Ultrasonic Transducers

Ultrasound is generated by piezoelectric materials which have the property of changing thickness when a voltage is applied across them. Lead zirconate titanate (PZT) is the most widely used. The piezoelectric effect derives from movements of a heavy, charged atom that is loosely bound within a complex crystal; when an electrical field is applied, the atom moves and distorts the crystal. PZT is a ceramic that is cast as a thin plate that may be disc-shaped or more usually is formed into a strip that is then sliced into several hundred tiny elements as an array, with metal electrodes on the two surfaces. It is polarised by heating it above a critical temperature (the Curie point, which is around 200°C) and then allowing it to cool in an electric field, a process similar to that used to polarise a magnet. When electrically pulsed, the crystal rings like a bell at a resonant frequency which is mainly determined by its thickness. Higher-frequency crystals are thinner and thus more difficult to manufacture. The piezoelectric effect is symmetrical, so that the same or a similar crystal is used as the receiver to produce small electrical signals when struck by an ultrasound wave.

The crystal is mounted in a conveniently shaped holder which contains the electrodes and any associated electronics as well as the lenses and matching layers required to improve the beam shape and enable efficient transfer of acoustic energy between the crystal and the patient (see later). The whole assembly is known as the probe or transducer.

The development of single crystal piezoelectric materials is improving the sensitivity and the bandwidth of transducers because the piezo domains are more truly aligned than in a traditional amorphous ceramic material. Manufacture is similar to silicon chip technology, seeding a molten pot of the material in a crucible and slowly cooling it to allow crystallization. The material is then machined to the required shape (usually as a multi-element array).

Propagation in Tissue

Ultrasound travels through tissue as a beam, which, for most clinical applications, is focused to around 1 mm or less in diameter at the focal zone. It propagates as a sequence of compression and rarefaction waves which are transmitted by the elastic forces between adjacent tissue particles. The particles move in the same direction as the wave—thus ultrasound is a longitudinal wave unlike the transverse waves that occur at the surface of water where the particles move up and down as the wave travels horizontally. The frequency of the oscillations is inversely proportional to the wavelength ( f = c/λ, where f is frequency, c is the velocity of ultrasound and λ is the wavelength).

The way in which the ultrasound wave is transmitted varies with the strength of the elastic forces between adjacent particles (which relates to the elasticity of the tissue and thus to the velocity of ultrasound) and with the masses of the particles (which determines density). These two factors determine the acoustic impedance (Z) of the tissue (Z ≅ ρc, where ρ is density and c is the velocity of ultrasound). When the particles are heavy, a given amount of energy is transmitted with small movements of the particles; when they are light, larger excursions occur, though it should be understood that the actual distance a particle is moved at diagnostic ultrasound intensities is less than a nanometre. In clinical practice, since the velocity of ultrasound in tissue is almost constant (at 1540 m s⁻¹), changes in impedance are mainly attributable to differences in density.

The constant speed of ultrasound in soft tissues allows the depth of reflectors to be calculated by measuring the delay in the return of echoes after the ultrasound pulse has been transmitted. This is the essence of the pulse-echo method used in both ultrasound imaging and most forms of Doppler ultrasound. (Note that the position of reflectors across the imaged plane is determined in a quite different manner, by the direction in which the ultrasound beam is transmitted; see below.)

Reflection

The other important mode of ultrasonic interaction with tissue is reflection. Some of the transmitted energy is reflected whenever the beam crosses an interface where the transmission properties change, the proportion depending on the degree of impedance mismatch (change of Z). The phenomenon is similar to that occurring in a rope that is fixed at one end and made to oscillate by shaking the free end up and down: provided the rope is of uniform construction, waves travel along it until they die out or reach the fixed end. But if a part of the rope is thicker or more rigid (or the reverse), then the waves are partly reflected back when they reach this ‘obstruction’. At the fixed end the same effect occurs but to a greater extent, all of the vibrational energy being returned as a full-strength ‘echo’ because this part of the rope cannot move at all.

Thus the intensity of the reflection depends on the degree of change in the rigidity or elasticity of the tissue (and potentially also of velocity, though this varies very little in soft tissues). Ultrasound that is not reflected passes through and is available for imaging deeper tissues. Only a small fraction (2–10%) is reflected at each soft- tissue interface but almost total reflection occurs at tissue–gas interfaces and some two-thirds of the incident ultrasound is reflected at a tissue–bone or tissue–calculus interface so that an acoustic ‘shadow’ is produced deep to these surfaces. They are essentially opaque to ultrasound, which therefore cannot be used to image aerated lung, nor generally where the tissue is covered by bone, for example, the brain.

