Relationship between stride interval variability and aging: use of linear and non-linear estimators for gait variability assessment in assisted living environments

Abstract

The aim of this study is to assess the impact of aging process in gait variability. Stride interval variability is estimated by using two approaches: (1) a non-linear fractal analysis (detrended fluctuation analysis) which evaluates the presence of long-range correlations in stride interval time series; and (2) a statistical dispersion measure (coefficient of variation) to quantify the magnitude of the stride interval fluctuations. Two groups of physically independent older adults, with different walking ability, have participated in the gait trials performed in an elderly care home. The estimated stride interval variability of the elders is compared to each other and to the variability coming from a young adult group used as control. To accomplish this, an infrastructure which uses wearables to acquire inertial data from the trunk of each participant is provided. Stride interval time series are made up of the estimated heel-strike events from previous inertial data. In addition, a service segments straight paths within the gait trials, discarding turns. The stride intervals from the segmented straight paths are stitched together to produce the long time series required to analyze gait variability. Despite the study has not provided conclusive results from an individual perspective, finding older adults who have less stride interval variability than younger ones. The inter-class analysis conducted has shown interesting findings about the relation between the subjective characterization of gait, aging and stride interval variability estimated through the two proposed approaches.

Appendix A: measuring the straightness of a trajectory fragment

The procedure tangentStraightness() presented in the flow diagram in Figure 6 is responsible for measuring the straightness of the trajectory enclosed by a fragment, to accomplish that the changes in the tangent to that piece of trajectory are computed; tangentStraightness() is mathematically defined as follows:

If the trajectory’s position at sample t is (x(t), y(t)), where x(t) is the timestamp and y(t) the yaw angle relative to this sample, then the tangent at this point is (dx(t), dy(t)), where dx(t) is the derivative of x at sample t. The tangent can be normalized dividing by ||(dx(t), dy(t))||. Therefore, an unit vector a(t) of the tangent to the trajectory at sample t is defined as:

$$\begin{aligned} a(t) = \frac{\left( dx(t),dy(t) \right) }{|| dx(t),dy(t)||} \end{aligned}$$

(5)

In order to measure the straightness of the trajectory framed in a particular fragment, the focus is set on integrating $||da(t)||^2$ along that portion of trajectory, where da(t) is the derivative of a at sample t. As our trajectories are sets of discrete data points rather than curves, finite differences must be used to approximate the derivatives. Therefore, a(t) becomes:

$$\begin{aligned} a(t)=\frac{ \frac{x(t+h)-x(t)}{h} , \frac{y(t+h)-y(t)}{h}}{\left\| \frac{x(t+h)-x(t)}{h},\frac{y(t+h)-y(t)}{h}\right\| } \end{aligned}$$

(6)

and da(t):

$$\begin{aligned} da(t) = \frac{a(t+h)-a(t)}{h} \end{aligned}$$

(7)

where the spacing parameter h, used in the finite differences, is initialized to 1 sample in this particular case. Then, we get a straightness value S by summing up $h||da(t)||^2$ for all points/samples belonging to the trajectory framed in a fragment:

$$\begin{aligned} S = \sum _{ trajectory }{h ||da(t)||^2} \end{aligned}$$

(8)

To reiterate, S will be zero for an ideal straight line and larger the more the trajectory enclosed by the fragment deviates from a line. We fix a threshold for S ($S>0.01$) in order to determine if the current fragment of trajectory under analysis is not considered straight, in other words, if it contains an abrupt change in direction or not.