June 22–26, 2014
Leipzig, Germany

Presentation Details

Name: (12a) Cardiac Arrhythmias in Mathematical Models of Ventricular Tissue: High-Performance Computing Studies
Time: Thursday, June 26, 2014
10:30 am - 11:00 am
Room:   Hall 4
CCL - Congress Center Leipzig
Breaks:10:30 am - 11:00 am Coffee Break
07:30 am - 10:30 am Welcome Coffee
Presenter:   Alok Ranjan Nayak, Indian Institute of Science
Abstract:   Cardiac arrhythmias, like ventricular tachycardia (VT) and ventricular fibrillation (VF), are a leading cause of sudden cardiac death. Thus, it is very important to study such arrhythmias. In such studies we must use interdisciplinary approaches with inputs from electrophysiology, bio-medical engineering, and cardiology, on the one hand, and nonlinear dynamics, physics, and computational science, on the other; methods from these areas must be used to develop and then study the complicated, nonlinear, partial-differential-equation (PDE) models for cardiac tissue. The solutions of such PDEs can show, inter alia, spiral- or scroll-wave turbulence and spatiotemporal chaos, which are believed to be mathematical analogs of VF. In the absence of medical intervention, VF incapacitates the pumping mechanism of the heart and a patient dies in a few minutes after the initiation of VF. Studies of spiral- and scroll-wave dynamics in cardiac tissue pose important challenges for in vivo and in vitro experimental studies and for in silico numerical studies of cardiac-tissue mathematical models.
We study two, recently developed state-of-the-art mathematical models of human ventricular tissue due to (a) ten-Tusscher, Noble, Noble, and Panfilov (the TNNP04 model) and (b) ten-Tusscher and Panfilov (the TP06 model). We have written an MPI code for this model and have run it on high-performance computing (HPC) platforms such as (a) the SGI Altix 350, (b) the IBM Regatta P690, (c) the IBM Cluster P720, (d) the IBM P575, and (e) the IBM Blue Gene/L. We have compared the performance of our code on these platforms.
We have carried out a detailed and systematic numerical study of spiral-wave dynamics in the TNNP04 and TP06 models of ventricular tissue in the presence of (a) conduction, (b) ionic, and (c) fibroblast-type inhomogeneities, and Purkinje fibers. In particular, we have used extensive numerical simulations to elucidate the interaction of spiral waves in these models with conduction and ionic inhomogeneities that occur commonly in cardiac tissue. Our studies show that spiral waves can continue to break up, as in VF, in the presence of a conduction inhomogeneity. They can, alternatively, get anchored to an obstacle and continue rotating around it, resulting in a situation similar to VT. In some cases, an obstacle can cause a spiral to move away from the tissue. Our ionicinhomogeneity studies show that they can suppress spiral wave like a conduction inhomogeneity but with richer dynamics observed in the rotating-spiral case. We have also shown that these final states depend very sensitively on the position, size and shape of the obstacle, reflecting the fractal-like boundary between different attractors in the underlying high-dimensional dynamical system. Our studies with fibroblast inhomogeneities show that a spiral wave can get anchored to a local fibroblast inhomogeneity like conduction inhomogeneity, or it can enter into the inhomogeneity like ionic inhomogeneity, depending on fibroblasts connections to myocytes. Our studies with Purkinje fibers show that inclusion of such fibers can convert a stable spiral (or broken spirals) to (a) a single spiral, (b) broken spirals, or (c) a system with no spirals at all. We also examine a control scheme, which has been suggested for the control of VT and VF via low-amplitude current-pulses algorithm; here we study this scheme in the presence of inhomogeneities and Purkinje fibers, in these models. We hope that our studies can help in developing effective methods for treating cardiac arrhythmias. Representative results are given in our poster.

Alok Ranjan Nayak & Rahul Pandit, Indian Institute of Science