1 Physics of Ultrasound J. Anthony Seibert Imaging systems using ultrasound have attained a large contraction of the crystal surface by an external power presence as point-of-care (PoC) devices across many source introduces energy into the medium as a series of clinical domains over the past 10 years. The success compressions and rarefactions, traveling as a wave front of ultrasound for this purpose is attributed to several in the direction of travel, known as a longitudinal wave, characteristics, including the low cost and portability as shown in Fig. 1.1. of ultrasound devices, the nonionizing nature of ultra- sound waves, and the ability to produce real-time Wavelength, Frequency, Speed images of the acoustic properties of the tissues and tis- The wavelength (λ) is the distance between any two sue structures in the body to deliver timely patient care, repeating points on the wave (a cycle), typically mea- among many positive attributes. An understanding of sured in millimeters (mm). Thefrequency (f) is the num- the basic physics of ultrasound, in addition to hands-on ber of times the wave repeats per second (s), also defined training, practice, and development of experience are of in hertz (Hz), where 1 Hz = 1 cycle/s. Frequency identi- great importance in its effective and safe use. This chap- fies the category of sound: less than 15 Hz is infrasound, ter describes the characteristics, properties, and produc- 15 Hz to 20,000 Hz (20 kHz) is audible sound, and tion of ultrasound; interaction with tissues, acquisition, above 20 kHz is ultrasound. Medical ultrasound typi- processing, and display of the ultrasound image; the cally uses frequencies in the million cycles/s megahertz instrumentation; achievable measurements, including (MHz) range, from 1 to 15 MHz, with some specialized blood velocity; and safety issues. ultrasound applications beyond 50 MHz. The period is the time duration of one wave cycle and is equal to 1/f. CHARACTERISTICS OF SOUND The speed of sound, c, is the distance traveled per unit time through a medium and is equal to the wavelength Sound is mechanical energy that propagates through a (distance) divided by the period (time). As frequency is continuous, elastic medium by the compression (high inversely equal to the period, the product of wavelength pressure) and rarefaction (low pressure) of particles and frequency is equal to the speed of sound, c = λf. The that comprise it. Compression is caused by a mechani- speed of sound varies substantially for different mate- cal inward deformation by an external force, such as an rials, based on compressibility, stiffness, and density expanding and contracting transducer crystal composed characteristics of the medium. For instance, air is highly of multiple elements in contact with the medium. During compressible and of low density, with a relatively low transducer surface expansion, an increase in the local speed of sound; bone is stiff and dense, with a relatively pressure at contact occurs. Contraction of the crystal very high speed of sound; and soft tissues have com- follows, causing a decrease in pressure. The mechanical pressibility and density characteristics with intermedi- energy imparted at the surface is transferred to adjacent ate speeds, as listed in Table 1.1. Of importance are the particles of the medium, which travels at the speed of average speeds for “soft tissue” (1540 m/s), fatty tissue sound through the medium. Continuous expansion and (1450 m/s), and air (330 m/s). To relate time with depth 2 CHAPTER 1 Physics of Ultrasound 3 Contraction Expansion Compression Wavelength, λ (mm) 1 cycle Pressure amplitude Transducer Rarefaction Fig. 1.1 Mechanical energy is generated from an expanding and contracting crystal in contact with a medium, introducing high-pressure (compression) and low-pressure (rarefaction) variations of the constituent particles that transfer the energy to adjacent particles as a longitudinal wave. TABLE 1.1 Density, Speed of Sound, In a homogeneous medium, ultrasound frequency and Acoustic Impedance for Tissues and and speed of sound are constant. When higher ultra- Materials Relevant to Medical Ultrasound sound frequency is selected, the wavelength becomes shorter, giving better detail and spatial resolution along Material Density (kg/m3) c (m/s) Z (rayls)* the direction of propagation. For instance, in soft tis- 2 Air 1.2 330 3.96 × 10 sue with a speed of 1540 m/s, a 5-MHz frequency has a 3 Lung 300 600 1.80 × 10 wavelength in tissue of λ = c / f ; 1540 m/s ÷ 5,000,000/s = Fat 924 1450 1.34 × 106 0.00031 m = 0.31 mm. A 10-MHz frequency has a wave- Water 1000 1480 1.48 × 106 length = 0.15 mm (Fig. 1.2). Although higher frequen- “Soft tissue” 1050 1540 1.62 × 106 cies provide better resolution, they