Wavelet-based neural network analysis of ophthalmic artery Doppler signals

Computers in Biology and Medicine 34 (2004) 601 – 613 http://www.intl.elsevierhealth.com/journals/cobm

Wavelet-based neural network analysis of ophthalmic artery Doppler signals Nihal Fatma G-uler∗ , Elif Derya Ubeyl˙ 2 Department of Electronics and Computer Education, Faculty of Technical Education, Gazi University, 06500 Teknikokullar, Ankara, Turkey Received 30 May 2003; received in revised form 15 September 2003; accepted 15 September 2003

Abstract In this study, ophthalmic artery Doppler signals were recorded from 115 subjects, 52 of whom had ophthalmic artery stenosis while the rest were healthy controls. Results were classi8ed using a wavelet-based neural network. The wavelet-based neural network model, employing the multilayer perceptron, was used for analysis of ophthalmic artery Doppler signals. A multilayer perceptron neural network (MLPNN) trained with the Levenberg–Marquardt algorithm was used to detect stenosis in ophthalmic arteries. In order to determine the MLPNN inputs, spectral analysis of ophthalmic artery Doppler signals was performed using wavelet transform. The MLPNN was trained, cross validated, and tested with training, cross validation, and testing sets, respectively. All data sets were obtained from ophthalmic arteries of healthy subjects and subjects su>ering from ophthalmic artery stenosis. The correct classi8cation rate was 97.22% for healthy subjects, and 96.77% for subjects having ophthalmic artery stenosis. The classi8cation results showed that the MLPNN trained with the Levenberg–Marquardt algorithm was e>ective to detect ophthalmic artery stenosis. ? 2003 Elsevier Ltd. All rights reserved. Keywords: Doppler signals; Wavelet transform; Multilayer perceptron neural network; Levenberg–Marquardt algorithm; Ophthalmic artery

1. Introduction Doppler ultrasound is widely used as a noninvasive method for the assessment of blood Cow in both the central and peripheral circulation. It may be used to estimate blood Cow, to image regions of blood Cow and to locate sites of arterial disease as well as Cow characteristics and resistance of ophthalmic arteries [1–4]. Doppler systems are based on the principle that ultrasound, emitted ∗

Corresponding author. Tel.: +90-312-212-3976; fax: +90-312-212-0059. E-mail address: [email protected] (N.F. G-uler).

0010-4825/$ - see front matter ? 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.compbiomed.2003.09.001

602

' N.F. G'uler, E.D. Ubeyl˙ * / Computers in Biology and Medicine 34 (2004) 601 – 613

