Simulations suggest walking with reduced propulsive force would not mitigate the energetic consequences of lower tendon stiffness

Abstract

Aging elicits numerous effects that impact both musculoskeletal structure and walking function. Tendon stiffness (kT) and push-off propulsive force (FP) both impact the metabolic cost of walking and are diminished by age, yet their interaction has not been studied. We combined experimental and computational approaches to investigate whether age-related changes in function (adopting smaller FP) may be adopted to mitigate the metabolic consequences arising from changes in structure (reduced kT). We recruited 12 young adults and asked them to walk on a force-sensing treadmill while prompting them to change FP (±20% & ±40% of typical) using targeted biofeedback. In models driven by experimental data from each of those conditions, we altered the kT of personalized musculoskeletal models across a physiological range (2-8% strain) and simulated individual-muscle metabolic costs for each kT and FP combination. We found that kT and FP independently affect walking metabolic cost, increasing with higher kT or as participants deviated from their typical FP. Our results show no evidence for an interaction between kT and FP in younger adults walking at fixed speeds. We also reveal complex individual muscle responses to the kT and FP landscape. For example, although total metabolic cost increased by 5% on average with combined reductions in kT and FP, the triceps surae muscles experienced a 7% local cost reduction on average. Our simulations suggest that reducing FP during walking would not mitigate the metabolic consequences of lower kT. Wearable devices and rehabilitative strategies can focus on either kT or FP to reduce age-related increases in walking metabolic cost.

Fig 1. Experimental design.

An overview of the (A) experimental and (B) computational methods to examine how tendon stiffness (k_T) and propulsive force (F_P) affect the metabolic cost of walking. In our experimental design (A), we asked participants to walk at their preferred speed while targeting specific F_P using visual biofeedback. We simulated their movement in numerous musculoskeletal models at a range of k_T levels (ε_o = 2%, 3.3% (model default), 4%, 6%, and 8%) and estimate d the metabolic cost for each condition (k_T & F_P). This figure is similar but not identical to a flowchart image we recently published [17].

Fig 2. Total average metabolic costs.

We show how average total metabolic cost varies across k_T (horizontal axis) and F_P intensity (vertical axis). This heatmap is color coded for the reference metabolic cost (default k_T and Norm F_P intensity) to be displayed in white, with higher costs in red and lower costs in blue. We found significant ANOVA main effects separately for k_T (horizontal arrow) and F_P (vertical arrow), but no interaction (no diagonal arrow) between them.

Fig 3. Total instantaneous metabolic costs.

We show instantaneous, whole-body metabolic cost as a percentage of the gait cycle, across both k_T (left minor axes) and F_P (right major axis). The average metabolic cost at default k_T and Norm F_P is normalized to white. We display higher costs in red, and lower costs in blue, with the color intensity profiles even between the two. At the top of the figure, we show periods with significant main effects for k_T (or ε_o) and F_P. The black horizontal bars indicate a significant repeated measures ANOVA main effect via statistical parameter mapping.

Fig 4. Individual muscle average metabolic costs.

Individual muscle metabolic costs respond uniquely across k_T and F_P. In this figure, we show the top 12 lower-body muscles that contribute to walking metabolic cost (Table 1). We oriented the heatmaps with proximal musculature (hip) towards the top, and distal musculature (ankle) towards the bottom. Like Fig 2, we normalized each heatmap for the default k_T and F_P values (3.3% and Norm, respectively) to be shown in white, with higher costs in red and lower costs in blue. Within each heatmap, we show significant ANOVA main effects via horizontal, vertical, and diagonal arrows indicating significant effects for k_T, and F_P, and interaction, respectively.

Fig 5. Individual muscle instantaneous metabolic costs.

Timing and intensity of individual-muscle metabolic costs change when varying k_T and F_P. In this figure, we show 12 lower-body muscles as in Fig 4, now including instantaneous metabolic cost across the gait cycle. These heatmaps are designed similar to the whole-body costs in Fig 3, with k_T on the left minor vertical axis, F_P on the right vertical major axis, and relative time (% GC) on the horizontal axis. We show significant ANOVA main effects from instantaneous statistical parametric mapping using blocks (ε_o and F_P) and shaded regions (interactions) along the top bar.

Fig 6. Activation, fiber length, and metabolic costs.

These scatterplots show general associations between the underlying muscle-tendon dynamics of activation and fiber length and their influence on the relationships between metabolic cost, F_P, and k_T. Each circle represents the subject-average outcome at a given activation, fiber length, metabolic cost, F_P, and k_T for the top dozen individual-muscle contributors to metabolic cost (also shown in Figs 4 and 5). We found a significant association between metabolic cost and mean activation (A) but not for normalized mean fiber length (B). F_P (C) seemed to have more mixed influence on the relationship between activation and fiber length, whereas k_T (strain, D) showed a strong effect for shorter fiber lengths and higher activations (downward & rightward shift from blue (most stiff) to pink (least stiff)).