Pendular Mechanism and Mechanical Work Dynamics in Bilateral Metatarsophalangeal Amputation Walking Mechanics: A Single-Case Velocity-Adjusted Analysis

Purpose: Loss of digital leverage can severely disrupt inverted pendulum mechanics and alter how mechanical work is distributed during walking. The biomechanical efficacy of prosthetic footwear in individuals with bilateral toe amputation remains poorly understood. This exploratory single-case study quantified the effects of custom prosthetic footwear on pendular recovery, mechanical work distribution, and functional mobility in a 52-year-old male with complete bilateral digital amputation (metatarsals preserved), while evaluating intervention effects relative to concurrent walking speed changes. Methods: Three-dimensional kinematic data were collected during barefoot and prosthetic footwear walking across 13 consecutive stride cycles (7 barefoot, 6 shod). Functional speed restoration was evaluated via the Locomotor Rehabilitation Index (LRI). Unadjusted condition differences were evaluated using Hedges’ g with bootstrap confidence intervals. To isolate intervention effects from walking velocity, a single-case multiple linear regression model incorporating a first-order autoregressive error structure [AR(1)] evaluated speed-adjusted intervention effects (β1) centered at grand mean speed (1.14 m/s). Results: Walking speed increased substantially from 0.88 ± 0.08 m/s barefoot (range: 0.76–0.98 m/s) to 1.45 ± 0.05 m/s with footwear (range: 1.38–1.52 m/s; Hedges’ g = 7.78), restoring size-controlled functional mobility (LRI increased from 57% to 94%). Unadjusted comparisons showed increases in pendular recovery (39% to 47%, g = 4.03); external mechanical work, Wext (0.460 to 0.608 J/kg/m, g = 4.85); forward work, Wf (0.286 to 0.627 J/kg/m, g = 5.92); and internal work, Wint (0.194 to 0.225 J/kg/m, g = 3.12). However, because walking speeds were distinctly separated with no overlap between conditions, parameter estimates at the mean speed rely on model extrapolation. When controlling for instantaneous stride speed via AR(1) regression (autocorrelation ρ = 0.38), speed-adjusted condition effects were non-significant for Wext (β1 = +0.085 J/kg/m, p = 0.265), Wf (β1 = +0.051 J/kg/m, p = 0.296), Wint (β1 = −0.007 J/kg/m, p = 0.680), and pendular recovery (β1 = +0.10%, p = 0.981), which is consistent with strong velocity dependence rather than intrinsic shifts in mechanical efficiency at a given speed. Vertical external work demonstrated a statistical trend toward elevation in the prosthetic condition (β1 = +0.162 J/kg/m, p = 0.062), which may reflect compensatory vertical body center of mass redirection to compensate for reduced distal forefoot lever propulsion during rollover. Conclusions: Prosthetic footwear substantially enhances functional gait mobility by enabling velocity restoration toward Froude-based optimal speed, although independent footwear and velocity effects cannot be fully decoupled without observations at overlapping speeds.