## Modelling the cardiac ventricular structural heterogeneities

Organization:
Institut de recherche en informatique et en automatique (INRIA)
Email:
mostafa.bendahmane at u-bordeaux2.fr and yves.coudiere at inria.fr
Job Description:

Position type: PhD Student
Functional area: Bordeaux (Talence)
Research theme: Computation sciences for biology, medicine and the environnement
Project: CARMEN
Scientific advisor: yves.coudiere$inria.fr and mostafa.bendahmane$u-bordeaux2.fr
HR Contact: cyril.gerboin@inria.fr

The IHU LIRYC is a collaborative research center dedicated to the complete understanding of normal and abnormal cardiac electrical excitation. In this context, the team CARMEN investigates the mathematical and computational issues underlying this research. The ventricular wall is a higly complex structure (see figure below): a network of branching and merging fibers rotating more than 100° from the outer to the inner wall. The fibers are bound together, tightly packed in sheets or laminae separated by layers of collagen. The organization of these laminae is highly complex. Until now, the complexity of the ventricular laminar architecture was largely ignored in whole-heart models: it was assumed to be functionally unimportant and there has been a lack of mathematical descriptions of the structures and quantitative data on their characteristics. Such data are now available at the IHU, using high precision imaging techniques to visualize laminae and electrophysiological techniques to record their electrical function (see [1]). In parallel, there is a growing awareness of the importance of structural abnormalities in a wide range of cardiac diseases, like in infarction and associated scars and ischemia. For instance, some life-threatening ventricular arrythmias are supposed to arise from the infarct scars because of propagation features related to the highly complex structure of these scars (inducing perturbed propagations of the action potential).

Mission:
The purpose of this work is to develop models of the heterogeneity of the cardiac tissue, test and validate them both at the cellular and the whole-heart level. We will focus on modelling infarct scars and their insertion in healthy tissues. In addition, models on both scales will be used to determine in which circumstances it is justifiable to neglect the smallest-scale inhomogeneities. Based on experimental data and from the literature, we expect to understand the microscopic packing of cells following the multi-scale technique (see [2]). With this technique and physiological quantitative data on the structure, we will develop generic models for the pattern of laminae in the heart, and of their remodelling in different types of cardiomyopathy. The second objective is to collaborate with T. Desplantez and O. Bernus in order to validate the models. For this purpose, experimental data will be provided from the single cell and multicellular scale by using the patch-clamp and microelectrode arrays techniques (T. Desplantez) and from the whole-heart scale by using the optical mapping technique (O. Bernus).

Descriptif du poste:
This project pertains to the field of mathematical modeling in cardiac electrophysiology from the microscopic to the macroscopic scales (like in [3]). We want to model the role of the heterogeneities of the cardiac tissue at several scales ranging i.e. from the µm to the mm in the propagation of the action potential. The heterogeneity comes from the nature of the tissue: a complex packing of excitable myocytes with fibroblasts, within the extracellular space and some sheets of collagen. First, we will study the description of the ventricular wall in the literature and from experimental data. The leading parameters and most important structural and functional features will be identified. Then, a novel homogenization method based on the ideas from [2] will be used to derive a model (partial differential equations) of the tissue's electrophysiology accounting for the predefined structural features. It will assume that the myocytes, extracellular space and fibroblasts are arranged in a non-periodic structure, but with known probability of density, forming laminae separated by collagen. At last, a finite element numerical technique will be used to compute approximate solutions of this model. These simulation will be compared to experimental data, in order to validate the models in view of the functional features identified earlier.

Profil:
The candidate will have a strong background in partial differential equation basics and numerical methods. An experience on homogenization techniques will be appreciated, although it is not required. He/she will be curious and interested in collaboration and interaction with scientists from the fields of biophysic and electrophysiology.

Avantages:
36 months. Monthly salary after taxes around 1 960 € (medical insurance included)

Informations complémentaires
In the interests of protecting its scientific and technological assets, INRIA is a restricted-access establishment. Consequently, it observes special regulations for welcoming foreign visitors from outside of the Schengen area. The final acceptance of each candidate thus depends on applying this security and defence procedure.
"Before applying, it is advised to contact the scientific advisor for more information on the research project (his/her e-mail is above-mentioned). You can also ask the HR contact for any administrative or practical information."
1. S.H. Gilbert, D. Benoist, A.P. Benson, E. White, S.F. Tanner, A.V. Holden, H. Dobrzynski, O. Bernus and A. Radjenovic. Visualization and quantification of whole rat heart laminar architecture using high spatial resolution contrast enhanced MRI. Am J Physiol - Heart and Circulatory Physiology, 302 H287-H298, 2012.
2. G. Allaire. Homogenization and Two-Scale Convergence. SIAM J. Math. Anal. 23, pp. 1482-1518, 1992.
3. A. Azzouzi and Y. Coudière and R. Turpault and N. Zemzemi. A mathematical model of Purkinje-Muscle Junctions. Mathematical Biosciences and Engineering, 4(8), 2011.

Job Categories: