ANALYSIS OF AUDITORY EVOKED POTENTIAL

by

VIKASH DAGA, B.E.

A THESIS

IN

ELECTRICAL ENGINEERING

Submitted to the Graduate Faculty of Texas Tech University in

Partial Fulfillment of the Requirements for

the Degree of

IVIASTER OF SCIENCE

IN

ELECTRICAL ENGINEERING

Approved

December, 2002

^

z^

ACKNOWLEDGEMENTS

v-'L ^h laccn tharkfiil to my advisor Dr. Mary Baker for her help, support and guidance

throughout the project. I am grateful to Dr. Dwayne Paschall for providing the data set and

guiding me and agreeing to be in my graduate committee to evaluate my work. I am also

grateful to Dr. Thomas Trost and for being in my graduate committee and evaluating my

work.

I am thankful to all my friends who provide me support through out my work and

study and especially thankful to Sri Raja for guiding me in some bad times. I am thankful

to my parents and my family for their support without which I would not have been where I

am right now. It is because of their love, guidance and encouragement that I was able to

make it so far.

11

TABLE OF CONTENTS

ACKNOWLEDGEMENTS ii

LIST OF TABLES v

LIST OF FIGURES vi

CHAPTER

1. INTRODUCTION 1

1.1 Aim of the thesis 1

1.2 Introduction to EEG and ABR 1

1.3 Earlier work and thesis outline 2

2. AUDITORY BRAINSTEM RESPONSE 3

2.1 Electroencephalography 3

2.2 Auditory evoked potential 3

2.3 Auditory brainstem response 5

2.4 Instrumentation 6

2.5 Interpreting ABR waveforms 9

2.6 Absolute latency 11

2.7 Interwave latency intervals 12

2.8 Latency curve 13

2.9 Clinical application 14

3. WAVELET TRANSFORMATION 16

3.1 Mathematical transformation 16

iii

3.2 Fourier transform 16

3.3 Short-time Fourier transform 17

3.4 Wavelet transform 17

3.5 Scale 18

3.6 Time and frequency resolution 20

3.7 Discrete wavelet transform 23

4. PROCEDURE 27

4.1 Introduction of data set 27

4.2 Data collection 27

4.3 Preprocessing 29

4.4 Slope method 30

4.5 Wavelet transform 32

4.6 Spectrogram approach 35

5. RESULT AND CONCLUSION 36

5.1 Slope method 36

5.2 Wavelet analysis 36

5.3 Conclusion 41

5.4 Future work 41

REFERENCES 43

IV

LIST OF TABLES

2.1 Summary of auditory evoked potentials 4

2.2 Normal values for adult females 10

5.1 Average and standard deviation of wave V latency 41

LIST OF FIGURES

2.1 Neural generators of the ABR in humans 6

2.2 Electrode placement for ABR recording 7

2.3 Block diagram of ABR recording 10

2.4 Normal ABR waveform of an adult male 12

2.5 Latency curve 13

2.6 Latency curve comparison 15

3.1 A cosine wave for s =1 19

3.2 A cosine wave for s > 1 19

3.3 A cosine wave for s < 1 20

3.4 Time and frequency diagram for wavelet transform 21

3.5 Time and frequency diagram of STFT 22

3.6 Time and frequency diagram of Fourier transform 22

3.7 Different levels of wavelet decomposition of signal 26

4.1 10-20 Intemational system for electrode placement 28

4.2 Test details 29

4.3 A typical waveform 30

4.4 Slope method 32

4.5 Daubechie wavelets 33

VI

4.6 Reconstmcted waveform 34

4.7 Spectrogram 35

5.1 Reconstmcted waveform at different wavelet coefficients 37

5.2 Latency curve comparison 38

5.3 Wave V latency for 80 dB 38

5.4 Wave V latency for 60 dB 39

5.5 Wave V latency for 55 dB 39

5.6 Wave V latency for 40 dB 40

5.7 Wave V latency for 20 dB 40

Vll

CHAPTER 1

E^JTRODUCTION

1.1 Aim of the thesis

Auditory brainstem response is the response of the auditory nervous system to an

acoustic stimulus. It is characterized by a series of peaks. The time of occmrence of these

peaks has clinical importance in assessing hearing disorders of patients and identifying

the region of disorder. The proper identification of the occmrence of these peaks is very

difficult due to noise in the signal as well as background EEG signals. The aim of the

thesis is to identify one of the several peaks (Wave V) with the help of various signal

processing techniques.

1.2 Introduction to EEG and ABR

Electroencephalography measures electrical signals from brain, recorded with the

help of electrodes placed on the scalp. EEG recordings are used to diagnosis various

neurological disorders. The EEG signal can be analyzed visually by neuroscientists to

yield some information, but computerized methods have been developed to analyze the

signals to get a better understanding of the human brain.

Auditory brainstem response occurs in the first 10-15 ms of the auditory evoked

potential. Auditory brainstem response is used in the following:

1. estimating the level in different patients.

2. screening newboms who are at risk for hearing loss.

3. evaluate patients with suspected retrocochlear pathology.

The Auditory brainstem response or ABR as it is commonly known, is identified

by the presence of various peaks which are produced when the stimulus is encoded by

neurons along the ascending auditory pathway. The various peaks in the ABR are named

as wave I, II, III and so on in order of their occurtence. The most important peak out of

these peaks is wave V peak which is produced by lateral lemniscus [1]. These peaks can

be identified in normal cases but in abnormal cases these peaks are hidden by the

presence of noise. The diagnosis is done by looking at the time of occiurence of the peak

which is known as the latency of the peak.

1.3 Earlier work and thesis outline

Automatic recognition of wave V in the auditory brainstem response has been the

subject of research for the past few years, and a lot of work has been done in the field.

