Plant Systems

One of the earliest reports of non-thermal effects produced by ultrasound comes from Harvey (1930) who reported cell wall disruption, twisting and tearing of organelles from cell walls, and cytoplasmic movement in Spirogyra, Nitella and Elodea. These effects were diminished if the gas tension in the plants was reduced prior to irradiation. Although no gas bubbles were obvious to the observer, it would appear that the effects seen were due to acoustic cavitation and streaming. Miller (1977) has...

The Equation Of Motion

As in any dynamical problem, a first line of approach is to specify the forces acting on the system in the present case, it is assumed that it is the (scalar) pressure, only, that maintains the motion. The force acting on any element of the continuous medium then depends on the pressure gradient, and Newton's second law may be written as (Beranek 1986) The unexpected notation for the time derivative (D Dt) is introduced because Newton's law, as stated, applies only to a particular particle,...

[bs bs bs0bs0 k

Where k is the concentration of the solute, and parameters related to the solvent are denoted by a subscript '0'. The relationship between these relative increments can be obtained by differentiating the well-known equation Figures 7.3a and 7.3b, taken from the review paper by Sarvazyan 1991, are plots showing measured values of p , bs and B A for various classes of molecules in biological tissues (data for four or more particular species per class) Figure 7.3a represents ' p - bs space' and...

Temperature Dependence

The parabolic shapes of the curves of speed vs. temperature for water and dilute aqueous solutions, discussed in Section 4.3.5, are shown in Figure 5.2. Figure 5.5 demonstrates the main features of the temperature dependence of sound speed in soft tissues. It is seen that fat tissue is distinguished not only in having a low sound speed but also in having a negative temperature coefficient (dc dT), whereas dc dT is positive for all of the non-fatty tissues that have been measured. This gives...

Acoustic Streaming

Acoustic streaming is the unidirectional circulation that may be set up by an acoustic field in a fluid. This results from a transfer of momentum to the liquid as it absorbs energy from the acoustic field. The velocity gradients associated with this fluid motion may be quite high, especially in the vicinity of boundaries within the field, and the shear stresses set up may be sufficient to cause changes and or damage. If the instantaneous pressure, density and velocity at a point in a...

Gailrter Haar

Institute of Cancer Research, Royal Marsden Hospital, UK As we have seen from Chapter 12 (and cf. Harvey & Loomis 1928) it has been known for some time that ultrasound interacts with tissue to produce biological change. Although there has been natural concern about possible hazard associated with diagnostic ultrasonic imaging, most of the early effort was put into using ultrasonically induced changes in tissue for therapeutic benefit. There is an extensive literature covering the subject of...

Radial Dependencies

The variation of particle pressure amplitude, normalised to the on-axis value, in the focal plane is given by where Jy is a Bessel function and Z KR where R r A (the normalised radial coordinate). From this it follows, for example, that the commonly used measure of the 'width' of the beam in the focal plane, defined as the distance between the first off-axis intensity minima, is given by Also, since from Chapter 1 intensity is proportional to the vector product of particle velocity and...

Calorimetry

Perhaps the most widely used approach to assessing the energy associated with various physical phenomena is to arrange for complete conversion of such energy to heat, and thus measurable temperature rise. So far as beams of ultrasonic energy are concerned, there are here, as with radiation force measurements, broadly two types of approach which may be adopted (a) to measure the total power associated with a beam, as defined by a particular aperture, and (b) to measure a local value of intensity...

Noise In Echography

At this point we need to take a look at the way that one of the particular characteristics of ultrasound images, their noise spectrum, is handled by human visual perception. As has already been pointed out, ultrasound, unlike the other phenomena used in mainstream medical imaging, is a coherent form of radiation and this has a profound effect on the nature and magnitude of the associated image noise that effectively limits contrast discrimination. As already outlined in Chapter 6 (Section 6.5),...

Reflection From A Planar Interface At Oblique Incidence

Reflection from an interface oriented orthogonally to the incident pulse is likely to occur only under special circumstances in medical pulse-echo investigations, and it is of some value to Figure 1.9. Definition of parameters used in calculating reflection from a planar interface, at oblique incidence Figure 1.9. Definition of parameters used in calculating reflection from a planar interface, at oblique incidence examine the case of oblique incidence. The problem cannot be tackled...

