadratichexahedrals
Maskingoperator:nodalintensityvalues FiniteElements
Method
Imageacquisition
FEMmeshMaskedfield+velocity
fieldPGmapping
Krittianetal.(2011),MedImageAnal,16:1029-1037
Imageacquisition
Velocitytracedetection
PGestimation
Bernoulli'sprinciple
Eulerequation
Yottietal.(2005),JAmCollCardiol,122:1771-1779
Noninvasive
Accurate
Automatic
IntroductionandMotivation Whichisthebesttechnique?
Imageacquisition
Computermodel
Boundaryconditions
Pressuresolution
Navier-StokessimulationsModeldriven
PoissonPressureEquation(PPE)Datadriven
Figueroaetal.(2009),AnnuRevBiomedEng,11:109-134
4DflowPC-MRIacquisition
Quadratichexahedrals
Maskingoperator:nodalintensityvalues FiniteElements
Method
Imageacquisition
FEMmeshMaskedfield+velocity
fieldPGmapping
Krittianetal.(2011),MedImageAnal,16:1029-1037
Noninvasive
Accurate
Automatic
IntroductionandMotivation Whichisthebesttechnique?
Imageacquisition
Computermodel
Boundaryconditions
Pressuresolution
Navier-StokessimulationsModeldriven
PoissonPressureEquation(PPE)Datadriven
Figueroaetal.(2009),AnnuRevBiomedEng,11:109-134
4DflowPC-MRIacquisition
Quadratichexahedrals
Maskingoperator:nodalintensityvalues FiniteElements
Method
Imageacquisition
FEMmeshMaskedfield+velocity
fieldPGmapping
Krittianetal.(2011),MedImageAnal,16:1029-1037
Noninvasive
Accurate
Automatic
Fast
IntroductionandMotivation Whichisthebesttechnique?
PoissonPressureEquation(PPE)Datadriven
4DflowPC-MRIacquisition
Quadratichexahedrals
Maskingoperator:nodalintensityvalues FiniteElements
Method
Imageacquisition
FEMmeshMaskedfield+velocity
fieldPGmapping
Krittianetal.(2011),MedImageAnal,16:1029-1037
Noninvasive
Accurate
Automatic
Fast
IntroductionandMotivation RelativepressuremappingusingPPEFEM
IntroductionandMotivation RelativepressuremappingusingPPEFEM
• Data-drivenapproach:pressurefieldisunknownbutvelocityfieldisprovided• DefinedapplyingdivergencetoNavier-Stokes'momentumconservationequation:
ReducedcomputationaltimeandcostsFormulationwithFiniteElementsMethodiseasy:
IntroductionandMotivation RelativepressuremappingusingPPEFEM
• Data-drivenapproach:pressurefieldisunknownbutvelocityfieldisprovided• DefinedapplyingdivergencetoNavier-Stokes'momentumconservationequation:
ReducedcomputationaltimeandcostsFormulationwithFiniteElementsMethodiseasy:
IntroductionandMotivation RelativepressuremappingusingPPEFEM
• Data-drivenapproach:pressurefieldisunknownbutvelocityfieldisprovided• DefinedapplyingdivergencetoNavier-Stokes'momentumconservationequation:
MRI
ReducedcomputationaltimeandcostsFormulationwithFiniteElementsMethodiseasy:
IntroductionandMotivation RelativepressuremappingusingPPEFEM
• Data-drivenapproach:pressurefieldisunknownbutvelocityfieldisprovided• DefinedapplyingdivergencetoNavier-Stokes'momentumconservationequation:
MESH
ReducedcomputationaltimeandcostsFormulationwithFiniteElementsMethodiseasy:
IntroductionandMotivation RelativepressuremappingusingPPEFEM
• Data-drivenapproach:pressurefieldisunknownbutvelocityfieldisprovided• DefinedapplyingdivergencetoNavier-Stokes'momentumconservationequation:
MASK
ReducedcomputationaltimeandcostsFormulationwithFiniteElementsMethodiseasy:
IntroductionandMotivation RelativepressuremappingusingPPEFEM
• Data-drivenapproach:pressurefieldisunknownbutvelocityfieldisprovided• DefinedapplyingdivergencetoNavier-Stokes'momentumconservationequation:
VELOCITY
ReducedcomputationaltimeandcostsFormulationwithFiniteElementsMethodiseasy:
IntroductionandMotivation RelativepressuremappingusingPPEFEM
• Data-drivenapproach:pressurefieldisunknownbutvelocityfieldisprovided• DefinedapplyingdivergencetoNavier-Stokes'momentumconservationequation:
PRESSURE
ReducedcomputationaltimeandcostsFormulationwithFiniteElementsMethodiseasy:
IntroductionandMotivation RelativepressuremappingusingPPEFEM
• Data-drivenapproach:pressurefieldisunknownbutvelocityfieldisprovided• DefinedapplyingdivergencetoNavier-Stokes'momentumconservationequation:
Finiteelementsedgesdonotmatchvessel'swallViscousterm(IIderivatives)compromisessolutionLowerSignal-to-NoiseRatioatwallsdoesnothelp!
