Contribution of muscle short-range stiffness to initial changes in joint kinetics and kinematics during perturbations to standing balance: A simulation study
Introduction
Simulating realistic musculoskeletal dynamics is critical to understanding neural control of muscle activity in sensorimotor feedback responses. Musculoskeletal responses to external perturbations are influenced by the initial mechanical response of the musculoskeletal system that precedes neurally-mediated changes in muscle activity (Horak and Macpherson, 1996, Ting et al., 2009). In particular, muscle short-range stiffness, a history-dependent property of muscles that is absent in Hill-type muscle models, likely plays an important role, yet its contributions to stabilizing musculoskeletal dynamics are not well understood.
In perturbed standing balance where baseline muscle activity is constant, the initial response to perturbations can be attributed solely to intrinsic mechanical properties of the body. Joint torques generated during the initial mechanical response to perturbations of standing are substantial despite minimal joint angle changes (Runge et al., 1999). However, the first small change in muscle activity due to spinal reflexes only occurs at ∼50 ms (Carpenter et al., 1999), and much larger balance-correcting effects are evoked ∼100 ms after perturbation onset (Horak and Macpherson, 1996). We refer to the period preceding neural changes in muscle activity at 50 ms as the initial mechanical response.
Short-range stiffness causes a rapid increase in muscle force upon muscle fiber stretch (Nichols and Houk, 1976), but its contributions to perturbed standing cannot be easily studied through experimentation. Short-range stiffness is observed when activated isometric muscle fibers are stretched and has been attributed to deformation of attached muscle cross-bridges (Campbell and Lakie, 1998). Due to actin-myosin overlap, short-range stiffness is highest at optimal fiber length (Campbell, 2014). In isolated muscle fibers, a stretch of less than a nanometer per half sarcomere length rapidly increases force to at least twice the pre-stretch isometric force, followed by a force plateau (Getz et al., 1998). Consistent with the effects of short-range stiffness, substantial increases in ankle joint torques in the absence of change in muscle activity are observed for joint angle perturbations smaller than 1° (Loram et al., 2007a, Loram et al., 2007b).
We currently lack dynamic simulations of whole-body movement that can be used to identify the functional role of short-range stiffness in perturbation responses. A phenomenological model in which short-range stiffness was proportional to the initial isometric force in each muscle (Cui et al., 2008) has been used to identify contributions of short-range stiffness to instantaneous arm endpoint stiffness in static postures using a musculoskeletal model of the arm (Hu et al., 2011). However, to our knowledge, models of short-range stiffness have yet to be implemented in dynamic musculoskeletal simulations of movement. Simulating muscle dynamics is computationally challenging and expensive, and therefore often neglected when computing muscle inputs that reproduce observed joint torques (Crowninshield and Brand, 1981).
Our recently-published dynamic optimization method based on direct collocation reduces the sensitivity of simulations to forward integration errors, allowing more efficient simulations of muscle dynamics in solving the muscle redundancy problem (De Groote et al., 2016). Solving skeletal and muscle dynamics independently further facilitates the rapid exploration of dynamic models of muscle force generation.
Here we identified the contributions of short-range stiffness to joint torques and angles in the initial mechanical response to perturbed standing using dynamic simulation. We developed a dynamic model of muscle short-range stiffness to augment a Hill-type muscle model. Dynamic optimization was used to assess whether a feasible set of muscle activations could reproduce the experimental joint torques. Joint torques during the initial mechanical response could only be reproduced with the addition of muscle short-range stiffness if muscle activations were assumed constant. Further, forward simulations were used to assess the effect of different models of muscle dynamics on joint kinematics. Forward simulations lacking short-range stiffness exhibit unrealistically large changes in joint angles in the initial mechanical responses. Our simulations provide evidence that short-range stiffness provides stability against perturbations before long-latency balance-correcting responses can intervene.
Section snippets
Methods
To assess the contribution of short-range stiffness to changes in joint torques during the initial mechanical response to perturbation, we first performed inverse dynamics (ID) analyses of perturbed standing balance during forward and backward translations of the support surface using a lower-limb musculoskeletal model in OpenSim (Delp et al., 2007; Fig. 1, gray boxes). We then identified constant muscle activation levels that accounted for the ID torques during the initial mechanical response
Results
During the initial mechanical response, joint torques changed substantially as a result of the support surface translation whereas changes in muscle activity were absent and changes in joint kinematics were small (Fig. 3). For subject 1, mean change in normalized EMG from baseline levels was less than 5% of the maximum observed EMG value for all muscles during both the 0–50 and 50–100 ms time bins after perturbation onset (Fig. 3B and C, top row). In contrast, increases of 16 ± 5% of the maximum
Discussion
Our musculoskeletal simulations demonstrate that short-range stiffness plays a substantial role in perturbed standing. In the initial 50 ms following a perturbation where muscle activity cannot be modified through sensorimotor feedback, we were only able to account for the rapid rise in joint torques by incorporating a dynamic model of muscle short-range stiffness. Moreover, forward simulations lacking short-range stiffness produced unrealistically large joint angle changes in the first 50 ms,
Conflict of interest statement
We wish to confirm that there are no known conflicts of interest associated with this publication and there has been no financial support for this work that could have influenced its outcome.
Acknowledgements
We gratefully acknowledge the support of FWO-V430116 N, NIH HD046922 and F32-NS087775.
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