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Modeling human arm endpoint stiffness and the feedforward control over the endpoint stiffness

The mechanical properties of the human arm are regulated to maintain stability across many tasks. The static mechanics of the arm can be characterized by estimates of endpoint stiffness, the static forces generated by a limb in response to external perturbations of posture, which is considered especially relevant for the maintenance of posture. At a fixed posture, endpoint stiffness can be regulated by changes in muscle activation, but which activation-dependent muscle properties contribute to this global measure of limb mechanics remains unclear. So my first study was to evaluate the role of muscle properties in the regulation of endpoint stiffness by incorporating scalable models of muscle stiffness into a three-dimensional musculoskeletal model of the human arm. Two classes of muscle models were tested: one characterizing short-range stiffness, and two estimating stiffness from the slope of the force-length curve. All models were compared to previously collected experimental data describing how endpoint stiffness varies with changes in voluntary force. We found that force-dependent variations in endpoint stiffness were accurately described by the short-range stiffness of active arm muscles. In contrast, estimates based on muscle force-length curves were less accurate in all measures, especially stiffness area. These results suggest that muscle short-range stiffness is a major contributor to endpoint stiffness of human arm. Furthermore, the developed model provides an important tool for assessing how the nervous system may regulate endpoint stiffness via changes in muscle activation.

Appropriate regulation of human arm mechanics is essential for completing the diverse range of tasks we accomplish each day. Endpoint stiffness is directional, resisting perturbations in certain directions more than others. It has been shown that humans can voluntarily control the orientation of the maximum stiffness to meet specific task requirements, although the limits on this control are poorly understood. Both neural and biomechanical factors may limit endpoint stiffness control. My second study was to quantify the biomechanical factors limiting the control of stiffness orientation. A realistic musculoskeletal model of the human arm coupled with a model of muscle stiffness developed in my first study was used to explore the range of endpoint stiffness orientations that could be achieved with changes in the feedforward control of muscle activation. We found that this range is constrained by the biomechanics of the neuromuscular system, and by the requirements of the specific task being performed by the subject. These constraints and the sensitivity to experimental conditions may account for some of the discrepancies in the literature regarding the ability to control endpoint stiffness orientation.



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