Application of FFT analyzed cardiac Doppler signals to fuzzy algorithm

Computers in Biology and Medicine 32 (2002) 435–444www.elsevier.com/locate/compbiomed

Application of FFT analyzed cardiac Doppler signalsto fuzzy algorithm

Inan G+uler ∗, F-rat Hardala/c, Necaattin Bar-/s/c-

Department of Electronics and Computer Education, Faculty of Technical Education, Gazi University,06500 Teknikokullar, Ankara, Turkey

Received 30 July 2001; accepted 2 February 2002

Abstract

Doppler signals, recorded from the output of tricuspid, mitral, and aorta valves of 60 patients, were trans-ferred to a personal computer via 16-bit sound card. The fast Fourier transform (FFT) method was applied tothe recorded signal from each patient. Since FFT method inherently cannot o8er a good spectral resolution athighly turbulent blood 9ows, it sometimes leads to wrong interpretation of cardiac Doppler signals. In orderto avoid this problem, :rstly six known diseased heart signals such as hypertension, mitral stenosis, mitralfailure, tricuspid stenosis, aorta stenosis, aorta insu=ciency were introduced to fuzzy algorithm. Then, theunknown heart diseases from 15 patients were applied to the same fuzzy algorithm in order to detect thekinds of diseases. It is observed that the fuzzy algorithm gives true results for detecting the kind of diseases.? 2002 Elsevier Science Ltd. All rights reserved.

Keywords: FFT method; Fuzzy logic; Cardiac Doppler; Heart diseases

1. Introduction

Ultrasonic Doppler blood 9ow measurement systems are widely used and are highly successfulnon-invasive techniques to detect heart diseases. In addition to estimates of stroke volume, the peakvelocity and maximum acceleration of aortic blood may yield additional information on the inotropicstate of myocardium. Continuous wave Doppler devices are most commonly used to provide velocity,not blood 9ow. With a pulsed Doppler system, the measurement of both arterial diameter and 9owvelocity are possible [1].

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

0010-4825/02/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved.PII: S 0010-4825(02)00021-5

436 I. G(uler et al. / Computers in Biology and Medicine 32 (2002) 435–444

Ultrasonic Doppler system is based on the frequency change (fd) of an emitted ultrasonic waveafter its backscattering by moving structures. The frequency change is a function of the emissionfrequency (f0), the velocity of moving structure (v) and the angle (�) between the ultrasonic beamand the direction of blood 9ow:

fd = 2f0vCos �=c; (1)

where c is the mean propagation velocity of ultrasound within tissues.Doppler signals obtained from heart valves have been analyzed by using di8erent spectral analysis

methods such as FFT, autoregressive, moving average, autoregressive-moving average and waveletmethods [2–5]. The output of a spectral analyzer is usually represented as a sonogram which illus-trates the time variation of the spectral characteristics of the Doppler signal. A number of parametersrelated to the blood 9ow may be extracted from the sonogram and these are of high clinical value.Although the spectral analysis methods have been applied to heart valves by the authors, thesespectral analyzed signals have not been applied to the fuzzy algorithm so far [2–4].

In this work, we applied FFT spectral analysis to the heart valves of 60 patients for obtainingspectral curves. When these curves were examined by the experts, there were some misleading fac-tors in the case of diagnosis. This is because the FFT method is insu=cient at highly turbulent9ows having data record length of more than 10 ms. In addition, FFT method su8ers from dis-tortions caused by sidelobe leakage e8ects. To overcome these problems, the cardiac data of 60patients having di8erent abnormalities are introduced to fuzzy algorithm in order to diagnose thekinds of heart diseases. After this introduction, cardiac data of 15 patients are investigated in thededicated fuzzy algorithm for testing purposes. The results show that the assessments of fuzzy algo-rithm of cardiac Doppler signals provided good results in terms of the diagnosis of kinds of cardiacdiseases.