by an ultrasonic transducer, is returned partially towards the transducer by the moving targets, thereby inducing a shift in frequency proportional to the emitted frequency and the velocity along the ultrasound beam. Studies in the literature have shown that Doppler ultrasound evaluation can give reliable information on both systolic and diastolic blood velocities of arteries and is useful in screening certain hemodynamic alterations in arteries [1–4]. Spectral analysis of the Doppler signals produces information concerning the blood Cow in the arteries [5]. However, arti8cial neural networks (ANNs) may o>er a potentially superior method of Doppler signal analysis to the spectral analysis methods. In contrast to the conventional spectral analysis methods, ANNs not only model the signal, but also make a decision as to the class of signal. Another advantage of ANN analysis over existing methods of Doppler signal analysis is that, after an ANN has trained satisfactorily and the values of the weights and biases have been stored, testing and subsequent implementation is rapid [6–8]. ANNs produce complicated nonlinear models relating the inputs (the independent variables of a system) to the outputs (the dependent predictive variables) [9,10]. The literature demonstrates an ability of ANNs to detect patterns enabling diagnosis of diseases [11,12]. A multilayer perceptron neural network (MLPNN) is the popular model that has been playing a central role in applications of neural networks. There are a number of training algorithms used to train a MLPNN and a frequently used one is called the backpropagation training algorithm [9,10,13]. However, backpropagation has some problems for many applications. Therefore, various algorithms have been introduced to address the problems of backpropagation algorithm. Second-order optimization methods such as the Levenberg–Marquardt algorithm have also been used for MLPNN training in recent years [14,15]. Recent advances in the 8eld of ANNs have made them attractive for analyzing signals. The application of ANNs has opened a new area for solving problems not resolvable by other signal processing techniques [11,12]. However, ANN analysis of Doppler shift signals is a relatively new approach [6–8,16–20]. In our previous study [20] for determining the MLPNN inputs, spectral analysis of ophthalmic artery Doppler signals was performed by using the Welch method (one of the fast Fourier transform-based methods). Since Cow in arteries is pulsatile and the moving targets have a random spatial distribution, the Doppler signal is time-varying and random. Therefore, wavelet transform (WT) [21,22] was used for spectral analysis of the ophthalmic artery Doppler signals, which is time-varying, in order to determine the MLPNN inputs presented in this study. The MLPNN presented in this study was trained, cross validated, and tested with the computed detail wavelet coeMcients of ophthalmic artery Doppler signals obtained from healthy subjects and subjects having ophthalmic artery stenosis. Furthermore, the MLPNN presented in the previous study [20] was trained with the least-mean squares backpropagation algorithm which had slow convergence. In order to improve convergence rate, the MLPNN presented in this study was trained with the Levenberg–Marquardt algorithm. The correct classi8cation rates and convergence rate of the wavelet-based neural network model presented in this study were found to be higher than the neural network model used in the previous study [20]. 2. Materials and method The procedure used in the development of the classi8cation system consisted of four parts: (i) measurement of ophthalmic artery Doppler signals, (ii) spectral analysis using the WT (128 detail

' N.F. G'uler, E.D. Ubeyl˙ * / Computers in Biology and Medicine 34 (2004) 601 – 613

Ultrasonic Transducer

Analog Doppler Unit

Recorder

Analog/Digital Interface Board

603

Computer & Printer

Fig. 1. Block diagram of measurement system.

wavelet coeMcients selected as neural network inputs), (iii) classi8cation using the MLPNN trained with the Levenberg–Marquardt algorithm, and (iv) classi8cation results (normal ophthalmic artery, stenosis in ophthalmic artery). These procedures are explained in the remainder of this paper. 2.1. Subjects In the present study, ophthalmic artery Doppler signals were obtained from 115 subjects. The group consisted of 56 females and 59 males with ages ranging from 19 to 65 years and a mean age of 33:5±0:5 years. Diasonics Synergy color Doppler ultrasonography was used during examinations and sonograms were taken into consideration. According to the examination results, 52 of 115 subjects su>ered from ophthalmic artery stenosis and the rest were healthy subjects (control group) who had no ocular or systemic disease. The group su>ering from ophthalmic artery stenosis consisted of 25 females and 27 males with a mean age 35:5 ± 0:5 years (range 23– 65) and the healthy subjects were 31 females and 32 males with a mean age 30:0 ± 0:5 (range 19 – 64). 2.2. Measurement of ophthalmic artery doppler signals Ophthalmic artery examinations were performed with a Doppler unit using a 10 MHz ultrasonic transducer. The block diagram of the measurement system is shown in Fig. 1. The system consisted of 8ve units. These were 10 MHz ultrasonic transducer, analog Doppler unit (Diasonics Synergy), recorder (Sony), analog/digital interface board (Sound Blaster Pro-16 bit), and a personal computer with a printer. The ultrasonic transducer was applied on a horizontal plane to the closed eyelids using sterile methylcellulose as a coupling gel. Care was taken not to apply pressure to the eye in order to avoid artifacts. The probe was most often placed at an angle of 60◦ from the midline pointing towards the orbital apex. Good and consistent signals were obtained at 37–42 mm depth. 2.3. Spectral analysis of ophthalmic artery doppler signals Diagnosis of arterial diseases is feasible by analysis of spectral shape and parameters [1–3,5]. Since Cow in arteries is pulsatile and the moving targets have a random spatial distribution, the Doppler signal is time varying and random. It is known that WT is better suited to analyzing nonstationary signals, since it is well localized in time and frequency. The property of time and frequency localization is known as compact support and is one of the most attractive features of the WT. The main advantage of the WT is that it has a varying window size, being broad at low frequencies and narrow at high frequencies, thus leading to an optimal time–frequency resolution in

