CLASSIFICATION OF INTERNAL CAROTID ARTERIAL DOPPLER SIGNALS USING WAVELET-BASED NEURAL NETWORKS

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1 CLASSIFICATION OF INTERNAL CAROTID ARTERIAL DOPPLER SIGNALS USING WAVELET-BASED NEURAL NETWORKS İnan GÜLER, Elf Derya ÜBEYLİ Department of Electroncs and Computer Educaton, Faculty of Techncal Educaton, Gaz Unversty, Teknkokullar, Ankara, Turkey, e-mal: Abstract Doppler ultrasound s a nonnvasve technque whch s wdely used n medcne for the assessment of blood flow n vessels. Therefore, Doppler ultrasonography s known as a relable technque, whch demonstrates the flow characterstcs and resstance of nternal carotd arteres n stenoss and occluson condtons. In ths study, nternal carotd arteral Doppler sgnals recorded from 130 subjects that 45 of them had suffered from nternal carotd artery stenoss, 44 of them had suffered from nternal carotd artery occluson and the rest of them had been healthy subjects were classfed usng waveletbased neural network. Spectral analyss of nternal carotd arteral Doppler sgnals was performed usng wavelet transform for determnng the neural network nputs. Multlayer perceptron neural network employng quck propagaton tranng algorthm was used to detect nternal carotd artery stenoss and occluson. The network was traned, cross valdated and tested wth subject s nternal carotd arteral Doppler sgnals. The correct classfcaton rate was 95.45% for healthy subjects, 92.00% for subjects havng nternal carotd artery stenoss and 95.65% for subjects havng nternal carotd artery occluson. The classfcaton results showed that multlayer perceptron neural network employng quck propagaton tranng algorthm was effectve to detect nternal carotd artery stenoss and occluson. Key Words: Doppler ultrasound, Wavelet transform, Multlayer perceptron neural network, Internal carotd artery 1. INTRODUCTION Doppler ultrasound has been a wdely used nonnvasve technque n clncal applcatons for detectng and evaluatng blood flow n vessels. Doppler ultrasonography works by emttng a focused ultrasound beam wth a base frequency f nto the body va a pezoelectrc transducer and detectng the change n frequency that occurs after the beam s reflected or scattered by movng targets. Ths Doppler shft frequency f D s proportonal to the speed of the movng targets: 2vf cosθ f D =, (1) c where v s the magntude of the velocty of target, f D s the Doppler shft frequency, f s the frequency of transmtted ultrasound, c s the magntude of the velocty of ultrasound n blood, and θ s the angle between ultrasonc beam and drecton of moton. Doppler ultrasonography s a relable technque, whch demonstrates the flow characterstcs and resstance of arteres n stenoss and occluson condtons. The 1

2 results of the studes n the lterature have shown that Doppler ultrasound s useful n screenng certan hemodynamc alteratons n arteres [1-3]. Artfcal neural networks (ANNs) produce complcated nonlnear models relatng the nputs (the ndependent varables of a system) to the outputs (the dependent predctve varables). ANNs are computatonal tools for pattern classfcaton that have been the subject of renewed research nterest durng the past 15 years [4-6]. The feld contnues to grow, and a wde varety of network formats and tranng algorthms are beng explored. A multlayer perceptron (MLP) s the popular model that has been playng a central role n applcatons of neural networks [6, 7]. There are many algorthms for tranng the MLP neural networks. The popular backpropagaton algorthm s smple but reportedly has some problems [4-6]. Varous related algorthms such as quck propagaton have been ntroduced to address the problems of backpropagaton algorthm [7]. Applcatons of ANNs n the medcal feld are numerous [8]. The numerous applcatons exhbt the sutablty of ANNs n pattern classfcaton ncludng dagnoss of dseases. However, neural network analyss of Doppler shft sgnals s a relatvely new approach [9, 10]. In ths study, nternal carotd arteral Doppler sgnals were obtaned from 130 subjects that 45 of them had suffered from nternal carotd artery stenoss, 44 of them had suffered from nternal carotd artery occluson and the rest of them had been healthy subjects and entered nto a database. Then the MLP neural network employng quck propagaton tranng algorthm was used to detect nternal carotd artery stenoss and occluson. For determnng the neural network nputs spectral analyss of nternal carotd arteral Doppler sgnals was performed usng the wavelet transform (WT). The network was traned, cross valdated and tested wth the subject records from the database. Tranng and testng performance of the neural network was analyzed for determnng whether the neural network was adequate to classfy data or not. 2. MATERIALS AND METHOD The procedure used n the development of the classfcaton system conssts of four parts: () measurement of nternal carotd arteral Doppler sgnals, () spectral analyss usng the WT (128 detal wavelet coeffcents selected as neural network nputs), () classfcaton usng MLP neural network employng quck propagaton tranng algorthm, (v) classfcaton results (normal nternal carotd artery, stenoss n nternal carotd artery, occluson n nternal carotd artery). These procedures are explaned n the remander of ths study. Internal carotd artery examnatons were performed wth a Doppler unt usng a 5 MHz ultrasonc transducer. The measurement system conssts of 5 MHz ultrasonc transducer, analog Doppler unt (Toshba 140A Color Doppler Ultrasonography), recorder (Sony), analog/dgtal nterface board (Sound Blaster Pro-16 bt), a personal computer wth a prnter. The ultrasonc transducer was appled on a horzontal plane to the neck usng water-soluble gel as a couplng gel. Care was taken not to apply pressure to the neck n order to avod artfacts. 2

