Key result
Combining dimensional and asymptotic analysis with the Mitchell-Schaeffer model enables accurate control and prediction of cardiac action potential propagation by reducing the model parameters into a new nondimensional form.
Why the study?
Simulating cardiac electrical activity with realistic anatomy requires understanding if a simplified ionic model can accurately reproduce action potential propagation and how to control model parameters effectively.
Should not change arrhythmia management; leaves open validation of nondimensional models for in silico cardiac research.
One of the current debate about simulating the electrical activity in the heart is the following: Using a realistic anatomical setting, i.e. realistic geometries, fibres orientations, etc., is it enough to use a simplified 2-variable phenomenological model to reproduce the main characteristics of the cardiac action potential propagation, and in what sense is it sufficient? Using a combination of dimensional and asymptotic analysis, together with the well-known Mitchell − Schaeffer model, it is shown that it is possible to accurately control (at least locally) the solution while spatial propagation is involved. In particular, we reduce the set of parameters by writing the bidomain model in a new nondimensional form. The parameters of the bidomain model with Mitchell − Schaeffer ion kinetics are then set and shown to be in one-to-one relation with the main characteristics of the four phases of a propagated action potential. Explicit relations are derived using a combination of asymptotic methods and ansatz. These relations are tested against numerical results. We illustrate how these relations can be used to recover the time/space scales and speed of the action potential in various regions of the heart.
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Yves Bourgault (2012) studied Cardiac electrophysiology. Nondimensional Mitchell-Schaeffer bidomain model was evaluated. Combining dimensional and asymptotic analysis with the Mitchell-Schaeffer model enables accurate control and prediction of cardiac action potential propagation by reducing the model parameters into a new nondimensional form.
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