Physical Principles, Ultrasonic Image Formation, and Artifacts

At first glance, two-dimensional (2-D) ultrasound images have much the same appearance as images made by two other common medical imaging modalities: X-ray computed tomography and magnetic resonance. However, ultrasonic images are formed by the reflection of pulses of energy from tissues, rather than by absorption of energy (as with X-ray images) or secondary emission of energy (as with magnetic resonance images). Thus, the principles of ultrasonic imaging bear more similarity to those of sonar or radar imaging than they do to other forms of medical imaging. Ultrasonic imaging has advantages, limitations, and artifacts that differ from those of other medical imaging modalities. These must be understood by the practitioner if the technique is to be used effectively.

The purpose of this chapter is to provide an introduction to the physical principles, design considerations, and sources of artifacts in ultrasonic imaging systems. Readers seeking to study this material in more depth are referred to the text by Kremkau, the chapter on echocardiography physics and instrumentation by Geiser in Marcus Cardiac Imaging, and the comprehensive textbook of echocardiography by Weyman.

Principles of ultrasound

Sound is defined as vibrations transmitted through an elastic medium that are capable of being detected by the human organs of hearing. Vibratory waves alternately cause compression and rarefaction (i.e., positive and negative changes in pressure within the medium through which they pass; Figure 1-1 ). The compression and rarefaction vary periodically over time at any fixed position in the medium and vary periodically in space for any fixed time during passage of the sound wave.

The number of cycles of a sound wave per unit time is called its frequency, which is measured in cycles per second, or hertz (abbreviated Hz and named after Heinrich Rudolf Hertz, a 19th century German physicist) or megahertz [MHz] = 10 ⁶Hz. The frequency f is the reciprocal of the period T, which is the time between successive pressure peaks or troughs (or other specific reference points) on the wave when measured at a fixed observation position, i.e.,

f=1T.f=1T.
f = 1 T .

Frequencies within the range of human hearing (about 20 to 20,000 Hz) are referred to as audio frequencies, while those above this range are referred to as ultrasonic frequencies. Echocardiography machines commonly operate in the frequency range of 2 to 10 million cycles per second (2 to 10 MHz). Some specialized ultrasound instruments (e.g., those made for intracoronary imaging) may operate at frequencies as high as 30 MHz.

At any fixed time, the distance between corresponding reference points on adjacent cycles of a sound wave is called the wavelength (λ). Frequency and wavelength are related by

c=f(λ)c=f(λ)
c = f ( λ )

where c is the speed of propagation in the medium. This relationship between frequency and wavelength requires specification of the medium through which the wave is traveling, because the speed of propagation of sound varies with the medium. The average propagation speed in soft tissues and blood is about 1540 m/s (1.54 mm/μs), the speed for which most medical ultrasound instruments are calibrated.

Among different media, the speed of sound propagation varies inversely with density (mass per unit volume) and directly with stiffness (tendency to resist compression). Paradoxically, sound usually travels faster in higher-density materials because they also tend to be stiffer and because stiffness differences among materials are usually larger than density differences. In general, the propagation speed of sound is low in gases, higher in liquids, and highest in solids. It is much faster in any tissue than in air (approximately 330 m/s).

The acoustic waves emitted by typical transesophageal echocardiography (TEE) transducers have a center frequency of 5 MHz, giving a wavelength of 0.308 mm (i.e., ≈0.3 mm) in tissue (by Equation 1-2 ). Wavelength is important to image quality, because physical principles limit the spatial resolution of an ultrasonic image to approximately 1 wavelength (p. 14). Thus, shorter wavelengths, obtained with higher frequencies (doubling the frequency halves the wavelength, so 10 MHz gives a wavelength of approximately 0.15 mm, again by Equation 1-2 ), produce better resolution. When the imaging frequency is selectable, the operator has to make a choice that balances the improved image quality with the reduced penetration obtained with higher frequencies. Accordingly, higher frequencies are used when imaging pediatric patients or shallow structures in adults.

As an acoustic wave passes from one medium into another, its frequency does not change. However, if the speed of propagation c differs between adjacent media, the wavelength of the sound will change upon passage from one medium to the other (by Equation 1-2 ).