' N.F. G'uler, E.D. Ubeyl˙ * / Computers in Biology and Medicine 34 (2004) 601 – 613

604

all frequency ranges [21,22]. Therefore, spectral analysis of ophthalmic artery Doppler signals was performed using the WT. All wavelet transforms can be speci8ed in terms of a low-pass 8lter h, which satis8es the standard quadrature mirror 8lter condition: H (z)H (z −1 ) + H (−z)H (−z −1 ) = 1;

(1)

where H (z) denotes the z-transform of the 8lter h. Its complementary high-pass 8lter can be de8ned as G(z) = zH (−z −1 ):

(2)

A sequence of 8lters with increasing length (indexed by i) can be obtained. i

Hi+1 (z) = H (z 2 )Hi (z); i

Gi+1 (z) = G(z 2 )Hi (z); i = 0; : : : ; I − 1

(3)

with the initial condition H0 (z) = 1. It is expressed as a two-scale relation in time domain hi+1 (k) = [h]↑2i ∗ hi (k); gi+1 (k) = [g]↑2i ∗ hi (k);

(4)

where the subscript [ · ]↑m indicates the up-sampling by a factor of m and k is the equally sampled discrete time. The normalized wavelet and scale basis functions ’i; l (k), i; l (k) can be de8ned as ’i; l (k) = 2i=2 hi (k − 2i l); i; l (k)

= 2i=2 gi (k − 2i l);

(5)

where the factor 2i=2 is an inner product normalization, i and l are the scale parameter and the translation parameter, respectively. The discrete wavelet transform decomposition can be described as s(i) (l) = x(k) ∗ ’i; l (k); d(i) (l) = x(k) ∗

i; l (k);

(6)

where S(i) (l) and di (l) are the approximation coeMcients and the detail coeMcients at resolution i, respectively [21,22]. In the present study, the wavelet coeMcients were computed using the Daubechies wavelet of order one. The detail wavelet coeMcients of ophthalmic artery Doppler signals obtained from one healthy subject (subject no: 10), and one subject having ophthalmic artery stenosis (subject no: 21) are given in Figs. 2 and 3, respectively. The detail wavelet coeMcients were computed using MATLAB software package. 2.4. Arti8cial neural networks ANNs may be de8ned as structures comprised of densely interconnected adaptive simple processing elements (neurons) that are capable of performing massively parallel computations for data

' N.F. G'uler, E.D. Ubeyl˙ * / Computers in Biology and Medicine 34 (2004) 601 – 613

605

50 40

Detail wavelet coefficients

30 20 10 0 -10 -20 -30 -40

0

20

40 60 80 100 Number of detail wavelet coefficients

120

140

Fig. 2. Detail wavelet coeMcients of ophthalmic artery Doppler signals obtained from one healthy subject (subject no: 10).

15

Detail wavelet coefficients

10

5

0

-5

-10

-15

-20

0

20

40 60 80 100 Number of detail wavelet coefficients

120

140

Fig. 3. Detail wavelet coeMcients of ophthalmic artery Doppler signals obtained from one subject having ophthalmic artery stenosis (subject no: 21).

processing and knowledge representation. ANNs can be trained to recognize patterns and the nonlinear models developed during training allow neural networks to generalize their conclusions and to make application to patterns not previously encountered [9,10]. The MLPNNs, which have features

606

' N.F. G'uler, E.D. Ubeyl˙ * / Computers in Biology and Medicine 34 (2004) 601 – 613

Outputs

Inputs

Input Layer

Hidden Layer 1

Hidden Layer N

Output Layer

Fig. 4. MLPNN topology.