2. Materials and methods

The measurement system consists of :ve functional blocks as shown in Fig. 1. These are 2.50 and3:75 MHz ultrasound transducers, an analog Doppler unit (Toshiba Sonolayer 140A-Echo equipment),Sony recorder, an analog=digital interface board (Sound Blaster Pro-16 bit), and a personal computer.The analog Doppler unit is capable of operating in both continuous and pulse wave modes. TheDoppler unit is also equipped with an imaging facility that makes it possible to focus the samplevolume to a desired location within the cardiac chambers. In this study, the Doppler unit is operatedin the pulse mode and the sample volume is located at the ventricular side of the valve ori:ce. Themeasurement angle is taken as 60◦.The signal at the output of the analog Doppler unit is recorded by a Sony recorder. The recorded

signal is then sampled and digitized into 16-bit data packets by using an A=D interface board. Thedigital data are then stored on the hard disk of the PC. The interface board o8ers a range of samplingfrequencies. The data stored as a sound :le on the hard disk of the PC are converted to a text :le byusing a simple algorithm implemented in C programming language. Spectral curves are then obtainedfrom this text :le using spectral analysis software developed in MATLAB. Then, FFT coe=cientsfrom the spectral curves are calculated to introduce to fuzzy algorithm.

I. G(uler et al. / Computers in Biology and Medicine 32 (2002) 435–444 437

UltrasonicTransducer Analog

DopplerUnit

SonyRecorder

A/Dinterface

board

PersonalComputer

Fig. 1. Block diagram of measurement system.

The frequency content of the signal will determine the sampling rate to be used, since the max-imum frequency (fm) analyzed is half of the sampling frequency (fs). Since fm is usually notknown a priori and depends upon the vessel on which the measurements are performed, it is usefulto implement the system such that it is capable of operating at various sampling frequencies. In thesystem, sampling frequencies are 2.56, 5.12, 10.24 and 20:48 kHz. These sampling frequencies arerelated to Doppler frequencies from 1.28 to 10:24 kHz, which are expected frequencies for cardiacmeasurements. In this work, measurements were performed at a sampling frequency of 20:48 kHz,so that the frequency aliasing, in the case of stenosis, would be avoided.

The number of signal samples required to form a frame depends heavily on the stationary conditionof the signal. In general, the Doppler signal is non-stationary. The signal may be assumed to bestationary for 10 ms or greater time periods if the 9ow is laminar and the velocity is not very high.However, this assumption is not valid for high velocity turbulence 9ows, such as the 9ow encounteredat the aortic arch, where the Doppler spectrum changes very rapidly. In this case frame length shouldbe shortened to validate the above assumption. On the other hand, very short frame lengths mayyield statistically poor spectral resolution. Therefore, selection of frame length is an important factorin Doppler spectral analysis. The frame length used in this study is 128 or 0:00625 s.

In order to take the FFT of a :nite Doppler signal, it must be framed with the powers of 2, such as64, 128, 256. Windowing technique is used to evaluate the frequency spectrum for the correspondingframe. By using hanning windowing, the appearance of non-existing frequency components in thespectrum is prevented. In addition, zero padding is applied to the same signal after the windowingprocess. This entails overhead on the process although it increases the readability of spectrum [5].

However, the performance of FFT method becomes insu=cient for recording blood 9ow in thestenosis where the speed of blood is high thus causing turbulences. It is also observed that thespectrum becomes wider and frequency resolution decreases in these areas. The long frame lengthalso makes the FFT method insu=cient in turbulent 9ow.

Before fuzzy algorithm, FFT analysis should be applied to Doppler signal in order to obtaincardiac Doppler data from spectral curve. Cardiac Doppler data are grouped into speci:c limits toconstruct fuzzy sets. Then, a rule base is constructed by considering all probable situations.Fuzzy algorithm: Fuzzy logic is a computational paradigm that provides a mathematical tool

for representing and manipulating information in a way that resembles human communication andreasoning processes [6]. A fuzzy variable (also called a linguistic variable; see Fig. 2) is characterizedby its name tag, a set of fuzzy values (also known as linguistic values or labels), and the membershipfunction of these labels; these latter assign a membership value, values �Label(u) to a given real valueu (R, within some prede:ned range (known as the universe of discourse)). While the traditionalde:nitions of Boolean logic operations do not hold, new ones can be de:ned. Three basic operations,and, or, and not are de:ned in fuzzy logic as follows [7,8]:


Fig. 2. Example of a fuzzy variable with two possible fuzzy values.

Fig. 3. Basic structure of a fuzzy inference system.

De�nition 1. �A and B(u) = �A(u) ∧ �B(u) = min{�A(u); �B(u)}.

De�nition 2. �A or B(u) = �A(u) ∨ �B(u) = max{�A(u); �B(u)}.

De�nition 3. �not A(u) =@�A(u) = 1− �A(u).

