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Fundação para a Ciência e a Tecnologia (FCT)

This paper presents a new sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point for Cohen-Grossberg neural networks with multiple time delays. The results establish a relationship between the network parameters of the neural system independently of the delay parameters. The results are also compared with the previously reported results in the literature.

ÖZET Bu tezin amacı kardiyolojik hastalıkların teşhis edilmesinde kullanılan ultrasonik görüntüleme yöntemlerini incelemektir. Bu nedenler önce ultrasonik dalgaların dokulardaki yayınım özellikleri incelenmiş ve dalga denklemi elde edilerek özel bir çözümü bulunmuştur. Bu çözümden hareketle dalganın dokulardaki yayınım özellikleri hakkında bilgi veren ve elektronik sistemlerde görüntü oluşturmada en çok kullanılan yansıma, zayıflama ve karakteristik empedans büyüklükleri incelenmiştir. ikinci olarak hareketli hedeflerin özellikle mitral kapakçık ve aort kapakçığının ekokardiyogramlarının elde edilmesinde sıkça kullanılan bir M-modu görüntüleme sistemi gerçekleştirilmiştir. Gerçekleştirilen bu M-modu görüntüleme sistemi» kurulan bir simülasyon sistemi üzerinde başarılar sonuçlar vermiştir. Son olarak bir M-modu görüntüleme sistemi ile kalp sistemine ait hangi hastalıkların teşhis edilebildiği ayrıntılı bir şekilde incelenmiştir. SUMMARY ECHOCARDIOGRAPHY Echocardiography is a diagnostic technique that utilizes ultrasound (high-frequency sound waves above the audible limit of 30 kHz) to produce an image of the beating heart in real time. A piezoelectric crystal is used to emit short bursts of high frequency, low intensity sound through the chest wall to the heart and then dedect reflections of this sound as it returns from the heart. Since movement patterns of several regions of the heart correlate with cardiac function and since changes in these patterns consistently appear in several types of cardiac disease» echocardiography has become a frequently used method for evaluation of the heart. Echocardiography has several advantages over other diagnostic tests of cardiac function: 1. It is noninvasived. e., no device must be inserted into any body cavity). 2. It is painless and requires no special preparation of the patient. 3. It is a safe prodecure and has no known harmfull effects. 4. The equipment is relatively mobile and may be transported to the bedside if necessary. 5. It may repeated as frequently as necessary allowing serial evaluation of a given disease process. 6. It produces an image instantaneously, which allows rapid diagnosis in emergent situations. VIPrior to discussing the mechanism of image production some common terms that govern the behaviour of ultrasound in soft tissue should be defined. Since ultrasound is propagated in waves» its behaviour in a medium is defined by fX=c, where f is the wave frequency, X. is the wavelength, and c is the acoustic velocity of ultrasound in the medium. The acoustic velocity for most tissues is similar and remains constant, for a given tissue. Frequency and wavelength are thus inversely related. As frequency is increased, wavelength will decrease, and as wavelength decreases the minimum distance between two structures also decreases. This is called the resolution of the instrument. As the frequency the ultrasound is increased, the penetration of the ultrasound signal into the body decreases. The optimal image for a given patient will be produced using a frequency that gives the highest possible resolution and adequate amount of penetration into the body. The term ultrasonic attenuation formally defines the more qualitative concept of tissue penetration. It is a complex parameter that is different for every tissue type and is defined as the rate of decrease in wave amplitude per distance at a given frequency. Acoustic impedance is the product of acoustic velocity and tissue density; thus this property is tissue specific but frequency independent. ' This property is important because it determines how much ultrasound will be reflected at an interface between two different types of tissue. When a short burst of ultrasound is directed at the heart, portions of this energy are reflected back to the receiver. It is these reflected waves that produce an image of the heart. VIIThere are two types of reflected waves: specular reflections and scattered reflections. Specular reflections occur at the interface between two types of tissue. The greater the difference in acoustic impedance between two tissues» the greater the amount of enegy that will be transmitted deeper into the heart. Scattered echoes are much weaker in energy. They are produced by small more weakly reflective objects. The transducer, which is placed on the skin and directed at the heart, is a piesoelectrik device. When subjected to an alternating electrical current, the serâmic crystal expands and contracts producing compressions and rarefactions in its environment, which become sound waves. In a typical imaging system a transducer may produce ultrasonic waves with a frequency range of 2-10 MHz. The waves are emitted as brief pulses lasting 1 /js every 100 jjs. During the remaining 99 /js the transducer is a receiver that dedects reflections from the heart. The same crystal, when excited by a reflected sound wave, will produce an electrical signal and send it back to the echocardiography for display. After the echoes are received they must be displayed in a usable format to give the maximal amount information. The original devices used an A-mode format that displayed depth on the x axis and amplitude of the signal on the y axis. In the B-mode the amplitudes of the returning echoes are displayed as dots of varying intensity. If the background white (zero intensity), then progressively stronger echoes will be displayed as progressively darker shades of gray with black represeting the highest intensity. VIIITo image the heart, the M-mode format (M for motion) was devised. In this format the returning echoes are displayed in an identical fashion to B-mode, but instead of constant spatial motion of the transducer baseline on the x axis, a displayer constantly records the B-mode signal and time becomes the parameter displayed on the x axis. The most recent advance in cardiac ultrasound is the application of the Doppler effect to allow analysis of blood flow within the heart and great vessels. The Doppler effect describes the cahange in frequency and wavelength that occurs with relative motion between the source of the waves and the receiver. The Doppler principle is applied to cardiac ultrasound in way: A beam of ultrasound is transmitted into the heart. The reflected impulses are then dedected by a receiver. If the target is moving, the frequency of the reflected echoes will be changed. The difference between the frequency of the transmitted and received echoes is called Doppler shift. It is related to the velocity of the target. In chapter 1 the advantages of echocardiographic imaging are given. In chapter 2 the wave equation is derived- describing the propagation of the important compressional waves through a supporting medium. Solutions to this differantional equation are presented and are examined for wave behavior, including a discussion interaction of phase velocity, wavelength, and frequency. This chapter also examines reflections of acoustic waves at boundaries, and equations are derived to predict the amount of the reflected and transmitted power at any IXgiven tissue interface. In adition to these ultrasonic attenuation in tissue is examined in this chapter. Chapter 3 describes the Doppler principle. Chapter 4 deals with the pulse-echo methods and the design of the practical bioinstrument. This chapter discuses the various imaging modes. These modes are A-mode, B-mode, and M-mode. An electronic circuit is designed for M-mode imaging in this chapter. In last chapter some hemodynamics inf ormations are given. 72