such as the ability to learn and generalize, smaller training set requirements, fast operation, ease of implementation and therefore most commonly used neural network architectures, have been adapted for detection of ophthalmic artery stenosis. As shown in Fig. 4, a MLPNN consists of (i) an input layer with neurons representing input variables to the problem, (ii) an output layer with neurons representing the dependent variables (what is being modeled), and (iii) one or more hidden layers containing neurons to help capture the nonlinearity in the data. 2.4.1. Multilayer perceptron neural networks Presently, the most widely used ANN type is a MLPNN which has been playing a central role in applications of neural networks. The MLPNN is a nonparametric technique for performing a wide variety of detection and estimation tasks [9,10,13]. In the MLPNN, each neuron j in the hidden layer sums its input signals xi after multiplying them by the strengths of the respective connection weights wji and computes its output yj as a function of the sum:
  wji xi ; (7) yj = f where f is the activation function that is necessary to transform the weighted sum of all signals impinging onto a neuron. The activation function (f) can be a simple threshold function, or a sigmoidal, hyperbolic tangent, or radial basis function. The sum of squared di>erences between the desired and actual values of the output neurons E is de8ned as 1 E= (ydj − yj )2 ; (8) 2 j where ydj is the desired value of output neuron j and yj is the actual output of that neuron. Each weight wji is adjusted to reduce E as rapidly as possible. How wji is adjusted depends on the training algorithm adopted [9,10,13]. Training algorithms are an integral part of ANN model development. An appropriate topology may still fail to give a better model, unless trained by a suitable training algorithm. A good training

' N.F. G'uler, E.D. Ubeyl˙ * / Computers in Biology and Medicine 34 (2004) 601 – 613

607

algorithm will shorten the training time, while achieving a better accuracy. Therefore, training process is an important characteristic of the ANNs, whereby representative examples of the knowledge are iteratively presented to the network, so that it can integrate this knowledge within its structure. There are a number of training algorithms used to train a MLPNN and a frequently used one is called the backpropagation training algorithm [9,10,13]. The backpropagation algorithm, which is based on searching an error surface using gradient descent for points with minimum error, is relatively easy to implement. However, backpropagation has some problems for many applications. The algorithm is not guaranteed to 8nd the global minimum of the error function since gradient descent may get stuck in local minima, where it may remain inde8nitely. In addition to this, long training sessions are often required in order to 8nd an acceptable weight solution because of the well-known diMculties inherent in gradient descent optimization. Therefore, a lot of variations to improve the convergence of the backpropagation were proposed. Optimization methods such as second-order methods (conjugate gradient, quasi-Newton, Levenberg–Marquardt) have also been used for ANN training in recent years. The Levenberg–Marquardt algorithm combines the best features of the Gauss-Newton technique and the steepest-descent algorithm, but avoids many of their limitations. In particular, it generally does not su>er from the problem of slow convergence [14,15]. Therefore, in this study the MLPNN was trained with the Levenberg–Marquardt algorithm. 2.4.2. Levenberg–Marquardt algorithm ANN training is usually formulated as a nonlinear least-squares problem. Essentially, the Levenberg–Marquardt algorithm is a least-squares estimation algorithm based on the maximum neighborhood idea. Let E(w) be an objective error function made up of m individual error terms ei2 (w) as follows: E(w) =

m 

ei2 (w) = f(w)2 ;

(9)

i=1

where ei2 (w) = (ydi − yi )2 and ydi is the desired value of output neuron i, yi is the actual output of that neuron. It is assumed that function f(·) and its Jacobian J are known at point w. The aim of the Levenberg–Marquardt algorithm is to compute the weight vector w such that E(w) is minimum. Using the Levenberg–Marquardt algorithm, a new weight vector wk+1 can be obtained from the previous weight vector wk as follows: wk+1 = wk + wk ;

(10)

where wk is de8ned as wk = −(JkT f(wk ))(JkT Jk + I)−1 :

(11)

In Eq. (11), Jk is the Jacobian of f evaluated at wk ,  is the Marquardt parameter, I is the identity matrix [14,15].

