Improving spring-mass parameter estimation in running using nonlinear regression methods [RESEARCH ARTICLE]

We present a method to model runners as spring–mass systems using nonlinear regression (NLR) and the full vertical ground reaction force (vGRF) time series without additional inputs and fewer traditional parameter assumptions. We derived and validated a time-dependent vGRF function characterized by four spring–mass parameters – stiffness, touchdown angle, leg length and contact time – using a sinusoidal approximation. Next, we compared the NLR-estimated spring–mass parameters with traditional calculations in runners. The mixed-effect NLR method (ME NLR) modeled the observed vGRF best (RMSE:155 N) compared with a conventional sinusoid approximation (RMSE: 230 N). Against the conventional methods, its estimations provided similar stiffness approximations (–0.2±0.6 kN m–1) with moderately steeper angles (1.2±0.7 deg), longer legs (+4.2±2.3 cm) and shorter effective contact times (–12±4 ms). Together, these vGRF-driven system parameters more closely approximated the observed vertical impulses (observed: 214.8 N s; ME NLR: 209.0 N s; traditional: 223.6 N s). Finally, we generated spring–mass simulations from traditional and ME NLR parameter estimates to assess the predicative capacity of each method to model stable running systems. In 6/7 subjects, ME NLR parameters generated models that ran with equal or greater stability than traditio...

Source: Journal of Experimental Biology - March 18, 2021 Category: Biology Authors: Burns, G. T., Gonzalez, R., Zernicke, R. F. Tags: RESEARCH ARTICLE Source Type: research