The Dynamics of Sustained Reentry in a Loop Model with Discrete Gap Junction Resistance

Dynamics of reentry are studied in a one dimensional loop of model cardiac cells with discrete intercellular gap junction resistance ($R$). Each cell is represented by a continuous cable with ionic current given by a modified Beeler-Reuter formulation. For $R$ below a limiting value, propagation is found to change from period-1 to quasi-periodic ($QP$) at a critical loop length ($L_{crit}$) that decreases with $R$. Quasi-periodic reentry exists from $L_{crit}$ to a minimum length ($L_{min}$) that is also shortening with $R$. The decrease of $L_{crit}(R)$ is not a simple scaling, but the bifurcation can still be predicted from the slope of the restitution curve giving the duration of the action potential as a function of the diastolic interval. However, the shape of the restitution curve changes with $R$.Comment: 6 pages, 7 figure

Evaluation of different statistical shape models for segmentation of the left ventricular endocardium from magnetic resonance images

International audienceStatistical shape models (SSMs) represent a powerful tool used in patient-specific modeling to segment medical images because they incorporate a-priori knowledge that guide the model during deformation. Our aim was to evaluate segmentation accuracy in terms of left ventricular (LV) volumes obtained using four different SSMs versus manual gold standard tracing on cardiac magnetic resonance (CMR) images. A database of 3D echocardiographic (3DE) LV surfaces obtained in 435 patients was used to generate four different SSMs, based on cardiac phase selection. Each model was scaled and deformed to detect LV endocardial contours in the enddiastolic (ED) and end-systolic (ES) frames of a CMR short-axis (SAX) stack for 15 patients with normal LV function. Linear correlation and Bland–Altman analyses versus gold-standard showed in all cases high correlation (r²>0.95), non-significant biases and narrow limits of agreement

Optimized schwarz methods and model adaptivity in electrocardiology simulations

[No abstract available

Mathematical Modeling and Simulation of Ventricular Activation Sequences: Implications for Cardiac Resynchronization Therapy

Next to clinical and experimental research, mathematical modeling plays a crucial role in medicine. Biomedical research takes place on many different levels, from molecules to the whole organism. Due to the complexity of biological systems, the interactions between components are often difficult or impossible to understand without the help of mathematical models. Mathematical models of cardiac electrophysiology have made a tremendous progress since the first numerical ECG simulations in the 1960s. This paper briefly reviews the development of this field and discusses some example cases where models have helped us forward, emphasizing applications that are relevant for the study of heart failure and cardiac resynchronization therapy

New Mathematical approaches in Electrocardiography Imaging inverse problem

International audienceImprove ECGI inverse problem reconstruction Introduce new mathematical approches to the field of the ECGI inverse problem Compare the performance of the new mathematical approaches to the state-of-the-art methods, mainly the MFS method used in commercial devices. In silico validation of the new approches. Assessment of some simplification hypothesis: Torso inhomogeneity Propose some uncertainty quantification apronches to deal with measurements errors Context and objectives Optimal control approach Mathematical model In silico gold standard Results Torso Heterogeneity effect Conclusions Forward model If we know the heart potential we can compute the electrical potential Inverse problem If we know the electrical potential and the current density at the outer boundary of the torso and we look for the electrical potential at the heart surface Computational heart and torso anatomical models + electrodes position Computational torso meshes: 250 nodes mesh (blue). More accurate FE mesh with 6400 nodes (green) Remarks Introducing the torso heterogeneity is natural with FEM. also anisotropy could be introduced The error is more important in the left ventricle Main results and perspectives New mathematical approches for solving the inverse problem in electrocardiography imaging based on optimal control Over all the 20 cases used in this study the optimal control method performs better than the MFS both in terms of relative error and correlation coefficient: Acknowledgment: This work was partially supported by an ANR grant part of "Investissements d'Avenir" program with reference ANR-10-IAHU-04. It is also supported by the LIRIMA international lab thought the EPICARD tea

Cardiac anisotropy in boundary-element models for the electrocardiogram

The boundary-element method (BEM) is widely used for electrocardiogram (ECG) simulation. Its major disadvantage is its perceived inability to deal with the anisotropic electric conductivity of the myocardial interstitium, which led researchers to represent only intracellular anisotropy or neglect anisotropy altogether. We computed ECGs with a BEM model based on dipole sources that accounted for a “compound” anisotropy ratio. The ECGs were compared with those computed by a finite-difference model, in which intracellular and interstitial anisotropy could be represented without compromise. For a given set of conductivities, we always found a compound anisotropy value that led to acceptable differences between BEM and finite-difference results. In contrast, a fully isotropic model produced unacceptably large differences. A model that accounted only for intracellular anisotropy showed intermediate performance. We conclude that using a compound anisotropy ratio allows BEM-based ECG models to more accurately represent both anisotropies