Once the medium has been specified, a sound wave that is a pure tone is characterized by its frequency and its amplitude. The amplitude of a wave is defined as the magnitude of the measurement from the baseline to the peak of the waveform. In the case of sound, it is measured in units of pressure within the medium (see Figure 1-1 ). The amplitude of the corresponding electrical signals within the ultrasound instrument is expressed in units of voltage. The power (rate of energy delivery) of a sound wave is proportional to the pressure amplitude squared (or voltage squared) and is measured in watts. Because the biologic effect of a sound wave is determined by the concentration of the power within the tissues, the output of ultrasound instruments is specified as intensity, or power per unit area (usually watts per square centimeter).

For introductory purposes, we consider sound waves that are generated for an indefinite time period, called continuous wave (CW) sound. However, CW signals are used in echocardiography only for purposes of some Doppler measurements (see Chapter 2 ). The use of pulsed wave (PW), rather than CW, ultrasound is necessary to construct images from the returned echoes. Pulses are brief bursts of sound (typically only a few cycles) transmitted into the medium, followed by a relatively long period of silence, during which the receiver in the ultrasound instrument awaits returned echoes ( Figure 1-2 ). In addition to the underlying frequency and amplitude of the pulses, a pulsed ultrasound signal is described by the pulse duration (PD, in microseconds) and the pulse repetition frequency (PRF, in Hz, also called the pulse repetition rate), which is the reciprocal of the pulse repetition period (PRP, in seconds). For any given speed of propagation, setting the PD also determines the pulse length in the medium. The pulse length is critical in that it limits the longitudinal or axial resolution of an ultrasound image (pp. 13-14).

Because the average propagation speed of sound in tissue is 1.54 mm/μs, a pulse travels 1 cm (10 mm) in 6.5 μs. Twice this time (13 μs) is required for each centimeter of round-trip travel from the transducer to a reflector and back. To display all objects uniquely within a typical 10-cm viewing window and avoid range ambiguity, there must be only a single ultrasonic pulse present within 10 cm of the transducer at any given time. This implies that the minimum time between transmitted pulses is 10 × 13 μs or 130 μs, or, equivalently, that the PRF must be no more than 1/130 μs ≈ 7700 Hz = 7.7 kHz (see Figure 1-2 ).

Together, the PD and PRF determine the duty cycle (DC, also called the duty factor), or the fraction of time that the pulse is “on.” (DC = PD/ PRP and is sometimes multiplied by 100 and cited as a percentage.) The DC and amplitude, in turn, determine the average power output by an ultrasound system, which determines the biologic effect on the tissues (pp. 18-19).

Because useful ultrasonic power levels vary over several orders of magnitude, power is usually expressed on a relative logarithmic scale called the decibel (dB, after Alexander Graham Bell: 1 bel = 10 dB), which is expressed as

relative power(dB)=10log10(PRp),relative power(dB)=10log10(PRp),
relative power ( dB ) = 10 log 10 ( P R p ) ,

where P is the power of the signal and R _pis the reference power level. For example, the control adjusting the transmitted power of an ultrasound instrument may be calibrated in decibels relative to the maximum possible transmitted power. Confusion can arise when signal strength is expressed as a function of the ratio of the acoustic pressures or the voltages measured at the transducer, rather than as a ratio of power levels. In this case, since power is proportional to the square of pressure or voltage, and the logarithm of a squared quantity is double that of the quantity itself, we must double the factor multiplying the logarithm term in Equation 1-3 , giving us 20log ₁₀( V / R _V), where V is the voltage of the signal and R _Vis the reference voltage level. Given that, log ₁₀(2) is approximately 0.3 and log ₁₀(0.5) is approximately −0.3, doubling the power (or multiplying the pressure or voltage by 2‾√≈1.4
2 ≈ 1.4
) corresponds to a 3 dB increase, while halving the power (or multiplying the pressure or voltage by 0.5‾‾‾√≈0.7
0.5 ≈ 0.7
) corresponds to a −3 dB change.

The loss of signal strength (or acoustic attenuation, described later) as a sound wave passes through tissue is an exponential function of the depth of penetration. Because the logarithm of an exponential function is a linear function, acoustic attenuation can be expressed as decibels per unit depth, making it a simple matter to calculate signal loss for any given depth of penetration.

Overall, the strength of useful returned echoes in ultrasound imaging may be as small as 10 ⁻¹⁰of the transmitted signal strength, corresponding to a power reduction of 10log ₁₀, 0.0000000001, or −100 dB. Other examples of power ratios and voltage or pressure ratios expressed in decibels are given in Table 1-1 .

TABLE 1-1

Examples of Power and Voltage or Pressure Ratios and Their Decibel Equivalents