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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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Scarle, Simon. (2009) 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. Computational Biology and Chemistry, Vol.33 (No.4). pp. 253-260. ISSN 1476-9271

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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.

Item Type: Journal Article
Subjects: R Medicine > RC Internal medicine
Divisions: Faculty of Science > Engineering
Library of Congress Subject Headings (LCSH): Arrhythmia -- Research, Xbox 360 (Video game console) -- Research, Turing (Computer program language), Heart -- Abnormalities -- Research
Journal or Publication Title: Computational Biology and Chemistry
Publisher: Elsevier Ltd
ISSN: 1476-9271
Official Date: August 2009
Volume: Vol.33
Number: No.4
Page Range: pp. 253-260
Identification Number: 10.1016/j.compbiolchem.2009.05.001
Status: Peer Reviewed
Access rights to Published version: Open Access
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URI: http://wrap.warwick.ac.uk/id/eprint/2514

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