Two main types of echoes are encountered clinically, depending on the structure of the reflecting surface (Table 3-1). Where this is smooth compared with the ultrasonic wavelength (i.e. the surface is flat over an extent of several millimetres) the reflected wave obeys Snell’s law for light and is reflected at an angle equal to the angle of incidence. By analogy these echoes are sometimes known as specular or mirror-like echoes. In the usual arrangement for ultrasound imaging, where the same transducer is used both for generation and reception of the ultrasound, only those smooth surfaces that lie close to right angles to the sound beam return these echoes. The directed reflection means that the echo is of high intensity: strength and directionality are the cardinal features of these echoes from flat surfaces. They arise from the linings of hollow viscera and blood vessels, from the valves of the heart, from organ capsules and fascial planes, from the skin and from gas and bone surfaces.

TABLE 3-1

Echo-Producing Mechanisms

Specular: mirror-like reflections from flat surfaces	Strong, directional echoes
Scattered: interference patterns from small parenchymal discontinuities	Weak, non-directional echoes

Where the irregularities in the surface are of the same order of size as the ultrasound wavelength itself, i.e. 0.01–1 mm, a different mechanism known as scattering produces echoes; here each small interface (e.g. a lobule of an organ, arterioles, venules, etc.) is vibrated by the mechanical shock it has received from the incident ultrasound pulse. The vibratory energy is re-radiated more-or-less equally in all directions, each discontinuity behaving as an isolated point source of ultrasound. Thus the echoes are isotropic and potentially detectable from any direction. However, because the energy is distributed across the surface of an expanding sphere, the signal received by the transducer from any single vibrating particle is weak and in practice is only detectable when several wavelets from adjacent particles happen to be superimposed and produce an additive effect. Low intensity and detectability from any angle are the cardinal features of these scattered echoes. They arise from soft-tissue parenchyma and thus are usually the more important diagnostically. It is important to note that the texture in the image is an interference pattern and is not a one-to-one representation of the histological reality. This is why tissues of very different structures (e.g. liver and spleen) can produce similar echo textures. Many soft tissue reflectors actually display properties that are intermediate between specular and scattered echoes.

Ultrasound is generally considered to be conducted in a linear manner whereby the waveform of the pulse is preserved with depth. In fact, this is not quite true and non-linear propagation is an important phenomenon in which the sine wave shape of the original pulse emanating from the transducer becomes distorted so that it comes to contain higher-frequency components or harmonics. This occurs because the speed of sound conduction increases with increasing density of the conducting medium (tissue or biological fluids) so that the compression part of the cycle travels slightly faster than the rarefaction part and this distorts the wave much in the way that an ocean wave builds and breaks as it approaches the shore (though the mechanism is not identical). The development of these harmonics depends on the sound intensity: higher acoustic powers produce stronger harmonics and therefore they are weak in the parts of the sound beam away from the central, desired portion. They are also weak for the first few millimetres of tissue depth because they take a few cycles to build up. These facts have been exploited in ultrasound systems that use software to select for the harmonics in the returning echoes by transmitting at, say, 1.5 MHz, and tuning the receiver to 3 MHz to remove the fundamental echoes. In doing so, the beam aberrations from side lobes and from reverberations in the superficial tissue layers are suppressed (see under ‘Resolution’). The tissue harmonic image is cleaner with higher contrast and this has been especially useful in echocardiography and in abdominal imaging (Fig. 3-1).

The direction in which the beam is sent can be determined mechanically or electronically. Mechanical steering systems were used widely but are now restricted to intracavitary techniques (endoscopic and intravascular). They use a simple, single element transducer which is mechanically swept through an arc, typically of 360°, by spinning it on a wheel (Fig. 3-4). The resulting image has a circular shape with the transducer itself at the centre and the tissues arranged around it with the intima closest to the transducer.

