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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

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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.

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Funding

This work was supported by Sun Yat-sen University, China, under Scientific Initiation Project (No.67000-18821109) for High-level Experts. M.-H. Chen was supported by the Ministry of Science and Technology of Taiwan under grant MOST 108-2115-M-006-019-.

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Correspondence to Ching-Hsing Luo or Min-Hung Chen.

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Xing-Ji Chen and Ching-Hsing Luo are first author

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Chen, XJ., Luo, CH. & Chen, MH. 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. Med Biol Eng Comput 58, 2131–2141 (2020). https://doi.org/10.1007/s11517-020-02220-x

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