Abstract
The EMI model represents excitable cells in a more accurate manner than traditional homogenized models at the price of increased computational complexity. The increased complexity of solving the EMI model stems from a significant increase in the number of computational nodes and from the form of the linear systems that need to be solved. Here, we will show that the latter problem can be solved by careful use of operator splitting of the spatially coupled equations. By using this method, the linear systems can be broken into sub-problems that are of the classical type of linear, elliptic boundary value problems. Therefore, the vast collection of methods for solving linear, elliptic partial differential equations can be used. We demonstrate that this enables us to solve the systems using shared-memory parallel computers. The computing time scales perfectly with the number of physical cells. For a collection of 512×256 cells, we solved linear systems with about2.5×108unknows. Since the computational effort scales linearly with the number of physical cells, we believe that larger computers can be used to simulate millions of excitable cells and thus allow careful analysis of physiological systems of great importance.
Highlights
Numerical simulations of excitable tissue have been performed using homogenized mathematical models
The main reason for this is that the cell itself is missing in the homogenized models
Spatial and Temporal Splitting The challenge we address in the present paper is to split the spatial coupling of the EMI model such that a solution algorithm can be founded on well-studied equations
Summary
Numerical simulations of excitable tissue have been performed using homogenized mathematical models. The bidomain model and the associated monodomain model have been very popular and provided important insights into the electrochemical processes underpinning every heartbeat. Introductions to these models can be found in, e.g., Refs. The extracellular space, the cell membrane and the intracellular space all exist everywhere in the computational domain. This approach has proven to be very useful in studying effects on a relatively large length scale (millimeters), but has obvious limitations when the length scale approaches the size of a cell (micrometers). The main reason for this is that the cell itself is missing in the homogenized models
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