The ability to perceive the direction of whole-body motion during standing may be critical to maintaining balance and preventing a fall. Our first goal was to quantify kinesthetic perception of whole-body motion by estimating directional acuity thresholds of support-surface perturbations during standing. The directional acuity threshold to lateral deviations in backward support-surface motion in healthy, young adults was quantified as 9.5 ± 2.4° using the psychometric method (n = 25 subjects). However, inherent limitations in the psychometric method, such as a large number of required trials and the predetermined stimulus set, may preclude wider use of this method in clinical populations. Our second goal was to validate an adaptive algorithm known as parameter estimation by sequential testing (PEST) as an alternative threshold estimation technique to minimize the required trial count without predetermined knowledge of the relevant stimulus space. The directional acuity threshold was estimated at 11.7 ± 3.8° from the PEST method (n = 11 of 25 subjects, psychometric threshold = 10.1 ± 3.1°) using only one-third the number of trials compared to the psychometric method. Furthermore, PEST estimates of the direction acuity threshold were highly correlated with the psychometric estimates across subjects (r = 0.93) suggesting that both methods provide comparable estimates of the perceptual threshold. Computational modeling of both techniques revealed similar variance in the estimated thresholds across simulations of about 1°. Our results suggest that the PEST algorithm can be used to more quickly quantify whole-body directional acuity during standing in individuals with balance impairments.
Although it is possible to produce the same movement using an infinite number of different muscle activation patterns owing to musculoskeletal redundancy, the degree to which observed variations in muscle activity can deviate from optimal solutions computed from biomechanical models is not known. Here, we examined the range of biomechanically permitted activation levels in individual muscles during human walking using a detailed musculoskeletal model and experimentally-measured kinetics and kinematics. Feasible muscle activation ranges define the minimum and maximum possible level of each muscle's activation that satisfy inverse dynamics joint torques assuming that all other muscles can vary their activation as needed. During walking, 73% of the muscles had feasible muscle activation ranges that were greater than 95% of the total muscle activation range over more than 95% of the gait cycle, indicating that, individually, most muscles could be fully active or fully inactive while still satisfying inverse dynamics joint torques. Moreover, the shapes of the feasible muscle activation ranges did not resemble previously-reported muscle activation patterns nor optimal solutions, i.e. static optimization and computed muscle control, that are based on the same biomechanical constraints. Our results demonstrate that joint torque requirements from standard inverse dynamics calculations are insufficient to define the activation of individual muscles during walking in healthy individuals. Identifying feasible muscle activation ranges may be an effective way to evaluate the impact of additional biomechanical and/or neural constraints on possible versus actual muscle activity in both normal and impaired movements.
Neuromusculoskeletal models solve the basic problem of determining how the body moves under the influence of external and internal forces. Existing biomechanical modeling programs often emphasize dynamics with the goal of finding a feed-forward neural program to replicate experimental data or of estimating force contributions or individual muscles. The computation of rigid-body dynamics, muscle forces, and activation of the muscles are often performed separately. We have developed an intrinsically forward computational platform (Neuromechanic, www.neuromechanic.com) that explicitly represents the interdependencies among rigid body dynamics, frictional contact, muscle mechanics, and neural control modules. This formulation has significant advantages for optimization and forward simulation, particularly with application to neural controllers with feedback or regulatory features. Explicit inclusion of all state dependencies allows calculation of system derivatives with respect to kinematic states and muscle and neural control states, thus affording a wealth of analytical tools, including linearization, stability analyses and calculation of initial conditions for forward simulations. In this review, we describe our algorithm for generating state equations and explain how they may be used in integration, linearization, and stability analysis tools to provide structural insights into the neural control of movement.