The aim of this study was to quantify the effect of cardiac anisotropy in the activation-based inverse problem of electrocardiography. Differences of the patterns of simulated body surface potential maps for isotropic and anisotropic conditions were investigated with regard to activation time (AT) imaging of ventricular depolarization. AT maps were estimated by solving the nonlinear inverse ill-posed problem employing spatio-temporal regularization. Four different reference AT maps (sinus rhythm, right-ventricular and septal pacing, accessory pathway) were calculated with a bidomain theory based anisotropic finite-element heart model in combination with a cellular automaton. In this heart model a realistic fiber architecture and conduction system was implemented. Although the anisotropy has some effects on forward solutions, effects on inverse solutions are small indicating that cardiac anisotropy might be negligible for some clinical applications (e.g., imaging of focal events) of our AT imaging approach. The main characteristic events of the AT maps were estimated despite neglected electrical anisotropy in the inverse formulation. The worst correlation coefficient of the estimated AT maps was 0.810 in case of sinus rhythm. However, all characteristic events of the activation pattern were found. The results of this study confirm our clinical validation studies of noninvasive AT imaging in which cardiac anisotropy was neglected.

Cardiac anisotropy: is it negligible regarding noninvasive activation time imaging?

Parallelized computation for computer simulation of electrocardiograms using personal computers with multi-core CPU and general-purpose GPU

Background: Many arrhythmias are triggered by abnormal electrical activity at the ionic channel and cell level, and then evolve spatio-temporally within the heart. To understand arrhythmias better and to diagnose them more precisely by their ECG waveforms, a whole-heart model is required to explore the association between the massively parallel activities at the channel/cell level and the integrative electrophysiological phenomena at organ level. Methods: We have developed a method to build large-scale electrophysiological models by using extended cellular automata, and to run such models on a cluster of shared memory machines. We describe here the method, including the extension of a language-based cellular automaton to implement quantitative computing, the building of a whole-heart model with Visible Human Project data, the parallelization of the model on a cluster of shared memory computers with OpenMP and MPI hybrid programming, and a simulation algorithm that links cellular activity with the ECG. Results: We demonstrate that electrical activities at channel, cell, and organ levels can be traced and captured conveniently in our extended cellular automaton system. Examples of some ECG waveforms simulated with a 2-D slice are given to support the ECG simulation algorithm. A performance evaluation of the 3-D model on a four-node cluster is also given. Conclusions: Quantitative multicellular modeling with extended cellular automata is a highly efficient and widely applicable method to weave experimental data at different levels into computational models. This process can be used to investigate complex and collective biological activities that can be described neither by their governing differentiation equations nor by discrete parallel computation. Transparent cluster computing is a convenient and effective method to make time-consuming simulation feasible. Arrhythmias, as a typical case, can be effectively simulated with the methods described.

/pdf/facilitating-arrhythmia-simulation-the-method-of-2zso6e3r8c.pdf

Facilitating arrhythmia simulation: the method of quantitative cellular automata modeling and parallel running.

In order to achieve a comprehensive understanding of complex biological systems, researchers must develop new techniques that incorporate key features of the system across all relevant spatial and temporal scales Recent advances in molecular biology and genetics have generated a wealth of experimental data that provides details with respect to gene-expression patterns and individual gene and protein functions, but integration of this information into meaningful knowledge of the complete system is a challenge borne by a new scientific era dependent on computational tools In this paper, we review new computational techniques, developed to reconstruct single-cell biochemical networks for generating quantitative descriptions of network properties, and agent-based models designed to study multicell interactions important in tissue patterning We also discuss the challenges and promises of combining these approaches in a single quantitative framework for advancing medical care for diseases that arise from a multitude of factors

Multiscale biosystems integration: coupling intracellular network analysis with tissue-patterning simulations

Personalized cardiac electrophysiology simulations have demonstrated great potential to study cardiac arrhythmias and help in therapy planning of radio-frequency ablation. Its application to analyze vulnerability to ventricular tachycardia and sudden cardiac death in infarcted patients has been recently explored. However, the detailed multi-scale biophysical simulations used in these studies are very demanding in terms of memory and computational resources, which prevents their clinical translation. In this work, we present a fast phenomenological system based on cellular automata (CA) to simulate personalized cardiac electrophysiology. The system is trained on biophysical simulations to reproduce cellular and tissue dynamics in healthy and pathological conditions, including action potential restitution, conduction velocity restitution and cell safety factor. We show that a full ventricular simulation can be performed in the order of seconds, emulate the results of a biophysical simulation and reproduce a patient’s ventricular tachycardia in a model that includes a heterogeneous scar region. The system could be used to study the risk of arrhythmia in infarcted patients for a large number of scenarios.

/pdf/an-automata-based-cardiac-electrophysiology-simulator-to-f9r34izm.pdf

An Automata-Based Cardiac Electrophysiology Simulator to Assess Arrhythmia Inducibility

Cellular automata are an important modeling paradigm for studying the dynamics of large, parallel systems composed of multiple, interacting components. However, to model biological systems, cellular automata need to be extended beyond the large-scale parallelism and intensive communication in order to capture two fundamental properties characteristic of complex biological systems: hierarchy and heterogeneity. This paper proposes extensions to a cellular automata language, Cellang, to meet this purpose. The extended language, with object-oriented features, can be used to describe the structure and activity of parallel molecular networks within cells. Capabilities of this new programming language include object structure to define molecular programs within a cell, floating-point data type and mathematical functions to perform quantitative computation, message passing capability to describe molecular interactions, as well as new operators, statements, and built-in functions. We discuss relevant programming issues of these features, including the object-oriented description of molecular interactions with molecule encapsulation, message passing, and the description of heterogeneity and anisotropy at the cell and molecule levels. By enabling the integration of modeling at the molecular level with system behavior at cell, tissue, organ, or even organism levels, the program will help improve our understanding of how complex and dynamic biological activities are generated and controlled by parallel functioning of molecular networks.

Cellular automata with object-oriented features for parallel molecular network modeling

The behaviors of cells in metazoans are context dependent, thus large-scale multi-cellular modeling is often necessary, for which cellular automata are natural candidates Two related issues are involved in cellular automata based multi-cellular modeling: how to introduce differential equation based quantitative computing to precisely describe cellular activity, and upon it, how to solve the heavy time consumption issue in simulation Based on a modified, language based cellular automata system we extended that allows ordinary differential equations in models, we introduce a method implementing asynchronous adaptive time step in simulation that can considerably improve efficiency yet without a significant sacrifice of accuracy An average speedup rate of 4–5 is achieved in the given example Strategies for reducing time consumption in simulation are indispensable for large-scale, quantitative multi-cellular models, because even a small 100 × 100 × 100 tissue slab contains one million cells Distributed and adaptive time step is a practical solution in cellular automata environment

/pdf/asynchronous-adaptive-time-step-in-quantitative-cellular-5f48xc5m4z.pdf

Asynchronous adaptive time step in quantitative cellular automata modeling.

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Facilitating arrhythmia simulation: the method of quantitative cellular automata modeling and parallel running.

Cellular automata with object-oriented features for parallel molecular network modeling

Asynchronous adaptive time step in quantitative cellular automata modeling.