Here A and B are fuzzy variables. Using such fuzzy operators one can combine fuzzy variables toform fuzzy-logic expressions, in a manner akin to Boolean logic. For example,if room temperature is Low, then increase ventilation fan speed.In Fig. 2, an example of a fuzzy variable with two possible fuzzy values labeled Low and High,

and orthogonal membership functions, plotted above as degree of membership versus input valuesare given. P and d de:ne the start point and the length of membership function edges, respectively.The orthogonality condition means that the sum of all membership functions at any point is one.An example, value u is assigned to the membership values �Low(u) = 0:7 and �High(u) = 0:3 (as canbe seen �Low(u) + �High(u) = 1).

A fuzzy inference system is a rule—based system that uses fuzzy logic, rather than Boolean logic,to reason about data [6]. Its basic structure includes four main components, as depicted in Fig. 3:(1) a fuzzi:er, which translates crisp (real-valued) inputs into fuzzy values; (2) an inference enginethat applies a fuzzy reasoning mechanism to obtain a fuzzy output; (3) a defuzzi:er, which translates


this latter output into a crisp value; and (4) a knowledge base, which contains both an ensembleof fuzzy rules, known as the rule base, and an ensemble of membership functions, known as thedatabase.

The decision-making process is performed by the inference engine using the rules contained inthe rule base. These fuzzy rules de:ne the connection between input and output fuzzy variables. Afuzzy rule has the form:

If antecedent then consequent;

where antecedent is a fuzzy-logic expression composed of one or more simple fuzzy expressionsconnected by fuzzy operators, and consequent is an expression that assigns fuzzy values to theoutput variables. The inference engine evaluates all the rules in the rule base and combines theweighted consequents of all relevant rules into a single fuzzy set using the aggregation operation.This operation is the analog in fuzzy logic of the average operator in arithmetic [7,9,10] (Aggregationis performed usually with the max operator).Fuzzy system parametersThe fuzzy rules used in this work are as follows:

Rule i: If Systole is Sj and Diastole is Dk then Class Cm;

where i=1; 2; : : : ; N rule number, j=1; 2; : : : ; P systole membership function number, k =1; 2; : : : ; Sdiastole membership function number, m= 1; 2; : : : ; T diagnosis class number. As given in Table 1,if the systole of the patient is 170 cm=s, then membership order of S1 set is 1. On the other hand,if the diastole of the patient is 70 cm=s, then membership order of D1 set is 1.

Some explanations which are considered in this work as follows:

• Fuzzy operators: min and max.• Input and output membership functions type: orthogonal, trapezoidal.• Defuzzi:cation method: weighted average.• Number of input membership functions: two input variables are used. First is systole that has

seven membership functions, denoted S1; S2; S3; S4; S5; S6 and S7, the other diastole has sevenmembership functions, denoted D1; D2; D3; D4; D5; D6 and D7.

• Number of output membership functions: This is the slope that of the seven membership functions,denoted C1; C2; C3; C4; C5; C6 and C7.

3. Results and discussions

Fig. 4 shows the spectral curves of seven di8erent diseases which have been diagnosed by cardiacexperts. All spectral curves have been constructed from cardiac Doppler signals using FFT method.These results are obtained by taking 120 000 samples. Each spectral curve is constructed o8-line in6 s. Sixty patients in this work are categorized as follows: 10 of healthy subjects, 15 of hypertension,8 of tricuspid insu=ciency, 5 of aorta stenosis, 5 of mitral insu=ciency, 10 of mitral stenosis and7 of aorta insu=ciency.

When the spectral curves are examined in Fig. 4, it is seen that the :rst peak (systole) occurswhen just the mitral valve opens by forcing the pressure of left atrium. Since the blood 9ows from


Fig. 4. Spectral curve of patients.


