Reduction of a cardiac pacemaker cell model using singular perturbation theory

Cardiac-cell models are now frequently used on the heart scale in model-based signal or image processing applications for understanding cardiac diseases. For these applications, it is necessary to design models representing a good trade-off between detailed description of the complex physiological phenomena on the cardiac-cell scale and available data on the heart scale. In order to contribute to this issue, a detailed cardiac cell model has been developed and is briefly presented. However, the computational burden associated with such a detailed model, the number of parameters and state variables used to describe the behavior of the cardiac electrical activity may render its practical application very difficult. To overcome this problem, singular perturbation theory has been applied to reduce the order of the detailed cardiac pacemaker cell model, while retaining the relevant dynamics with respect to the real system. The model exhibits three time scales (Tikhonov generalized form). Validation results show the ability of the reduced order model to match some of the behavioral features of the detailed model, such as the excitability, but fails to reproduce other features, such as the shape of pacemaker action potential. This drawback is the consequence that our cardiac pacemaker cell model has a non-Tikhonov asymptotic structure.