Section: New Results

Computational Physiology

Personalisation of Cardiac Electrophysiology Model for simulation of Patient-Specific Ventricular Tachycardia (VT)

Participants : Jatin Relan [ Correspondant ] , Hervé Delingette, Maxime Sermesant, Nicholas Ayache.

This work is funded by the FP7 European Project euHeart.

Modeling of the cardiac electrophysiology has been an important research interest for the last few decades, but in order to translate this work to the clinics, there is an important need for personalisation of such models, i.e. estimation of the model parameters that best fit the simulation to the clinical data. In this work, we propose a method to personalize a 3D simplified ionic monodomain electrophysiology model, the Mitchell-Schaeffer (MS) model. The personalization is performed using the 2D epicardial depolarization and repolarization maps obtained ex-vivo from optical imaging of porcine healthy heart. The model parameters are estimated by matching the simulated and experimental conduction velocities, Action Potential Duration (APD) and APD Restitution (see Fig. 13 ). APD restitution is defined as the relationship of the succeeding APD with the preceeding diastolic interval (DI). After personalisation of the model, we evaluate the prediction ability of the model for different epi- and endocardial pacing scenarios [62] . This personalisation strategy could also be applied to clinical data where the 2D optical data can be replaced by 2D endo- or epicardial electro-anatomical mapping of the patient. The model is also used to simulate clinical VT-Stim Protocol to induce VT in patients, which is used to plan ablation lines in radio-frequency ablation therapy [63] , [64] .

Figure 13. Estimated parameters of MS model used for prediction of cardiac electrophysiology for different pacing scenario i.e. Right Ventricle Endocardium, and simulation of clinical VT-Stim protocol for induction of VT [62] .

Data assimilation for the estimation of the mechanical parameters of the heart model.

Participants : Florence Billet [ Correspondant ] , Maxime Sermesant, Hervé Delingette, Nicholas Ayache.

In this work, we build a patient-specific model by coupling an electromechanical model [24] and cine-MRI data. To achieve this personnalisation, we have to estimate both the state (i.e the position and the velocity) and the parameters of the electromechanical model. Thus, we first estimated the state of the heart by using a proactive deformable model [48] (see Fig. 14 ). Second, we used variational assimilation methods to estimate some mechanical parameters of the heart.

Figure 14. Short axis (top) and long axis (bottom) views at different times of the cardiac cycle. Contours of the mesh estimated with the proactive deformable model are surimposed with the images. Colors correspond to the intensity of the image forces applied on the heart surfaces [48] .

(a) t = 0.01 s (b) t = 0.337 s (c) t = 0.574 s (d) t = 0.921 s

Biomechanical modeling of the knee joint

Participants : Tobias Heimann [ Correspondant ] , François Chung, Olivier Clatz, Hervé Delingette.

Within the EU project 3D Anatomical Human, our goal is the construction of subject-specific models of the knee joint to predict exact movement patterns for the lower limbs. To this end, we developed a highly efficient finite element model for ligament tissue, which features realistic anisotropic behavior and non-linear stress-strain response [54] . The collagen fiber directions required for this model are estimated automatically from ligament geometry. Using this material model and segmentations from MRI data, we implemented an interactive simulation of a subject-specific joint in the Open Source software SOFA (see Fig. 15 ). Current work focuses on improving collision detection and response by employing implicit surface descriptions.

Figure 15. 3D finite element model of a subject-specific knee joint with cruciate and collateral ligaments.

Biomechanical Liver Modeling

Participants : Stéphanie Marchesseau, Erik Pernod, Tobias Heimann, Hervé Delingette [ Correspondant ] .

In the context of the Passport European project, a realistic biomechanical model of the liver has been developed based on the SOFA platform. This model relies on visco-elasticity for large displacements (non-linear elasticity) and also a poro-elastic behavior to cope with the blood motion within the hepatic parenchyma. Specific attention has been paid to the optimized formulation of hyperelastic materials on a linear tetrahedral FEM mesh. To this end, we chose to isolate in the strain energy the terms involving the infinitesimal volume change J in order to optimize the assembly of the nodal forces and stiffness matrices. Furthermore, we have described the visco-elasticity of the liver using Prony series where parameters have been estimated from rheological experiments performed at the University of Strasbourg.

Comparison with analytical curves and other FEM software confirmed the accuracy of the visco-elastic formulation model. Additional work needs to be done in order to combine poro-elasticity with the visco-elastic model of the liver and to build a realistic patient specific liver model suitable for real-time surgery simulation.

Adaptive Tetrahedral Meshing for Personalized Cardiac Simulations

Participants : Hans Lamecker [ Correspondant ] , Tommaso Mansi, Jatin Relan, Hervé Delingette.

This project was funded by the European Commission (FP7 - ICT-2007-224495: euHeart)

Personalized simulation for therapy planning in the clinical routine requires fast and accurate computations. The aim of this project was to analyze the meshing requirements for finite-element simulations of ventricular tachycardia and Tetralogy of Fallot. We have evaluated and benchmarked a variety of existing meshing software systems. Based on the insights gained from this study, we have developed a pipeline for generating high-quality, adaptive meshes (Fig. 16 ). The results indicate how to construct computationally efficient meshes in electrophysiological and electromechanical cardiac simulations [57] .

Figure 16. Four meshes with varying number of layers in the myocardium wall for studying discretization effects in electromechanical simulations.

Interactive Medical Simulation based on the SOFA Platform

Keywords : Manifold triangulation, manifold tetraedrisation, resection, incision, edge swapping, point snapping.

Participants : Erik Pernod [ Correspondant ] , Hervé Delingette.

SOFA is a software platform developed jointly with mainly the Alcove and Evasion project teams. Several developments have been performed in order to improve the topological description of meshes in SOFA. For instance, manifold triangulations and tetrahedrisations have been implemented as specialization of generic triangulations classes. Furthermore, the handling of topological changes has be extended to cope with manifold triangulation by avoiding the removal or additional of triangles when it violates the manifold constraint.

In addition, the method for interactively cutting triangular meshes has been much improved by allowing the incision path to go through existing vertices and edges in order to minimize the number of created triangles. The creation of several connected components during the simulation of incision is now possible.

The support of several input and output file formats has been improved and streamlined by defining mesh loaders factory in SOFA. For instance, this allows us to import in SOFA all meshes and anatomical information (e.g. fiber orientation) used in our proprietary platform MIPS. Finally, in order to simulate the propagation of electrical potentials in the heart, we have developed a software module that implements reaction-diffusion partial differential equations on a triangular or tetrahedral mesh.