Velocity of blood flow (v)

(a)

Velocity of blood flow (v)

(b)

(c)

S 1 S 2 S 3 S 4 S 5 S 6 S 7

cm /s165 170 171 175 176 180 181 185 186 190 191 195 196 200

µ s

D 1 D 2 D 3 D 4 D 5 D 6 D 7

cm /s65 72 73 79 80 86 87 93 94 100 101 107 108 115

µ d

C 1 C 2 C 3 C 4 C 5 C 6 C 7

slope

µ c

0.3

4

0.3

5

0.3

6

0.3

8

0.3

9

0.4

0

0.4

1

0.4

2

0.4

3

0.4

5

0.4

6

0.5

9

0.6

0

0.6

5

Fig. 5. Membership functions (a) systole, (b) diastole, (c) slope (output).

left atrium to left ventricule, the pressure of left atrium decreases so that the blood velocity decreases.This causes a decrease in the amplitude of the spectral curve. This point is a valley between twopeaks. After all these events, the M-shaped spectral curve is obtained as shown in Fig. 4a. Whenthe slope between systole and diastole is small on the envelope of spectral curve of patients, thismeans a degeneration on the envelope of the M-shaped spectral curve as shown in Fig. 4b–g.

Fig. 5a shows the velocity of blood at systole in the range of 165–200 cm=s. Fig. 5b showsvelocity of blood at diastole in the range of 65–115 cm=s. In this work, the slope is calculated asslope = (systole − diastole)=time [11]. The slope values in Fig. 5c are grouped and fuzzi:ed in therange of 0.34–0.65. This grouping is achieved by membership functions. The rule base is formedby considering all probable conditions of the grouping as shown in Table 1.

In Table 1, C1 represents hypertension, C2 represents tricuspid insu=ciency, C3 represents aortastenosis, C4 represents mitral insu=ciency, C5 represents mitral stenosis, C6 represents aorta in-su=ciency, and C7 represents normal subject. Process state variables (inputs) are represented asS1; S2; : : : ; S7 systole; D1; D2; : : : ; D7 diastole in seven sets. In order to test the system, FFT an-alyzed cardiac Doppler signal taken from 15 patients are classi:ed statistically as shown inTable 2.


Table 1Rule base

D \ S S1 S2 S3 S4 S5 S6 S7

D1 C4 C3 C2 C2 C2 C1 C1D2 C5 C5 C4 C3 C3 C3 C2D3 C6 C6 C6 C5 C5 C5 C4D4 C6 C6 C6 C6 C6 C6 C5D5 C6 C6 C6 C6 C6 C6 C6D6 C7 C7 C6 C6 C6 C6 C6D7 C7 C7 C7 C7 C6 C6 C6

Table 2Value of test data

Patient no. Measurement location Systole (cm=s) Diastole (cm=s) SD

1 Mitral valve 195 68 312 Aorta 181 73 303 Mitral valve 192 82 284 Tricuspid valve 186 65 345 Mitral valve 193 112 276 Mitral valve 195 114 267 Mitral valve 192 64 288 Mitral valve 195 75 379 Mitral valve 188 80 2810 Mitral valve 192 110 3111 Tricuspid valve 188 67 3512 Mitral valve 190 82 3013 Mitral valve 195 116 2714 Mitral valve 197 79 3515 Mitral valve 197 115 28

Since there are two input variables (systole and diastole) which have seven sets, 7× 7= 49 rulesare de:ned as follows:

Rule 1. If Systole is S1 and Diastole is D1 then Class C4 = mitral insu=ciency,Rule 2. If Systole is S1 and Diastole is D2 then Class C5 = mitral stenosis,Rule 3. If Systole is S1 and Diastole is D3 then Class C6 = aorta insu=ciency,Rule 7. If Systole is S1 and Diastole is D7 then Class C7 = healthy,Rule 22. If Systole is S4 and Diastole is D1 then Class C2 = tricuspid insu=ciency,Rule 30. If Systole is S5 and Diastole is D2 then Class C3 = aorta stenosis,Rule 43. If Systole is S7 and Diastole is D1 then Class C1 = hypertension.

All these rules are given in Table 1. For example, if the systole of the patient is 170 cm=s, thenthe membership order of S1 set is 1. On the other hand, if the diastole of the patient is 70 cm=s,then the membership order of D1 set is 1. According to these inputs, Rule 1 is activated and thepatient belonging to C4 set has mitral insu=ciency.


Table 3Classi:cation rates

Name of data Correct classi:cation number Correct classi:cation rate (%)

Training data (60 part) 59 98.33Test data (15 part) 15 100

The values in Table 2 are evaluated in the fuzzy algorithm, for example, 1st patient (patient no.1) has 195 cm=s blood velocity in systole belonging to S6 set and 68 cm=s blood velocity in diastolebelonging to D1 set. These results emphasize that C1 set in rule base is the active output, whichrepresents hypertension. Similarly, all the other data are tested. The test results of 15 patients show5 of normal subject (C7), 2 of tricuspid insu=ciency (C2), 3 of mitral stenosis (C5), 2 of mitralinsu=ciency (C4), one of aorta stenosis (C3), 2 of hypertension (C1).

