simulation of soft tissue deformation for medical...
TRANSCRIPT
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Simulation of soft tissue
deformation for medical
applications
Hervé Delingette
[email protected] INRIA SOPHIA ANTIPOLIS March 20th , 2014
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Context
in v
ivo Medical
Images
and
Bio-signals
The Digital Patient
CT ScanMRI
ECG
Medical Records
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Context
Personalisation
in v
ivo Medical
Images
and
Bio-signals
Geometry
Physics
Physiology
Cognition
Computational
Models
&
Tools
in silico
Sta
tist
ics
The Digital Patient
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Soft Tissue Deformation in Medicine
• Water content of human Body is 50-75%
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Soft Tissue Deformation in Medicine
• Water content of human Body is 50-75%
• Cause of Deformation :
– Muscle :
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MR Imaging ofKnee joint@3DAH
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Soft Tissue Deformation in Medicine
• Water content of human Body is 50-75%
• Cause of Deformation :
– Muscle :
– Heart :
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Cardiac MR Imaging
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Soft Tissue Deformation in Medicine
• Water content of human Body is 50-75%
• Cause of Deformation :
– Muscle :
– Heart :
– Respiration :
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Augmented Reality IHU Strasbourg
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Soft Tissue Deformation in Medicine
• Water content of human Body is 50-75%
• Cause of Deformation :
– Muscle :
– Heart :
– Respiration :
– Pathologies
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Simulation of Glioblastoma Growth
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Soft Tissue Deformation in Medicine
• Water content of human Body is 50-75%
• Cause of Deformation :
– Muscle :
– Heart :
– Respiration :
– Pathologies
– Surgical tools
- 9Liver Surgery Simulation
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Application of soft tissue deformation
• Image Registration :
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Cardiac Motion Tracking based on Biomechanical model
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Application of soft tissue deformation
• Image Registration :
• Image Segmentation
• Therapy Training
• Therapy Planning
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Holy Grail of Soft Tissue Deformation
• The 4Ps:
– Precise
– Performant
– Personalized
– Predictive
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Accurate Modeling
• Use Physically (=biomechanical) based models
– Model verification
– Simplest Suitable Model
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Accurate Modeling
• Use Physically (=biomechanical) based models
• Image Based Validation :
– Huge amount of data acquired every day
– Only visible motion
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Cine-MRI : visible motion tagged-MRI : “true” motion
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Holy Grail of Soft Tissue Deformation
• The 4Ps:
– Precise
– Performant
– Personalized
– Predictive
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Computational Speed
• Why is it important ?
– Models Compatible with clinical practice
• Training : Real Time !
• Diagnosis : Few minutes
• Planning : Few hours
– Important for
• Model Personalization
• Uncertainty Estimation
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How to speed up computation
• Possible approaches (can be combined):
– Fast assembly of Force vectors / Stiffness matrices• Geometric View of Linear Finite Elements
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TriangleTetrahedra
� � ���� � ���
�� � � �� ⋅ � ���
Shape Function Shape Vector
Displacement NodalDisplacement
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How to speed up computation
• Possible approaches (can be combined):
– Fast assembly of Force vectors / Stiffness matrices• Geometric View of Linear Finite Elements• Use mesh topology to store matrices• Link between discrete & continuum mechanics
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Established equivalence between :
• Linear Strain / Stress Elasticity • Spring mass systems on Triangles / Tetrahedra with tensile / angular
and volumetric springs
H. Delingette. Triangular Springs for Modeling Nonlinear Membranes .IEEE Transactions on Visualization and Computer Graphics, 14(2), March/April 2008
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Compressible St Venant Kirchhoff
• Efficient stiffness matrix computation
������ � � ������ �� � �� ��� ���
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AffineTransformation
Linear ElasticStiffness Matrix
Cope with inverted elements
Cope with Large Deformation
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How to speed up computation
• Possible approaches (can be combined):
– Fast assembly of Force vectors / Stiffness matrices• Geometric View of Finite Elements• MJED
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S. Marchesseau, T. Heimann, S. Chatelin, R. Willinger, and Hervé Delingette.Fast porous visco-hyperelastic soft tissue model for s urgery simulation: application to liver surgery .Progress in Biophysics and Molecular Biology, 103(2-3):185-196, 2010
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Fast Assembly of Stiffness Matrices
• For Hyper-elastic materials– Existence of a strain energy W
• Multiplicative Jacobian Energy Decomposition– Decompose W according to :
• J=|F| Jacobian of deformation gradient � � ��• I1, I2, I3, invariants of Deformation tensor C = (Right Cauchy Green)
– Simplify term ��� and
�!�� !
