Sensitivity of the Wolf’s and Rosenstein’s Algorithms to Evaluate Local Dynamic Stability from Small Gait Data Sets: Response to Commentaries by Bruijn et al.

Abstract

Assessing gait stability using the Largest Lyapunov Exponent (k1) has become popular, especially because it may be a key measure in evaluating gait abnormalities in patient populations. However, clinical settings usually involve having small gait data sets and accurate determination of k1 estimates from such sets is difficult. In an effort to address this issue, Cignetti et al. recently identified that k1 estimates using the algorithm of Wolf et al. (W-algorithm) were more sensitive than those using the algorithm of Rosenstein et al. (R-algorithm) in order to capture age-related decline in gait stability from small data sets. Thus, they advocated the use of the former algorithm. Some concerns about the study were expressed afterwards by Bruijn et al. and we welcome the opportunity to discuss them in the present letter. Bruijn et al. expressed four concerns about the validity of the methods used by Cignetti et al. that could have biased the results. First, they indicate that although speed difference between young adults (YA) and older adults (OA) was not significant, it does not exclude speed as a confounder of the aging effect on gait stability. Although we agree that a perfect matching of YA and OA with respect to speed would definitely avoid confounding, such matching is highly unlikely as YA walk usually faster than OA. Accordingly, matching statistically the two groups in terms of average speed appears to be the best compromise between ecological validity and methodological validity. However, a mean to further avoid the confounding of speed on k1 is to evaluate group difference by using analyses of covariance (ANCOVAs) instead of using analyses of variance (ANOVAs), thus controlling for speed effect. As reported in Table 1, results from ANCOVAs run on the data sets of Cignetti et al. confirmed previous results obtained using ANOVAs. In particular, with respect to the main effect of age, k1 remained significantly larger in OA as compared to YA regardless the size of the data set (i.e., 3600, 7200, and 10,800 data points) when using the W-algorithm. Such result was obtained only for the largest data set (i.e., 10,800 data points) when using the R-algorithm. Therefore, the difference in k1 between YA and OA reported by Cignetti et al. is not biased by the inter-group difference in walking speed. Second, Bruijn et al. argued that the time series of YA might have counted more strides than those of OA due to shorter stride time, increasing artificially k1. However, the stride time was the same in YA and OA with mean ± standard error values of 1.27 ± 0.03 and 1.26 ± 0.05 s, respectively (Table 2). These data are in agreement with previous studies that reported similar values of stride time in both YA and OA populations. Accordingly, k1 exponents were estimated in the study of Cignetti et al. from a similar number of strides for both groups. Specifically, the time series with 3600 data points contained 47 strides in both YA and OA, the time series with 7200 data points contained 94 strides in YA and 95 strides in OA, and the time series with 10,800 data points contained 141 strides in YA and 143 strides in OA (Table 2). Hence, Bruijn et al. were mistaken in assuming that an intergroup difference in stride time could have biased the difference in k1 between YA and OA in Cignetti et al.’s study. A third concern expressed by Bruijn et al., closely related to the previous one, relates with the fact that Cignetti et al. did not normalize time using average stride time when estimating k1 with the W-algorithm, Address correspondence to Fabien Cignetti, Nebraska Biomechanics Core Facility, University of Nebraska at Omaha, 6001 Dodge Street, Omaha, NE 68182-0216, USA. Electronic mail: fabien. cignetti@univ-amu.fr Annals of Biomedical Engineering, Vol. 40, No. 12, December 2012 ( 2012) pp. 2507–2509 DOI: 10.1007/s10439-012-0665-6