title: Quadratic adaptive algorithm for solving cardiac action potential models.
abstract: An adaptive integration method is proposed for computing cardiac action potential models accurately and efficiently. Time steps are adaptively chosen by solving a quadratic formula involving the first and second derivatives of the membrane action potential. To improve the numerical accuracy, we devise an extremum-locator (el) function to predict the local extremum when approaching the peak amplitude of the action potential. In addition, the time step restriction (tsr) technique is designed to limit the increase in time steps, and thus prevent the membrane potential from changing abruptly. The performance of the proposed method is tested using the Luo-Rudy phase 1 (LR1), dynamic (LR2), and human O'Hara-Rudy dynamic (ORd) ventricular action potential models, and the Courtemanche atrial model incorporating a Markov sodium channel model. Numerical experiments demonstrate that the action potential generated using the proposed method is more accurate than that using the traditional Hybrid method, especially near the peak region. The traditional Hybrid method may choose large time steps near to the peak region, and sometimes causes the action potential to become distorted. In contrast, the proposed new method chooses very fine time steps in the peak region, but large time steps in the smooth region, and the profiles are smoother and closer to the reference solution. In the test on the stiff Markov ionic channel model, the Hybrid blows up if the allowable time step is set to be greater than 0.1ms. In contrast, our method can adjust the time step size automatically, and is stable. Overall, the proposed method is more accurate than and as efficient as the traditional Hybrid method, especially for the human ORd model. The proposed method shows improvement for action potentials with a non-smooth morphology, and it needs further investigation to determine whether the method is helpful during propagation of the action potential.
authors.affiliation: Department of Mathematics, National Cheng Kung University, 1 University Road, Tainan 701, Taiwan.
authors.forename: Min-Hung
authors.initials: MH
authors.lastname: Chen
authors.affiliation: Department of Engineering and Maintenance, Kaohsiung Medical University Chung-Ho Memorial Hospital, 100 Tzyou 1st Road, Kaohsiung 807, Taiwan.
authors.forename: Po-Yuan
authors.initials: PY
authors.lastname: Chen
authors.affiliation: Department of Electrical Engineering, National Cheng Kung University, 1 University Road, Tainan 701, Taiwan; Institute of Medical Science and Technology, National Sun Yat-Sen University, 70 Lienhai Road, Kaohsiung 80424, Taiwan. Electronic address: robinluo@mail.ncku.edu.tw.
authors.forename: Ching-Hsing
authors.initials: CH
authors.lastname: Luo
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000465:Algorithms; D000818:Animals; D003198:Computer Simulation; D006168:Guinea Pigs; D006321:Heart / Q000502:physiology; D006329:Heart Conduction System / Q000502:physiology*; D006801:Humans; D008955:Models, Cardiovascular
keywords: Action potential; Adaptive method; Cardiac action potential model; Computer simulation; Numerical method