PRESSURE
ReducedcomputationaltimeandcostsFormulationwithFiniteElementsMethodiseasy:
IntroductionandMotivation RelativepressuremappingusingPPEFEM
• Data-drivenapproach:pressurefieldisunknownbutvelocityfieldisprovided• DefinedapplyingdivergencetoNavier-Stokes'momentumconservationequation:
Finiteelementsedgesdonotmatchvessel'swallViscousterm(IIderivatives)compromisessolutionLowerSignal-to-NoiseRatioatwallsdoesnothelp!
PRESSUREHigherresolutionisnotthesolution!
ReducedcomputationaltimeandcostsFormulationwithFiniteElementsMethodiseasy:
IntroductionandMotivation RelativepressuremappingusingPPEFEM
• Data-drivenapproach:pressurefieldisunknownbutvelocityfieldisprovided• DefinedapplyingdivergencetoNavier-Stokes'momentumconservationequation:
Finiteelementsedgesdonotmatchvessel'swallViscousterm(IIderivatives)compromisessolutionLowerSignal-to-NoiseRatioatwallsdoesnothelp!
PRESSUREHigherresolutionisnotthesolution!
IntroductionandMotivation RelativepressuremappingusingPPEFEM
• Data-drivenapproach:pressurefieldisunknownbutvelocityfieldisprovided• DefinedapplyingdivergencetoNavier-Stokes'momentumconservationequation:
Integrationoftheboundaryregionbyautomaticfittingofasmoothtubularcomputationalmeshtothesegmentationdomain
Low-SNRanddataissuesareaddressedbythereconstructionofthevelocityprofileviaaStokes-drivendegreesoffreedomrepopulationinthenear-wallregion
Stokes'enhancedPPEapproach
Methods HybridStokes'enhancedPPEFEMapproach
• UsesPPEFEMstandardapproach(data-driven)inthecoreregion• UsesStokes'theory(model-driven)toreconstructvelocityintheboundaryregion• Mainhypothesisisthatviscoustermdrivesmotionnearthevessels'wall:
Methods HybridStokes'enhancedPPEFEMapproach
• UsesPPEFEMstandardapproach(data-driven)inthecoreregion• UsesStokes'theory(model-driven)toreconstructvelocityintheboundaryregion• Mainhypothesisisthatviscoustermdrivesmotionnearthevessels'wall:
Methods HybridStokes'enhancedPPEFEMapproach
• UsesPPEFEMstandardapproach(data-driven)inthecoreregion• UsesStokes'theory(model-driven)toreconstructvelocityintheboundaryregion• Mainhypothesisisthatviscoustermdrivesmotionnearthevessels'wall:
Methods HybridStokes'enhancedPPEFEMapproach
Imageacquisition
Segmentation+Walls
detection
Template
definition
Imageregistration+Meshpersonalization
Wallsvelocityreconstruction(Stokes)
Relativepressuremapping(PPEFEM)
• UsesPPEFEMstandardapproach(data-driven)inthecoreregion• UsesStokes'theory(model-driven)toreconstructvelocityintheboundaryregion• Mainhypothesisisthatviscoustermdrivesmotionnearthevessels'wall:
Methods HybridStokes'enhancedPPEFEMapproach
Imageacquisition
Segmentation+Walls
detection
Template
definition
Imageregistration+Meshpersonalization
Wallsvelocityreconstruction(Stokes)
Relativepressuremapping(PPEFEM)
Materials Validationtestcase
Materials Validationtestcase
Imageacquisition TemplategenerationInsilicophantomCylindricalstraightpipe3DPoiseuilleflow(viscousonly)
Resolution:2mm3SimulatedGaussiannoise,
8longitudinalelms8circumferentialelms12radialelms8boundaryelms(25%lumen)
Originalimage
Noisyimage,SNR=5
Materials Validationtestcase
Imageacquisition TemplategenerationInsilicophantomCylindricalstraightpipe3DPoiseuilleflow(viscousonly)
Resolution:2mm3SimulatedGaussiannoise,
8longitudinalelms8circumferentialelms12radialelms8boundaryelms(25%lumen)
Originalimage
Noisyimage,SNR=5
Materials Validationtestcase
Imageacquisition TemplategenerationInsilicophantomCylindricalstraightpipe3DPoiseuilleflow(viscousonly)
Resolution:2mm3SimulatedGaussiannoise,
8longitudinalelms8circumferentialelms12radialelms8boundaryelms(25%lumen)
Originalimage
Noisyimage,SNR=5
Materials Validationtestcase
