Appropriate Mother Wavelets for Continuous Gait Event Detection Based on Time-Frequency Analysis for Hemiplegic and Healthy Individuals

Abstract

Gait event detection is a crucial step towards the effective assessment and rehabilitation of motor dysfunctions. Recently, the continuous wavelet transform (CWT) based methods have been increasingly proposed for gait event detection due to their robustness. However, few investigations on determining the appropriate mother wavelet with proper selection criteria have been performed, especially for hemiplegic patients. In this study, the performances of commonly used mother wavelets in detecting gait events were systematically investigated. The acceleration signals from the tibialis anterior muscle of both healthy and hemiplegic subjects were recorded during ground walking and the two core gait events of heel strike (HS) and toe off (TO) were detected from the signal recordings by a CWT algorithm with different mother wavelets. Our results showed that the overall performance of the CWT algorithm in detecting the two gait events was significantly different when using various mother wavelets. By using different wavelet selection criteria, we also found that the accuracy criteria based on time-error minimization and F1-score maximization could provide the appropriate mother wavelet for gait event detection. The findings from this study will provide an insight on the selection of an appropriate mother wavelet for gait event detection and facilitate the development of adequate rehabilitation aids.

Keywords: acceleration signal; appropriate mother wavelet; gait event detection; hemiplegic gait; wavelet-selection criteria.

Figure 1

Experimental setup for force sensitive resistor (FSR) and accelerometer sensors placement in preparation for gait data acquisition. (a) A pair of FSR sensors were placed under the big toe and heel of the insole; (b) the placement of the insole into the shoe; (c) the placement of the accelerometer on the tibialis anterior muscle under the knee joint of right leg; (d) a bandage was used to firmly fix the sensors.

Figure 2

Conceptualization of the proposed general CWT algorithm with three main phases: (1) Pre-processing of the acceleration signals; (2) Tracking the gait events and gait cycles through time-frequency analysis; (3) Distinguishing HS and TO gait events.

Figure 3

Continuous wavelet transform (CWT) plots of the acceleration signals during walking from one healthy subject (a) and one hemiplegic subject (b), where two mother wavelets (“db6” and “morl”) were adopted for comparison. The underlying scale relationship between the gait events (HS and TO) and gait cycles are illustrated.

Figure 4

Temporal representation of HS and TO gait event detection based on the proposed general CWT algorithm. The first local minima of $x_{event}$ corresponded to the estimated HS event (orange circle). The second local maxima of the further differentiated $x_{event}$ corresponded to the estimated TO event (purple circle). Each gait cycle bound was defined as the maximum points of $x_{cycle}$. Vertical dashed lines indicated the time-errors between the estimated event and the reference event from the FSR method.

Figure 5

Averaged time-error values of the estimated HS and TO gait events over all the healthy subjects (a) and all the hemiplegic subjects (b) when using 32 commonly applied mother wavelets. The vertical dashed lines indicate the standard deviation.

Figure 6

Bland–Altman plots of time agreement between the proposed modified CWT algorithm and the FSR method for HS and TO gait event detection in the healthy group (a) and the hemiplegic group (b). The time agreement results of selecting the optimal wavelet “db6” are shown on the left side whereas results of the commonly used wavelet “gaus1” with rather poor performance are shown on the right side. Positive times correspond to delays in the gait event detection of the proposed modified CWT algorithm with respect to the reference FSR method. The horizontal axis represents the average time measures for detecting gait events by both methods, and the vertical axis is the time error between the two methods. The dashed line from top to down respectively represent the 95% CI upper limit, the mean, 95% CI lower limit of the time difference (in seconds).

Figure 7

Averaged F1-scores of HS and TO gait event detection over all the healthy subjects (blue line) and over all the hemiplegic subjects (red line) across different mother wavelets. The vertical dashed lines indicate the standard deviation.

Figure 8

Averaged cross-correlation coefficients between the anterior–posterior knee acceleration signal and specific mother wavelet function for healthy subjects (a) and hemiplegic subjects (b). Vertical dotted line indicates the standard deviation.

Figure 9

Averaged energy-to-Shannon entropy ratios of CWT coefficients for healthy subjects (blue line) and hemiplegic subjects (red line) across different mother wavelets (p > 0.05). Vertical dotted line indicates the standard deviation.