Abstract
• Fractional-order based model for long-tailed transient behavior of biological systems. • Approximations to achieve a “pseudo-steady-state” in non-ideal relaxation processes. • Analysis of rational functions, asymptotically equivalent to Mittag-Leffler pattern for long times. • Application to safe and efficacious protocols of stimulation and electrical characterization. This paper discusses the complexity of distributed relaxation processes in biological systems, particularly with regard to the slowest timescale phenomena that influence the modeling of physiological events. Specifically, our main interest is to determine the optimal excitation time at which the transient response , described in terms of relatively slow decays and memory effects, can be considered negligible. We estimate the time scale required for the Mittag-Leffler function to reach and stay within a range about the final value (dc “pseudo-steady state”). From numerical computations, we consider the problem of approximating holding times with common and rational (Padé-type) asymptotic approximations for comparative purposes. It is important to understand the physiological processes and to explore new mathematical models, based on efficient approximations, in order to design safe, controllable, and effective protocols for the electrical stimulation of excitable cells and the characterization of biological tissues.
Published Version
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