Various approaches like partem recognition and neural network and signal processing

techniques have been used for automatic detection of wave V peaks. Habrakan [2] used

neural networks to extract features to identify peak V in brainstem auditory evoked

potenfial. Wilson [3] used discrete wavelet analysis for the peak identification.

In this thesis. Chapter 2 describes about the evoked potential and gives a brief

description of auditory brainstem response. Chapter 3 describes the basics of wavelet

transformation and the reason for it being used in the thesis. Chapter 4 gives details about

the procedure followed, from data collection to processing. Chapter 5 summarizes the

result and conclusion as well as the future scope of the work.

CHAPTER 2

AUDITORY BRAINSTEM RESPONSE

2.1 Electroencephalography

Neurons exchange information in the form of electric signals. The recording of

this electrical activity of the neurons is called electroencephalography, or EEG. An

Austrian psychiatrist Hans Bergerin was the first to measure these signals in the late

1920s.

EEG signals are used for clinical and research purposes. The most common

method of recording an EEG signal is by placing surface electrodes on the scalp. The

electrical response to specific stimuli is known as the evoked potential. The evoked

potential can be a visual evoked potential caused by a flash of light or an auditory evoked

potential caused by an audio click.

2.2 Auditory evoked potential

Electrical potentials recorded due to an acoustic stimulus is known as an auditory

evoked potential. The auditory stimulus can be a click, tone burst, white noise, and

others. Latency is the time interval between the presenting of the stimuli and the

occurtence of the cortesponding response. Auditory evoked potentials are usually divided

into three time epochs each with different latencies. These are [4]:

1. fast response - latency of 0-10 ms,

2. middle response - latency of 10-50 ms and

3. slow response - latency of 50-500 ms.

Table 2.1 gives a list of all the auditory evoked potentials that occur in the first

500 ms after the onset of the stimulus along with their latencies, neural generators and the

places where the potentials are recorded [1].

Table 2.1 Summary of auditory evoked potentials [1]

Response Electrocochleography

Auditory Brainstem Response

Frequency Following Response

SNio Response

Middle Latency Response (MLR)

40 Hz Response

Late Potentials (Ni-P2 P300, CNV)

Latency 0.2-4.0 ms

1.5-10.0 ms

6-25 ms

8-12 ms

10-80 ms

Every 25 ms

80-500 ms

Recording Site Middle ear at the pronmontory

Vertex to earlobe or mastoid

Vertex to earlobe or mastoid

Vertex to earlobe or mastoid Vertex to earlobe or mastoid

Vertex to earlobe or mastoid Vertex to earlobe or mastoid

Generator(s) Coclea (CM andSP) Vlllth nerve (AP) Vllth nerve (AP) Brainstem nuclei tracts Vllth nerve (AP) Brainstem nuclei tracts Not known

Thalamus, primary auditory cortex? Not known

Primary auditory and association cortex

Stimulus Pulses

Pulses Tonebursts

Tones

Tonebursts

Pulses Tonebursts Tones

Pulses Tonebursts Tones Pulses Tonebursts Tones

2.3 Auditory brainstem response

The ABR is a sequence of electrical potentials that are generated in the brainstem

and central auditory pathway in response to a stimulus in the ear. ABR occurs as the fast

response of the auditory evoked potenfial [4]. ABR reflects the transmission of the

stimuli through the brain stem auditory pathways. A normal waveform is usually

characterized by a series of 5 to 7 peaks that occur within 12 ms after the onset of the

stimulus. These peaks are labeled in roman numerals from wave I to wave VII. These

peaks are the response of the various neurons present in the brainstem auditory pathway

of the stimuli. The various neurons responsible for the peaks are these [1]:

a. Vlllth nerve for the wave I,

b. Lateral nemuscus for wave II,

c. Oliver bundle for wave III,

d. Lateral lemniscus for wave IV and

e. Inferior colliculus for wave V.

The most prominent peaks are the wave I, III, V. The latencies of these peaks for

normal persons is generally [1]:

a. 1.6 ms for wave I,

b. 3.7 ms for wave III and

c. 5.4 ms for wave V.

Figure 2.1 shows the ascending auditory pathway and the neural generators

responsible for the various peaks. The figure is that of cochlear nerve fibers and the

neurons responsible for the generafion of peaks are shown [4].

DCNi

A A A / T r i I

"""rt-

1 ' -"^ i ^.

MG

Figure 2.1 Neural generators of the ABR in humans (reproduced from "The Auditory Brainstem Response" edited by John T. Jacobson, P.27)

2.4 Instrumentation

An instrument that captures and stores auditory evoked potential has to perform

four major functions. These include generafing an acousfic stimulus, amplification of the

electric potential and averaging and storing the signal. These are explained in detail

below.

2.4.1 Generation of an acoustic stimulus and recording

The stimulus most often used in ABR recording is an acoustic stimulus, which is

a click with time duration of 100 microseconds. The intensity of the stimulus is measured

in decibels and ranges from 80 dB to 20 dB.

The ABR is recorded by artaching electrodes to the surface of the patient's scalp.

The most common method of clinical ABR recording uses four electrodes, one at the

vertex (referted as Gi), two electrodes at the inner surface of both the ear lobes or over

the mastoids (G2), and the ground electrode at the forehead. The electrode artangement is

shown in Figure 2.2. In the Intemational 10-20 system, which is most commonly used,

the Gi electrode position is called Cz, while the G2 positions are called Ai and A2,

respectively, for left and right ears.

Figure 2.2 Electrode placement for ABR recording (reproduced from "Auditory Evoked Potentials" by Lind J. Hood and Charles I. Berlin, P. 12)

Electrodes are placed after cleaning the skin and then placing conductive

electrode paste or gel on the skin and electrode. The electrode is securely attached with

tape. The impedance of the electrodes is measured to determine whether it is within the

acceptable limits.

