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Simulation of soft tissue deformation for medical applications Herv 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

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Simulation of soft tissue deformation for medical applications

Hervé Delingette

Herve.Delingette@inria.fr

Asclepios INRIA SOPHIA ANTIPOLIS

March 20th , 2014

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Context

in vivo

Medical Images and Bio-signals

The Digital Patient

CT Scan MRI ECG Medical Records

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SLIDE 3

Context

Personalisation

in vivo

Medical Images and Bio-signals

Geometry Physics Physiology Cognition Computational Models & Tools

in silico

Statistics

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 of Knee joint @3DAH

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SLIDE 6

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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SLIDE 7

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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SLIDE 8

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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SLIDE 9

Soft Tissue Deformation in Medicine

  • Water content of human Body is 50-75%
  • Cause of Deformation :

– Muscle : – Heart : – Respiration : – Pathologies – Surgical tools

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Liver Surgery Simulation

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SLIDE 10

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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SLIDE 15

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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SLIDE 17

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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Triangle Tetrahedra

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Shape Function Shape Vector Displacement Nodal Displacement

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SLIDE 18

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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Affine Transformation Linear Elastic Stiffness 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 surgery 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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SLIDE 23

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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SLIDE 24

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 2011 EMETTEUR - NOM DE LA PRESENTATION

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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

Simulated Observations Measured Observations

Patient Data

Data processing

,...) , , ( K µ σ

Global Parameters

Calibration

Local Parameters

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 k from dx!!

dx F k =

?

k

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Parameter Observability

  • Can estimate combination of parameters from observation

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dx Only estimate spring stiffness k1+k2 from 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/k2 from displacements !! k1 k2 k1 k2 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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SLIDE 36

solid mechanics

Clinical applications Diagnosis Therapy planning

blood flow

Cardiac data Personalization

electro-physiology perfusion & metabolism

Physiological Modeling of the Heart

Cardiac modeling

anatomy

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A Multiphysics Problem

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Electrophysiology Modeling Simulate Action Potential Propagation Mechanical Modeling Action Potential Controls Active Stress Orthotropic Passive Material Flow Modeling Arterial Pressure Valve Opening / Closure

Strong Anisotropy due to the cardiac fibers

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SLIDE 38

Simulating the Cardiac Cycle

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Isovolumetric Contraction Ejection Isovolumetric Relaxation Filling

Stéphanie Marchesseau

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Complex Muscle Modeling

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Contractile Sarcomere Energy dissipation in Sarcomere Due 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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SLIDE 40

Longitudinal Motion: Apico-basal Shortening Radial Motion: Wall Thickening

Simulating the Healthy Heart

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  • 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 Calibration 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 Sciences The Guy's, King's and St Thomas' School of Medicine St Jude Ensite

  • K. Rhode
  • A. Rinaldi
  • R. Rezavi
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Parameter Observability

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Cine-MRI Estimate ratio of stiffnesses and contractilities Cine-MRI

+

LV Pressure Estimate stiffnesses

  • r contractilities
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Personalization of Local Contractility

Observations = LV AHA Regional Volumes LV barycenter Vreg

To optimize 17 local contractility parameters after calibration

  • f up to

7 global parameters

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Measured vs. Simulated Regional 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 using Reduced Order Unscented Kalman Filtering from Regional Volumes. Medical Image Analysis 2013

Euheart Project

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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 after

LV endocardia Coronary sinus RV endocardia

dP/dt

measured simulated measured simulated

dP/dt

Simulated CRT

resynchronizatio n

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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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SLIDE 51

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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Acknowledgments

Post-doc / engineer : Erik Pernod, Federico Spadoni Phd 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 Moireau Sisyphe INRIA : Michel Sorine Shacra INRIA : Stéphane Cotin, Christian Duriez KCL : 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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