Combination of “generalized Trotter operator splitting” and “quadratic adaptive algorithm” method for tradeoff among speedup, stability, and accuracy in the Markov chain model of sodium ion channels in the ventricular cell model

The fast hybrid operator splitting (HOS) and stable uniformization (UNI) methods have been proposed to save computation cost and enhance stability for Markov chain model in cardiac cell simulations. Moreover, Chen-Chen-Luo’s quadratic adaptive algorithm (CCL) combined with HOS or UNI was used to imp...

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Bibliographic Details
Published in:Medical & biological engineering & computing Vol. 58; no. 9; pp. 2131 - 2141
Main Authors: Chen, Xing-Ji, Luo, Ching-Hsing, Chen, Min-Hung
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2020
Springer Nature B.V
Subjects:
Accuracy
Adaptive algorithms
Algorithms
Asymptotic methods
Asymptotic properties
Biomedical and Life Sciences
Biomedical Engineering and Bioengineering
Biomedicine
Computation
Computer Applications
Computer simulation
Human Physiology
Imaging
Ion channels
Markov analysis
Markov chains
Mathematical models
Mean square errors
Model accuracy
Original Article
Radiology
Root-mean-square errors
Sodium channels
Splitting
Stability
Tradeoffs
Ventricle
Operator splitting
Ventricular cell model
Sodium ion channel
Adaptive algorithm
Markov chain model
ISSN:0140-0118, 1741-0444, 1741-0444
Online Access:Get full text
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Summary:The fast hybrid operator splitting (HOS) and stable uniformization (UNI) methods have been proposed to save computation cost and enhance stability for Markov chain model in cardiac cell simulations. Moreover, Chen-Chen-Luo’s quadratic adaptive algorithm (CCL) combined with HOS or UNI was used to improve the tradeoff between speedup and stability, but without considering accuracy. To compromise among stability, acceleration, and accuracy, we propose a generalized Trotter operator splitting (GTOS) method combined with CCL independent of the asymptotic property of a particular ion-channel model. Due to the accuracy underestimation of the mixed root mean square error (MRMSE) method, threshold root mean square error (TRMSE) is proposed to evaluate computation accuracy. With the fixed time-step RK4 as a reference, the second-order GTOS combined with CCL (30.8-fold speedup) for the wild-type Markov chain model with nine states (WT-9 model) or (7.4-fold) for the wild-type Markov chain model with eight states (WT-8 model) is faster than UNI combined with CCL (15.6-fold) for WT-9 model or (1.2-fold) for WT-8 model, separately. Besides, the second-order GTOS combined with CCL has 3.81% TRMSE for WT-9 model or 4.32% TRMSE for WT-8 model more accurate than 72.43% TRMSE for WT-9 model or 136.17% TRMSE for WT-8 model of HOS combined with CCL. To compromise speedup and accuracy, low-order GTOS combined with CCL is suggested to have the advantages of high precision and low computation cost. For high-accuracy requirements, high-order GTOS combined with CCL is recommended. Graphical abstract
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ISSN:0140-0118
1741-0444
1741-0444
DOI:10.1007/s11517-020-02220-x