2.4.2 Amplification

The amplifier used in measuring auditory evoked potential is a differential

amplifier. It amplifies only the difference voltage of the electrodes and cancels the

common voltage. This helps in reducing the noise from, for example, the building power

lines, which is common to both the electrodes. Evoked potentials have their amplitudes

in the order of 0.1-0.5 microvolt, so the gain of the amplifier is on the order of 100,000.

This increases the amplitude to a range where it can be better identified and analyzed [4].

2.4.3 Signal averaging

Before averaging the signal is passed through an analog-to-digital converter. A

signal averager is then used to increase the signal-to-noise ratio (SNR). The signal is

assumed to be a sum of ABR and noise. Let x(j) be the EEG signal, a(j) is the ABR signal

and n(j) is the noise where/ which varies from 1 to k (total number of sample points), is

the number of sampled points. The EEG signal can be written mathematically as

x(j) = a(j) + n(j) 2.1

and represents one recorded waveform. If w records are collected a matrix of ^ columns

and m rows can be formed. Each sampled point can be represented as:

8

MW = a(ij) + ri(ij) 2.2

where / goes from 1 to m. Since the ABR signal is identical to each of these records, die

equation can be rewritten as:

x(ij) = aO) + n(ijf 2.3

The noise is assumed to be random, so it will differ in each record and hence the index /

cannot be removed from the noise part. The SNR can be taken as the ratio of the RMS

energy of ABR signal and the RMS energy of noise. The RMS of ABR signal is aQ'), for

a particular value of time the ABR signal is constant. The noise is assumed to be of

Gaussian distribution with mean value zero and variance a^. The RMS value of n(ij)

equals its standard deviation a. So for a particular value of time the SNR of the record is

a(j)/ a. When the average of all the records is taken the variance of the noise, which is m

independent samples from the same distribution is a /m, and hence its RMS value is

a/m^''^. So the over all SNR of the ABR signal is m^''^ a(j)l a which is m^'^ times of the

SNR of a single record. Finally, the resultant waveform is stored in a digitized format in a

computer. The various fiinctions performed by the instmment are shown in Figure 2.3.

2.5 Interpreting ABR waveforms

Some well-defined peaks characterize an ABR waveform. Parameters associated

with these peaks which help in diagnosis of hearing disorders are (i) latency (in ms), (ii)

latency difference between primary peaks (interpeak latency), (iii) peak amplitude

(microvolt), (iv) I-V amplitude ratio, and (v) waveform morphology. The values of these

parameters depend on the age as well as the sex of the subjects. Table 2.2 shows values

of these parameters for aduh females [1].

Stimulus! Section ;

Earphones i i

Calibrated Attenuator

i I

Stimulus Generator

SUBJECT

1

i 1

» C\Bf,i tieCuuuc:]

' r

Amplifiers and filters

A/D Converter

1 r

Averager

!Recording and i Amplification 1 Section

1 Averaging • ^prt inn

CVA converter Computer

Plotter

Storing Section

Figure 2.3 Block diagram of ABR recording

Table 2.2 Normal values for adult females [1]

Parameter Presence of waveform components Expected latency at 75dB Wave I Wave III WaveV Interwave latency intervals Wave I-III Wave III-V Wave I-V Wave V latency-intensity function between 50 and 70 dB Wave V/I amplitude ratio

Normal Value Usually Waves I,III,V at slow rates

1.6 msec +/- 0.2msec 3.7 msec +/- 0.2 msec 5.6 msec +/- 0.2 msec

2.0 msec +/- 0.4msec 1.8 msec +/- 0.4 msec 3.8 msec +/- 0.4 msec 0.3 msec/10 dB

Greater than 1.0

10

2.6 Absolute latency

The absolute latency is the time difference between the onset of the acoustic

stimulus and the time of occurtence of the peak of the averaged response. Figure 2.4

shows the concept of measuring the absolute latency and the interpeak latency [4]. A

peak is considered as that part of the wave where the dovmward slope starts. Most of the

time the waveforms have well-defined peaks but sometimes two peaks merge with each

other.

The absolute latency of wave V has received the most widespread clinical

attention in differential diagnosis of otoneurological disorders as well as in estimating

hearing sensitivity. The importance of wave V peak is due to its robust character and

reliability under varying measurement condition and due to its predictability with

decreasing stimulus intensity. An increase in latency with decrease in the stimulus

intensity is common to all neural system; that is, neural firing becomes less frequent as

the magnitude of the stimulus decreases [1].

Figure 2.4 shows a normal ABR waveform. The peaks are marked by roman

numerals. Labeled in the figure are absolute Wave V latency, the wave V amplitude, inter

peak latency of I-II, I-V and III -V. The diagram has been labeled by following the

Jewert scheme for peak labeling [4].

11

Wave V Absolute Lofency

MSEC

Figure 2.4 Normal ABR waveform of an adult male. (Reproduced from "The Auditory Brainstem Response" edited by John T. Jacobson, P.66)

2.7 Interwave latency intervals

The time difference between the different peaks of the ABR waveform is known

as interwave latency interval. The typical value of the interwave latency interval for

waves I-III and III-V is approximately 2 ms and for the wave I-V interval is about 4.0 ms.

Interwave latency intervals provide information regarding the synchrony and integrity of

the brainstem pathways from a nerve to the other nuclei, since each peak is the response

of a group of neurons.

