Modeling of Isometric Muscle Properties via Controllable Nonlinear Spring and Hybrid Model of Proprioceptive Receptors

This work investigates the macroscopic behavior of skeletal muscles from a system-theoretic perspective. Based on data available in the literature, we propose an initial evaluation model for isometric force generation, i.e., force produced at a constant muscle length or in quasi-static conditions, as a function of muscle length and neuronal excitation frequency. This model enables a more physics-inspired representation of isometric force by employing a nonlinear spring framework with controllable properties such as stiffness and rest length. Finally, we introduce a hybrid dynamical filter model to describe components of the sensory system responsible for relaying information about muscle length and its rate of change back to the Central Nervous System. As an application case, we present the modeling of the oculomotor system, highlighting the relevance of the proposed modeling approach in a physiologically meaningful control task.