Physical Principles of Medical Ultrasonics
[...]... necessarily Physical Principles of Medical Ultrasonics, Second Edition Edited by C R Hill, J C Bamber and G R ter Haar & 2004 John Wiley & Sons, Ltd: ISBN 0 471 97002 6 2 PHYSICAL PRINCIPLES OF MEDICAL ULTRASONICS negligible in hard tissues, such as bone, and the treatment below must be seen as ultimately pertaining to soft tissues only, for waves in the medical frequency range The neglect of shear... number of theoretical descriptions of wave scattering The focus of this chapter, however, is to describe some of the solutions of the homogeneous wave equation, equation (1.24), and to investigate them in order to acquire an understanding of the acoustic fields utilised in medical applications of ultrasound Despite the fact that the vast majority of soft tissues are clearly inhomogeneous, the solutions of. .. uses of ultrasound have continued to develop and are now being joined by methods employing strongly focused beams of ultrasound for minimally invasive surgical destruction of deep tissue structures Technologically, much of this development has been empirical; often without benefit of any systematic knowledge of the physics and biophysics underlying the essential phenomena Valuable though much of this... essentially entails a good grasp of the principles of the propagation of ultrasound waves in tissue-like media Many treatments of the subject emphasise continuous waves, but it is the transient (pulsed) wave that is utilised in the vast majority of cases This chapter therefore aims to avoid the simplifying assumption of harmonic waves, except to introduce it as a case of special interest, or where it... be given by s¼ pðr, tÞ %0 C 2 ð1:32Þ 8 PHYSICAL PRINCIPLES OF MEDICAL ULTRASONICS Other wave variables are less conveniently expressed in terms of the pressure For example, equation (1.12) shows that, in general, a first-order differential equation would have to be solved in order to establish the behaviour of the particle velocity field, uðr, tÞ, from the (gradient of the) pressure wave Specifying xðr,... indebted to a number of individuals and publishers for permission to use illustrative material, the sources of which are indicated in the text Kit Hill Jeff Bamber Gail ter Haar 1 Basic AcousticTheory S J LEEMAN Institute of Cancer Research, Royal Marsden Hospital, UK 1.1 INTRODUCTION No true understanding of medical ultrasound methods is possible without an appreciation of the physics of ultrasound, and,... addresses the principles and methods of application of ultrasound to the investigation of human pathology and physiology This is a subject that is commonly referred to as imaging or sonography and, although, as will be seen, its scope is considerably wider than such terms imply, much of it is concerned with the formation of images that are to be presented to a human observer, whose characteristics often turn... VARIABLES The description of the ultrasound field in terms of the pressure is, for most measurement purposes, the most direct and convenient, since pressure is the primary physical variable that is detected by most of the hydrophones and receiving transducers in general use However, the space–time behaviour of a number of other wave variables may be used to describe the field, and one of these may be deemed... special interest, or where it significantly reduces the complexity of the analysis A study of pulse propagation requires the specification of a wave equation, which, in the case of interest here, rests heavily on the ability to specify a model of the (mechanical) behaviour of tissue-like media At present, such a model still eludes the medical ultrasound community, but it will be seen below that some... Coordinate system for calculating the on-axis pressure field of a planar, disk transducer ð1:68Þ 16 PHYSICAL PRINCIPLES OF MEDICAL ULTRASONICS pðz, tÞ ¼ %0 pffiffiffiffiffiffiffiffiffiffi z 2 þR 2 ð T dR.an ðt À R=CÞ ð1:69Þ z The integration is easily affected by noting that an ðt À R=CÞ @ @ nn ðt À R=CÞ ¼ ÀC nn ðt À R=CÞ @t @R where nn denotes the (normal) velocity of the transducer face The on-axis field that results is . oyal Marsden H ospital, Sutton, S urrey , UK Physical Principles of Medical Ultrasonics Physical Principles of Medi cal Ultraso ni cs Second Edition Ed. appreciation of the physics of ultrasound, and, for most applications, that essentially entails a good grasp of the principles of the propagation of ultrasound