simulation of soft tissue deformation for medical...

Simulation of soft tissue

deformation for medical

applications

Hervé Delingette

[email protected] INRIA SOPHIA ANTIPOLIS March 20th , 2014

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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• Cause of Deformation :

– Muscle :

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MR Imaging ofKnee joint@3DAH




– Muscle :

– Heart :

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Cardiac MR Imaging




– Muscle :

– Heart :

– Respiration :

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Augmented Reality IHU Strasbourg




– Muscle :

– Heart :

– Respiration :

– Pathologies

- 8

Simulation of Glioblastoma Growth




– Muscle :

– Heart :

– Respiration :

– Pathologies

– Surgical tools

- 9Liver Surgery Simulation

Application of soft tissue deformation

• Image Registration :

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Cardiac Motion Tracking based on Biomechanical model

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


• 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



– 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

Compressible St Venant Kirchhoff

• Efficient stiffness matrix computation

��

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AffineTransformation

Linear ElasticStiffness Matrix

Cope with inverted elements

Cope with Large Deformation



– 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

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




– Reduced Models (POD)

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– Reduced Models (POD)

– Parallelization (MT, GPU)

– Dedicated Software

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Excalibur SOFA

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

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Deformable Augmented Reality@Shacra – IHU Strasbourg

Haptic Feedback@Shacra

Pre-stressed Cutting

With Shacra Team, Inria Lille

00 MOIS 2011EMETTEUR - NOM DE LA PRESENTATION - 32

Hugo Talbot

EndoVascular Simulator of Cardiac RadioFrequency Ablation


• 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

35

dx

Cannot estimate spring stiffness kfrom dx!!

dx

Fk =

?k


• Can estimate combination of parameters from observation

36

dx

Only estimate spring stiffness k1+k2from dx and F!!

k1

k2

F


• Can estimate combination of parameters from observation

37

dx2

Can estimate the ratio of spring stiffness k1/k2from displacements !!

k1 k2k1k2

dx1

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

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

Simulating the Cardiac Cycle

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IsovolumetricContractionEjectionIsovolumetricRelaxationFilling

Stéphanie Marchesseau

Complex Muscle Modeling

42

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]

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.

Simulating the Healthy Heart

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Circumferential Motion:Twist / Torsion, Inverse Rotation between Base and Apex

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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46

Cine-MRI

Estimate ratio of stiffnesses

and contractilities

Cine-MRI

+

LV Pressure

Estimate stiffnesses

or contractilities

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


• The 4Ps:

– Precise

– Performant

– Personalized

– Predictive

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51

Predictive Value?• Predict the effect of a Cardiac Resynchronization

Therapy (CRT)

Currently, up to 30% of implantations are not successful

53

Virtual Pacemaker

before afterLV endocardia

Coronary sinus

RV endocardia

dP/dt

measuredsimulated

measuredsimulated

dP/dt

Simulated CRT

resynchronization

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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