avelet Transforms for Compound Nerve Action Potential Analysis

An attempt has been made to characterize Compound Nerve Action ~ o ~ ~ n t i a ~ s from normals and Hanseniasis patients using wavelet transforms. The work reported here involves classification of peripheral potentials recorded at the elbow of normals and Nanseniasis patients following electrical stimula~ion of the median nerves. Employing the system developed by the first author, nerve conduction data has been obtained from 8 normals and 8 Hanseniasis patients. The gical data so collected was preprocessed to energy of the various responses and was analyzed using the Discrete Wavelet Transform. A new arameter defined in the transform domain and termed as Eaesgy Ratio, could clearly demarcate nseniasis patients at a particular scale. ~ ~ ~ 0 ~ ~ s : Compound nerve action potential, wavelet transform, Hanseniasis, Intra-scale Interepoch Energy Ratio, scalogram. Hansens's disease is primarily a neuropathy. Stu&es on nerve conduc~on velocities (NCV) have been reported in the affect of patients. While a general reduction in NCV observed, there is an overlap between the ranges of NCVs for normal nerves and those affected by thus NCVs by themselves cannot en normal and Hanseniasis nerves. It is the dominant response [see Fig. la]. The patient spectra and thus, classification thought that a method of analysis that looks at the time d is~but ion of energies at different frequency bands could possibly distinguish between n o d and abnormal waveforms. ~ ~ o n g the Time-Frequency Representations ("FR) which could be used for this purpose, the wavelet transform introduced by Grossman and Morlet [2] is seen to be the most appropriate. The Discrete Wavelet Transform (DWT) has also been successfirlly used in many other biomedical applications such as ECG signal compression [3], late potential detection [4] and evoked potential analysis [5 ] . Proceedings RC IEEE-EMBS & 14th BMESI 1995 2.70 METHOD Data acquisition employed a custom built evoked potential system [6]. Median nerves of 8 normal subjects and 8 patients were electrically stimulated at the wrist to evoke a minimal thumb twitch. Responses were recorded from the elbow at a location medial to the brachial artely. Each recorded waveform was an average of 16 responses of 20 ms duration digitized at a rate of 16.67 kHz. For further processing, a window of length 256 samples was selected from each response and. scaled to normalize its energy. The goal of the wavelet transform is to decompose any into a summation of wavelets at arbitrary signal f(x) different scales and shifts as given below. l k The integer j denotes different levels of wavelets, starting with j=O; integer k covers the number of wavelets in each level, namely from k=0 to 2 -1. The DWT is an algorithm for computing a, + ~ when f(x) is sampled at equally spaced intervals over OCx <I. The DWT algorithm was discovered by h4allat [7] and is therefore also known as Mallat's Pyramid algorithm. As the number of the wavelet coefficients increases, a wavelet becomes smoother and resembles a smoothly windowed harmonic function. Daubeclies wavelet of 8 taps [SI was foun our analysis. The scalogram or time-frequency energy distribution of f(x) at various levels is obtained by ~ ~ n g eq. (1) and is given by 0 i k When comparing energies across various leveldscales, it is important to take care of the scaling factor (112 ), which is dependent on the wavelet levelj. However, the current study examined the distribution of signal energy across time epochs within each scale. For this, the signal at each scale was divided into two equal epochs and the ratio of the energy in the first half of the signal to that in the second half was obtained for each scale. This ratio, designated as Intra-scale Inter-Epoch Energy Ratio at levelj (IIER,) is defined as, 21-1-1 I 21-1 200 0 -200 0 20 40 60 80 a 00 120 Fig. 1. A Compound Nerve Action Potential from a patient and its scalogram RESULTS AND DiSCUSSiON Figs. l a and l b show, respectively, a sample waveform from a patient and its scalogram represented as a gray scale image with eight levels of quantization. The dominant peak in the waveform gives rise to the bright segment seen in the initial portion of scale 5. Figs. 2a and 2b show the values of the IIER at scales 5 and 3 respectively for all the normals and patients. As there was a wide difTerence between the ranges of values of IIER for normals and patients at scale 5, the logarithm of this ratio has been plotted. It can be clearly seen that the ratio is much higher for normals than for patients at this scale. On the other hand, there is a complete overlap and consequently, absence of any observable pattern between the values for the two groups at scale 3. These scales correspond roughly to frequency bands of 520-1040 Hz (scale 5) and 130 to 260 Hz (scale 3). Thus the value of IIERs could be used to distinguish a normal nerve from a pathological nerve affected by Hanseniasis. ” + ” normals ”o” patients