Comparison of subject-specific musculoskeletal model calibration strategies on muscle force and fatigue estimation

Abstract

Muscle force and fatigue modeling and simulation are powerful tools for rehabilitation, sports performance, ergonomics, and injury prevention. However, their accuracy is challenged by dynamic mechanical and physiological factors. Since musculoskeletal models are typically derived from cadaver data and scaled to individuals, careful subject-specific calibration is recommended to achieve accurate simulation results. This study investigates how different muscle models and calibration strategies affect the accuracy of muscle force estimation at the elbow level. Two models-a simplified static model and a rigid-tendon Hill-type model-were compared. Several calibration approaches were tested using isometric and isokinetic measurements to identify the parameters that most enhance model performance. The models were used to estimate muscle forces, and their outputs were compared to experimental data collected from seventeen healthy subjects. In the first phase, estimations were made during short maximal voluntary contractions (MVCs) without fatigue, in order to isolate muscle force from fatigue effects. In the second phase, the calibrated parameters from each strategy were used to estimate muscle forces and fatigue during a short-duration, high-intensity dynamic exercise by incorporating a muscle fatigue model. The highest accuracy was achieved with the Hill-type model, which involved refining individual muscle length and force parameters based on concentric and eccentric MVCs and adjusting two parameters of the force-velocity relationship. However, incorporating subject-specific muscle fatigue parameters did not significantly improve force estimation under fatigue conditions.

Keywords: Biomechanics; Muscle fatigue model; Muscle force dynamics; Musculotendon model; Rehabilitation; Sport performance.

Fig. 1

a Isokinetic dynamometer; b 7-muscle arm model

Fig. 2

Hill-type musculotendon model. The MTU fibers are modeled as an active contractile element (CE) in parallel with a passive elastic component (PE). These elements are in series with a nonlinear elastic tendon (SE). The pennation angle α denotes the angle between the MTU fibers and the tendon. Superscripts MT, M, and T indicate musculotendon, MTU fiber, and tendon, respectively [28]

Fig. 3

Preliminary comparison of the estimated torques from the original and adjusted models with experimental measurements for a healthy subject during DYN and ISOM6

Fig. 4

Maximum isometric torques of elbow flexors estimated with the different approaches versus experimental (red) for a healthy subject during ISOM6

Fig. 5

Maximum dynamic (concentric and eccentric) torques of elbow flexors estimated with the different approaches versus experimental (red) for a healthy subject during DYN

Fig. 6

Maximum dynamic and isometric fatigued torques of elbow flexors estimated with the different approaches versus experimental (red) for a single subject during DYN-FAT, DYN-FAT-R1 and DYN-FAT-R2

Fig. 7

Dynamic and isometric fatigued torque of elbow flexors (orange) and target load (black) estimated with PHYS3-DYN versus experimental (red) for a single subject during DYN-FAT, DYN-FAT-R1 and DYN-FAT-R2