On the dynamical stability of skeletal muscle

TL;DR

This paper investigates the stability of skeletal muscle models, demonstrating that intrinsic mechanical properties can stabilize muscle contractions in regions previously thought unstable, and proposes a convex, robust 1D model.

Contribution

It introduces a stabilized 1D Hill-type muscle model incorporating 3D deformation, enhancing simulation robustness without sacrificing efficiency.

Findings

Traditional models can exhibit divergent dynamics in the dip region.

Activation-independent properties can stabilize muscle contractions.

The new model maintains stability and efficiency in simulations.

Abstract

There has been debate for over 70-years about whether active skeletal muscle is dynamically stable at lengths greater than its optimal length. The stability of computational muscle models is a critical issue, as it directly affects our ability to simulate muscle deformation across different operating lengths, especially at lengths where muscles are known to remain functional despite model-predicted instabilities. In this study, we revisit the question of dynamical stability of ODE-based models of skeletal muscle. In particular, we investigate whether activation-independent tissue properties can provide stability to contractions along the dip region of the total force-length curve. First, using a combination of analytical tools (eigenvalue analysis and non-dimensionalization) and numerical simulations, we confirm that traditional Hill-type muscle models can display divergent dynamics in this region. Then, we propose a stabilized version of a 1D Hill-type muscle model that incorporates the 3D nature of skeletal muscle deformation. This results in a completely convex force-length relationship that can bring robustness to numerical simulations, while preserving the computational efficiency of 1D models. Our findings suggest that activation-independent intrinsic mechanical properties of muscle are sufficient to stabilize contractions even in the dip region, offering new insight into how muscles maintain functional integrity during active stretch.