A simple and efficient adaptive time stepping technique for low‐order operator splitting schemes applied to cardiac electrophysiology. (6th January 2023)

• Record Type: Journal Article
• Authors: Ogiermann, Dennis; Perotti, Luigi E.; Balzani, Daniel
• Is Part Of: International journal for numerical methods in biomedical engineering. Volume 39:Number 2(2023)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2023-01-06
• Subjects: bidomain model -- computational cardiology -- reaction tangent controller -- reaction–diffusion splitting; Biomedical engineering -- Periodicals; Imaging systems in medicine -- Periodicals; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 610.28
• DOI: 10.1002/cnm.3670
• Languages: English
• ISSNs: 2040-7939

Abstract

Abstract: We present a simple, yet efficient adaptive time stepping scheme for cardiac electrophysiology (EP) simulations based on standard operator splitting techniques. The general idea is to exploit the relation between the splitting error and the reaction's magnitude—found in a previous one‐dimensional analytical study by Spiteri and Ziaratgahi—to construct the new time step controller for three‐dimensional problems. Accordingly, we propose to control the time step length of the operator splitting scheme as a function of the reaction magnitude, in addition to the common approach of adapting the reaction time step. This conforms with observations in numerical experiments supporting the need for a significantly smaller time step length during depolarization than during repolarization. The proposed scheme is compared with classical proportional–integral–differential controllers using state‐of‐the‐art error estimators, which are also presented in details as they have not been previously applied in the context of cardiac EP with operator splitting techniques. Benchmarks show that choosing the time step as a sigmoidal function of the reaction magnitude is highly efficient and full cardiac cycles can be computed with precision even in a realistic biventricular setup. The proposed scheme outperforms common adaptive time stepping techniques, while depending on fewer tuning parameters. Abstract : A new method is proposed to adaptively control the time step length of operator splitting schemes for the bidomain model as a function of the reaction component. The proposed method is analyzed with work‐precision studies using as baseline schemes from reaction–diffusion problems applied to the bidomain model. Our novel method outperforms these general schemes by an order of magnitude, while preserving similar accuracy in subject‐specific biventricular setups.