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Efficient simulation of cardiac electrical propagation using high order finite elements.

Arthurs CJ, Bishop MJ, Kay D - J Comput Phys (2012)

Bottom Line: We detail the hurdles which must be overcome in order to achieve theoretically-optimal errors in the approximations generated, including the choice of method for approximating the solution to the cardiac cell model component.We place our work on a solid theoretical foundation and show that it can greatly improve the accuracy in the approximation which can be achieved in a given amount of processor time.Our results demonstrate superior accuracy over linear finite elements at a cheaper computational cost and thus indicate the potential indispensability of our approach for large-scale cardiac simulation.

View Article: PubMed Central - PubMed

Affiliation: Department of Computer Science, University of Oxford, Oxford, United Kingdom.

ABSTRACT
We present an application of high order hierarchical finite elements for the efficient approximation of solutions to the cardiac monodomain problem. We detail the hurdles which must be overcome in order to achieve theoretically-optimal errors in the approximations generated, including the choice of method for approximating the solution to the cardiac cell model component. We place our work on a solid theoretical foundation and show that it can greatly improve the accuracy in the approximation which can be achieved in a given amount of processor time. Our results demonstrate superior accuracy over linear finite elements at a cheaper computational cost and thus indicate the potential indispensability of our approach for large-scale cardiac simulation.

No MeSH data available.


Plot comparing the action potential in an isolated cellmodel using the standard Luo-Rudy 1991 formulation and the Noble-formmodification. Left: Noble-form modified LR91 action potential in an isolatedcell. On this scale, differences caused by the modification would be hardlynoticeable. Right: original LR91 transmembrane potential subtracted fromNoble-form LR91 transmembrane potential. Note that the scales on the y-axesdiffer.
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f0015: Plot comparing the action potential in an isolated cellmodel using the standard Luo-Rudy 1991 formulation and the Noble-formmodification. Left: Noble-form modified LR91 action potential in an isolatedcell. On this scale, differences caused by the modification would be hardlynoticeable. Right: original LR91 transmembrane potential subtracted fromNoble-form LR91 transmembrane potential. Note that the scales on the y-axesdiffer.

Mentions: Fig.3 shows the AP differencebetween the standard LR91 model and the modified Noble-form LR91; they arequite minor. Given the fact that cell models are generated from experimentaldata naturally prone to experimental error [44], these differences are probably not worth beingconcerned with, especially given that the discontinuities do not appear tobe biologically justified. We must check for and remove such discontinuitieswhen using a particular cell model for simulation.


Efficient simulation of cardiac electrical propagation using high order finite elements.

Arthurs CJ, Bishop MJ, Kay D - J Comput Phys (2012)

Plot comparing the action potential in an isolated cellmodel using the standard Luo-Rudy 1991 formulation and the Noble-formmodification. Left: Noble-form modified LR91 action potential in an isolatedcell. On this scale, differences caused by the modification would be hardlynoticeable. Right: original LR91 transmembrane potential subtracted fromNoble-form LR91 transmembrane potential. Note that the scales on the y-axesdiffer.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4067136&req=5

f0015: Plot comparing the action potential in an isolated cellmodel using the standard Luo-Rudy 1991 formulation and the Noble-formmodification. Left: Noble-form modified LR91 action potential in an isolatedcell. On this scale, differences caused by the modification would be hardlynoticeable. Right: original LR91 transmembrane potential subtracted fromNoble-form LR91 transmembrane potential. Note that the scales on the y-axesdiffer.
Mentions: Fig.3 shows the AP differencebetween the standard LR91 model and the modified Noble-form LR91; they arequite minor. Given the fact that cell models are generated from experimentaldata naturally prone to experimental error [44], these differences are probably not worth beingconcerned with, especially given that the discontinuities do not appear tobe biologically justified. We must check for and remove such discontinuitieswhen using a particular cell model for simulation.

Bottom Line: We detail the hurdles which must be overcome in order to achieve theoretically-optimal errors in the approximations generated, including the choice of method for approximating the solution to the cardiac cell model component.We place our work on a solid theoretical foundation and show that it can greatly improve the accuracy in the approximation which can be achieved in a given amount of processor time.Our results demonstrate superior accuracy over linear finite elements at a cheaper computational cost and thus indicate the potential indispensability of our approach for large-scale cardiac simulation.

View Article: PubMed Central - PubMed

Affiliation: Department of Computer Science, University of Oxford, Oxford, United Kingdom.

ABSTRACT
We present an application of high order hierarchical finite elements for the efficient approximation of solutions to the cardiac monodomain problem. We detail the hurdles which must be overcome in order to achieve theoretically-optimal errors in the approximations generated, including the choice of method for approximating the solution to the cardiac cell model component. We place our work on a solid theoretical foundation and show that it can greatly improve the accuracy in the approximation which can be achieved in a given amount of processor time. Our results demonstrate superior accuracy over linear finite elements at a cheaper computational cost and thus indicate the potential indispensability of our approach for large-scale cardiac simulation.

No MeSH data available.