Time-normalized velocity profiles of discrete movements have traditionally been studied to identify characteristics of human motion independent of movement distance and movement duration [2426, 50, 51]. Thus, in contrast to our previous analysis of volitional command bandwidth through relative phase, the analysis of time-normalized subtalar eversion to inversion velocity profiles may elucidate limitations of the human neuromuscular system related to mechanical consistency. By not distinguishing between symmetric and parallel coordination modes, thus disregarding any temporal and high level decision error from choosing between performing subtalar inversion or eversion, kinematic patterns observed across populations and frequencies may more closely relate to the way generalized movements are realized physiologically through lower level muscle synergies and individual muscle activations.

Average time-normalized velocity profiles from maximum eversion to maximum inversion were calculated from the non-amputee group’s right subtalar movements under blind symmetry instruction at 1.4 Hz and 2.2 Hz. Average time-normalized velocity profiles generated by subjects with amputation were calculated for both intact subtalar and optimized subtalar model outputs under the same conditions. Moderately slow 1.4 Hz and moderately fast 2.2 Hz subtalar trajectories were selected due to their significantly different relative phase distributions. The beginning and end indices for each individual movement were determined by detecting when speed rose above and fell below 3% of the maximum movement speed.

Additionally, lognormal distributions with bounded support (LGNB) have been shown to accurately describe human-generated velocity profiles from the ankle, subtalar, and wrist [5052]. A LGNB distribution described by

was fitted to each average velocity profile using an iterative least squares curve fit solver, where D is total displacement of the movement, t0 the time of the impulse command, t1 the end time of the movement, μ and σ2 the mean and variance of ln(t-t0). A thorough description of this equation as it applies to human movement is given by Plamondon et al. [50]. Coefficients of determination were calculated for the generated LGNB velocity profiles. Standard deviations of the average velocity profiles were calculated and graphed per normalized time point. Further reading about these methods, including velocity profile rejection criteria, can be found in a study on discrete volitional ankle-subtalar movements by Michmizos et al. [52].

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