Hip and ankle responses for reactive balance emerge from varying priorities to reduce effort and kinematic excursion: A simulation study

Abstract

Although standing balance is important in many daily activities, there has been little effort in developing detailed musculoskeletal models and simulations of balance control compared to other whole-body motor activities. Our objective was to develop a musculoskeletal model of human balance that can be used to predict movement patterns in reactive balance control. Similar to prior studies using torque-driven models, we investigated how movement patterns during a reactive balance response are affected by high-level task goals (e.g., reducing center-of-mass movement, maintaining vertical trunk orientation, and minimizing effort). We generated 23 forward dynamics simulations where optimal muscle excitations were found using cost functions with different weights on minimizing these high-level goals. Variations in hip and ankle angles observed experimentally (peak hip flexion=7.9-53.1°, peak dorsiflexion=0.5-4.7°) could be predicted by varying the priority of these high-level goals. More specifically, minimizing center-of-mass motion produced a hip strategy (peak hip flexion and ankle dorsiflexion angles of 45.5° and 2.3°, respectively) and the response shifted towards an ankle strategy as the priority to keep the trunk vertical was increased (peak hip and ankle angles of 13.7° and 8.5°, respectively). We also found that increasing the priority to minimize muscle stress always favors a hip strategy. These results are similar to those from sagittal-plane torque-driven models. Our muscle-actuated model facilitates the investigation of neuromechanical interactions governing reactive balance control to predict muscle activity and movement patterns based on interactions between neuromechanical elements such as spinal reflexes, muscle short-range stiffness, and task-level sensorimotor feedback.

Keywords: Forward dynamics; Kinematics; Posture; Simulation.

Figure 1. Overview of simulation methods

(A) The forward dynamics simulations used a detailed musculoskeletal model with 23 degrees-of-freedom (DoF) and 46 muscles per leg. (B) Translation of the support-surface was achieved by prescribing the displacement, velocity, and acceleration of the anterior-posterior translation of the toe segment of the model using experimentally measured values. (C) Optimal muscle excitation parameters were found using a simulated annealing algorithm. (D) Muscle excitation signals were identical across legs and were not allowed to change for 100 ms after perturbation onset to account of neural conduction delays. The shape of the muscle excitation in the subsequent time period was defined by cubic interpolation of 15 equally-spaced spline points for a total simulation duration of 1.5 s. (E) The cost function included terms for minimizing center-of-mass excursion, trunk orientation excursion, and muscle stress. The weights for each of these three terms (k's) were varied to determine the effect of each parameter (see Table 2 for values). A terminal cost was also included that brought the model back to its initial state at the end of the simulation. (F) Once the optimization converged, center-of-mass excursion, trunk orientation, and hip, knee, and ankle angles were used to characterize the response and compared across each resulting simulation.

Figure 2. Simulated kinematics when minimizing only center-of-mass versus only trunk orientation excursion

In response to identical perturbations, minimizing center-of-mass (CoM) versus trunk orientation excursion produced very different responses. The time-course of the simulated response (left panels) and peak values (right panels) are shown for (A) CoM excursion, (B) trunk orientation, (C) hip angle, and (D) ankle angle. Greater hip and trunk motion and smaller CoM excursion were generated when minimizing CoM excursion only (red solid line) versus trunk orientation excursion only (blue dashed line). Ankle deviations were small in both cases, but were in opposite directions (plantarflexion vs. dorsiflexion). The simulated responses were generally in agreement with the range observed experimentally in an individual of a height and mass similar to the model that was subjected to sixty perturbations of identical magnitude as the simulated perturbations (gray box plots in right panel).

Figure 3. Effect of varying priorities to minimize center-of-mass and trunk orientation excursion

When the priority to minimize both center-of-mass (CoM) and trunk orientation excursion were differentially weighted, a spectrum of kinematic patterns were produced that were intermediate to those found in simulations minimizing only CoM or trunk orientation excursion. As the relative weight to minimize trunk orientation versus CoM excursion increased (left to right): (A) peak trunk orientation (solid blue line) decreased while peak CoM (dashed red line) increased and (B) peak hip angle decreased (solid orange line) while ankle dorsiflexor angle (dashed purple lines) increased slightly, with no discernable changes in peak knee angle (dotted black line).

Figure 4. Effect of minimizing muscle stress on response kinematics

The peak (A) center-of-mass (CoM) excursion, (B) trunk orientation, (C) hip angle, and (D) ankle angle are shown across increasing (left to right) ratios of priority to minimize trunk orientation vs. CoM excursion (x-axis, increasing trunk to CoM weight ratio) for low (light green circles), medium (green x's), and high (dark green triangles) priority to minimize muscle stress. As the priority to minimize muscle stress increased (light to dark lines): (A) peak CoM showed no consistent change, (B) peak trunk orientation and (C) peak hip angle increased and (D) peak ankle angle had minimal changes across all trunk to CoM weight ratios. The extent of these changes in trunk and hip angles with increasing priority to minimize muscle stress was larger when the priority to minimize trunk orientation was also high (e.g. Cond7 vs Cond1). (E) As expected, average muscle stress (normalized to the medium condition) decreased as the priority to minimize muscle stress was increased.

Figure 5. Effect of repeated perturbations on experimental kinematic response

The peak (A) center-of-mass (CoM) excursion, (B) trunk orientation, (C) hip angle, and (D) ankle angle are shown across sets of repeated perturbations of identical magnitude (left to right). Experimental kinematics were collected from one individual (male, 36 years old) of similar height and weight (177.0 cm, 75.0 kg) as the model (180.0 cm, 71.2 kg). The subject was first habituated to 20 forward perturbations and then unexpectedly given a series of 20 backward perturbations of identical magnitude as that applied in the simulations. This was repeated a total of three times. Only the response to the backward perturbations are shown. Post-hoc analyses using least- squares linear fits (thick red lines) were used to examine changes in experimental kinematics (thin black lines) over repeated backwards perturbations. There was a trend for the response strategy to shift towards an ankle strategy as the subject adapted to the perturbations with a reduction in both peak (B) trunk orientation and (C) hip angle.