Imageacquisition TemplategenerationInsilicophantomCylindricalstraightpipe3DPoiseuilleflow(viscousonly)
Resolution:2mm3SimulatedGaussiannoise,
8longitudinalelms8circumferentialelms12radialelms8boundaryelms(25%lumen)
Originalimage
Noisyimage,SNR=5
Materials Validationtestcase
Imageacquisition TemplategenerationInsilicophantomCylindricalstraightpipe3DPoiseuilleflow(viscousonly)
Resolution:2mm3SimulatedGaussiannoise,
8longitudinalelms8circumferentialelms12radialelms8boundaryelms(25%lumen)
Originalimage
Noisyimage,SNR=5
Materials Validationtestcase
Imageacquisition TemplategenerationInsilicophantomCylindricalstraightpipe3DPoiseuilleflow(viscousonly)
Resolution:2mm3SimulatedGaussiannoise,
8longitudinalelms8circumferentialelms12radialelms8boundaryelms(25%lumen)
Originalimage
Noisyimage,SNR=5
Stokes'enhancedPPE(SePPE)vsDirectPPE(DPPE)pressuregradientpercentagerelativeerror:
Sensitivityanalysis• Lumendetectionerror• SNR• Segmentationthreshold
Materials Validationtestcase
Imageacquisition TemplategenerationInsilicophantomCylindricalstraightpipe3DPoiseuilleflow(viscousonly)
Resolution:2mm3SimulatedGaussiannoise,
8longitudinalelms8circumferentialelms12radialelms8boundaryelms(25%lumen)
Originalimage
Noisyimage,SNR=5
Stokes'enhancedPPE(SePPE)vsDirectPPE(DPPE)pressuregradientpercentagerelativeerror:
Results
Sensitivityanalysistolumendetectionerror
Results
Sensitivityanalysistolumendetectionerror
Results
SePPEoutperformsDPPE!• WithSePPEunderestimationoflumenleadstopressuregradientoverestimationandviceversa• PressuregradientisalwaysunderestimatedwithDPPE• Performanceisstillacceptablewithlow-to-moderate εφ
• Lumendetectionerrorcomputedas
Results
SensitivityanalysistoSNRandsegmentationthreshold
Results
SePPEperformsbetterthanDPPE!• Highsensitivitytosegmentationthreshold• Bothmethodsperformpoorlyforhighlevelofnoise
• 20simulationsrunforeachsetofparameterstoavoidvariabilityofresults• SNRwithintherange[5÷15]• Segmentationthresholdasapercentageoftheanalyticalpeakvelocity• Physiologicallyrelevantnoise[7.5÷12.5]andsegmentationthreshold[7.5%÷12.5%]inred
SensitivityanalysistoSNRandsegmentationthreshold
Results
Discussion
Discussion • Laminarviscousdissipationishigheratthevessels'boundary• ViscousgradientsarenotcapturedcorrectlywithPPE
✓ SePPEmethodisfullyautomatic✓ PPEenablescomputationoftime-dependent,convectiveandviscousgradientsseparately✓ Velocityreconstructionreduceserrorinviscousgradientirrespectiveoflumendetectionerrorx Segmentationisfundamental!(lumendetectionerror<5%toget80%accuracyingradients)x OptimalsegmentationthresholdchoiceisfunctionofSNRlevelx 3DPoiseuilleflowisnotrepresentativeofphysiologicalaorticflows(noinertialterms)
Discussion
• Performingvalidationtestsonmorerealisticinsilicocases(Womersleypulsatileflowfield)• UsingNavier-Stokes'simulationtoreconstructvelocityprofileinboundaryregion
• Laminarviscousdissipationishigheratthevessels'boundary• ViscousgradientsarenotcapturedcorrectlywithPPE
✓ SePPEmethodisfullyautomatic✓ PPEenablescomputationoftime-dependent,convectiveandviscousgradientsseparately✓ Velocityreconstructionreduceserrorinviscousgradientirrespectiveoflumendetectionerrorx Segmentationisfundamental!(lumendetectionerror<5%toget80%accuracyingradients)x OptimalsegmentationthresholdchoiceisfunctionofSNRlevelx 3DPoiseuilleflowisnotrepresentativeofphysiologicalaorticflows(noinertialterms)
Hybridmethodimprovesestimationoflaminarviscousdissipation
Discussion
• Performingvalidationtestsonmorerealisticinsilicocases(Womersleypulsatileflowfield)• UsingNavier-Stokes'simulationtoreconstructvelocityprofileinboundaryregion
• Laminarviscousdissipationishigheratthevessels'boundary• ViscousgradientsarenotcapturedcorrectlywithPPE
Thankyouforyourattention.
Questions?