References

Tissue as a Voigt body for propagation of ultrasound. Ultrasonic Imaging 1, 136-143. Ahuja, A.S. and Hendee, W.R. (1978). Effects of particle shape and orientation on propagation of sound in suspensions. J. Acoust. Soc. Am. 63, 1074-1080. Akiyama, I., Nishida, Y., Nakajima, M. and Yuta, S. (1983). On the measurement of frequency dependent attenuation in biological tissue using broadband pulsed ultrasound. IEEE Ultrasonics Symposium Proc. 2, Cat. No. 83CH1947-1, 80-805....

Sonoluminescence

The phenomenon of sonoluminescence is the emission of light from media irradiated with ultrasound, and is generally thought to be an indicator of inertial (transient) cavitation activity, although the mechanism of light generation is still not fully understood. Fogging of photographic plates as a result of ultrasonic irradiation was first described by Marinesco and Trillat in 1933, and the phenomenon was first attributed to ultrasonically induced light emission (sonoluminescence) by Frenzel and...

Distributed Scatterers Morerealistic

The above description deals with the simplified situation of a single scatterer. In real situations the signals will be scattered from multiple targets, with a variety of velocities. In these circumstances it is no longer practical to think of the returning signal as simply shifted by a single Doppler frequency. Instead, the returned signal will contain a spectrum of frequencies. This range of frequencies, or spectral broadening, is induced by a number of processes (Figure 10.5). These include...

Acoustic Wave 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 to be more appropriate than the pressure, in particular applications. Of course, relationships...

N

If the scatterers are arranged in a three-dimensional lattice, then Figure 6.4. Polar plots of the differential scattering cross-section for a sphere, using the Born approximation, for three different values of ka. Note that for ka 10.0a log scale is used l, m, n are integers, a, b, c are repeat vectors.

The Directivity Spectrum Approach

The directivity spectrum (Healey et al. 1997) is essentially a generalisation of the angular spectrum, and is the basis of a field description and prediction method that handles transient fields with ease, and is not encumbered by evanescent waves. In this case, the starting point is the observation that a general solution of the canonical lossless wave equation may be written The formal proof of equation (1.86) is non-trivial, but it may be directly verified by substitution into the wave...

Info

Planesource Radiators Images

Stability) over a wide range of spot frequencies, but it is generally unsuitable for diagnostic or dosimetric applications. The ferroelectric ceramics, such as the lead zirconate-titanates, have relatively high electromechanical coupling coefficients and are appreciably sensitive off resonance, with corresponding potential for at least moderate bandwidth operation. Their high dielectric coefficient implies that even quite small devices can be made without impracticably high values of electrical...

The Phenomenon Of Scattering

Scattering is the fundamental information-coding phenomenon that lies at the heart of investigative ultrasound methods. Systematic interest in the subject dates only from the 1970s (Chivers 1977, 1978 Hill et al. 1978) and a very useful overview of developments in the field in the ensuing 20 years has been given by Shung and Thieme (1993). In this chapter we shall outline a theoretical basis for understanding the phenomenon (building on the foundations laid in Chapter 1), describe the principal...

E02

Typical field from a physiotherapy transducer. (a 1cm diameter disc operating at 1.1MHz) (a) axial plots of peak positive pressure, peak negative pressure and intensity (b) transaxial profile of intensity measured 1 cm from transducer face (c) transaxial profile of intensity measured 2 cm from transducer face (d) two- and three-dimensional transaxial profiles of intensity measured 4cm from transducer face (e) transaxial profile of intensity measured 8 cm from transducer face....

Measurement Of Nonlinearity

There are two main methods for determining the parameter B A. The finite amplitude method, of which there have been various embodiments (Law et al. 1981 Cobb 1983 Cain et al. 1986 Zhang & Dunn 1987), is based on the measurement of the second harmonic generated during propagation of a sinusoidal wave equation (4.46) . Two transducers are used, as in the variable path attenuation measurement (Section 4.4.1.2). The second harmonic pressure, p2(z), as a function of propagation distance, z, is...

Dormec Medicine

Standard Methods for Measuring Performance of Pulse-Echo Ultrasound Imaging Equipment. American Institute of Ultrasound in Medicine, Rockville, MD. AIUM NEMA (1989). Acoustic Output Measurement and Labeling Standard for Diagnostic Equipment. American Institute of Ultrasound in Medicine, Rockville, MD. Anderson, M.E. and Trahey, G.E. (1998). The direct estimation of sound speed using pulse-echo ultrasound. J. Acoust. Soc. Am. 104, 3099-3106. Anglesen, B.A.J. (2000). Ultrasound...