– Allow for some precomputation
– Extended for Visco-elasticity, anisotropy
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MJED Computational Speed -Up
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On average 2.7 times faster !
Models for hyperelasticity
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How to speed up computation
• Possible approaches (can be combined):
– Fast assembly of Force vectors / Stiffness matrices• Geometric View of Finite Elements• MJED
– Reduced Models (POD)
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How to speed up computation
• Possible approaches (can be combined):
– Fast assembly of Force vectors / Stiffness matrices• Geometric View of Finite Elements• MJED
– Reduced Models (POD)
– Parallelization (MT, GPU)
– Dedicated Software
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Excalibur SOFA
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SOFA : www.sofa -framework.org
• Developed by several INRIA teams since 2004
• API for medical simulation :
– Focused on but not limited to real-time applications
– Modular : components structured inside a graph
– Support for GPU ( Cuda / Opencl)
– Well developed for Mechanical deformation (solid, fluid,
FEM. CG methods), Collision Detection, Visualization, Haptics
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SOFA in Action
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Deformable Augmented Reality@Shacra – IHU Strasbourg
Haptic Feedback@Shacra
Pre-stressed Cutting
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With Shacra Team, Inria Lille
00 MOIS 2011EMETTEUR - NOM DE LA PRESENTATION - 32
Hugo Talbot
EndoVascular Simulator of Cardiac RadioFrequency Ablation
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Holy Grail of Soft Tissue Deformation
• The 4Ps:
– Precise
– Performant
– Personalized
– Predictive
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Parameters
Electromechanical Model
Equations
SimulatedObservations
Measured Observations
Patient Data
Data
processing
,...),,( 0 Kµσ
GlobalParameters
Calibration
LocalParameters
Local
Personalization
Model Personalization• Amounts to solve an inverse problem
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Parameter Observability
• Not all parameters can be estimated from observations
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dx
Cannot estimate spring stiffness kfrom dx!!
dx
Fk =
?k
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Parameter Observability
• Can estimate combination of parameters from observation
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dx
Only estimate spring stiffness k1+k2from dx and F!!
k1
k2
F
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Parameter Observability
• Can estimate combination of parameters from observation
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dx2
Can estimate the ratio of spring stiffness k1/k2from displacements !!
k1 k2k1k2
dx1
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Biophysical Model Personalization
• Not just “Parameter Fitting” :
– Sensitivity analysis to extract most important params
– Parameters constrained by physics and physiology
• Avoid overfitting by adapting model complexity to that of the
measurements
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solid mechanics
Clinical applications
Diagnosis
Therapy planning
blood flow
Cardiac data
Personalizationelectro-physiology
perfusion & metabolism
Physiological Modeling of the Heart
Cardiac modeling
anatomy
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A Multiphysics Problem
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Electrophysiology Modeling
SimulateAction PotentialPropagation
Mechanical Modeling
Action PotentialControls
Active Stress
Orthotropic PassiveMaterial
Flow Modeling
Arterial Pressure
Valve Opening / Closure
Strong Anisotropy due to the cardiac
fibers
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Simulating the Cardiac Cycle
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IsovolumetricContractionEjectionIsovolumetricRelaxationFilling
Stéphanie Marchesseau
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Complex Muscle Modeling
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Contractile Sarcomere
Energy dissipation in SarcomereDue to friction
Elasticity of the Z-line (titine)
Elasticity of the Collagen
Energy dissipation in the Collagen
[Bestel 2009,Chapelle 2012]
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Longitudinal Motion:Apico-basal Shortening
Radial Motion:Wall Thickening
Simulating the Healthy Heart
43S. Marchesseau, H. Delingette, M. Sermesant, M. Sorine, K. Rhode, S.G. Duckett, C.A. Rinaldi, R. Razavi, & N. Ayache. Preliminary Specificity Study of the Bestel-Clément-Sorine Electromechanical Model of the Heart using ParameterCalibration from Medical Images. Journal of the Mechanical Behavior of Biomedical Materials, 2012.