12

2.8 Latency curve

The latency of the various waveforms mcreases as the mtensity is reduced. The

change in the latency is slow for stimulus intensity from 90 dB to 60 dB but is rapid

between 60 dB and 25 dB. A typical function can be plotted using wave V latency for

different values of intensity, such a graph is called a latency intensity function. Figure 2.5

shows a typical latency-intensity plot. The solid line is the latency curve of wave V of

normal hearing subjects. The dotted line represents the limits of+/- 3 standard deviations

8.5

8.0

7.5

n E .£ 7.0 >, o c _i

> 5

6.5

6,0

5.5

5.0

dBH ipea

1

LN 20 < SPL) (56)

1 30 (66)

i 40

(76)

1

50 (86)

1 60 (96)

- - —

1 70

(106)

1 80

(116)

1 90

(126)

Intensity

Figure 2.5 Latency curve (reproduced from "Auditory Evoked Potentials" by Lind J. Hood and Charles I. Berlin, pg 19)

13

2.9 Clinical application

The latency-intensity plot is used to identify cochlear hearing loss. The slope of

the latency curve of a person having cochlear loss will be steeper then the latency curve

of a normal person. Delay in latency of all major peaks but the interpeak latency within

normal limits signifies conductive hearing loss. The shift in the latency is due to the

reduction of the signal intensity which artives at the cochlea. This can also be caused by

human ertor like placement of earphones over the ear canals or shifts in ear phones due to

patients' movement. Figure 2.6 shows a comparison of latency curve for normal hearing,

cochlear loss and conductive hearing loss [1].

Prolongation of peaks latencies, prolongation of interpeak latencies and waveform

deformation, e.g., (absence of peaks) signifies presence of tumors in the Vlllth nerve

pathway. Tumors can also be indicated if the amplitude ratio of wave V/I is less than 0.5

[1].

14

^^^^^^^Kt'

^ B

•

7.5

7.0

£

ie.s c «J -J > 0)

S 6.0

5.5

5.0

dBHLI '*! (dB SPL)

1 1 \

Cochlear >. \ i

\ > « ^ Tv Conductive or \ » \ retrocochlear

\ \ \ /

/ \ \ % Normal 111 A^ '

^^ \ W \

N^ \ >v X

^ ^

1 1 1 1 ! 1 1 1 20 30 40 50 60 70 80 90

(56) (66) (76) (86) (96) (106) (116) (126) Intensity

Figure 2.6 Latency curve comparison (reproduced from "Auditory Evoked Potentials" by Lind J. Hood and Charles I. Beriin, P.21 )

15

CHAPTER 3

WAVELET TRANSFORMATION

3.1 Mathematical transformation

A mathematical transform is often used to extract information from a signal which

is not observable in the raw signal. A "raw signal" is one which has not been processed.

The signal obtained by applying any of the available mathematical transformation is a

processed signal. Some commonly used mathematical transform is Fourier transform,

Hilbert transformation, and wavelet transformation.

3.2 Fourier transform

The Fourier transform is used to extract the frequency information of a time-based

signal. The mathematical representation of Fourier transform is:

00

Xio))= \xit)expi-jcot)dt 3.1

- 0 0

00

xit)= jXia))expijo)t)dco. 3.2 - 0 0

In the above equations, t represents time, 6) represents frequency in radians per second,

and X denotes the signal in time domain and X denotes the signal in frequency domain.

Equation (3.1) is called the Fourier transform ofx(t) whereas equation (3.2) is called the

inverse transform Fourier transform ofX(a)), which is x(t).

16

A Fourier transform gives information of the frequencies present in the signal. It

will not give any temporal resolution.

3.3 Short-time Fourier transform

The Short-Time Fourier transform is a modified version of the Fourier transform.

In the Fourier transform the entire signal is multiplied by the sine and cosine function. In

STFT, the entire signal is divided into small time windows and the Fourier transform is

applied to the windowed signal. The time precision of the signal depends on the length of

the window. If the length of the window is infinite, then the Fourier transform is obtained

and time precision is minimum. The mathematical representation of STFT is:

STFT^it',0)) = j[xit)W* it -t')]expi-jo)t)dt. 3.3

W(t) is a window function and * is its complex conjugate.

The STFT maps a time function signal into a two-dimensional function of time

and frequency. The fixed length of the windowed signal, which gives limited time

precision to the transformed signal, limits the use of STFT.

3.4 Wavelet transform

EEG signals usually consist of low frequency component for a long durations and

high frequency component for short durations. Since high frequency component occur for

short durations so they should be analyzed with wide window. To overcome the

17

disadvantages of Fourier transform and short-time Fourier transform, the wavelet

transform is used. The wavelet transform utilizes wavelet functions, giving temporal

information on the coefficients.

The mathematical representation of wavelet transformation is:

rt-T^ vp;(r,.) = -i=Jx(0^* dt 3.4 y s J

where ^ f (r, s) is the wavelet transformation of signal x(t) and i// (t) is the transforming

function and it is called the wavelet.

A wavelet is similar to the sine and cosine function of the Fourier transform. In

the Fourier transform, the sine and cosine waves have various frequencies. Similarly, in

the wavelet transform, the wavelets have dilated and shifted versions. The difference

between the sine or cosine function of the Fourier transform and wavelet of wavelet

transformation is that the sine and cosine function is of infinite duration whereas the

wavelet is of finite duration. This property of the wavelet gives it its time resolution

property.

3.5 Scale

A wavelet transform maps a time-based signal into functions of scale and time.

The scale is similar to the frequency of the signal and is inversely related to frequency:

scale = (1 /frequency). 3.5

A scale basically compresses or dilates the wavelet and hence controls the frequency

component. Large scales cortcspond to dilated or stretched out signals and small scale

18

cortesponds to compressed signals. In terms of mathematics, if f(t) is a signal, tiien f(st) is

a compressed signal if s>l and is a stretched out signal if s<l [5].

