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WAVELETS ANALYSIS FOR NERVE SIGNALS PROCESSING: A PERSPECTIVE FOR LOWER LIMB

PROSTHESIS CONTROL

Bagna M 1, Atsma J.W 2, Gingras D 1, Bédard S 2 1 Université de Sherbrooke, 2 Victhom Human Bionics1

denis.gingras@imsi.usherbrooke.ca

1 Introduction The current research addresses the problem of designing a gait phase detection algorithm as part of a control system to interface signals recorded from nerves in the residual stump of an amputee with an artificial prosthesis limb. This paper focuses on the design of Electro-Neuro-Gram (ENG) data processing algorithms. Experiments of ENG signals recording and three amplitude enhancement algorithms are presented. A gait phases segmentation algorithm based on a template matching method is also described. It was found that wavelets analysis combined with Rectification-Bin-Integration (RBI) method followed by template matching can achieve near perfect gait pattern segmentation using only one ENG signal recording.

2 Experiments Following anesthesia, a cat was implanted with a cuff electrode on the left hind limb

peroneal nerve. After the animal had recovered from surgery (3 weeks) ENG was recorded during two different sessions, while the animal was walking on a treadmill at a 0.6 m/s speed. The recorded ENG signal was band-pass filtered and sampled at a frequency of 30 kHz. A goniometer was placed over the ankle to record the joint angle during walking.

Figure 1: Signals recorded during first recording session. First graph: Whole raw ENG signal recorded from the cat walking on a treadmill during session 1. Second graph: Synchronized ankle angle recording during the session. Note a 2 second recording without movement indicated by the box (left figure). This signal portion can be considered as noise part of the recording.

Figure 1 shows sample data recorded during the first session. A 2 second noise portion was recorded during no movement. Distribution and quartiles tests analyses have shown that this noise, denoted η, can be considered white and uncorrelated with the ENG and thus, the Signal-to-Noise-Ratio (SNR) of the recorded signals can be calculated using equation (1).

2 22

10 102 210log 10 log signalENGSNR η

η η

σ σσσ σ

−= =

, (1)

2σ being the variance of the indexed signal. We found a SNR of 6.43 dB and 7.83 dB for ENG signals recorded during session 1 and 2

respectively.

This work is supported by Victhom Human Bionics Inc.

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EN

G (µ

volts

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3 Amplitude enhancement algorithms The goal of the analysis is to segment recorded ENG signals into swing and stance phases.

Hoffer et al. [1] show that segmentation characteristics are explicit in the amplitude time domain rather than in the frequency description of the signals. Thus, algorithms that reveal ENG amplitude variations over phases are considered.

The RBI [1] method consists of averaging the absolute value of the signal by summing samples over a finite window length. The ENG signal of length N is divided into M parts of length L. For each part we calculate the RBI as in (2) and replace all the samples by this value:

1

1( ) ( ) , 1,...,

L

n

RBI k ENG n k ML =

= =∑ . (2)

Thus, our version of the RBI algorithm conserves only one sample over each window. The resulting signal is a signal of length M and sampling frequency of Fs/L, where Fs is the sampling frequency of the original signal. The RBI method increases the SNR up to 12.43dB for ENG signal 1 and 14.32dB for ENG signal 2.

In the discrete wavelet transform method proposed here, we tested the Symlet 7 and Daubechies 4 wavelets suggested in [2] and the Coiflet 5 wavelet that we selected after experimenting with many others to perform ENG signals decomposition. To assess the performance of each wavelet at each decomposition level, we use the SNR at level i defined in [3] and given by:

−=

2

2

10log10i

ii

w

wwsiSNR

η

η

σσσ

, (3)

where 2

iwsσ is the variance of the wavelet transform at level i of the signal portion and 2

iwησ the variance of the wavelet transform of the noise portion. The best wavelet and

decomposition level will achieve the highest SNR. The results for the three different wavelets and various decomposition levels are shown in figure 2.

Figure 2: SNR calculated for different decomposition levels using: (a) Daubechies 4 wavelet, (b) Symlet 7 wavelet and (c) Coiflet 5 wavelet. From theses figures, level 5 achieves best SNR for both ENG signals 1 and 2 and for all three wavelets tested. 0 level means no decomposition applied (raw signal SNR). Circled trace is signal’s 1 SNR variation and crossed trace for signal 2.

Obviously, one can see that fifth level decomposition performed the best SNR for the three

wavelets and, though not significant difference was found between the three wavelets, the Coiflet 5 gives the best SNR. Thus, from our experiment, the Coiflet 5 wavelet with five decomposition levels is optimal for the ENG signals. The wavelet decomposed signal is called the W-ENG signal. The wavelet decomposition increases the SNR up to 12.55 dB for signal ENG 1 and to 12.73 dB for signal ENG2.