In this work, 60 data are used for training, and 15 data are used for test purposes. When theclassi:cation results are compared with the expert results, 1 false classi:cation in 60 data is obtained.On the other hand, the 15 test data are completely classi:ed as true. The results are given in Table 3.

4. Conclusion

FFT analyzed cardiac Doppler signals of 60 patients were introduced to fuzzy algorithm. Then,15 patients, cardiac Doppler signals were compared with the data of 60 patients in fuzzy algorithmso that the probable errors of FFT were removed. The results show that the fuzzy algorithm in thediagnosis of di8erent Doppler signals o8ers good results.

References

[1] D.H. Evans, W.N. McDicken, R. Skidmore, Woodcock, Doppler Ultrasound: Physics, Instrumentation and ClinicalApplication, Wiley, Chicester, 1989.

[2] I. G+uler, F. Hardala/c, S. M+uld+ur, Determination of aorta failure with the application of FFT, AR and wavelet methodsto Doppler technique, Comput. Biol. Med. 31 (2001) 229–238.

[3] I. G+uler, S. Kara, N.F. G+uler, M.K. Kiymik, Application of AR and FFT spectral analysis to tricuspid and mitralvalve stenosis, Comput. Methods Programs Biomed. 49 (1996) 29–36.

[4] I. G+uler, S. Kara, Detection of mitral stenosis by pulsed Doppler 9owmeter and autoregressive spectral analysis, FirstRegional Conference on IEEE Engineering, Medical and Biological Society and Biomedical Engineering Society,India, 2.91–2.92, India.

[5] S.M. Kay, S.L. Marple, Spectrum analysis—a modern perspective, Proc. IEEE 69 (1981) 1380–1419.[6] R.R. Yager, L.A. Zadeh, Fuzzy Sets, Neural Networks, and Soft Computing, Van Nostrand Reinhold, New York,

1994.[7] C.A. Pena-Reyes, M. Sipper, A fuzzy-genetic approach to breast cancer diagnosis, Artif. Intell. Med. 17 (1999)

131–155.[8] L.A. Zadeh, Fuzzy logic = computing with words, IEEE Trans. Fuzzy Systems 4 (2) (1996) 103–111.[9] D.L. Hudson, M.E. Cohen, Neural Networks and Arti:cial Intelligence for Biomedical Engineering, IEEE Press,

Piscataway, 2000.[10] Y. Hao, L.C., Sheppard, Regulating mean arterial pressure in post-surgical cardiac patients. A fuzzy logic system to

control administration of sodium nitroprusside, IEEE Eng. Med. Biol. Mag. 13 (5) (1994) 671–677.[11] J. Miao, P.J. Benkeser, F.T. Nichols, A computer based statistical pattern recognition for Doppler spectral waveforms

of intracranial blood 9ow, Comput. Biol. Med. 26 (1996) 53–63.


Inan G!uler graduated from Erciyes University in 1981. He took his M.S. degree from Middle East Technical University in 1985, andhis Ph.D. degree from I stanbul Technical University in 1990, all in Electronic Engineering. Between 1988 and 1989 he worked in theDepartment of Medical Physics and Clinical Engineering at Leicester Royal In:rmary, where he studied the experimental part of his Ph.D.He is a professor at Gazi University where he is Head of Department. His interest areas include biomedical systems, biomedical signalprocessing, biomedical instrumentation, and electronic circuit design. He has written more than 70 articles on biomedical engineering.

F#rat Hardala%c graduated from F-rat University in 1987. He took his M.S. and Ph.D. degrees from F-rat University in 1993 and 1997,respectively, all in electronic engineering. Then, he was appointed as an Assistant Professor at Biophysics Department, Faculty of Medicineat F-rat University. His interest areas include biophysics, biomedical systems, and signal processing. He has written numerous articles onrelated areas.

Necaatin Bar#%s%c# graduated from Gazi University in 1994. He took his M.S. degree in 1999, in computer technology. He is a researchassistant at the Department of Electronics and Computer Technology at Gazi University. His interest area is biomedical computing.

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Application of FFT analyzed cardiac Doppler signals to fuzzy algorithm