Effects of walking speed, strength and range of motion on gait stability in healthy older adults

Abstract

Falls pose a tremendous risk to those over 65 and most falls occur during locomotion. Older adults commonly walk slower, which many believe helps improve walking stability. While increased gait variability predicts future fall risk, increased variability is also caused by walking slower. Thus, we need to better understand how differences in age and walking speed independently affect dynamic stability during walking. We investigated if older adults improved their dynamic stability by walking slower, and how leg strength and flexibility (passive range of motion (ROM)) affected this relationship. Eighteen active healthy older and 17 healthy younger adults walked on a treadmill for 5min each at each of 5 speeds (80-120% of preferred). Local divergence exponents and maximum Floquet multipliers (FM) were calculated to quantify each subject's inherent local dynamic stability. The older subjects walked with the same preferred walking speeds as the younger subjects (p=0.860). However, these older adults still exhibited greater local divergence exponents (p<0.0001) and higher maximum FM (p<0.007) than the younger adults at all walking speeds. These older adults remained more locally unstable (p<0.04) even after adjusting for declines in both strength and ROM. In both age groups, local divergence exponents decreased at slower speeds and increased at faster speeds (p<0.0001). Maximum FM showed similar changes with speed (p<0.02). Both younger and older adults exhibited decreased instability by walking slower, in spite of increased variability. These increases in dynamic instability might be more sensitive indicators of future fall risk than changes in gait variability.

Figure 1.

Schematic Representation of State-space Construction. (A) The original time series of raw data define the states (q₁, q₂, …) of the system. (B) These states are combined to form the system’s trajectory in state space (only a 3-dimensional state space is shown here used for illustrative purposes). (C) Expanded view of a typical local region. A small perturbation moves the system at S(t) to its closest neighbor S(t*). Local divergence is computed by measuring the Euclidean distances between the subsequent points, denoted d_j(i). The local dynamic stability of the system is defined by how quickly, on average, the two trajectories diverge away from each other. Rates of divergence, λ*_S and λ*_L, were calculated from the slopes of the mean log divergence curve (Eq. 2). (D) Poincaré sections are defined to be orthogonal to the mean (i.e., limit) cycle. The system state, S_k, at stride k evolves to S_k+1 one stride later. Floquet multipliers quantify, on average, whether the distances between these states and the system fixed point, S*, grow or decay after one cycle (Eq. 5).

Figure 2.

Spatio-temporal gait metrics vs. walking speed. 1.0×PWS is preferred walking speed. Error bars denote between-subject standard deviations within each group. Note that symbols for Older and Young groups have been offset slightly for clarity. ANOVA results for differences between age groups (p_a), walking speeds (p_s) and group × speed interactions (p_ix) are shown. Older adults exhibited shorter stride times at all 5 walking speeds. They also exhibited slightly shorter step lengths, but the differences did not quite reach statistical significance.

Figure 3.

(A) Sample local divergence curves for the 1.0×PWS walking speed for each age group. Solid lines are group averages. Dashed lines indicate ±1 between-subject standard deviation bands. The slopes of these curves define local dynamic stability (Fig. 1C). (B) Local divergence exponents (λ*) vs. Speed and Age. Error bars denote standard deviations within each group. Note that symbols for Older and Young groups have been offset slightly for clarity. Older adults exhibited greater short-term (λ*_S; p < 10⁻¹³), but not long-term (λ*_L; p = 0.192) local instability. Both groups exhibited decreased local dynamic instability at slower speeds and increased instability at faster speeds (p < 0.001).

Figure 4.

Short-term local divergence exponents (λ*_S) vs. composite strength and range of motion (ROM) scores. Each symbol represents that average value for one subject, averaged across speeds. Composite strength and ROM scores were both correlated with λ*_S. These correlations explain some, but not all, of the age-related differences in λ*_S (Table 2).

Figure 5.

A) Maximum Floquet multipliers (FM) across the entire gait cycle for the 1.0×PWS walking speed for each age group. Solid lines are group averages. Dashed lines indicate ±1 between-subject standard deviation bands. Maximum FM were consistent across the gait cycle. A few trials displayed a spike at ~20% or ~70% of the gait cycle, but this was not consistent between subjects or groups. Similar results were obtained at the other walking speeds. B) Maximum FM values vs. Speed for both age groups for the Poincaré sections at 0%, 25%, 50% and 75% of the gait cycle. Error bars denote ±1 between-subject standard deviation within each group. Note that symbols for Older and Young groups have been offset slightly for clarity. Older adults (squares) displayed higher Maximum FM. The horizontal bracket at the 75% Poincaré section denotes significant Tukey’s LSD post-hoc comparisons at p < 0.005. Maximum FM at the 0.8× and 0.9×PWS speeds were significantly different from those at both the 1.1× and 1.2×PWS speeds.

Figure 6.

Maximum Floquet multipliers (FM) vs. composite strength and range of motion (ROM) scores. Each symbol represents that average value for one subject, averaged across speeds. Correlations are shown for Maximum FM computed at Poincaré sections at 0% and 25% of the gait cycle. Results from 50% and 75% were similar. Composite strength and ROM scores were only slightly correlated with Maximum FM. These correlations explained little of the age-related differences in Maximum FM (Table 2).