The Nature Of The Transfer Function

The foregoing has provided an outline of the practicalities of launching, steering and echo-detecting the wave packets used in pulse-echo interrogation of tissues, and we can now consider the acoustic physics of the 'interrogation' process in imaging parlance, the nature of the transfer function by which the system interprets an object as a set of image data. An exact description of the situation that we need to model here would entail a three-dimensional, scattering-ensemble object...

Absorption Dispersion Attenuation And Scattering As Related Phenomena

Historically, the subject of the mechanisms of acoustic wave propagation has developed such that the topics of absorption and scattering are usually, as in this book, dealt with separately. Such a distinction between propagation phenomena is, however, in some senses artificial and may become difficult to maintain. As pointed out by O'Donnell et al. (1978, 1981), one grey area lies within a general discussion of acoustic loss mechanisms, particularly in relation to speed dispersion. There is no...

Variation of Cavitation Intensity Threshold with Frequency

Pictures Related Ultrasonics

Hill (1972) has collated data on the behaviour of cavitation as a function of frequency. It can be seen that, in general, as the ultrasonic frequency is increased, a higher intensity is required to produce cavitation (Figure 12.14). Figure 12.14. Frequency dependence of cavitation threshold in air-equilibrated water. Collated data from different sources, quoted by Hill (1972) Figure 12.14. Frequency dependence of cavitation threshold in air-equilibrated water. Collated data from different...

Piezoelectric transducer

Principle of a scanning acoustic microscope (SAM), operating here in simple transmission mode. Transmission-reflection, stereo, dark-field and C-mode are other configurations potentially available Figure 11.3. Principle of a scanning acoustic microscope (SAM), operating here in simple transmission mode. Transmission-reflection, stereo, dark-field and C-mode are other configurations potentially available practical limit to which is imposed by the attenuation coefficient and sound...

Phase Tracking Methods

This class of motion detectors relies on the signal processing technique of cross-correlation to match specific reflections in consecutive pulse echoes. As noted in Section 10.2.1, when using PW techniques the time delay of the reflected signal provides information related to the depth of the scatterer in the medium. If, by comparison of two echo signals, the echoes associated with a particular scatterer or group of scatterers can be matched from one signal to the next, then the time shift...

Radiation Pressure

Equation (1.131) may be rewritten in a form suggestive of a conservation equation for the momentum density, Tu (p + tU2) + ( TU) 0 (1.136) Here, analogous to the interpretation of equation (1.38), the entity p + Tu2 represents a (one-dimensional) momentum density flux vector. Note that its definition incorporates the acoustic pressure, rather than the total pressure this is because it is assumed, as before, that the static pressure in the medium in the absence of the wave is a constant. Thus a...

Viscoelasticity Semisolid Media

Maxwell Element

In Chapter 1, and thus far in the present chapter, the viscous nature of liquids has been emphasised. In the classical case of a perfectly viscous (Newtonian) liquid the applied stress is always proportional to the rate of change in the resulting strain, but is independent of the strain itself, which is not maintained. The correspondingly ideal, perfectly elastic, solid follows Hooke's law in which stress is always proportional to strain and is independent of the rate of strain. All real...

Simple Continuous Wa Ve Motion Detection

Continuous Wave Ultrasound Beam Shape

In the simple case of a single reflector sited in a continuous sinusoidal ultrasound field (Figure 10.1) the measured echo signal will have both an amplitude related to the strength of the reflection and an associated phase-offset given by the frequency and time of flight of the sound wave. If the reflector is stationary, both the amplitude and phase of the returning signal will remain constant relative to the transmitted signal. As soon as the target moves, depending on the direction of the...

General Observations

A valuable compendium of published values for the speed of sound has been provided by Duck (1990). Typical ranges for these values are shown here in Figure 5.3, where data have been chosen from measurements on a variety of tissues of both man and other mammalian species. For comparison, values for a few non-biological media have also been included in the figure. No particular species variation for the speed of sound in a given tissue type has been noted, although the sparseness of the data, and...

Sonochemistry

One indicator of cavitation activity within an irradiated sample is the occurrence of chemical reactions typical of the presence of energy-rich species such as ionised and excited molecules, ions and free radicals. These chemical reactions are thought to be indicative of collapse (inertial or transient) cavitation and are attributed to the electrical and thermal effects discussed in the previous section (Section 12.3.5.3). Although the chemistry is not understood completely, it is generally...

