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Numerical simulations of the human heart can guide medical doctors and researchers only if properly validated. This work presents a computational framework to validate mathematical models of cardiac electrophysiology at the tissue level. Specifically, we focus on the transmural wedge experiment as proposed by Antzelevitch in 1996. This experimental setup is easily reproduced and allows to probe key modeling assumptions and components before organ level simulations are performed. Our results highlight the need to further investigate the conductivity tensor, which, by modifying wave propagation, will affect the ECG morphology at the organ level.

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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.

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