AMERICAN SOCIETY OF BIOMECHANICS
Presented at the Twenty-First Annual Meeting
of the American Society of Biomechanics
Clemson University, South Carolina
September 24-27, 1997
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| AMERICAN SOCIETY OF BIOMECHANICS
Presented at the Twenty-First Annual Meeting |
In this paper we present a method of analyzing animal gait using wavelets. Time series data such as joint trajectories can be decomposed by the discrete wavelet transform to represent components of different frequency bandwidth. Differences between two similar trajectories were detected by comparing the components of the same bandwidth. Hind limb function of three clinically normal Greyhound dogs was evaluated prior to and 10 days after inducing Wallerian degeneration in the tibial nerve. A discrete wavelet transform was used to decompose each joint trajectory into components of different frequency bandwidth from which mean square maps and modified scalegrams were constructed. Alterations in the gait patterns during tibial nerve dysfunction were identified and described by comparing the mean square maps and modified scalegrams.
A common method to identify gait abnormalities was to compare profiles of joint rotations of normal and pathological individuals. Although such techniques are simple to implement, they do not allow for an accurate quantitative measure of the discrepancies or deviations in the kinematic quantity when comparing profiles that are very similar in nature. Borrowing from the techniques of signal analysis, researchers in the biomechanics area have used the Fourier transform to break down the kinematic time series data into components of different frequency bandwidths. The coefficients associated with these components were then compared to detect discrepancies between normal and pathological subjects. One significant disadvantage in using this method is that the frequency information cannot be correlated to time. This is a consequence of evaluating the Fourier transform integral from -infty to +infty and the frequency information obtained is an average over the entire length of the signal. This disadvantage is overcome by the wavelet analysis which provides an alternative method of analyzing the signal. The wavelet transform is an expansion of compactly supported functions (i.e, they equal zero everywhere except within a specific interval). These functions are referred to as wavelets and are used to decompose the signal into its constituent components. The original signal may be regained by adding all the wavelet components together.
The purpose of the study reported here was to utilize the discrete wavelet transform and the associated mean square maps to analyze two-dimensional kinematic data obtained from the hind limbs of three normal Greyhound dogs. The analysis was repeated on data collected from the dogs during an episode of tibial nerve dysfunction. We hypothesized that by comparing the energy distribution in different components of the transform, we could identify and specifically locate the discrepancies between the patterns of normal and abnormal gaits.
The opportunity to study kinematic data from dogs during an episode of tibial nerve damage arose as an adjunct to the development of a model of nerve regeneration. Three conditioned female Greyhound dogs, weighing between 22 and 35 kg were studied. A few days after acquiring the kinematic data from the dogs at the trot, they were clinically induced with Wallerian degeneration of the tibial nerve fibers on the left hind limb. On the tenth day following surgery, kinematic data were collected for the 3 dogs. Nerve regeneration typically resulted in functional recovery within 3 months.
Traditional graphs of flexion/extension movements for both conditions of gait were compared along with their corresponding mean square maps to distinguish abnormalities. From visual comparison of the flexion/extension angle graphs, we could not distinguish any dramatic pattern differences before and after surgery in the coxofemoral and femorotibial angles. Several recognizable differences were noted in the tarsal joint angles.
The coefficients obtained after applying the discrete wavelet transform were arranged in eight levels (since the length of each dataset was 2^7 i.e. 128 points) with the index of each level indicating the wavelet scale. The energy distribution by components at different levels were computed by summing the squares of the wavelet coefficients at each level and expressed as a percentage of the total signal energy.
When we compared the energy distribution patterns of two similar trajectories for each dog, the lower level components were very similar. Differences in the trajectories were distributed in the higher frequency components (higher levels). Therefore, trajectories of the same joints were assumed to be built on the same basic component, with differences in individual gait patterns being embedded in the higher frequency components. To magnify the discrepancies in the energy distribution at the higher levels, we excluded the components at levels -1 and 0 and computed the energy distribution for the remaining levels.
The most obvious differences were observed in the energy distribution patterns for the tarsal joint. For dog~1 after surgery, the energy distribution at level 1 was lesser by 20 percent and level 2 indicated an increase of 20 percent. Energy distribution levels for the tarsal joint angles of dog~2 exhibited a reduction of about 10 percent after surgery. The energy contribution for the tarsal joint angles of dog~3 had dropped by almost 40 percent at level 1 and at the same time, the energy contribution at level 2 had increased by 37 percent after surgery (Figure 1).
The results of visual evaluation of the energy patterns shown in the levels of the mean square maps of the tarsal joints (Figure 2) were most dramatic, easily recognized and consistent among dogs. After surgery, the maps for each dog had a notable increase in energy at level~1 during the stance phase of the gait cycle. At the other two joints, the patterns were inconsistent.
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