Electronic sector systems (also known as phased arrays) have replaced mechanical systems for most applications. Here the beam direction is controlled by building up interference patterns between the waves transmitted from an array of a large number of small transducer elements. The usual arrangement consists of numerous PZT elements (512 in state-of-the-art systems), each 1 mm or less in width and 5–10 mm in length, stacked up to form a strip. Each has separate electrical contacts and the pulses to each element are serially delayed from one end of the array to the other. These minute differences in timing occur within the short time needed to form an individual pulse and they produce interference patterns in which the troughs and peaks of the pressure waves add where they coincide and subtract where they are out of phase (hence the term ‘phased array’) (Fig. 3-5). This results in a beam that is directed to one side. For the next pulse, a slightly different set of delays is applied to adjust the steering. During receipt of the returning echoes the electrical signals from the individual elements are delayed before they are summed in the beam former, exploiting the same summing and cancelling approach; the aggregate signal produced is the electronic equivalent of mechanically angling the transducer face in the required direction. Though the concept is fairly easy to understand, the underlying mathematics is complex and generally requires dedicated hardware; however, software emulations have been developed so that beam forming can be performed in a PC, opening the way to cheaper and more flexible machines. The resulting image has a triangular or sector shape which has the important practical advantage of requiring only a small skin contact area (or footprint), although it provides only a limited display of the superficial tissues.

The operation of electronic linear array transducers is a little simpler. They are longer than phased arrays and the beam is moved across the imaged plane by firing the elements in groups, starting from one end of the array and stepping along to the other (Fig. 3-6). This produces an image with a rectangular shape, best suited for the superficial structures that are of prime interest in small parts imaging (Fig. 3-7). In a simple variant, the linear array is shaped as a curve so that the field of view is almost trapezoidal, as with sector imaging, but with a longer skin line. This compromise is particularly useful when both superficial and deeper structures need to be imaged, for example in obstetrics (Fig. 3-8).

The ultrasound emitted from a point source spreads in a hemisphere but, as the source is enlarged, it forms a beam with near-parallel sides for a few centimetres of depth before the beam diverges again (Fig. 3-9). The changeover is the transition between the near (Fresnel) and far (Fraunhofer) zones. In fact it represents the point beyond which the ultrasound waves from the edge of the transducer arrive less than a wavelength later than those from the transducer centre so that larger aperture transducers have longer near fields. The beam is actually formed by the same interference effects that are exploited to steer the beam in electronic transducers and occur because the compression and rarefaction phases of the ultrasound pulse add in the direction of the beam but cancel elsewhere.

Adding a converging lens (usually a curved layer of plastic bonded to the front of the piezo material), or simply shaping the transducer face into a shallow dish, acts to narrow the beam (Fig. 3-9). This can be thought of as working in the same way as an optical lens, i.e. by beam refraction, but a more useful concept is based on the fact that the lens conducts ultrasound more rapidly than tissue, so that waves emanating from the transducer edge are fractionally ahead of those from the centre as they enter the tissue. Thus interference patterns are set up across the sound field that emphasise the centre region of the ultrasound beam and cancel ultrasound waves that otherwise would spread laterally.

The same effect can be produced with a multi-element array by sending the transmit pulses to the outer elements fractionally ahead of those to more central elements—this is the electronic equivalent of shaping the transducer surface into a dish (Fig. 3-10). Focusing also occurs on receipt of the echoes, in a reciprocal fashion. While electronic focusing is complex, it confers two benefits. First, the focal position can be altered by changing the delays within the transmit pulse so that the probe can be optimised for each clinical situation—with a mechanical probe the focus is fixed and so the entire probe must be exchanged if the focal zone needs to be altered. In addition, with electronic focusing on receipt of the echoes, the focus can be set close to the transducer initially (to optimise resolution of superficial tissues) and then progressively refocused deeper into the body to track the train of echoes returning from deeper interfaces. This dynamic focusing optimises resolution over the entire depth of the image.

Tight focusing of the ultrasound beam has the undesired effect of accentuating its divergence in the far field, so that the beam is only optimal over a short depth (Fig. 3-9D). While such a transducer would be appropriate for structures where only a narrow strip of tissue is of interest, e.g. the retina in the eye, generally a better compromise is to use weak focusing together with as large an aperture as can reasonably be maintained in contact with the skin.

In practice, the ultrasound beam achieved is far from perfect (Fig. 3-11). Not only is the optimum beam width achieved over only a relatively short focal depth but also its profile, a bell-shaped curve across the beam, leads to smearing of signals from strong reflectors since they are detected from some distance off-axis (Fig. 3-12). In addition, the real beam has side lobes which are emitted at steep angles from the main beam so that unwanted echoes may be received from interfaces that lie a long way off-axis. These signals further smear the image, particularly when strong reflectors such as gas bubbles lie in their direction. These limitations also apply across the imaging plane, so that out-of-plane reflectors may also interfere. Minimising the loss of spatial and contrast resolution that results from these deficiencies is a major emphasis of the art and science of transducer design and is an area where marked progress continues to be made (see tissue harmonic imaging, above and Fig. 3-1).