Noninertial Cavitation Threshold

Hsieh and Plesset (1961) have shown that the rate at which gas flows into a bubble during rarefaction, dm dt, is given by where D is the diffusion constant and C1 is the gas concentration in the liquid in the absence of the bubble. This expression ignores surface tension effects. Surface tension may be included if the right-hand side is multiplied by (Neppiras 1980b) Similarly, the rate at which gas diffuses out of the bubble during compression is given by where C0 is the saturation gas...

Thermal And Mechanical Indices

The only country to regulate acoustic output from diagnostic ultrasound scanners is the USA. The 'Standard for real-time display of thermal and mechanical indices on diagnostic ultrasound equipment' (AIUM NEMA 1992), known colloquially as the ODS, has been adopted as a means of satisfying the 'track 3' path of the Food and Drug Administration's 510000 requirement for acoustic outputs. The output indices that have been chosen are the thermal index (TI) and the mechanical index (MI). Mechanical...

Radiation Forces Due to Gas Bubbles

If a bubble exists in an irradiated fluid it will oscillate with the field, thus acting as a secondary source that will interact with the particles around it. An attractive force of the same form as the Figure 12.21. Four acoustic streaming regimes. The bubble is excited by the surface on which it sits. (a) Surface-contaminated bubble low-amplitude oscillations in a liquid of low viscosity. (b) As (a) but with a wider range of amplitudes and viscosities. (c, d) Patterns obtained when surface...

Largetarget Methods

A considerable variety of designs of large-target, total-power measurement devices has been described, mostly using reflecting rather than absorbing targets (to avoid thermal anomalies consequent on heating), and differing principally in their designed sensitivity range and in their method of force measurement. Included here are devices based on standard analytical balances, as illustrated in Figure 3.4a (Hill 1970 Rooney 1973) electromagnetically compensated null-deflection devices (Farmery...

Nonthermal Effects

The non-thermal mechanisms by which ultrasound may act on tissue have been outlined in Chapter 12. As far as consideration of physiological effects is concerned, these mechanisms may be divided into two classes cyclic and non-cyclic. Cyclic effects arise from the periodic nature of the sound pressure field and have been referred to as 'micro-massage' (Summer & Patrick 1964). This oscillatory motion may help in loosening adhesions present in soft tissue injuries. The main non-cyclic effect...

Introduction

No true understanding of medical ultrasound methods is possible without an appreciation of the physics of ultrasound, and, for most applications, that 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...

Published Data On Attenuation And Absorption Coefficients

Excellent discussions of this subject already exist (Carstensen 1979 Dunn et al. 1969 Dunn & O'Brien 1976 Johnston et al. 1979 Wells 1975), and a number of tables of published data on ultrasonic properties of tissues have been compiled, notably those due to Duck (1990), but see also publications by Chivers and Parry (1978), Goldman and Hueter (1956), Goss et al. (1978, 1980). This material will not be reproduced here in detail, although it does form the basis for the whole of this section....

Impedance Change

As bubbles form in an irradiated fluid, the acoustic properties of that fluid are altered. The change in acoustic impedance of the medium reflects the amount of cavitation activity within Figure 12.12. (a) Solutions to the Rayleigh-Plesset equation for bubbles driven at 4.5 MHz for which the ratio of bubble radius to equilibrium radius is presented as a grey scale and is plotted against equilibrium radius and time. (b) Fourier transform of (a) showing the presence of the fundamental, first...

Overview Of Scattering Theory

The theory of scattering by human tissue has been reviewed by Chivers (1977) and Insana and Brown (1993), and a brief account of some of the approaches will be given to put in context some of the detailed theories of later sections. Many of these treatments are included in a comprehensive treatise by Ishimaru (1978), who considers scattering of a number of different forms of radiation. The case when the wavelength used, 1, is much less than the scale of the inhomogeneities, a (where a is some...

Formation Of Cavities

The origin of cavities that grow and become active under the action of an externally applied acoustic field has been the subject of some controversy. A detailed discussion of this complex topic is contained in Leighton (1994). Large bubbles of radius R will rise in a fluid at a velocity, defined by Stokes' viscous drag and the buoyant force, given by where p0 is the liquid density and z is the liquid viscosity. A 10 mm bubble in water, for example, rises at the rate of 0.2mms-1. Smaller...