For example, let f(st) be cos(s*(7c/4)*t) and s assumes tiie value of 1, 2, K2 tiien tiie

resultant waveform is shoym in Figures 3.1-3.3.

f(st) where s = 1

ID 20 30 40 a ] 60 Time

100

Figure 3.1 A cosine wave for s =1

1

D.8

0.8

0.4

0.2 0>

• n

i 0

-0.4

-0.61-

-0.8

-1

f(st) where s > 1

TT

10 20 30 40 50 Time

90 100

Figure 3.2 Figure 3.1 A cosine wave for s >1

19

Figure 3.3 A cosine wave for s <1

3.6 Time and frequency resolution

The biggest advantage of the wavelet transform over other transforms is the

varying resolution of time and frequency. The different resolutions of time and frequency

can be best explain by Figure 3.4. In the figure, the ordinate is time and the abscissa is

frequency. Each box in the diagram represents a value of the wavelet transform for

different resolution of frequency and time. Although each box has different yvddth and

height, the area of each box is the same. This signifies that each value of the wavelet

transform covers an equal portion in time-frequency plane but yvith different resolution.

At low frequency, the y^dth is greater than the height which means that wavelet

transform gives good frequency resolution but poor time resolution at low frequency;

similarly at high frequency the transform gives better time resolution but poor frequency

20

resolution [5]. In the diagram, it is seen that none of the boxes has zero area which means

the value of a particular point in time and frequency cannot be known. ue

ncy

kreq

c q

o

E o o 0)

• Q

0 • D

X

Time

Figure 3.4 Time and frequency diagram for wavelet transform

The time and frequency diagram of STFT will consist of squares since it has fixed

resolution in time and frequency. This is shown in Figure 3.5.

21

13

cr

Time

Figure 3.5 Time and frequency diagram of STFT

The time and frequency diagram for the Fourier transform will consist of

rectangles with width covering the entire time scales because no information of time is

present in a Fourier transform. This is shown in Figure 3.6

o

cr i-t

Time

Figure 3.6 Time and frequency diagram of Fourier Transform

22

3.7 Discrete wavelet transform

The wavelet transform calculated by using the continuous wavelet transform

formula given in equation 3.4. This formula can be used only for continuous time signals.

For discrete time signals, the discrete wavelet transform is used [5].

In the discrete wavelet transform, the signal is passed through various low-pass

and high-pass filters. The frequency resolution is controlled by the cut-off frequencies of

these filters. After passing the signal through various filters, the signal is upsampled or

downsampled to control the time resolution of the signal. Downsampling is removing

some of the samples from the signal, which decreases the sampling rate of frequency. For

example, to doymsample a signal by 2, every other sample points of the signal have to be

ignored. Upsampling is increasing the sampling rate by adding new sample points with

linear interpolation, in the signal [5].

In discrete wavelet transform, the signal is passed first through a low-pass filter

and high-pass filter. Filtering a signal is mathematically convolving the impulse response

of the filter with the signal and can be expressed as:

00

y[n] = x[n]h[n] = X * l - M « " 1 3.6 * = - o o

where y[n] is the resultant signal, x[n] is the original signal and h[n] is the impulse

response of the filter.

After passing through the filters, the signal is sub-sampled to satisfy the N\ quist

criteria. Initially the signal spanned from 0 - TT radians per second. When the signal is

passed through a high-pass filter then the resultant signal has frequency component from

23

71/2 - n radians per second and hence the frequency resolution has doubled. Similarly, the

signal resultant from a low-pass filter will have frequency range from 0 - 7r/2 radians per

second. After passing the signal through the filters, k is downsampled by 2. This

downsampling reduces the time resolution of the signal by 2. This is the first level of

decomposition. The coefficient of wavelet obtained for the signal passed through the high

pass filter is called the detail coefficient and for the low-pass filter it is called the

approximate coefficient. The low-pass filter signal is again passed through a high-pass

and a low-pass filter, resulting in a second level decomposition and then sub-sampled. As

the decomposition level increases the frequency resolution increases and the time

resolution decreases due to decrease in the sample points. This process is also known as

subband coding.

For example, suppose a signal x[n] has 512 points and is passed through the first-

level decomposition having high-pass filter with impulse response h[n] and resultant

signal yHi[n] and low-pass filter with impulse response l[n] and resultant signal yLi[n]

where the subscript 1 denotes the first level of decomposition. The resultant signals are

subsampled by 2 leaving both yHi[n] and yLi[n] with 256 points each and thus halved the

resolution in time. The frequency resolution of yHi[n] is n/2 - n radians per second and

yLi[n] is 0 - 71 radians per second. The low-pass signal is again passed through the high-

pass and low-pass filter yielding yH2[n] and yL2[n] each having 128 sample points and the

frequency band spans from 7i/4 - 7i/2 radians per second and 0 - 7i/4 radians per second.

The signal in the second decomposition level has half the time resolution and t\s ice the

frequency resolution then the first level decomposition. As the level of decomposition

24

increases, the time resolution decreases and the frequency resolution increases by a factor

of 2. The process of decomposition of the low pass filtered signal continues till the

number of sample points is 2. For this example the level of decomposition will be 8 [5].

In the Figure 2.5, the decomposition of the signal has been shown. In the figure

h[n] is a high-pass filter, whereas l[n] is a low-pass filter. These two filters filter the

signal, and then it is doymsampled by 2. The equation f = 0 - 7r shows that the filtered

signals frequency span is from 0 to 7i radians per second.

