Derivation of the Gait Deviation Index for Spinal Cord Injury

Abstract

The Gait Deviation Index (GDI) is a dimensionless multivariate measure of overall gait pathology represented as a single score that indicates the gait deviation from a normal gait average. It is calculated using kinematic data recorded during a three-dimensional gait analysis and an orthonormal vectorial basis with 15 gait features that was originally obtained using singular value decomposition and feature analysis on a dataset of children with cerebral palsy. Ever since, it has been used as an outcome measure to study gait in several conditions, including spinal cord injury (SCI). Nevertheless, the validity of implementing the GDI in a population with SCI has not been studied yet. We investigate the application of these mathematical methods to derive a similar metric but with a dataset of adults with SCI (SCI-GDI). The new SCI-GDI is compared with the original GDI to evaluate their differences and assess the need for a specific GDI for SCI and with the WISCI II to evaluate its sensibility. Our findings show that a 21-feature basis is necessary to account for most of the variance in gait patterns in the SCI population and to provide high-quality reconstructions of the gait curves included in the dataset and in foreign data. Furthermore, using only the first 15 features of our SCI basis, the fidelity of the reconstructions obtained in our population is higher than that when using the basis of the original GDI. The results showed that the SCI-GDI discriminates most levels of the WISCI II scale, except for levels 12 and 18. Statistically significant differences were found between both indexes within each WISCI II level except for 12, 20, and the control group (p < 0.05). In all levels, the average GDI value was greater than the average SCI-GDI value, but the difference between both indexes is larger in data with greater impairment and it reduces progressively toward a normal gait pattern. In conclusion, the implementation of the original GDI in SCI may lead to overestimation of gait function, and our new SCI-GDI is more sensitive to larger gait impairment than the GDI. Further validation of the SCI-GDI with other scales validated in SCI is needed.

Keywords: gait deviation index (GDI); gait impairment; singular value decomposition; spinal cord injury (SCI); three-dimensional (3D) kinematic gait data; walking index for spinal cord injury (WISCI).

FIGURE 1

Diagram showing the steps followed to obtain the three reduced order bases compared in this article. The column on the left, with matrices in blue, represents the process followed in the original article by Schwartz and Rozumalski (2008), whereas the green matrices on the right correspond to the steps performed in this work, using SCI gait data. Note that the reduced order SCI basis with 15 features, located in the middle at the bottom of the diagram is merely the set of the first 15 features of the 21-feature reduced order SCI basis. We compare the results of the three criteria in red when using this basis because the number of features in the basis determines the order of the reconstructions of the gait curves. Thus, it is fair to compare the quality of the reconstructions of the same order.

FIGURE 2

Kinematic reconstructions of a validation stride using the three bases. The black line is the original curve, the blue line is the result when using the SCI basis with m = 21, the red dashed line corresponds to the reconstruction with the SCI basis with m = 15, and the gray dashed line is the reconstruction with the CP basis (Schwartz and Rozumalski 2008). For all nine angles, the reconstructions with the original CP basis provide the largest deviation from the original curve.

FIGURE 3

Histograms of the SCI-GDI stratified by the WISCI II level (12–20 and control). The dotted line represents the normal distribution curve fitted to the data within each level. The vertical black line indicates the control mean.

FIGURE 4

Average ± one standard deviation for GDI (black) and SCI-GDI (red) for each WISCI II level. In all levels, GDI values are greater than SCI-GDI values. WISCI II levels with a statistically significant difference between both indexes are marked with a circle.

FIGURE 5

Strong linear correlation between GDI and SCI-GDI was found (r = 0.993). The linear regression between both indexes, represented by the continuous line, is given by the equation $SCI\_GDI=1.0573\ast GDI-7.5915$ . The dashed line indicates the 1:1 axis. For all the samples, GDI values are larger than SCI-GDI values. The difference between both indexes is larger in data with greater impairment and it reduces progressively toward a normal gait pattern.