608

' N.F. G'uler, E.D. Ubeyl˙ * / Computers in Biology and Medicine 34 (2004) 601 – 613

3. Results and discussion 3.1. Application of MLPNN to ophthalmic artery doppler signals ANN architectures are derived by trial and error and the complexity of the neural network is characterized by the number of hidden layers. There is no general rule for selection of appropriate number of hidden layers. A neural network with a small number of neurons may not be suMciently powerful to model a complex function. On the other hand, a neural network with too many neurons may lead to over8tting the training sets and lose its ability to generalize which is the main desired characteristic of a neural network. The most popular approach to 8nding the optimal number of hidden layers is by trial and error. In the present study, after several trials it was seen that one hidden layered network achieved the task in high accuracy. The most suitable network con8guration found was ten neurons for the hidden layer. In the hidden layer and the output layer, sigmoidal function was used, which introduced two important properties. Firstly, the sigmoid is nonlinear, allowing the network to perform complex mappings of input to output vector spaces, and secondly it is continuous and di>erentiable, which allows the gradient of the error to be used in updating the weights. The MLPNN was trained by using the Levenberg–Marquardt algorithm. For the Levenberg– Marquardt algorithm, the Marquardt parameter () was set to 0.01. The MLPNN was implemented by using MATLAB software package (MATLAB version 6.0 with neural networks toolbox). Selection of the ANN inputs is the most important component of designing the neural network based on pattern classi8cation since even the best classi8er will perform poorly if the inputs are not selected well. Input selection has two meanings: (1) which components of a pattern, or (2) which set of inputs best represent a given pattern. Since the detail wavelet coeMcients contain a signi8cant amount of information about the Doppler signal, the computed detail wavelet coeMcients (128 detail wavelet coeMcients) of ophthalmic artery Doppler signals of each subject were used as the MLPNN inputs. The adequate functioning of ANN depends on the sizes of the training set and test set. In this study, 48 of 115 subjects were used for training and the rest for testing. A practical way to 8nd a point of better generalization is to use a small percentage (around 20%) of the training set for cross validation. For obtaining a better network generalization ten training subjects were selected randomly to be used as a cross validation set. The training set consisted of 21 subjects su>ering from ophthalmic artery stenosis and 27 healthy subjects. The testing set consisted of 31 subjects su>ering from ophthalmic artery stenosis and 36 healthy subjects. The cross validation set consisted of 8ve subjects su>ering from ophthalmic artery stenosis and 8ve healthy subjects. The outputs of the MLPNN were represented by unit basis vectors: [0 1]=normal ophthalmic artery, [1 0]=stenosis in ophthalmic artery. 3.2. Performance analysis of MLPNN The MLPNN was trained with the training set, cross validated with the cross validation set, and checked with the test set. In this study, performance analysis of the MLPNN is examined in two parts: training performance and testing performance.

' N.F. G'uler, E.D. Ubeyl˙ * / Computers in Biology and Medicine 34 (2004) 601 – 613

609

0.12 Training MSE Cross validation MSE 0.1

MSE

0.08

0.06

0.04

0.02

0

0

100

200

300 Epoch

400

500

600

Fig. 5. Training and cross validation MSE curves of the MLPNN.