25

Decomposition level 1

x[n]

i h[n]

f=nll -n

Downsamplin

l[n]

f=0 -nil

Decomposition level 2 i

h[n]

i=nt4-ni:

h[n]

f=;r/8- nl4

l[n]

f = 0-71/4

iDecomposition

level 3

l[n]

f=0-;r/8

Figure 3.7 Different levels of wavelet decomposition of signal

26

CFL\PTER 4

PROCEDURE

4.1 Introduction of data set

The data was obtained from the Communication Disorders department of Texas

Tech Health Science center. There were 10 patients, of which 1 was normal and 9 were

abnormal cases. Each patient was considered a dataset, yvdth different number of records.

Each record has 256 points with different time spans.

4.2 Data collection

The subjects were seated in a recliner chair in a relaxed position or in sleep.

Before applying the electrodes on the ears the ear canals were checked with an otoscope

to see that they were clean. Electrodes were applied to the Cz and both mastoids. In

accordance with 10-20 Intemational System for scalp mapping, these sites cortcspond to

abbreviations Fz, A2(for right ear lobe) and Ai (for left earlobe).

The EEG data was stored in a host computer. The files were stored with an

extension of *.ep. The files were accessed by a DOS batch file epcfg.bat. The signal

values were then extracted into ASCII fortnat with the file EP2ASC.BAT. The ASCII

values were saved into Excel files. The entire analysis on the dataset was done in Matlab,

which was used to extract the data from the excel files and do the processing.

Figure 4.1 shows the 10-20 Intemational System for electrode positioning.

27

NASION

' ^^ (^ V

if4

*n I _r_5^...@..„,.(^,_.0_„0 .

< fA?

LEFT RIGHT

INION

Figure 4.1 10-20 Intemational system for electrode placement [4].

Figure 4.2 shows the details of the test performed. The patient is called as

"Subject 3". Each record is shoyvn as either gray or white. The two items on the first row

of each record are the date of the test performed and the time of the test. The first column

shows the number of the record as well as the chaimel. The second column shows the

name of the test performed, AEP is auditory evoked potential. The third column is the

total time span of the record. The next column shows the ear in which the stimulus is

applied. The next column is the type of stimulus used, as in this case it is a toneburst. The

next column is the stimulus frequency followed by the intensity of the stimulus and the

stimulus rate. The last two columns show the number of readings taken for a record and

the number of artifacts (times when the signal went to the instrument limits).

28

PATIENT :

REC-CHAN

NUMBER

01/04/80

^ 1_ 1

"01/04/80 2 1

01/04/80 3 1

01/04/80 4 1

piiyiGJi/eo

C 5 1 01/04/80

Subject 3

TEST TEST STIN NANE EPOCH LOC 17:54:12 W^^mww^mw^ AEP 15.10 RIGHT EAR 17:56:41

AEP 15.10 RIGHT EAR 17:59:11

AEP 15.10 RIGHT EAR

AEP 15.10 RIGHT EAR

18:04135 'WKKk AEP 15.10 RIGHT EAR 18:07:29

6 1 AEP 15.10 RIGHT EAR

7 1 01/04/80 8 1

wmwm 9 1

01/04/80 10 1

AEP 15.10 RIGHT EAR 18:12:49 AEP 15.10 RIGHT EAR

18:15 r'fS^^^^^^^^^^^^ AEP l^O^mm EAR 18:17:34"^

AEP 15.10 RIGHT EAR

[Fl] Preuious page [FZ] Next page

STIH

TVPE

A^TBURSI

A TBURST

JjmiBST

A TBURST

Ifif IBURST

A TBURST

A TBURST

A TBURST &-y

A TBURST

A TBURST

STIM FREQ

1

1

1

1

1

1

1

1

1

1

[F3] Printer

KHz

KHz

KHz

KHz

KHz

KHz

KHz

KHz

KHz

KHz

STIM INTMS

STIM RATE

80dB

80dB

80dB

60dB

60dB

11.3

11.3

11.3

11.3

11.3

40dB^|^1.3

40dB 11.3

20dB

[ESC] exit

11.3

NUMBER

STIM ART

1200

1200

1200

1200

1200

1200

18

16

6

6

9

0

120(|^^ 0

1200

1200

1200

4

6

58

Figure 4.2 Test details

4.3 Preprocessing

The data were normalized in terms of power, so that each record has same power.

The formula used for normalization was:

x, x norm. =

yl(x[+x[+Z+xl)

where X/ is the original value of each sample,

n is 256, the total number of sample points,

29

xnorm^ is the normalized value.

The normalized data was used to extract various features from the signal, which

were then used to identify the wave V peak. Two approaches were used to identify the

wave V peak, the slope method, the wavelet transform.

4.4 Slope method

The aim was to pick a peak, and slope as a characteristic associated with a peak

can be used to identify the peak. Most of the work done [2, 3] in the past for automatic

detection of wave V were usually done on normal waveforms but the data used here were

highly affected either by noise or most of them were patients so abnormal. A typical

waveform data looked like as shoyvn in Figure 4.3.

ja record number-2 original signal

Figure 4.3 A typical waveform

30

The first step was filtering the data to eliminate the noise from the ABR signal.

The power spectrum of the signal was drawn for all the signals. The cutoff frequenc\ of

the signal was determined to be around 1750 Hz, while recording values from patients,

filter of range 0 - 3000 Hz was used, and the signals had the power line noise of 60 Hz.

Hence a band pass filter was used of range 70 - 1750 Hz. The response of various filters

was observed and Chebyshev II had the least distorted filtered waveform. The frequency

range of filter used was consistent with the frequency range given by [3] for the various

peaks.

After filtering the signals, the local maxima and minima were identified and

slopes associated to the maxima were calculated. To calculate the slope, two values were

required on amplitude scale one was the local maxima and the other was the local

minima. The minima in this case were considered as the point was the waveform shape

changes and not the immediate dip after the peak. For example, in Figure 4.4 are shown

the original waveform on the top and the filtered waveform at bottom. The maxima and

the minima are marked. The slope was calculated for the peak A of the waveform.

