Transmission Delays in Negative Feedback Physiological Systems: The Case of the Muscle Stretch Reflex

The behavior of physiological systems is more easily understood thanks to the definition of appropriate mathematical models that facilitate the implementation of in silico experiments. Starting from the description and study of the similarities between the various negative feedback physiological systems, the objective of the present work is to study the particular paradigmatic case of the neuromuscular reflex arc, i.e. the physiological control system that regulates the dynamics of the muscle stretch reflex, introducing some transmission delays along the afferent and efferent nerve fibres to better simulate the real behavior. The existence of the equilibrium points is therefore evaluated and discussed. The main results show how the extent of the delays along the nerve fibers affects the system's stability. The mathematical model is able to capture these dynamics and allows us to determine the transmission delay threshold above which the system becomes unstable. The capability of the mathematical model to reliably capture and describe the behavior of physiological systems could support the design of physiologically-inspired digital twins, able to mimic, monitor, and predict the dynamics of biological functions in both healthy and disease states.