3.2.1. Training performance of MLPNN The training set provided to the MLPNN was representative of the whole space of concern so that the trained MLPNN had the ability of generalization. In training, a representative training set with examples was presented iteratively to the MLPNN and the output activations were calculated using the MLPNN weights. An error term, based on the di>erence between the output of MLPNN and desired output, was then propagated back through the MLPNN to calculate changes of the interconnection weights. The square di>erence between the output of MLPNN and the desired output over training iterations was plotted for observing how well the MLPNN was trained. The curve of the mean square error (MSE) versus iteration is the training curve. In general, it is known that a network with enough weights will always learn the training set better as the number of iterations is increased. However, this decrease in the training set error is not always coupled to better performance in the test. When the network is trained too much, the network memorizes the training patterns and does not generalize well. The training holds the key to an accurate solution, so the criterion to stop training must be very well described. Cross validation is a highly recommended criterion for stopping the training of a network. When the error in the cross validation increases, the training should be stopped because the point of best generalization has been reached. In Fig. 5, the error in training set and the cross validation set is shown on the same graph. The values of minimum MSE and 8nal MSE during training and cross validation are given in Table 1. In this study as it is seen from Table 1, training was done in 600 epochs since the cross validation error began to rise at 600 epochs. Since MSE (Fig. 5) converged to a small constant approximately zero in 600 epochs, the MLPNN trained with the Levenberg–Marquardt algorithm was determined to be successful. However, in our previous study [20] the MLPNN trained with the least-mean squares backpropagation algorithm had a slow convergence and MSE converged to a small constant of approximately zero in 3000 epochs. Thus, the convergence rate of wavelet-based neural network model presented

610

' N.F. G'uler, E.D. Ubeyl˙ * / Computers in Biology and Medicine 34 (2004) 601 – 613

Table 1 The values of minimum and 8nal MSE during training and cross validation Network

Training

Cross validation

Number of epochs Minimum MSE Final MSE

600 0.000106 0.000106

600 0.000153 0.000153

in this study was found to be higher than the neural network model used in the previous study [20]. 3.2.2. Testing performance of MLPNN After a training phase for testing the MLPNN, 67 test data that the network had not seen before was applied to the network. The MLPNN applied its past experience to test data and produced a solution based on the training and topology of the MLPNN. The evaluation of testing performance of the MLPNN was performed by assessment of classi8cation results, the values of statistical parameters, and performance evaluation parameters. In classi8cation, the aim is to assign the input patterns to one of several classes, usually represented by outputs restricted to lie in the range from 0 to 1, so that they represent the probability of class membership. While the classi8cation is carried out, a speci8c pattern is assigned to a speci8c class according to the characteristic features selected for it. In this study, there were two classes: normal or stenosis. Classi8cation results of the MLPNN were displayed by a confusion matrix. The confusion matrix showing the classi8cation results of the MLPNN is given below. Confusion matrix Output/desired

Result (normal)

Result (stenosis)

Result (normal) Result (stenosis)

35 1

1 30

According to the confusion matrix, one normal subject was classi8ed incorrectly by the MLPNN as a subject having ophthalmic artery stenosis and one subject having ophthalmic artery stenosis was classi8ed as a normal subject. The test performance of the MLPNN was determined by the computation of the following statistical parameters: Speci8city: number of correct classi8ed normal subjects/number of total normal subjects, Sensitivity: number of correct classi8ed subjects having stenosis/number of total subjects having stenosis, Accuracy: number of correct classi8ed subjects/number of total subjects. The values of these statistical parameters are given in Table 2. The MLPNN classi8ed normal subjects and subjects having stenosis with an accuracy of 97.22% and 96.77%, respectively. The normal subjects and subjects having stenosis were classi8ed with an accuracy of 97.01%. The correct

' N.F. G'uler, E.D. Ubeyl˙ * / Computers in Biology and Medicine 34 (2004) 601 – 613

611

Table 2 The values of statistical parameters Statistical parameters

Values (%)

Speci8city Sensitivity Accuracy

97.22 96.77 97.01

Table 3 The values of performance evaluation parameters during test process Performance

Result (normal)

Result (stenosis)

