General Engineering Principles in Diagnostic Ultrasound

DURING THE PAST 25 YEARS, there has been an explosive growth in the development of various medical imaging techniques [1], namely, computerized tomography, digital radiography, magnetic resonance imaging, and ultrasound, among others. Ultrasound is particularly suited to situations where exposure to ionizing radiation is undesirable, such as inn obstetrics and neonatal monitoring, and to imaging moving structures such as the heart valves. In this article, general engineering and physical principles that are needed to better understand the past and new developments in ultrasonic imaging are reviewed. The audible range of sound for the human ear is from 20 Hz Figure 1. 'A sinusoidal acoustic wave. to 20 KHz. Ultrasound is a sound wave with frequency higher than 20 KHz. As a wave, it transports energy and can be described in terms of a number of wave parameters. For electromagnetic waves, the parameters are electric field, FUNDAMENTALS OF ACOUSTIC PROPAGATION magnetic field, dielectric constant, etc. For ultrasound, equivIf the disturbance produced by the source is small, acousalent parameters are pressure, density, temperature, particle tical propagation in a liquid medium is a function of time, t, displacement, etc. Unlike electromagnetic waves, sound and distance, z; governed by the following equation [21: requires a medium through which to travel. It cannot propa2W po _2_ gate through a vacuum. To better visualize how sound waves (1) propagate, the medium can be approximated as a three az2 B at2 dimensional structure of spheres, representing atoms or molecules, separated by perfect elastic springs. When a whez-direio,andae, respectively, particle displacement in particle is pushed from its neutral position, the disturbance or the z-direction, density of the medium, and bulk modulus of force is transmitted to the adjacent particles by the springs, the medium. This second-order differential equation is called setting up a chain reaction. When the driving force oscillates the wave equation. Similar equations can also be derived for sinusoidally, the particles respond in the same way. If the other acoustical parameters such as pressure or density. The driving source produces particle displacement parallel to the solution of this equation should have the form of f(z ± ct); propagation direction, the wave is called a compression or the sinusoidal solution is: longitudinal wave; if it produces displacement perpendicular W= W t ± kz) (2) to the propagation direction, the wave is called a shear or W oe transverse wave. Ultrasound waves used in medical applicawwhere co = angular frequency =27rf, k wlxc Is the wave tions are, with very few exceptions, longitudinal. number, and c = (BIpo)1/2* The distance traveled by the particle in the acoustic Equation (2) indicates that two waves exist, one travelling propagation is called particle displacement and usually Is in in the + z direction and one in the z direction. The direction the order of a few microns. Likewise, the velocity of the of the displacement parallels the direction of wave propagaparticle oscillating back and forth is called particle velocity. It tion. Solid media can also support a shear wave, which is not should be noted that this velocity is different from the rate of of major importance in diagnostic ultrasound. energy propagating through the medium, which is defined as The pressure change, Pz' associated with this disturbance the phase velocity or the sound propagation velocity. The is related to the particle or medium velocity, uz = aWh3t, by sound velocity is much greater than the particle velocity, the following equation: Although the particle itself moves but a few microns, its perturbations are transmitted to other particles over a much ,z= + (3) farther distance. Regions of compression and rarefaction are produced when The ratio of pressure to medium velocity is defined as the a sinusoidal sound wave is propagated through a medium. characteristic acoustic impedance of the medium: Particle displacement is largest in the rarefaction region and smallest in the compression region. The displacement of a z=Pz= ±P0C (4) particle, W, versus both distance, z, and time, t, are Z sinusoidal, as shown in Fig. 1. The wavelength (X) is the distance over which one cycle occurs; the period Tis the time The acoustic velocity and impedance for a few common for one cycle to occur. Thus: materials and biological tissues are listed in Table 1. (For a Tc= more comprehensive listing, see references [3] and [4].) The intensity of a wave is defined as the average power where c = sound propagation velocity. Since frequency, f, carried by the wave per unit area normal to the direction of equals 1IT, we have: propagation. For ultrasonic propagation, the intensity, i, is related to the medium velocity and pressure by the following fX = c relationship: