Abstract
Hill-type muscle models are widely used within the field of biomechanics to predict and understand muscle behaviour, and are often essential where muscle forces cannot be directly measured. However, these models have limited accuracy, particularly during cyclic contractions at the submaximal levels of activation that typically occur during locomotion. To address this issue, recent studies have incorporated effects into Hill-type models that are oftentimes neglected, such as size-dependent, history-dependent, and activation-dependent effects. However, the contribution of these effects on muscle performance has yet to be evaluated under common contractile conditions that reflect the range of activations, strains, and strain rates that occur in vivo. The purpose of this study was to develop a modelling framework to evaluate modifications to Hill-type muscle models when they contract in cyclic loops that are typical of locomotor muscle function. Here we present a modelling framework composed of a damped harmonic oscillator in series with a Hill-type muscle actuator that consists of a contractile element and parallel elastic element. The intrinsic force-length and force-velocity properties are described using Bézier curves where we present a system to relate physiological parameters to the control points for these curves. The muscle-oscillator system can be geometrically scaled while preserving dynamic and kinematic similarity to investigate the muscle size effects while controlling for the dynamics of the harmonic oscillator. The model is driven by time-varying muscle activations that cause the muscle to cyclically contract and drive the dynamics of the harmonic oscillator. Thus, this framework provides a platform to test current and future Hill-type model formulations and explore factors affecting muscle performance in muscles of different sizes under a range of cyclic contractile conditions.
Highlights
One of the primary functions of skeletal muscle is to perform work by cyclically contracting to move an external load during locomotion
One of the primary functions of skeletal muscle is to generate work and power to move the body during locomotor tasks such as walking and running
This study demonstrates a forward-dynamic modelling framework that links a Hill-type muscle model to an oscillating external load
Summary
One of the primary functions of skeletal muscle is to perform work by cyclically contracting to move an external load during locomotion. For the last half-century, experimental work-loop studies have provided insight into how muscle force and length, and work, depend on interactions between neural excitation and the external load placed on the muscle during cyclic contractions. These interaction effects are supported by early in vitro studies examining the behaviour of invertebrate flight muscles coupled to external loads with different elastic, viscous and inertial properties [1,2]. The behaviour of muscle depends on the demands of the task in addition to the properties of the muscle
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