The Contributions of Individual Muscle–Tendon Units to the Plantarflexor Group Force–Length Properties

Musculotendon Parameters in Lower Limb Models: Simplifications, Uncertainties, and Muscle Force Estimation Sensitivity

Musculotendon parameters are key factors in the Hill-type muscle contraction dynamics, determining the muscle force estimation accuracy of a musculoskeletal model. Their values are mostly derived from muscle architecture datasets, whose emergence has been a major impetus for model development. However, it is often not clear if such parameter update indeed improves simulation accuracy. Our goal is to explain to model users how these parameters are derived and how accurate they are, as well as to what extent errors in parameter values might influence force estimation. We examine in detail the derivation of musculotendon parameters in six muscle architecture datasets and four prominent OpenSim models of the lower limb, and then identify simplifications which could add uncertainties to the derived parameter values. Finally, we analyze the sensitivity of muscle force estimation to these parameters both numerically and analytically. Nine typical simplifications in parameter derivation are identified. Partial derivatives of the Hill-type contraction dynamics are derived. Tendon slack length is determined as the musculotendon parameter that muscle force estimation is most sensitive to, whereas pennation angle is the least impactful. Anatomical measurements alone are not enough to calibrate musculotendon parameters, and the improvement on muscle force estimation accuracy will be limited if the source muscle architecture datasets are the only main update. Model users may check if a dataset or model is free of concerning factors for their research or application requirements. The derived partial derivatives may be used as the gradient for musculotendon parameter calibration. For model development, we demonstrate that it is more promising to focus on other model parameters or components and seek alternative strategies to further increase simulation accuracy.

Elastic energy storage across speeds during steady-state hopping of desert kangaroo rats (Dipodomys deserti)

Small bipedal hoppers, including kangaroo rats, are thought to not benefit from substantial elastic energy storage and return during hopping. However, recent species-specific material properties research suggests that, despite relative thickness, the ankle extensor tendons of these small hoppers are considerably more compliant than had been assumed. With faster locomotor speeds demanding higher forces, a lower tendon stiffness suggests greater tendon deformation and thus a greater potential for elastic energy storage and return with increasing speed. Using the elastic modulus values specific to kangaroo rat tendons, we sought to determine how much elastic energy is stored and returned during hopping across a range of speeds. In vivo techniques were used to record tendon force in the ankle extensors during steady-speed hopping. Our data support the hypothesis that the ankle extensor tendons of kangaroo rats store and return elastic energy in relation to hopping speed, storing more at faster speeds. Despite storing comparatively less elastic energy than larger hoppers, this relationship between speed and energy storage offer novel evidence of a functionally similar energy storage mechanism, operating irrespective of body size or tendon thickness, across the distal muscle-tendon units of both small and large bipedal hoppers.

Changes in neural drive to calf muscles during steady submaximal contractions after repeated static stretches

KEY POINTS

Repeated static-stretching interventions consistently increase the range of motion about a joint and decrease total joint stiffness, but findings on the changes in muscle and connective-tissue properties are mixed. The influence of these stretch-induced changes on muscle function at submaximal forces is unknown. To address this gap in knowledge, the changes in neural drive to the plantar flexor muscles after a static-stretch intervention were estimated. Neural drive to the plantar flexor muscles during a low-force contraction increased after repeated static stretches. These findings suggest that adjustments in motor unit activity are necessary at low forces to accommodate reductions in the force-generating and transmission capabilities of the muscle-tendon unit after repeated static stretches of the calf muscles.

ABSTRACT

Static stretching decreases stiffness about a joint, but its influence on muscle-tendon unit function and muscle activation is unclear. We investigated the influence of three static stretches on changes in neural drive to the plantar flexor muscles, both after a stretch intervention and after a set of maximal voluntary contractions (MVCs). Estimates of neural drive were obtained during submaximal isometric contractions by decomposing high-density electromyographic signals into the activity of individual motor units from medial gastrocnemius, lateral gastrocnemius and soleus. Motor units were matched across contractions and an estimate of neural drive to the plantar flexors was calculated by normalizing the cumulative spike train to the number of active motor units (normalized neural drive). Mean discharge rate increased after the stretch intervention during the 10% MVC task for all recorded motor units and those matched across conditions (all, P = 0.0046; matched only, P = 0.002), recruitment threshold decreased for motor units matched across contractions (P = 0.022), and discharge rate at recruitment was elevated (P = 0.004). Similarly, the estimate of normalized neural drive was significantly greater after the stretch intervention at 10% MVC torque (P = 0.029), but not at 35% MVC torque. The adjustments in motor unit activity required to complete the 10% MVC task after stretch may have been partially attenuated by a set of plantar flexor MVCs. The increase in neural drive required to produce low plantar-flexion torques after repeated static stretches of the calf muscles suggests stretch-induced changes in muscle and connective tissue properties.

Estimation of the force-velocity properties of individual muscles from measurement of the combined plantarflexor properties

The force-velocity (F-V) properties of isolated muscles or muscle fibers have been well studied in humans and other animals. However, determining properties of individual muscles in vivo remains a challenge because muscles usually function within a synergistic group. Modeling has been used to estimate the properties of an individual muscle from the experimental measurement of the muscle group properties. While this approach can be valuable, the models and the associated predictions are difficult to validate. In this study, we measured the in situ F-V properties of the maximally activated kangaroo rat plantarflexor group and used two different assumptions and associated models to estimate the properties of the individual plantarflexors. The first model (Mdl1) assumed that the percent contributions of individual muscles to group force and power were based upon the muscles' cross-sectional area and were constant across the different isotonic loads applied to the muscle group. The second model (Mdl2) assumed that the F-V properties of the fibers within each muscle were identical, but because of differences in muscle architecture, the muscles' contributions to the group properties changed with isotonic load. We compared the two model predictions with independent estimates of the muscles' contributions based upon sonomicrometry measurements of muscle length. We found that predictions from Mdl2 were not significantly different from sonomicrometry-based estimates while those from Mdl1 were significantly different. The results of this study show that incorporating appropriate fiber properties and muscle architecture is necessary to parse the individual muscles' contributions to the group F-V properties.