Review of Modelling Techniques for In Vivo Muscle Force Estimation in the Lower Extremities during Strength Training

Abstract

Background: Knowledge of the musculoskeletal loading conditions during strength training is essential for performance monitoring, injury prevention, rehabilitation, and training design. However, measuring muscle forces during exercise performance as a primary determinant of training efficacy and safety has remained challenging.

Methods: In this paper we review existing computational techniques to determine muscle forces in the lower limbs during strength exercises in vivo and discuss their potential for uptake into sports training and rehabilitation.

Results: Muscle forces during exercise performance have almost exclusively been analysed using so-called forward dynamics simulations, inverse dynamics techniques, or alternative methods. Musculoskeletal models based on forward dynamics analyses have led to considerable new insights into muscular coordination, strength, and power during dynamic ballistic movement activities, resulting in, for example, improved techniques for optimal performance of the squat jump, while quasi-static inverse dynamics optimisation and EMG-driven modelling have helped to provide an understanding of low-speed exercises.

Conclusion: The present review introduces the different computational techniques and outlines their advantages and disadvantages for the informed usage by nonexperts. With sufficient validation and widespread application, muscle force calculations during strength exercises in vivo are expected to provide biomechanically based evidence for clinicians and therapists to evaluate and improve training guidelines.

Figure 1

Muscle and joint forces are quantified in vivo by combining experimental measurements (yellow) with computational biomechanics (orange). Different measurement parameters (black arrows) or computational optimizations (black arrows) are required to achieve different output parameters (green) in inverse dynamics or forward dynamics processes. For forward dynamics simulations (red arrows), usually applied to dynamic ballistic movement exercises such as the squat jump, joint dynamics such as joint angles, joint net moment, or muscle kinematics are derived by finding an optimal set of muscle kinetics using computational modelling. For inverse dynamics analysis (blue arrows), usually applied to low-speed exercises such as the squat, joint moments, muscle forces, and finally joint contact forces are derived from joint angles and net joint moments.

Figure 2

The Hill-type muscle-tendon model, showing muscle and tendon forces (F ^M, F ^T), as well as the series-elastic (SE), parallel-elastic (PE), and contractile (CE) elements of the muscle length (l) and stiffness (k) of the whole muscle-tendon actuator (M, T). a(t) represents the activation of the CE (adapted from Pandy and coworkers [12]).

Figure 3

(a) Schematic representation of the musculoskeletal model for the vertical jump and (b) the four-segment multibody model with lumped masses and mass moments of inertia for the foot, shank, thigh, and head/arms/trunk (Pandy and coworkers [12]).