3 2.1. Spectral Analyss of Internal Carotd Arteral Doppler Sgnals The Doppler sgnal contans a wealth of nformaton about blood flow occurrng wthn the sample volume of the Doppler ultrasonography. The most complete way to dsplay ths nformaton s to perform spectral analyss. Dagnoss of arteral dseases s feasble by analyss of spectral shape and parameters. Snce flow n arteres s pulsatle and the movng targets have a random spatal dstrbuton, the Doppler sgnal s tme-varyng and random. Therefore, spectral analyss of nternal carotd arteral Doppler sgnals was performed usng the WT. It s known that wavelets are better suted to analysng nonstatonary sgnals, snce they are well localzed n tme and frequency. The property of tme and frequency localzaton s known as compact support and s one of the most attractve features of the WT. The man advantage of the WT s that t has a varyng wndow sze, beng broad at low frequences and narrow at hgh frequences, thus leadng to an optmal tme-frequency resoluton n all frequency ranges [3, 11, 12]. All wavelet transforms can be specfed n terms of a low-pass flter h, whch satsfes the standard quadrature mrror flter condton: 1 1 H ( z) H ( z ) + H ( z) H ( z ) = 1 (2) where H (z) denotes the z-transform of the flter h. Its complementary hgh-pass flter can be defned as 1 G ( z) = zh ( z ). (3) A sequence of flters wth ncreasng length (ndexed by ) can be obtaned: 2 H ( z) = H ( z ) H ( ) + 1 z 2 1( z) = G( z ) H ( z) G +, = 0, K, I 1 (4) wth the ntal condton H 0 ( z) = 1. It s expressed as a two-scale relaton n tme doman h k) h h ( [] ) [ g] h ( ) + 1( = 2 k 1( k) = 2 k g + (5) where the subscrpt [] m ndcates the up-samplng by a factor of m and k s the equally sampled dscrete tme. The normalzed wavelet and scale bass functons ϕ ( ), ψ ( ) can be defned as / 2 ϕ, l ( k) = 2 h ( k 2 l), l k, l k / 2 ψ, l ( k) = 2 g ( k 2 l) (6) / 2 where the factor 2 s an nner product normalzaton, and l are the scale parameter and the translaton parameter, respectvely. The dscete wavelet transform decomposton can be descrbed as s l) = x( k) ( ) ( ) ( ϕ, l k ( ) ( l) x( k) ψ, l ( k ( ) ( l d = ) (7) where s ) and d (l) are the approxmaton coeffcents and the detal coeffcents at resoluton, respectvely [11, 12]. 3

