Modeling of active skeletal muscles: a 3D continuum approach incorporating multiple muscle interactions

Abstract

Skeletal muscles have a highly organized hierarchical structure, whose main function is to generate forces for movement and stability. To understand the complex heterogeneous behaviors of muscles, computational modeling has advanced as a non-invasive approach to evaluate relevant mechanical quantities. Aiming to improve musculoskeletal predictions, this paper presents a framework for modeling 3D deformable muscles that includes continuum constitutive representation, parametric determination, model validation, fiber distribution estimation, and integration of multiple muscles into a system level for joint motion simulation. The passive and active muscle properties were modeled based on the strain energy approach with Hill-type hyperelastic constitutive laws. A parametric study was conducted to validate the model using experimental datasets of passive and active rabbit leg muscles. The active muscle model with calibrated material parameters was then implemented to simulate knee bending during a squat with multiple quadriceps muscles. A computational fluid dynamics (CFD) fiber simulation approach was utilized to estimate the fiber arrangements for each muscle, and a cohesive contact approach was applied to simulate the interactions among muscles. The single muscle simulation results showed that both passive and active muscle elongation responses matched the range of the testing data. The dynamic simulation of knee flexion and extension showed the predictive capability of the model for estimating the active quadriceps responses, which indicates that the presented modeling pipeline is effective and stable for simulating multiple muscle configurations. This work provided an effective framework of a 3D continuum muscle model for complex muscle behavior simulation, which will facilitate additional computational and experimental studies of skeletal muscle mechanics. This study will offer valuable insight into the future development of multiscale neuromuscular models and applications of these models to a wide variety of relevant areas such as biomechanics and clinical research.

Development and verification of a physiologically motivated internal controller for the open-source extended Hill-type muscle model in LS-DYNA

“…Despite these advantages, some aspects such as volumetric shape or the shift of muscle mass during contraction cannot be properly modelled using Hill-type models such as the EHTM. Thus, recent studies have focused on the creation of constitutive three-dimensional muscle models to describe the processes and effects of muscle contraction in more detail (Almonacid et al 2022 ; Saini et al 2022 ; Zeng et al 2023 ). While these models thus offer a more wholistic perspective on the topic of skeletal muscle behaviour and have shown to achieve more realistic results than their discrete, on-dimensional counterparts in some cases (Hedenstierna and Halldin 2008 ), one critical downside concerning their widespread use remains unresolved.…”

Emerging Innovations in Preoperative Planning and Motion Analysis in Orthopedic Surgery

“…This muscle behavior, in passive and active scenarios, marked by a certain deformability between elongation and shortening, corresponds to information about relaxation and contraction, which is difficult to measure in practice, especially during complex movements. Physical and computerized muscle models have been developed for measuring muscle length and moment arms in healthy individuals [95][96][97][98]. Figure 5 demonstrate an example of a biomechanical analysis of the muscles in the upper limb using the Newcastle shoulder model [99].…”

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“…The muscle was modeled as a fiber-reinforced composite in which the strain energy density function includes the contribution from the isotropic matrix embedding the muscle fiber and the contribution from the muscle fibers [23]. The strain energy density function of the muscle contains the following terms:…”