are also more readily Kidney 1041 1565 1.63 × 106 attenuated, and depth penetration can be inadequate for Blood 1058 1560 1.65 × 106 certain examinations, such as for the heart and abdomen. Liver 1061 1555 1.65 × 106 Intensity Muscle 1068 1600 1.71 × 106 The amount of ultrasound energy imparted to the 6 Skull bone 1912 4080 7.8 × 10 medium is dependent on the pressure amplitude vari- 7 PZT 7500 4000 3.0 × 10 ations generated by the degree of transducer expan- *Acoustic impedance is the product of density and speed of sion and contraction, controlled by the transmit gain sound. The rayl is the named unit, with base units of kg/m2/s. applied to a transducer. Power is the amount of energy Acoustic impedance directly relates to the propagation charac- per unit time introduced into the medium, measured in teristics of ultrasound in a given medium and between media. milliwatts (mW). Intensity is the concentration of the power per unit area in the ultrasound beam, typically expressed in mW/cm2. Signals used for creating images interactions in the patient, medical ultrasound devices are derived from ultrasound interactions in the tissues assume a speed of sound of 1540 m/s, despite slight dif- and the returning intensity of the produced echoes. ferences in actual speed for the various tissues encoun- Absolute intensity depends on the method of ultrasound tered. Changes in the speed of sound can affect how production and can result in heating or mechanical dis- ultrasound travels through the tissues and may result ruption of tissues, as discussed later in this chapter. in unexpected artifacts (see Chapter 2 on speed artifact and refraction artifact). The product of the density and INTERACTIONS OF ULTRASOUND WITH speed of sound is known as the acoustic impedance. This TISSUES characteristic of the tissues is intrinsic in the generation of ultrasound echoes, which return to the transducer to Interactions of ultrasound are chiefly based on the acous- create the ultrasound image. More detail is in the next tic impedance of tissues and result in reflection, refrac- section on ultrasound interactions. tion, scattering, and absorption of the ultrasound energy. 4 SECTION 1 Principle of Ultrasound between two tissues that have a difference in acoustic impedance (Fig. 1.3A). The fraction of incident inten- sity Ii reflected back to the transducer (Ir) is the intensity 2 MHz λ = 0.77 mm reflection coefficient,I R , calculated as 2 Ir Z2 ‐ Z1 RI = = Ii ( Z2 + Z1 ) The subscripts 1 and 2 represent tissues that are prox- λ = 0.31 mm 5 MHz imal and distal to the boundary. The intensity trans- mission coefficient, T , is defined as the fraction of the λ = 0.29 mm Fat I incident intensity that is transmitted across an inter- face, equal to TI = 1 – RI. For a fat–muscle interface, the intensity reflection and transmission coefficients are cal- = 0.15 mm culated as 10 MHz λ 2 Ir 1.71 − 1.34 RI, Fat → Muscle = = = 0.015 ; Ii 1.71 + 1.34 0 0.2 0.4 0.6 0.8 1.0 TI, Fat → Muscle = 1 − RI, Fat → Muscle = 0.985 Distance (mm) Fig. 1.2 Wavelength and frequency are inversely proportional, A high fraction of ultrasound intensity is transmit- determined by the speed of sound in the medium. For soft tissue, with an average speed of 1540 m/s, the wavelength is directly ted at tissue boundaries for tissues that have similar calculated as the speed of sound divided by the frequency in acoustic impedance. For tissues with large differences cycles/s. As frequency remains constant in different media, wave- of acoustic impedance, such as air-to-tissue or tissue- length must change. Shown is the wavelength for a 5-MHz fre- to-bone boundaries, most of the intensity is reflected, quency in fat (red line), with a speed of sound of 1450 m/s. with no further propagation of the ultrasound pulse. At a muscle–air interface, nearly 100% of incident intensity Acoustic Impedance is reflected, making anatomy unobservable beyond an Acoustic impedance, Z, is a measure of tissue stiffness air-filled cavity. Acoustic coupling gel placed between and flexibility, equal to the product of the density and the transducer and the patient’s skin is a critical part of speed of sound: Z = ρc, where ρ is the density in kg/m3 the standard ultrasound imaging procedure to ensure and c is the speed of sound in m/s, with the combined good transducer coupling and to eliminate air pockets units given the name rayl, where 1 rayl is equal to 1 kg/ that would reflect the ultrasound. For imaging beyond (m2s). Air, soft tissues, and bone represent the typical lung structures, avoidance of the ribs and presence of low, medium, and high ranges of acoustic impedance a “tissue conduit” are necessary to achieve propagation values encountered in the patient, as listed in Table 1.1.