4 The wavelet coeffcents were computed usng the Daubeches wavelet of order 4. Snce the detal wavelet coeffcents contan a sgnfcant amount of nformaton about the Doppler sgnal, the computed detal wavelet coeffcents (128 detal wavelet coeffcents) of each subject s nternal carotd arteral Doppler sgnals were used as the MLP neural network nputs. The detal wavelet coeffcents were computed usng MATLAB software package. The detal wavelet coeffcents of nternal carotd arteral Doppler sgnals obtaned from healthy subject (subject no: 8), subject havng nternal carotd artery stenoss (subject no: 15) and subject havng nternal carotd artery occluson (subject no: 21) are gven n Fgures 1-3, respectvely Detal wavelet coeffcents Number of detal wavelet coeffcents Fgure 1. Detal wavelet coeffcents of nternal carotd arteral Doppler sgnals obtaned from healthy subject (subject no: 8) Detal wavelet coeffcents Number of detal wavelet coeffcents Fgure 2. Detal wavelet coeffcents of nternal carotd arteral Doppler sgnals obtaned from subject havng nternal carotd artery stenoss (subject no: 15) 4

5 Detal wavelet coeffcents Number of detal wavelet coeffcents Fgure 3. Detal wavelet coeffcents of nternal carotd arteral Doppler sgnals obtaned from subject havng nternal carotd artery stenoss (subject no: 21) 2.2. MLP Neural Network ANNs consst of a great number of processng elements (neurons), whch are connected wth each other; the strengths of the connectons are called weghts. For the modelng of physcal systems, a MLP neural network s commonly used. It conssts of a layer of nput neurons, a layer of output neurons and one or more hdden layers. In order to cope wth nonlnearly separable problems, addtonal layer(s) of neurons placed between the nput layer (contanng nput nodes) and the output layer are needed leadng to the MLP archtecture. The most popular approach to fndng the optmal number of hdden layers s by tral and error [4-6]. In the present study, the MLP neural network conssted of one nput layer, one hdden layer, and one output layer and the decson about the number of hdden layers n use was determned emprcally (Fgure 4). Drecton of Actvaton Propagaton Inputs Outputs Input Layer Hdden Layer Output Layer Drecton of Error Propagaton Fgure 4. MLP neural network 5

6 In ANNs, the knowledge les n the nterconnecton weghts between neurons. Therefore, tranng process s an mportant characterstc of the ANN methodology, whereby representatve examples of the knowledge are teratvely presented to the network, so that t can ntegrate ths knowledge wthn ts structure [4-6]. There are a number of tranng algorthms used to tran a MLP and a frequently used one s called the backpropagaton tranng algorthm [6, 7]. However, backpropagaton has some problems such as slow convergence for many applcatons. The quck propagaton tranng algorthm, whch was put forward by Fahlman [7], s a modfed backpropagaton algorthm developed to speed up the tranng of the network. In MLP neural network, each neuron j n the hdden layer sums ts nput sgnals x after multplyng them by the strengths of the respectve connecton weghts w and computes ts output y j as a functon of the sum: ( w x ) y, (8) j = f where f s actvaton functon that s necessary to transform the weghted sum of all sgnals mpngng onto a neuron. In ths study, the actvaton functon for hdden neurons was the conventonal sgmodal functon wth the range between zero and one. The sum of squared dfferences between the desred and actual values of the output neurons E s defned as: E 1 2 = ( y dj y j ), (9) 2 j where y dj s the desred value of output neuron j and y j s the actual output of that neuron. Each weght w s adjusted by addng an ncrement w to t. w s selected to reduce E as rapdly as possble. How w s computed depends on the tranng algorthm adopted. Quck propagaton algorthm s then nvoked to adjust all the weghts n the network and gves the change w (k) n the weght of the connecton between neurons and j at teraton k as: E w ( k) = α + µ w ( k 1), (10) w ( k) where α s called the learnng coeffcent, w ( k 1) s the weght change n the mmedately preceedng teraton and µ s the momentum coeffcent and defned as E / w ( k) µ =. ( E / w ( k 1)) ( E / w ( k)) In ths study, learnng coeffcent was determned emprcally and α was taken as RESULTS AND DISCUSSION MLP neural network employng quck propagaton tranng algorthm was mplemented by usng MATLAB software package (MATLAB verson 6.0 wth neural networks toolbox). Selecton of the network nputs s the the most mportant component of desgnng the neural network based on pattern classfcaton snce even the best 6