As a third method, we retained the fifth level approximation signal (coiflet 5, fifh level decomposition) as the de-noised ENG signal and then applied the RBI algorithm to the resulting signal. The result of the combination of the two operations is the WRBI-ENG signal. This method had a performance in SNR up to 23.77dB for ENG signal 1 and 23.90dB

Decomposition level

SN

R

(a) (b) (c)

BIOSIGNAL 2006 for ENG signal 2, which is the best performance we obtained from the three methods.

Figure 3 shows the results of the three algorithms applied to ENG signal 1 using a RBI window length of L = 5 ms.

Figure 3: Results of application of a) RBI, b) wavelet decomposition W-ENG and c) WRBI-ENG for signal 1. Corresponding goniometric variations (top of each figure) and processed signals shown are normalized. Notice the clear segmentation characteristics in the WRBI-ENG signal (c) that do not appear in the RBI-ENG (a), and the amplitude characteristics that appeared in the W-ENG signal (b).

4 Template matching and segmentation Once the amplitude characteristics are enhanced in the signals, the next step is to segment

the processed signals into stance and swing phases. The template matching method consists of choosing a signal portion that represents a

sample of the desired signal in a repetitive or periodic recording, and perform correlation analysis over the whole recording. For application of QRS complex detection to ECG signal, the author in [4] introduces the following normalized correlation coefficient:

[ ][ ][ ] [ ]∑ ∑

∑−

=

−

=

−

=

−−−

−−−=

1

0

1

0

22

1

0

)()(

)()()(

N

n

N

n

N

nxy

yknyxnx

yknyxnxkγ , (4)

where x is the template, y the ENG signal and x and y the averages over the N samples considered. Parameter k is the time index of the signal y at which the template is placed. Here, we selected a template representing a whole gait cycle for each WRBI-ENG signal. The calculated correlation coefficient exhibits 2 majors peaks per cycle that are correlated to the transition instant between the stance and the swing phases in the processed ENG. We then applied a threshold to detect theses peaks in the correlation signal. As was observed for the goniometric signal and reported in the literature [1], the stance phase duration within a cycle is greater than the swing phase. We thus segment the overall signal by comparing distance between two consecutive detected peaks to the previous calculated distance and assign a value 1 (stance phase) if the present distance is greater than the previous one, and 0 (swing phase) otherwise. Figure 4 shows the results of template matching and signal segmentation over a 10 s sample of WRBI-ENG1. Over 32 gait cycles in signal 1 and 40 cycles in signal 2, 100% of the transition peaks within the cycles in both signals were detected. In signal 1, 4 cycles were not well segmented into stance and swing phases while in signal 2, 1 cycle segmentation was missed.

a) RBI-ENG

b) W-ENG

c) WRBI-ENG

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Figure 4: Results of template matching and segmentation algorithms: A: The correlation coefficient calculated over time is juxtaposed to the WRBI-ENG signal and corresponding goniometric signal portion. Note that the peaks of the correlation coefficient occur at the same occurrence of the peaks in the signal. B: A threshold value of 0.023 is applied to the correlation signal to detect the peaks in the signal. C: Phases segmentation using inter-peaks distance algorithm. Stance is identified with 1 value while swing is assigned a 0 value. The goniometric and processed ENG signals have been normalized.

5 Conclusions In this document, we introduced an ENG signal processing algorithm combining wavelet

analysis and RBI. The method was demonstrated to improve the amplitude segmentation characteristics over the signal. A template matching algorithm was used to detect the relevant peaks in the processed signals and an interpeak distance algorithm was used to identify the stance and swing phases during the gait cycles. From a mathematical point of view, this signal processing procedure can be applied for any ENG signal processing application where the control is performed over the signals amplitude characteristics as foot drop correction or bladder monitoring. The next step in the goal of nerve signals integration in the control of the artificial limb is the developpment of an artificial intelligent system that can interpret the gait phases and tranform the signals into activation commands.

References [1] Hoffer J.A et al, Neural signals for command control and feedback in functional

neuromuscular stimulation: A review, Journal of Rehabilitation Research 1996; 22:145-57 [2] Diedreich A, et al., Analysis of Raw Microneurographic recordings Based on Wavelets

De-noising Technique and Classification Algorithm: Wavelet analysis in Microneurography, IEEE Transactions in Biomedical Engineering 2003; 50:41-50

[3] Akay M., “Time Frequency and wavelets in biomedical signal processing,” IEEE- PRESS, 1997; 739 pp. [4] Rangaraj M. R., Biomedical Signal Analysis: A case study approach, IEEE Press Series

in Biomedical Engineering 2002; 516 pp.

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