What have we learned from mathematical models of defibrillation and postshock arrhythmogenesis? Application of bidomain simulations.
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Biomedical subjects
Gernot Plank
Publications and source records attributed to Gernot Plank.
Three-dimensional models of individual cardiac histoanatomy: tools and challenges.
There is a need for, and utility in, the acquisition of data sets of cardiac histoanatomy, with the vision of reconstructing individual hearts on the basis of noninvasive imaging, such as MRI, enriched by reference to detailed atlases of serial histology obtained from representative samples. These data sets would be useful not only as a repository of knowledge regarding the specifics of cardiac histoanatomy, but could form the basis for generation of individualized high-resolution cardiac structure-function models. The current article presents a step in this general direction: it illustrates how whole-heart noninvasive imaging can be combined with whole-heart histology in an approach to achieve automated construction of histoanatomically detailed models of cardiac 3D structure and function at hitherto unprecedented resolution and accuracy (based on 26.4 x 26.4 x 24.4 microm MRI voxel size, and enriched by histological detail). It provides an overview of the tools used in this quest and outlines challenges posed by the approach in the light of applications that may benefit from the availability of such data and tools.
Animals↗
Defibrillation depends on conductivity fluctuations and the degree of disorganization in reentry patterns.
UNLABELLED: Defibrillation depends on conductivity and disorganization. INTRODUCTION: Cardiac fibrillation is the deterioration of the heart's normally well-organized activity into one or more meandering spiral waves, which subsequently break up into many meandering wave fronts. Delivery of an electric shock (defibrillation) is the only effective way of restoring the normal rhythm. This study focuses on examining whether higher degrees of disorganization requires higher shock strengths to defibrillate and whether microscopic conductivity fluctuations favor shock success. METHODS AND RESULTS: We developed a three-dimensional computer bidomain model of a block of cardiac tissue with straight fibers immersed in a conductive bath. The membrane behavior was described by the Courtemanche human atrial action potential model incorporating electroporation and an acetylcholine- (ACh) dependent potassium current. Intracellular conductivities were varied stochastically around nominal values with variations of up to 50%. A single rotor reentry was initiated and, by adjusting the spatial ACh variation, the level of organization could be controlled. The single rotor could be stabilized or spiral wave breakup could be provoked leading to fibrillatory-like activity. For each level of organization, multiple shock timings and strengths were applied to compute the probability of shock success as a function of shock strength. CONCLUSIONS: Our results suggest that the level of the small-scale conductivity fluctuations is a very important factor in defibrillation. A higher variation significantly lowers the required shock strength. Further, we demonstrated that success also heavily depends on the level of organization of the fibrillatory episode. In general, higher levels of disorganization require higher shock strengths to defibrillate.
Acetylcholine↗
Parallel multigrid preconditioner for the cardiac bidomain model.
The bidomain equations are widely used for the simulation of electrical activity in cardiac tissue but are computationally expensive, limiting the size of the problem which can be modeled. The purpose of this study is to determine more efficient ways to solve the elliptic portion of the bidomain equations, the most computationally expensive part of the computation. Specifically, we assessed the performance of a parallel multigrid (MG) preconditioner for a conjugate gradient solver. We employed an operator splitting technique, dividing the computation in a parabolic equation, an elliptical equation, and a nonlinear system of ordinary differential equations at each time step. The elliptic equation was solved by the preconditioned conjugate gradient method, and the traditional block incomplete LU parallel preconditioner (ILU) was compared to MG. Execution time was minimized for each preconditioner by adjusting the fill-in factor for ILU, and by choosing the optimal number of levels for MG. The parallel implementation was based on the PETSc library and we report results for up to 16 nodes on a distributed cluster, for two and three dimensional simulations. A direct solver was also available to compare results for single processor runs. MG was found to solve the system in one third of the time required by ILU but required about 40% more memory. Thus, MG offered an attractive tradeoff between memory usage and speed, since its performance lay between those of the classic iterative methods (slow and low memory consumption) and direct methods (fast and high memory consumption). Results suggest the MG preconditioner is well suited for quickly and accurately solving the bidomain equations.
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