Physiologically-constrained decomposition of vertical ground reaction forces using gaussian basis functions: A full-curve approach to gait characterization.

Abstract

We aimed to test whether a healthy-derived, phase-anchored μ template can approximate pathological vGRF waveforms and quantify deviations relative to normative patterns. Traditional peak-based metrics capture only fragments of gait dynamics. This study introduces a physiologically anchored model that reconstructs the entire vertical ground-reaction-force (vGRF) curve with eight Gaussian basis functions, each linked to a specific sub-phase of stance. Ninety-one published vGRF traces representing healthy walking and running, post-stroke recovery stages, total-hip-arthroplasty gait, transtibial and foot-prosthesis use, and athletic sprinting were digitised, amplitude- and time-normalised, and fitted with constrained non-linear optimisation. Position parameters (μ) were restricted to ± 1 standard deviation around phase-specific mean values, while amplitudes (A) and widths (σ) were freely optimised. The model reproduced GRF morphology with coefficients of determination (R²) from 0.95 to 0.99 and root-mean-square errors below 0.03 body-weight across all conditions. Fixed μ values alone reconstructed a reference walking curve with R² = 0.996, demonstrating the validity of the phase template. Radar plot visualisations of A and σ revealed characteristic deviations that were obscured in peak-based analysis: elevated mid-stance loads and diminished push-off in post-stroke gait, broadened mid-stance components after hip arthroplasty, and attenuated late-stance amplitudes in prosthetic limbs. The eight-component Gaussian model provides a concise 24-parameter representation of vGRF trajectories, enabling accurate, interpretable and storage-efficient gait profiling. Its phase-anchored structure enhances diagnostic sensitivity, supports progress monitoring in rehabilitation, and is readily transferable to wearable or large-scale database applications. Radar plots offer an exploratory summary of gait morphology, supporting objective comparisons within and between individuals.