7 classfer wll perform poorly f the nputs are not selected well. Input selecton has two meanngs: 1) whch components of a pattern, or 2) whch set of nputs best represent a gven pattern. In ths study, the detal wavelet coeffcents (128 detal wavelet coeffcents) of each subject s nternal carotd arteral Doppler sgnals were used as the MLP neural network nputs. The outputs of the network were represented by unt bass vectors: [0 0 1] = normal nternal carotd artery [0 1 0] = stenoss n nternal carotd artery [1 0 0] = occluson n nternal carotd artery The adequate functonng of the neural network depends on the szes of the tranng set and test set. In ths study, 60 of 130 subjects were used for tranng and the rest of them were used for testng. For obtanng a better network s generalzaton 15 of tranng subjects were used as cross valdaton set. MLP neural network employng quck propagaton was traned wth the tranng set and checked wth the test set. In ths study, performance analyss of the neural network s examned n two parts as tranng performance and testng performance. Tranng set provded to the neural network s representatve of the whole state space of concern so that the traned neural network has the ablty of generalzaton. In tranng, a representatve tranng set wth examples s presented teratvely to the neural network and the output actvatons are calculated usng the network weghts. An error term, based on the dfference between the output of network and desred output, s then propagated back through the network to calculate changes of the nterconnecton weghts. The square dfference between the output of network and the desred output over tranng teratons s plotted for observng how well the network s traned. The curve of the mean square error (MSE) versus teraton s called as the tranng curve (Fgure 5). When the network s traned too much, the network memorzes the tranng patterns and does not generalze well. The tranng holds the key to an accurate soluton, so the crteron to stop tranng must be very well descrbed. Cross valdaton s a hghly recommended crteron for stoppng the tranng of a network. In Fgure 5, the error n tranng set and the valdaton set s shown on the same graph. When the error n the cross valdaton ncreases, the tranng should be stopped because the pont of best generalzaton has been reached. In ths study as t s seen from Table 1, tranng was done n 2500 epochs and number of epochs was determned accordng to the error of cross valdaton. The values of mnmum MSE and fnal MSE durng tranng and cross valdaton are gven n Table 1. Snce MSE (Fgure 5) s convergng to a small constant approxmately zero n 2500 epochs, tranng of the neural network s determned as successful. Table 1. The values of mnmum and fnal MSE durng tranng and cross valdaton Network Tranng Cross valdaton Number of epochs Mnmum MSE Fnal MSE

8 MSE Tranng MSE Cross Valdaton MSE Fgure 5. Tranng and cross-valdaton MSE curves of MLP neural network After tranng phase, testng of the MLP neural network was done. The data, that the network had not seen before, was appled to the network for testng the network performance. Snce tranng was successful and the network s topology was correct, t appled ts past experence to test data and produced a good soluton. Testng performance was analyzed by assessng the classfcaton results, the values of performance evaluaton parameters and statstcal parameters. In classfcaton, the am s to assgn the nput patterns to one of several classes, usually represented by outputs restrcted to le n the range from 0 to 1, so that they represent the probablty of class membershp. Whle the classfcaton s carred out, a specfc pattern s assgned to a specfc class accordng to the characterstc features selected for t. In ths study, there were three classes as normal, stenoss and occluson whch were ndcatng stuatons of subjects nternal carotd arteres. Classfcaton results of the network were dsplayed by a confuson matrx. In a confuson matrx, each cell contans the number of exemplars classfed for the correspondng combnaton of desred and actual network outputs. The confuson matrx showng the classfcaton results of ths network s gven below. Confuson matrx Epoch Output/Desred Result (normal) Result (stenoss) Result (occluson) Result (normal) Result (stenoss) Result (occluson) When ths confuson matrx s examned, t s seen that one normal subject classfed ncorrectly by the network as a subject havng stenoss, one subject havng stenoss classfed as a normal subject, one subject havng stenoss classfed as a subject havng occluson and one subject havng occluson classfed as a subject havng stenoss. 8

