A mass-flowing muscle model with shape restrictive soft tissues: correlation with sonoelastography

Skeletal muscles are always embedded in sheets of connective tissues, which influences muscle biomechanics by shaping the fascicle geometry and encapsulating muscular mass flow. However, existing Hill-type muscle models typically take surrounding tissues into account as a nonlinear spring, without consideration of the muscle geometry and inertia. In this paper, a new muscle model is proposed to simultaneously account for soft tissue constraints on the muscle's shape together with mass flow during stretch. To accomplish this, a mass-variable cable element of the muscle-tendon unit, with parameterization of its geometrical influence on the force-producing capability, is newly formulated based on an arbitrary Lagrangian-Eulerian description. Also, sliding joints are presented to further constrain possible mass flow of the elements via epimuscular soft tissue connections between adjacent muscle bellies. Available experimental data from cat soleus and rat gastrocnemius medialis muscles validates the proposed method. For further verification, a planar model of the triceps surae is developed by integration of this modeling framework, and subject-specific simulations of the passive ankle dynamometry tests are performed and correlated with sonoelastographic evaluations of two male participants. The results confirm that the flow of the muscle mass can alternate its force-generating behaviors, and the established model provides an accurate prediction of muscle behavior under transverse loading. The proposed muscle element could be integrated with larger musculoskeletal models to better investigate biomechanical functions of muscles during locomotion, such as heel impact or vibration responses of the spine, when dynamic effects are substantial.