Combination of “quadratic adaptive algorithm” and “hybrid operator splitting” or uniformization algorithms for stability against acceleration in the Markov model of sodium ion channels in the ventricular cell model

The Markovian model has generally been used for cardiac electrophysiological simulations. However, the Markovian model is so stiff that speeding up the computation of the algorithms with variable time-steps always results in simulation instability. In particular, the unstable simulations always occu...

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Bibliographic Details
Published in:Medical & biological engineering & computing Vol. 57; no. 6; pp. 1367 - 1379
Main Authors: Chen, Xing-Ji, Luo, Ching-Hsing, Chen, Min-Hung, Zhou, Xiang
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2019
Springer Nature B.V
Subjects:
Acceleration
Adaptive algorithms
Algorithms
Biomedical and Life Sciences
Biomedical Engineering and Bioengineering
Biomedicine
Computation
Computer Applications
Computer simulation
Human Physiology
Imaging
Ion channels
Low voltage
Markov analysis
Markov chains
Original Article
Radiology
Simulation
Sodium
Sodium channels
Splitting
Stability
Ventricle
Ventricular cell model
Action potential
Computer simulation
Adaptive algorithm
Markovian model of sodium channel
ISSN:0140-0118, 1741-0444, 1741-0444
Online Access:Get full text
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Summary:The Markovian model has generally been used for cardiac electrophysiological simulations. However, the Markovian model is so stiff that speeding up the computation of the algorithms with variable time-steps always results in simulation instability. In particular, the unstable simulations always occur at a low voltage rate or current change, while transition rates in the Markovian model are changing markedly. The uniformization (UNI) method allows for a Markovian model simulation with high stability but also a high computation cost. To save computation costs with variable time-steps, we propose a speed increasing idea that is a compromise to the trade-off between stability and acceleration by combining Chen-Chen-Luo’s “quadratic adaptive algorithm” (CCL) method with “hybrid operator splitting” (HOS) into the solver (CCL + HOS solver). The computation cost of this CCL + HOS solver is approximately 24 times lower than the CCL + UNI solver, and the CCL + HOS solver can function 295 times faster in comparison to the HOS solver with a fixed time-step (DT). The suggested optimal solver should be CCL + HOS solver with a maximum time-step at 0.1 ms due to its high speed with low error. Additionally, the CCL method has much better performance and stability than the hybrid method in this single-cell model simulation.
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ISSN:0140-0118
1741-0444
1741-0444
DOI:10.1007/s11517-019-01956-5