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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.

Abstract：

: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.

journal_name

Med Biol Eng Comput

journal_title

Medical & biological engineering & computing

authors

Chen XJ,Luo CH,Chen MH

doi

10.1007/s11517-020-02220-x

subject

Has Abstract

pub_date

2020-09-01 00:00:00

pages

2131-2141

issue

eissn

0140-0118

issn

1741-0444

pii

10.1007/s11517-020-02220-x

journal_volume

pub_type

杂志文章

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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.