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Implications of the Turing completeness of reaction-diffusion models, informed by GPGPU simulations on an XBox 360: Cardiac arrhythmias, re-entry and the Halting problem

Paper ID Volume ID Publish Year Pages File Format Full-Text
15292 1401 2009 8 PDF Available
Title
Implications of the Turing completeness of reaction-diffusion models, informed by GPGPU simulations on an XBox 360: Cardiac arrhythmias, re-entry and the Halting problem
Abstract

In the arsenal of tools that a computational modeller can bring to bare on the study of cardiac arrhythmias, the most widely used and arguably the most successful is that of an excitable medium, a special case of a reaction-diffusion model. These are used to simulate the internal chemical reactions of a cardiac cell and the diffusion of their membrane voltages. Via a number of different methodologies it has previously been shown that reaction-diffusion systems are at multiple levels Turing complete. That is, they are capable of computation in the same manner as a universal Turing machine. However, all such computational systems are subject to a limitation known as the Halting problem. By constructing a universal logic gate using a cardiac cell model, we highlight how the Halting problem therefore could limit what it is possible to predict about cardiac tissue, arrhythmias and re-entry.All simulations for this work were carried out on the GPU of an XBox 360 development console, and we also highlight the great gains in computational power and efficiency produced by such general purpose processing on a GPU for cardiac simulations.

Keywords
Heart; Re-entry; Cardiac arrhythmias; Excitable media; Halting problem; GPGPU
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Implications of the Turing completeness of reaction-diffusion models, informed by GPGPU simulations on an XBox 360: Cardiac arrhythmias, re-entry and the Halting problem
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Publisher
Database: Elsevier - ScienceDirect
Journal: Computational Biology and Chemistry - Volume 33, Issue 4, August 2009, Pages 253–260
Authors
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Subjects
Physical Sciences and Engineering Chemical Engineering Bioengineering
Get Full-Text Now
Don't Miss Today's Special Offer
Price was $35.95
You save - $31
Price after discount Only $4.95
100% Money Back Guarantee
Full-text PDF Download
Online Support
Any Questions? feel free to contact us