31

Figure 4.4 Slope method

The formulae for the slope is

Slope= (PA - Dc)/(Tc- TA)

where PA is the amplitude of peak A, Dc is the amplitude of dip C, Tc is the time of

occurtence of C and Tc is the time of occvurence of TA-

4.5 Wavelet transform

The normalized signal was decomposed into 5 levels using the MATLAB

fiinction "wavedec" . Only the low pass filter signal was continuously decomposed using

32

the filter. The mother wavelet used for the decomposition was Daubechie 5. The dB5 is

the most widely used mother wavelet for EEG signals. The shape of various Daubechie

wavelets is shown below in Figure 4.5. After each level of decomposition the number of

points of the signal was decreased by a factor of 2. So the first level of signal had 128

points, the second level of signal had 64 points and so on. The entire signal at a particular

level was then reconstructed by using the command "waverec". These reconstructed

waveforms were used to extract the various features:

i. slope of the peaks (the difference in the ampliUide of the wave peak and the next

possible minima and the downward slope is taken),

ii. inter peak latencies (the time difference between all peaks),

iii. amplitude ratio (the ratio of the amplitudes of the various peaks), and

iv. peaks latencies (the time of occurtence of the peaks).

* I } > • X 4 • 1 4 * » i * * * • t

db2 db3 db4 db5 db6

« 1 I* i<

db7 db8 db9 db10

Figure 4.5 Daubechie wavelets

33

These features were extracted and tabulated m an excel file. Peak latency was taken

as the feature to be used for classification. The algorithm followed to pick the wave V

peak was as follows:

1. The waveform was normalized so that the lowest pomt of the waveform is

zero amplitude.

2. The mean value of all the available peaks was taken.

3. The peaks whose amplitude was greater than the mean value were selected as

the possible peaks.

4. The peaks from the short listed ones were seen in time frame in the following

order: 6-7 msec, 7-9 msec, 5-6 msec and 9-10 msec.

5. The first peak to fall in this range was selected as peak V, and if there was no

peak in these time intervals then it was assumed that the peak W2is absent.

05

> o u 'E .E 0

ampl

itude

cn

*-• > O.B o 1 0.6

•ffl 0 .4 T3

to.2 t " 0

ja record number-1 original signal

^ ^ ^ peakV/ \ J

\ / \ y \ /^

1 1 1 1 \ _ / i 1

2 4 B 8 10 12 time in seconds, , _ .._

ja record number -1 reconstructed level a3 using db5

^^ ' 'N peakV / \ y

\ / ^ / \ X"^

, 1 1 1 \ y i — 1

2 4 6 0 10 12

^^^H^amv:Mxmi!aiss:is!S£mm^^^ l ' ' "^ '" SBCOndS

1

14

x i o '

1

14

xlD'^

Figure 4.6 Reconstructed waveform.

34

4.6 Spectrogram approach

Before identifying the wave V from the signal, an approach was made to classify

the data set into normal and abnormal cases. The data set was known to have 1 normal

case and 9 abnormal cases. The STFT method was used to determine to what degree it

could cortoborate the clinical results. The total length of the signal was divided into 41

windows using a Kaiser Windowing function. Among the dataset only "ja" in Figure 4.7

was normal. There was a visible difference between the normal cases and abnormal cases

in the frequency range of 2000 to 4000Hz.

8000

7000

6000

w

u c

5000 -,

o- 4000 h

3000

2000

1000

0

'ii*

spectrogram ofjal using kaiser(16,5) — r r x — - . 1 f—

I *«> m

w

x10 i Figure 4.7 Spectrogram

35

CHAPTER 5

RESULT AND CONCLUSION

The previous chapters discussed about the theory of ABR and Wavelet transfonn

and the various processing steps taken to identify the wave V peak. In tiiis chapter we

will discuss the results of the various processing steps.

5.1 Slope method

Only about 30% of the peaks identified by the expert were selected by the slope

method. The slope alone can't be used as a feature to select peak V.

5.2 Wavelet analysis

The wavelet transform used to filter the signal and then locate the peak by using

the algorithm was much more successful then the slope method. Out of 10 patients, wave

V identification were 80% for 7 patients within a limit of 0.3 ms and 60% for 3 patients

within a limit of 0.3 ms. in terms of over all results out of 120 waveforms used 95 were

identified cortectly giving an overall 78% classification. Figure 5.1 shows the

reconstructed wave for "ag" record 10 at 8th level of decomposition. In the figure, "s'' is

the original signal, "ag" is the approximate coefficient at level 8, "dg", "d;", "de", ''ds",

"d4", "ds", "d2" and "di" are the detail coefficient at levels 8 to 1 respectively.

36

Figure 5.3 shows the latency curve for tiie clinically identified peak V and the

wavelet identified peak V.

Figures 5.2 through 5.6 compare tiie classification of wave V peak latency

determined by our clinical specialist and tiie peak V identified by tiie wavelet transfonn

37

for different intensity of stimulus. The X axis has tiie wave V latency and tiie Y axis has

the number of records.