Displacement Detectors

Particle displacement is another measure of the acoustic field which, under linear plane wave conditions, is simply related to the acoustic pressure, with which it can then be used interchangeably (cf. Section 1.3 and Table 2.2). Correspondingly, it can be used as a means of calibrating a pressure-sensitive hydrophone. An early device to use this approach was the capacitance microphone (Filipczynski 1969), which can be so arranged that an acoustic field is incident normally to one face of an...

Harmonic Pumping

Equation (1.132) is reminiscent of the wave equation with non-linear terms added, but it is no trivial matter to obtain a general solution, as for the linearised case. One approach is adopted whereby the acoustic variables appearing in that equation are expanded as follows t - o e i + e2 2 + (1-141) p ep1 + e2p2 + (1-142) u Wi + e2 u2 + (1 143) In these approximations, the (dimensionless) parameter e < < 1 so that the magnitude of each term in the expansion is approximately a factor e...

Molecular Aspects Of Soft Tissue Mechanics

Deformation Mechanics Soft Tissue

From the point of view of mechanics, soft tissue represents an intermediate case between solids and liquids. Similarly to liquids, soft tissues are commonly characterised as 'incompressible' materials, which means that the ratio between shear and bulk moduli is close to zero, i.e. G K. Typically, shear moduli of soft tissues are in the range of 103-107 Pa, whereas bulk moduli are close to that of water and in the narrow range 2-3 x109 Pa, as indicated in Figure 7.1 (Sarvazyan 1975 Madsen et al....

Hydrophone Calibration By Reciprocity Methods

The theorem of reciprocity in acoustics was originally stated by Rayleigh and has been discussed in detail by McLean (1940) and Foldy and Primakoff (1945, 1947). Its systematic application to the calibration of hydrophones has been described by Ludwig and Brendel (1988) and, for present purposes, it can be stated in the following terms. If a transducer operated as a projector is driven with a current j, the free-field sound pressure amplitude at a point d metres from the acoustic centre of the...

Beam Formation By Transducer Arrays

Hitherto the discussion of this chapter has been based on the formation of beams by transducers having a constant pattern of phase exitation (and or sensitivity) over their surfaces. A considerable increase in flexibility results, however, if it is possible to vary and control the phase relationships over the transducer surface in practice this can be achieved by physically dividing the surface into a number of separate elements and introducing between them relative phase shifts in the...

Hydrophones

The development and characterisation of hydrophones for medical applications have been subjects of interest for some considerable time (Hill 1970 Reid & Sikov 1973) and have now reached the point of formal international agreement on recommended methods (IEC 1987, 1991a, b). The measurement of highly inhomogeneous fields calls, ideally, for a device with linear dimensions much less than an acoustic wavelength in the propagation medium (e.g. 0.1 mm for 15 MHz in water). There are, broadly, two...

A A

Demodulation Ultrasound

Sd(t) r cos(2ot + dot + j) + cos(dot + j) Low-pass filtering to remove the higher (2o) frequency components gives Figure 10.6. Simple coherent demodulation. The reflected signal is multiplied by a reference signal with the frequency of the originally transmitted signal, to produce a signal beating at the Doppler frequency. Low-pass filtering then yields the pure Doppler signal Figure 10.6. Simple coherent demodulation. The reflected signal is multiplied by a reference signal with the frequency...

Noncavitational Sources Of Shear Stress

In an attempt to study the effects of acoustic streaming and associated shear stresses and velocity gradients, such as those set up around stable, oscillating bubbles, several different applicators designed to produce extremely localised vibrations have been devised. A commonly used applicator for this type of work has been the oscillating wire. Several authors have described the use of a fine wire, tapering to 5-20 mm at the tip and driven longitudinally at frequencies around 25 kHz, to study...

M

O o a o o o co cd 00 o 00 co Figure 12.24. a Cumulative number of events appearance of bubbles in guinea pig leg plotted as a function of time for different intensities in two different animals. See text for details. Source Adapted from ter Haar and Daniels 1981 . b Variation of number of events with applied pressure. It can be seen that the appearance of bubbles is reduced when the ambient pressure is increased. Source Adapted from ter Haar and Daniels 1982 . c Number of events plotted against...

The Canonical Inhomogeneous Wave Equation Of Linear Acoustics

Numerous texts consider the derivation of an acoustic wave equation, but the standard, if slightly ageing, reference is still the book by Morse and Ingard 1968 . In order to arrive at a tractable equation which governs the propagation of a pressure wave inside a medium as complicated as soft tissue, some simplifications will clearly have to be made. Foremost among these is the specification of the physical nature of the medium itself. One of the simplest, but nonetheless realistic, starting...