Causal interactions and dynamic stability between limbs while walking with imposed leg constraints

Abstract

Aim: To investigate the dynamics of the motor control system during walking by examining the complexity, stability, and causal relationships of leg motions. Specifically, the study focuses on gait under both bilateral and unilateral constraints induced by a passive exoskeleton designed to replicate gastrocnemius contractures.

Methods: Kinematic data was collected as 10 healthy participants walked at a self-selected speed. A new Complexity-Instability Index (CII) of the leg motions was defined as a function of the Correlation Dimension and the Largest Lyapunov Exponent. Causal interactions between the leg motions are explored using Convergent Cross Mapping.

Results: Normal walking is characterized by a high mutual drive of each leg to the other, where CII is lowest for both legs (complexity of each leg motion is low and stability high). The effect of the bilateral emulated contractures is a reduced drive of each leg to the other and an increased CII for both legs. With unilateral emulated contracture, the mechanically constrained leg strongly drives the unconstrained leg, and CII was significantly higher for the constrained leg compared to normal walking.

Conclusion: Redundancy in limb motions is used to support causal interactions, reducing complexity and increasing stability in our leg dynamics during walking. The role of redundancy is to allow adaptability above being able to satisfy the overall biomechanical problem; and to allow the system to interact optimally. From an applied perspective, important characteristics of functional movement patterns might be captured by these nonlinear and causal variables, as well as the biomechanical aspects typically studied.

Keywords: clinical gait analysis; exoskeleton; nonlinear dynamics; pathological gait; symmetry.

FIGURE 1

Example of device used by Attias et al. (2016) to replicate contractures on healthy participants. The exoskeleton, designed and built-in collaboration with the Giglio Partners Orthopedic group (Geneva, Switzerland) bilaterally embraced the pelvis, thigh and shank with plastic cuffs that did not occlude retroreflective markers placed on the skin. Unilateral and bilateral contractures were induced using ropes in relation to the muscle insertions and termination for the gastrocnemius muscle. In depth description of the exoskeleton design is reported in previous work (Attias et al., 2016; Goodman et al., 2004; Houx et al., 2012).

FIGURE 2

Mean and standard deviations of the Complexity Instability Index (CII) for the left (red) and right (green) leg in the three experimental conditions; the normal walking condition (No_Exoskeleton), bilateral exoskeleton (Bilateral) and unilateral exoskeleton (Unilateral; where the left leg is the constrained leg) condition. In the unilateral exoskeleton condition, the left leg is the constrained leg.

FIGURE 3

Mean and standard deviations of the causal drive of the left to the right leg (red) and right to left leg (green) across the three experimental conditions; the normal walking condition (NormalWalking), bilateral exoskeleton (Bilateral) and unilateral exoskeleton (Unilateral; where the left leg is the constrained leg) conditions.