MSE MAE Minimum absolute error Maximum absolute error r

0.000235 0.015621 0.006587 0.162108 0.986273

0.000358 0.017964 0.007889 0.190215 0.971403

classi8cation rates of the MLPNN presented in the previous study [20] were 90.63% for normal subjects and 88.89% for subjects having ophthalmic artery stenosis. Thus, the accuracy of wavelet-based neural network model presented in this study was found to be higher than the neural network model used in the previous study [20]. The di>erence between the output of the network and the desired response is referred to as the error and can be measured in di>erent ways. In this study, MSE, mean absolute error (MAE), minimum absolute error, maximum absolute error, and correlation coeMcient (r) were used for measuring error of the MLPNN. The sizes of MSE and MAE can be used to determine how well the network output 8ts the desired output, but they may not reCect whether the two sets of data move in the same direction. The correlation coeMcient solves this problem. The correlation coeMcient is limited within the range [ − 1; 1]. When r = 1 there is a perfect positive linear correlation between network output and desired output, which means that they vary by the same amount. When r = −1 there is a perfectly linear negative correlation between network output and desired output, that means they vary in opposite ways. When r = 0 there is no correlation between network output and desired output. Intermediate values describe partial correlations. The values of performance evaluation parameters of the presented MLPNN are given for normal subjects and subjects having ophthalmic artery stenosis in Table 3. The classi8cation results, the values of statistical parameters and performance evaluation parameters indicated that testing of the MLPNN trained with the Levenberg–Marquardt algorithm was successful. 4. Summary ANNs are able to generalize well and are capable of solving nonlinear problems. In addition, they are robust and tolerant of faults and noise, due to their highly parallel nature. ANNs may o>er a

612

' N.F. G'uler, E.D. Ubeyl˙ * / Computers in Biology and Medicine 34 (2004) 601 – 613

potentially superior method of Doppler signal analysis to the spectral analysis techniques. In contrast to the conventional spectral analysis techniques, ANNs not only model the signal, but also make a decision as to the class of signal. Another advantage of ANN analysis over existing techniques of ophthalmic artery waveform analysis is that, after an ANN has trained satisfactorily and the values of the weights and biases have been stored, testing and subsequent implementation is rapid. In this study, a wavelet-based neural network model employing the multilayer perceptron was presented for analysis of ophthalmic artery Doppler signals. The MLPNN trained with the Levenberg–Marquardt algorithm was used to detect stenosis in ophthalmic arteries. The MLPNN was trained, cross validated, and tested with the computed detail wavelet coeMcients of ophthalmic artery Doppler signals obtained from healthy subjects and subjects having ophthalmic artery stenosis. Performance indicators and statistical measures were used for evaluating the MLPNN. The classi8cation of healthy subjects and subjects having stenosis were done with an accuracy of 97.22% and 96.77%, respectively. Based on the accuracy of the MLPNN detections, it can be concluded that the classi8cation of ophthalmic artery Doppler signals is feasible by a MLPNN trained with the Levenberg–Marquardt algorithm. References [1] D.H. Evans, W.N. McDicken, R. Skidmore, J.P. Woodcock, Doppler Ultrasound: Physics, Instrumentation and Clinical Applications, Wiley, Chichester, 1989. [2] B. Sigel, A brief history of Doppler ultrasound in the diagnosis of peripheral vascular disease, Ultrasound Med. Biol. 24 (1998) 169–176. [3] ˙I. G-uler, F. HardalaQc, E.D. Ubeyli, Determination of Behcet disease with the application of FFT and AR methods, Comput. Biol. Med. 32 (2002) 419–434. [4] H.C. Fledelius, Ultrasound in ophthalmology, Ultrasound Med. Biol. 23 (1997) 365–375. [5] P.J. Vaitkus, R.S.C. Cobbold, K.W. Johnston, A comparative study and assessment of Doppler ultrasound spectral estimation techniques part II: methods and results, Ultrasound Med. Biol. 14 (1988) 673–688. [6] I.A. Wright, N.A.J. Gough, F. Rakebrandt, M. Wahab, J.P. Woodcock, Neural network analysis of Doppler ultrasound blood Cow signals: a pilot study, Ultrasound Med. Biol. 23 (1997) 683–690. [7] I.A. Wright, N.A.J. Gough, Arti8cial neural network analysis of common femoral artery Doppler shift signals: classi8cation of proximal disease, Ultrasound Med. Biol. 24 (1999) 735–743. [8] M. Akay, Y.M. Akay, W. Welkowitz, Automated noninvasive detection of coronary artery disease using wavelet-based neural networks, IEEE Proceedings of the 16th Annual International Conference on Engineering Advances: New Opportunities for Biomedical Engineers, Vol. 1, Baltimore, USA, 1994, pp. A12–A13. [9] S. Haykin, Neural Networks: A Comprehensive Foundation, Macmillan, New York, 1994. [10] I.A. Basheer, M. Hajmeer, Arti8cial neural networks: fundamentals, computing, design, and application, J. Microbiol. Meth. 43 (2000) 3–31. [11] A.S. Miller, B.H. Blott, T.K. Hames, Review of neural network applications in medical imaging and signal processing, Med. Biol. Eng. Comput. 30 (1992) 449–464. [12] W.G. Baxt, Use of an arti8cial neural network for data analysis in clinical decision making: the diagnosis of acute coronary occlusion, Neural Comput. 2 (1990) 480–489. [13] B.B. Chaudhuri, U. Bhattacharya, EMcient training and improved performance of multilayer perceptron in pattern classi8cation, Neurocomputing 34 (2000) 11–27. [14] M.T. Hagan, M.B. Menhaj, Training feedforward networks with the Marquardt algorithm, IEEE Trans. Neural Networks 5 (6) (1994) 989–993. [15] R. Battiti, First- and second-order methods for learning: between steepest descent and Newton’s method, Neural Comput. 4 (1992) 141–166. [16] N. Baykal, J.A. Reggia, N. Yalabik, A. Erkmen, M.S. Beksac, Feature discovery and classi8cation of Doppler umbilical artery blood Cow velocity waveforms, Comput. Biol. Med. 26 (1996) 451–462.

