Simulation of soft tissue deformation for medical applications Hervé Delingette March 20th , 2014 Asclepios INRIA SOPHIA ANTIPOLIS Herve.Delingette@inria.fr
Context The Digital Patient ECG Medical CT Scan in vivo Medical Records MRI Images and Bio-signals - 2
Context The Digital Patient Medical in silico in vivo Computational Statistics Geometry Images Models Physics & and Physiology Tools Cognition Bio-signals Personalisation - 3
Soft Tissue Deformation in Medicine • Water content of human Body is 50-75% - 4
Soft Tissue Deformation in Medicine • Water content of human Body is 50-75% • Cause of Deformation : – Muscle : MR Imaging of Knee joint @3DAH - 5
Soft Tissue Deformation in Medicine • Water content of human Body is 50-75% • Cause of Deformation : – Muscle : – Heart : Cardiac MR Imaging - 6
Soft Tissue Deformation in Medicine • Water content of human Body is 50-75% • Cause of Deformation : – Muscle : – Heart : – Respiration : Augmented Reality IHU Strasbourg - 7
Soft Tissue Deformation in Medicine • Water content of human Body is 50-75% • Cause of Deformation : – Muscle : – Heart : – Respiration : – Pathologies Simulation of Glioblastoma Growth - 8
Soft Tissue Deformation in Medicine • Water content of human Body is 50-75% • Cause of Deformation : – Muscle : – Heart : – Respiration : – Pathologies – Surgical tools Liver Surgery Simulation - 9
Application of soft tissue deformation • Image Registration : Cardiac Motion Tracking based on Biomechanical model - 10
Application of soft tissue deformation • Image Registration : • Image Segmentation • Therapy Training • Therapy Planning - 11
Holy Grail of Soft Tissue Deformation • The 4Ps: – Precise – Performant – Personalized – Predictive - 12
Accurate Modeling • Use Physically (=biomechanical) based models – Model verification – Simplest Suitable Model - 13
Accurate Modeling • Use Physically (=biomechanical) based models • Image Based Validation : – Huge amount of data acquired every day – Only visible motion Cine-MRI : visible motion tagged-MRI : “true” motion - 14
Holy Grail of Soft Tissue Deformation • The 4Ps: – Precise – Performant – Personalized – Predictive - 15
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 - 16
How to speed up computation • Possible approaches (can be combined): – Fast assembly of Force vectors / Stiffness matrices • Geometric View of Linear Finite Elements Nodal Displacement Displacement � � � � � � � � � � � � � � � � ⋅ � � � ��� Triangle Tetrahedra Shape Vector Shape Function - 17
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 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 - 18
Compressible St Venant Kirchhoff • Efficient stiffness matrix computation ��� � �� � �� � �� � �� � �� �� � � �� � � Affine Linear Elastic Transformation Stiffness Matrix Cope with inverted elements Cope with Large Deformation - 19
How to speed up computation • Possible approaches (can be combined): – Fast assembly of Force vectors / Stiffness matrices • Geometric View of Finite Elements • MJED S. Marchesseau, T. Heimann, S. Chatelin, R. Willinger, and Hervé Delingette. Fast porous visco-hyperelastic soft tissue model for surgery simulation: application to liver surgery . Progress in Biophysics and Molecular Biology , 103(2-3):185-196, 2010 - 21
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) � and � ! � – Simplify term �� � ! – Allow for some precomputation – Extended for Visco-elasticity, anisotropy - 22
MJED Computational Speed-Up Models for hyperelasticity On average 2.7 times faster ! - 25
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) - 26
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 Excalibur SOFA - 27
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 28
SOFA in Action Pre-stressed Cutting Deformable Augmented Reality @Shacra – IHU Strasbourg Haptic Feedback @Shacra - 29
EndoVascular Simulator of Cardiac RadioFrequency Ablation Hugo Talbot With Shacra Team, Inria Lille EMETTEUR - NOM DE LA PRESENTATION 00 MOIS 2011 - 32
Holy Grail of Soft Tissue Deformation • The 4Ps: – Precise – Performant – Personalized – Predictive - 33
Model Personalization • Amounts to solve an inverse problem Patient Data Data Measured Observations processing Electromechanical Model Simulated Parameters Observations ( σ , µ , ,...) K Equations 0 Local Global Local Parameters Parameters Personalization Calibration - 34
Parameter Observability • Not all parameters can be estimated from observations Cannot estimate spring stiffness k from dx!! k F ? k = dx dx 35
Parameter Observability • Can estimate combination of parameters from observation k 1 F Only estimate spring stiffness k 1 +k 2 from dx and F!! k 2 dx 36
Parameter Observability • Can estimate combination of parameters from observation k 1 k 1 k 2 k 2 dx 1 dx 2 Can estimate the ratio of spring stiffness k 1 /k 2 from displacements !! 37
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 38
Physiological Modeling of the Heart Therapy planning anatomy Personalization electro-physiology blood flow Diagnosis perfusion solid mechanics & metabolism Clinical Cardiac data Cardiac modeling applications - 39
Strong Anisotropy due to the cardiac fibers A Multiphysics Problem Electrophysiology Mechanical Modeling Flow Modeling Modeling Orthotropic Passive Material Simulate Arterial Pressure Action Potential Propagation Controls Action Potential Active Stress Valve Opening / Closure - 40
Simulating the Cardiac Cycle Isovolumetric Isovolumetric Ejection Contraction Relaxation Filling Stéphanie Marchesseau - 41
Complex Muscle Modeling Elasticity of the Z-line (titine) Energy dissipation in Sarcomere Due to friction Contractile Sarcomere Elasticity of the Collagen Energy dissipation in the Collagen [Bestel 2009, 42 Chapelle 2012]
Simulating the Healthy Heart Longitudinal Motion: Radial Motion: Apico-basal Shortening Wall Thickening S. 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 Parameter 43 Calibration from Medical Images . Journal of the Mechanical Behavior of Biomedical Materials, 2012.
Simulating the Healthy Heart Circumferential Motion: Twist / Torsion, Inverse Rotation between Base and Apex 44
Personalization from In vivo Clinical Measurements R. Rezavi K. Rhode A. Rinaldi King’s College, division of Imaging Sciences The Guy's, King's and St Thomas' School of Medicine St Jude Ensite - 45
Parameter Observability Estimate ratio of stiffnesses and contractilities Cine-MRI Estimate + stiffnesses or contractilities Cine-MRI LV Pressure 46
Personalization of Local Contractility Observations = V reg LV AHA Regional Volumes LV barycenter To optimize 17 local contractility parameters after calibration of up to 7 global parameters - 47
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