Phenomenological Muscle Constitutive Model With Actin–Titin Binding for Simulating Active Stretching

Abstract

The force produced by a muscle depends on its contractile history, yet human movement simulations typically employ muscle models that define the force–length relationship from measurements of fiber force during isometric contractions. In these muscle models, the total force–length curve can have a negative slope at fiber lengths greater than the fiber length at which peak isometric force is produced. This region of negative stiffness can cause numerical instability in simulations. Experiments have found that the steady-state force in a muscle fiber following active stretching is greater than the force produced during a purely isometric contraction. This behavior is called residual force enhancement. We present a constitutive model that exhibits force enhancement, implemented as a hyperelastic material in the febio finite element software. There is no consensus on the mechanisms responsible for force enhancement; we adopt the assumption that the passive fiber force depends on the sarcomere length at the instant that the muscle is activated above a threshold. We demonstrate the numerical stability of our model using an eigenvalue analysis and by simulating a muscle whose fibers are of different lengths. We then use a three-dimensional muscle geometry to verify the effect of force enhancement on the development of stress and the distribution of fiber lengths. Our proposed muscle material model is one of the few models available that exhibits force enhancement and is suitable for simulations of active lengthening. We provide our implementation in febio so that others can reproduce and extend our results.