' N.F. G'uler, E.D. Ubeyl˙ * / Computers in Biology and Medicine 34 (2004) 601 – 613

613

[17] M.S. Beksac, F. BaQsaran, S. Eskiizmirliler, A.M. Erkmen, S. Y-or-ukan, A computerized diagnostic system for the interpretation of umbilical artery blood Cow velocity waveforms, Eur. J. Obstet. Gynecol. Reprod. Biol. 64 (1996) 37–42. [18] J.H. Smith, J. Graham, R.J. Taylor, The application of an arti8cial neural network to Doppler ultrasound waveforms for the classi8cation of arterial disease, Int. J. Clin. Monitor. Comput. 13 (1996) 85–91. ˙I. G-uler, Neural network analysis of internal carotid arterial Doppler signals: predictions of stenosis [19] E.D. Ubeyli, and occlusion, Expert Syst. Appl. 25 (2003) 1–13. [20] ˙I. G-uler, E.D. Ubeyli, Detection of ophthalmic artery stenosis by least-mean squares backpropagation neural network, Comput. Biol. Med. 33 (2003) 333–343. [21] J-M. Girault, D. Kouame, A. Ouahabi, F. Patat, Micro-emboli detection: an ultrasound Doppler signal processing viewpoint, IEEE Trans. Biomed. Eng. 47 (2000) 1431–1439. [22] Y. Zhang, Y. Wang, W. Wang, B. Liu, Doppler ultrasound signal denoising based on wavelet frames, IEEE Trans. Ultrason. Ferroelectr. Frequency Control 48 (2001) 709–716. Nihal Fatma Guler graduated from Erciyes University in 1981. She took her M.S. degree from Middle East Technical University in 1985, and her Ph.D. degree from Erciyes University in 1990, all in Electronic Engineering. She is a professor at the Department of Electronics and Computer Education at Gazi University. Her interest areas include biomedical systems, biomedical signal processing, biomedical instrumentation, electronic circuit design, neural network, and arti8cial intelligence. Elif Derya Ubeyl˙% graduated from CQukurova University in 1996. She took her M.S. degree in 1998, in electronic engineering. She is a research assistant at the Department of Electronics and Computer Education at Gazi University. Her interest area is biomedical signal processing, neural network, and arti8cial intelligence.