Extending the Law of Intersegmental Coordination: Implications for Powered Prosthetic Controls

TL;DR

This work addresses the elevated metabolic cost of walking in transfemoral amputees by extending the Law of Intersegmental Coordination (ISC) to 3D elevation angles and dynamics through Elevation Space Moments (ESM). It maps anatomical joint torques to a reduced elevation-space via $M = (J_\alpha(q)^T)^{\dagger} \tau$ and relates external power to both joint- and elevation-space representations with $P_T = \tau^T \dot q = M^T \dot \alpha$ and $\dot \alpha = J_\alpha(q) \dot q$, enabling a moment-based coordination analysis. The authors introduce the ISC3d toolbox, demonstrate planar covariation in elevation angles for AB gait, and show altered ISC in amputee gait with passive and powered prostheses; ESM reveal reduced coordination in amputees, suggesting that imposing a covariation constraint could guide prosthetic control toward healthier thigh kinematics. A CVP-constrainedPred approach demonstrates potential for predicting shank profiles that preserve healthy thigh behavior, hinting at a pathway to reduce hip compensations and metabolic cost in powered prosthetic control, while highlighting the need for broader datasets and 3D real-time implementations.

Abstract

Powered prostheses are capable of providing net positive work to amputees and have advanced in the past two decades. However, reducing amputee metabolic cost of walking remains an open problem. The Law of Intersegmental Coordination (ISC) has been observed across gaits and has been previously implicated in energy expenditure of walking, yet it has rarely been analyzed or applied within the context of lower-limb amputee gait. This law states that the elevation angles of the thigh, shank and foot over the gait cycle are not independent. In this work, we developed a method to analyze intersegmental coordination for lower-limb 3D kinematic data, to simplify ISC analysis. Moreover, inspired by motor control, biomechanics and robotics literature, we used our method to broaden ISC toward a new law of coordination of moments. We find these Elevation Space Moments (ESM), and present results showing a moment-based coordination for able bodied gait. We also analyzed ISC for amputee gait walking with powered and passive prosthesis, and found that while elevation angles remained planar, the ESM showed less coordination. We use ISC as a constraint to predict the shank angles/moments that would compensate for alterations due to a passive foot so as to mimic a healthy thigh angle/moment profile. This may have implications for improving powered prosthetic control. We developed the ISC3d toolbox that is freely available online, which may be used to compute kinematic and kinetic ISC in 3D. This provides a means to further study the role of coordination in gait and may help address fundamental questions of the neural control of human movement.

Figures (10)

• Figure 1: Schematic of (a) elevation angles ($\alpha_i$) and moments ($M_i$) in the sagittal plane, and (b) anatomical joint flexion angles ($\phi_j$) and their internal joint torques ($\tau_{\phi_j}$). Ankle dorsiflexion is assumed as positive. All moments are defined in the positive direction of their associated angle.
• Figure 2: Elevation angles of the thigh (T), shank (S) and foot (F) computed from \ref{['eq:calc_elevation_angles']}. Able bodied mean curves with shaded standard deviations (left), amputees with a passive prosthesis (middle) and amputees with a powered prosthesis (right). The amputated (A) side is indicated by a dashed line, and the contralateral (C) side as a solid line, as in AB data. For this and \ref{['fig:2_elevation_cvp', 'fig:3_elevation_pcs', 'fig:4_shank_foot', 'fig:6_elevation_moments', 'fig:7_elevation_moments_pcs', 'fig:mainFigure_Demonstration']} means across subjects for three speeds are shown; slower speed corresponds to more transparent colors.
• Figure 3: Elevation angles Covariation Plane. The amputated leg (AL) is indicated by a dashed line, and contralateral leg (CL) as a solid line. The plane of each loop, defined by the first and second PCs, is shown as a grid. The trajectory progresses in gait phase counterclockwise. The top (bottom) of the loop is linked to the heel strike (toe-off) events, respectively.
• Figure 4: Principal Component scores of the elevation angles (as in \ref{['fig:1_elevation_angles']}), with indices ordered by decreasing PC variance for amputated (A) and contralateral (C) legs.
• Figure 5: Mean Shank-Foot coordination which is adopted from borghese_kinematic_1996.