9 The szes of MSE and mean absolute error (MAE) can be used to determne how well the network output fts the desred output, but they may not reflect whether the two sets of data move n the same drecton. The correlaton coeffcent ( r ) solves ths problem. When r s close to 1 there s a perfect postve lnear correlaton between network output and desred output, whch means that they vary by the same amount. The values of these performance evaluaton parameters are gven n Table 2. From Table 2, one can see that the values of MSE and MAE are low and the correlaton coeffcents are close to 1. The values of these performance evaluaton parameters ndcated that test performance of the neural network was hgh. Table 2. The values of performance evaluaton parameters Performance evaluaton parameters Result (normal) Result (stenoss) Result (occluson) MSE MAE r The test performance was determned by the computaton of the followng statstcal parameters: Specfcty: number of correct classfed normal subjects / number of total normal subjects Senstvty (stenoss): number of correct classfed subjects havng stenoss / number of total subjects havng stenoss Senstvty (occluson): number of correct classfed subjects havng occluson / number of total subjects havng occluson Accuracy: number of correct classfed subjects / number of total subjects The values of these statstcal parameters are gven n Table 3. As t s seen from Table 3, the neural network classfed normal subjects wth the accuracy of 95.45%, subjects havng stenoss wth the accuracy of 92.00%, subjects havng occluson wth the accuracy of 95.65%. The normal subjects, subjects havng stenoss and subjects havng occluson were classfed wth the accuracy of 94.29%. Table 3. The values of statstcal parameters Statstcal parameters Values Specfcty 95.45% Senstvty (stenoss) 92.00% Senstvty (occluson) 95.65% Accuracy 94.29% 4. CONCLUSION ANNs are able to generalze well and are capable of solvng nonlnear problems. ANNs may offer a potentally superor method of Doppler sgnal analyss to the spectral analyss technques. In contrast to the conventonal spectral analyss technques, ANNs 9

10 not only model the sgnal, but also make a decson as to the class of sgnal. Another advantage of ANN analyss over exstng technques of nternal carotd artery waveform analyss s that, after an ANN has traned satsfactorly and the values of the weghts and bases have been stored, testng and subsequent mplementaton s rapd. In ths study, the MLP neural network employng quck propagaton tranng algorthm was used to detect stenoss and occluson n nternal carotd arteres. The neural network was traned, cross valdated and tested wth the computed detal wavelet coeffcents of each subject s nternal carotd arteral Doppler sgnals. Performance ndcators and statstcal measures were used for evaluatng the neural network. The classfcatons of healthy subjects, subjects havng stenoss and subjects havng occluson were done wth the accuracy of 95.45%, 92.00%, and 95.65%, respectvely. Based on the accuracy of the neural network s detectons, t can be mentoned that the classfcaton of nternal carotd arteral Doppler sgnals s feasble by the MLP neural network employng quck propagaton tranng algorthm. REFERENCES 1. D.H. Evans, W.N. McDcken, R. Skdmore, J.P. Woodcock, Doppler Ultrasound: Physcs, Instrumentaton and Clncal Applcatons, Wley, Chchester, İ. Güler, S. Kara, N.F. Güler, M.K. Kıymık, Applcaton of autoregressve and fast Fourer transform spectral analyss to trcuspd and mtral valve stenoss, Computer Methods and Programs n Bomedcne, 49, 29-36, İ. Güler, F. Hardalaç and S. Müldür, Determnaton of aorta falure wth the applcaton of FFT, AR and wavelet methods to Doppler technque, Computers n Bology and Medcne, 31, , S. Haykn, Neural networks: A comprehensve foundaton, Macmllan, New York, I.A. Basheer, M. Hajmeer, Artfcal neural networks: fundamentals, computng, desgn, and applcaton, Journal of Mcrobologcal Methods, 43, 3-31, B.B. Chaudhur, U. Bhattacharya, Effcent tranng and mproved performance of multlayer perceptron n pattern classfcaton, Neurocomputng, 34, 11-27, S.E. Fahlman, An emprcal study of learnng speed n backpropagaton networks, Computer Scence Techncal Report, CMU-CS , A.S. Mller, B.H. Blott, T.K. Hames, Revew of neural network applcatons n medcal magng and sgnal processng, Medcal & Bologcal Engneerng & Computng, 30, , I.A. Wrght, N.A.J. Gough, F. Rakebrandt, M. Wahab, J.P. Woodcock, Neural network analyss of Doppler ultrasound blood flow sgnals: A plot study, Ultrasound n Medcne & Bology, 23(5), , İ. Güler, E.D. Übeyl, Detecton of ophthalmc artery stenoss by least-mean squares backpropagaton neural network, Computers n Bology and Medcne, 2003, (n press). 11. P.I.J. Keeton, F.S. Schlndwen, Applcaton of wavelets n Doppler ultrasound, Sensor Revew, 17(1), 38-45, Y. Zhang, Y. Wang, W. Wang, B. Lu, Doppler ultrasound sgnal denosng based on wavelet frames, IEEE Transactons on Ultrasoncs, Ferroelectrcs, and Frequency Control, 48(3), ,