8

^ 7.8 (0

E 7.6 -i" 7.4, c © 7 2 (0

> 7 -% 6.8 -

^ 6.6 -

6.4 -

2

Latency Curve

r,,...—

0 40 55 60

Intensity (dB)

8

4 Clinical \^lue

> • Was^let value

0

Figure 5.2 Latency curve comparison

38

Intensity 80 dB

>4 c3

-•1 0 X',J^!&^i^/ii/^i^>/y/;M^^l^ifS/^^^^

-•—wavelet identified

clinically identifieq

1 3 5 7 9 11 13 15 17 19 21 23 Record

Figure 5.3 Wave V latency for 80 dB

o (0

E

o c (0

10 9 8 7 6 5 4 3 2 1 0

Intensity 60 dB

" f — I — ' I '" ''1 1 — " ' r - t——I—-r-

-•—wavelet identified

-•—clinically identified

1 3 5 7 9 11 13 15 17 Record

Figure 5.4 Wave V latency for 60 dB

39

9i

87 ie c5 >.4

Q>2

-J1

u

Intensity 55 dB

F-^:.^Jr:^--^<^::»^^^-^ T ^ 5 > i M r v ^ ^ ^^---^^K^V

'

IE r I 1 ' • " ' • * — • " • "

—•—wavelet identified 1 1 1

—•—clinically identified

1 3 5 7 9 11 13 15 17 Record

Figure 5.5 Wave V latency for 55 dB

12

0

Intensity 40 dB

-•—wavelet identified

••—clinically identified

" T ^' I r

1 2 3 4 5 6 7 8 9 1011 1213

Record

Figure 5.6 Wave V latency for 40dB

40

Intensity 20 dB

-•—wavelet identified

•—clinically identified

1 2 3 4 5 6 7 8 9 10

Record

Figure 5.7 Wave V latency for 20dB

Table 5.1 compares the average values and standard deviation of wave V latency

between clinically identified peaks and wavelet identified peaks.

Table 5.1 Average and standard deviation of wave V latency

Intensity 80 60 55 40 20

Clinically Identified Average Lat.

7.29 7.46 7.02 7.47 7.10

Standard dev. 0.97 0.70 0.55 0.81 0.70

Wavelet Resulted Average Lat.

7.36 7.92 6.92 7.32 6.91

Standard dev. 0.76 0.87 0.50 0.91 0.79

The other features, like the slope of the reconstructed waveform, the interpeak

latencies and the amplitude ratio yield no results. The spectrogram approach had shoyvn

some results but the values obtained fi-om the spectrogram could not be quantified and

hence it was a qualitative result and not quantitative.

41

5.3 Conclusion

The reconstructed wave of wavelet decomposition level 3 using Daubechie 5

mother wavelet can be used as feature to extract the wave V peak from the waveform.

Wilson [3] has shoym that the wavelet used does not significantiy effect peak

identification.

5.4 Future work

Along with one more features the automated identification accuracy of wave V

can be improved. The other wavelets can potentially be used to extract features for

identification. The spectrogram approach could be used to classify the cases into normal

and abnormal.

42

REFERENCES

1. Linda J. Hood, Charles I. Berlin, Auditory Evoked Potentials, Austm, Pro-ed, 1986.

2. Habraken JBA, van Gils MJ, Cluitmans PJM. Identification of Peak V in Brainstem Auditory Evoked Potentials with Neural Networks. Computers in Biology and Medicine, 23 (5), pp. 369-380, 1993.

3. Wayne J. Wilson, Mark Winter, Gill Kert and Farzin Aghdasi, "Signal Processing of the Auditory Brainstem Response: Investigating into the use of Discrete Wavelet Analysis", Procs. South African IEEE Symposium on Communications and Signal Processing - COMSIG'98, University of Cape Toym, Rondebosch, September 7-8 1998, pp 17-22.

4. John T. Jacobson, The Auditory Brainstem Response, College-Hill Press, Inc, San Diego, CA, 1985.

5. Wavelet tutorial http://engineering.rowan.edu/~polikar/WAVELETS/WTtutorial.html

6. Ernest J. Moore, Bases of Auditory Brain-Stem Evoked Responses, Grune & Stratton, New York, 1983.

7- Barbara Burke Hubbard, The world According to Wavelets, A K Peters Wellesley, Wellesley, Ma, 1998.

8. Agostino Abbate, Casimer M. DeCusatis, Pankaj K. Das, Wavelets and Subbands, Birkhauser, Boston, MA, 2002.

9. J. Robert Boston, "Automated Interpretation of Brainstem Auditory Evoked Potentials: A Prototype System", IEEE Transactions on Biomedical Engineering, vol. 36, pp. 528-532, May 1989

10. Wayne J. Wilson, Mark Winter, Cartnel Nohr and Farzin Aghdasi, "Signal Processing of the Auditory Brainstem Response: Clinical effects of variations in Fast Fourier Transform Analysis", Procs. South African IEEE Symposium on Communications and Signal Processing - COMSIG'98, University of Cape Town, Rondebosch, September 7-8 1998, pp 23-28

43

11. M.J. van Gils. Peak Identification in Auditory Evoked Potentials using Artificial Neural Networks, Ph.D. Thesis, Eindhoven University of Technology, The Netherlands, 1995.

12. Wilson, W.J., and Aghdasi, F., "Discrete Wavelet Analysis of tiie Auditory Brainstem Response: Effects of Stimulus Intensity and Subject Age Gender and Test Ear", Proceedings of the IEEE AFRICON'99 conference, Vol. 1, pp. 291-296, September 1999.

13. Wilson, W.J., and Aghdasi, F., "Discrete Wavelet Analysis of the Auditory Brainstem Response: Effects of Stimulus Intensity and Subject Age Gender and Test Ear", Proceedings of the IEEE AFRICON'99 conference. Vol. 1, pp. 291-296, September 1999.

14. Hanrahan, H. E. (1990). Extraction of features in auditory brainstem response (ABR) signals. COMSIG 90, Proceedings of the third South African Conference on Communications and Signal Processing, IEEE catalog number 90TH0314-5/90, 61-66.

15. http://yvww.vanaga.es/fcps/filtered.htm

16. http://yvww.audiospeech.ubc.ca/haplab/aep.htm

44

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