Kinematic variability and local dynamic stability of upper body motions when walking at different speeds

Abstract

A ubiquitous characteristic of elderly and patients with gait disabilities is that they walk slower than healthy controls. Many clinicians assume these patients walk slower to improve their stability, just as healthy people slow down when walking across ice. However, walking slower also leads to greater variability, which is often assumed to imply deteriorated stability. If this were true, then slowing down would be completely antithetical to the goal of maintaining stability. This study sought to resolve this paradox by directly quantifying the sensitivity of the locomotor system to local perturbations that are manifested as natural kinematic variability. Eleven young healthy subjects walked on a motorized treadmill at five different speeds. Three-dimensional movements of a single marker placed over the first thoracic vertebra were recorded during continuous walking. Mean stride-to-stride standard deviations and maximum finite-time Lyapunov exponents were computed for each time series to quantify the variability and local dynamic stability, respectively, of these movements. Quadratic regression analyses of the dependent measures vs. walking speed revealed highly significant U shaped trends for all three mean standard deviations, but highly significant linear trends, with significant or nearly significant quadratic terms, for five of the six finite-time Lyapunov exponents. Subjects exhibited consistently better local dynamic stability at slower speeds for these five measures. These results support the clinically based intuition that people who are at increased risk of falling walk slower to improve their stability, even at the cost of increased variability.

Introduction

Every year, one-third of community-dwelling elderly and 60% of nursing home residents fall and these falls cause 70% of accidental deaths among the elderly (Fuller, 2000). Most falls occur during whole-body movements like walking (Tinetti et al., 1995; Berg et al., 1997; Niino et al., 2000) and these falls are associated with even greater risks of serious injury (Tinetti et al., 1995). Developing a better understanding of the control mechanisms governing dynamic stability during walking is, therefore, essential for determining the underlying causes of these falls.

Elderly and patients with gait abnormalities almost always walk slower than healthy controls. Slow gait occurs with neurological disorders affecting the central (Alexander, 1996; Thaut et al., 1999) or peripheral (Dingwell and Cavanagh, 2001) nervous systems, muscular (Lohmann Siegel et al., 2004) or orthopedic (Powers et al., 1999) disorders, and with normal aging (Alexander, 1996; Lord et al., 1996). Perhaps intuitively, elderly with a history of falls walk slower than elderly non-fallers (Kerrigan et al., 2000). In prospective studies, however, while some found that slow gait predicts future falls (Luukinen et al., 1995; Bergland et al., 2003), others found that it does not (Lord et al., 1996; Maki, 1997; Hausdorff et al., 2001a, Hausdorff et al., 2001b).

These people may slow down because of specific limiting impairments that prevent them from walking faster. Slower speeds in elderly subjects are associated with decreased joint movements and joint kinetics (Olney et al., 1994; Judge et al., 1996; Kerrigan et al., 2001). However, it is not clear if these biomechanical changes were the cause or the result of the slower walking speeds. Young healthy subjects exhibit similar changes during slow walking (Winter, 1983) and in studies that specifically controlled for gait speed, some found that biomechanical differences persisted (DeVita and Hortobagyi, 2000; Kerrigan et al., 2000), while others did not (Alexander, 1996; Kerrigan et al., 1998). The alternative possibility is that elderly and patients with gait disabilities slow down because doing so reflects a “safer” or “more cautious” gait strategy (Winter et al., 1990; Courtemanche et al., 1996; DeVita and Hortobagyi, 2000), just as healthy subjects naturally slow down when walking on slippery surfaces like ice. Elderly subjects also slow down when their stability is challenged, such as when negotiating obstacles (Hahn and Chou, 2004) or walking over irregular terrain (Menz et al., 2003; Richardson et al., 2004). In fact, older people who walk faster may be more likely to trip and fall than those who walk more slowly (Pavol et al., 1999, Pavol et al., 2001).

One potentially confounding problem with the theory that people slow down to be more stable is that when young healthy subjects (for whom stability is not an issue) walk either slower or faster, their movements become more variable (Winter, 1983; Öberg et al., 1993, Öberg et al., 1994). It is commonly believed that greater variability indicates greater instability. Indeed, most proposed indices of locomotor “stability” quantify some aspect of gait variability (Winter, 1989; Yack and Berger, 1993; Holt et al., 1995) and increased locomotor variability has been prospectively associated with an increased risk of falling in elderly subjects (Maki, 1997; Hausdorff et al., 2001a, Hausdorff et al., 2001b). Healthy elderly also exhibit increased step width variability (Owings and Grabiner, 2004a, Owings and Grabiner, 2004b), which may have implications for lateral stability (Kuo, 1999; Bauby and Kuo, 2000). When walking over irregular surfaces that induce small perturbations, elderly and patients with diabetic neuropathy exhibit increased variability as well as slower walking speeds (Menz et al., 2003, Menz et al., 2004; Richardson et al., 2004). However, correlations do not always imply causation. Thus, it remains an open question whether being more variable actually causes you to be at greater risk of falling. Neuropathic patients who are known to have a high risk of falling demonstrated increased kinematic variability during walking, but these differences were more strongly correlated with their slower walking speeds than with their sensory loss (Dingwell and Cavanagh, 2001).

Resolving this paradox requires gaining a better understanding of how walking speed affects dynamic stability. Stability can generally be defined as the capacity of a system to respond to perturbations (Full et al., 2002). While increased gait variability may be a clinically valid predictor of future falls (Maki, 1997; Hausdorff et al., 2001a, Hausdorff et al., 2001b), these measures do not quantify how the neuromuscular control system responds to perturbations and therefore cannot provide direct measures of stability itself. The present study applied a more dynamically rigorous approach that quantifies local dynamic stability (Dingwell and Cusumano, 2000), or the resilience of the locomotor system to the infinitesimally small (i.e. “local”) perturbations that occur naturally during walking. Global stability, the capacity of the system to respond to larger perturbations, such as tripping or slipping, was not assessed. Patients with diabetic neuropathy who walked slower and were more variable, simultaneously exhibited better local dynamic stability (Dingwell et al., 2000). Post-hoc regression analyses suggested this improved local dynamic stability was related to their slower walking speeds. However, those subjects were tested only at their preferred walking speeds (PWS), so no definitive assessment of how speed affects local dynamic stability was possible. Therefore, the purpose of the present study was to directly examine how both kinematic variability and local dynamic stability vary across a range of walking speeds. We focused our analyses on upper body motions because maintaining dynamic stability of the upper body is a primary objective of human locomotion (MacKinnon and Winter, 1993; Prince et al., 1994). We hypothesized that variability of these motions would exhibit a quadratic relationship that increased at both slower and faster walking speeds (Winter, 1983; Öberg et al., 1993, Öberg et al., 1994). In contrast, however, we hypothesized that local dynamic stability would improve as speed decreased.