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Simulating the Healthy Heart
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Circumferential Motion:Twist / Torsion, Inverse Rotation between Base and Apex
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Personalization from In vivo Clinical
Measurements
King’s College, division of Imaging SciencesThe Guy's, King's and St Thomas' School of Medicine
St Jude Ensite
K. Rhode A. RinaldiR. Rezavi
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Parameter Observability
46
Cine-MRI
Estimate ratio of stiffnesses
and contractilities
Cine-MRI
+
LV Pressure
Estimate stiffnesses
or contractilities
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Personalization of Local Contractility
Observations
=
LV AHA
Regional Volumes
LV
barycenter
Vreg
To optimize17 local contractility parameters after calibration of up to 7 global parameters
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Measured vs. SimulatedRegional Volumes
Measurements
Personalized
Simulation
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Mechanical Personalization
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Marchesseau, S., Delingette, H., Sermesant, M., Cabrera-Lozoya, R., Tobon-Gomez, C., Moireau, P., Figueras, R., Lekadir, K., Hernandez, A., Garreau, M., Donal, E., Leclercq, C., Duckett, S., Rhode, K., Rinaldi, C., Frangi, A., Razavi, R., Chapelle, D., and Ayache, N. Personalization of a Cardiac Electromechanical Model usingReduced Order Unscented Kalman Filtering from Regional Volumes. Medical Image Analysis 2013
EuheartProject
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Holy Grail of Soft Tissue Deformation
• The 4Ps:
– Precise
– Performant
– Personalized
– Predictive
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Predictive Value?• Predict the effect of a Cardiac Resynchronization
Therapy (CRT)
Currently, up to 30% of implantations are not successful
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Virtual Pacemaker
before afterLV endocardia
Coronary sinus
RV endocardia
dP/dt
measuredsimulated
measuredsimulated
dP/dt
Simulated CRT
resynchronization
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Importance of Estimating Uncertainty
• Predicting the future is difficult !!
• Estimate source of uncertainty
– Image / Data Noise or distorsion
– Image Processing
– Model Errors (False hypothesis)
– Errors in parameters / BC / IC
– Discretization errors
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Conclusion
• Need for soft tissue models to match clinical constraints in
terms of speed and accuracy.
• Must adapt model complexity to each given problem but
keeping a predictive value.
• Personalization leads to difficult inverse problems :– Parameters observability
– Data assimilation techniques
• Access to rich experimental data is key
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AcknowledgmentsPost-doc / engineer : Erik Pernod, Federico SpadoniPhd Students : Hugo Talbot, Stéphanie Marchesseau,
Tommaso Mansi, Jatin Relan, Jean-Marc Peyrat, Florence Billet, Loic Le Folgoc, Adityo Prakosa
Asclepios INRIA : Maxime Sermesant, Nicholas Ayache, Reo INRIA : Miguel Fernandez, Jean-Frédéric Gerbeau, Macs INRIA : Dominique Chapelle, Philippe MoireauSisyphe INRIA : Michel SorineShacra INRIA : Stéphane Cotin, Christian DuriezKCL : N. Smith, K. Rhode, R. Razavi, Toronto HSC : M. Pop, G. Wright,Creatis : P. Croisille, P. Clarysse
Funding : EuHeart, MedYMA, Health-e-Child, INRIA
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"In theory there is no difference between theory and practice.
In practice there is.“
Yogi Berra
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