Chapter 1

Physics and basic principles

Stephen Alerhand¹, Ole Graumann^2,3,4 and Bret P. Nelson¹

¹Division of Emergency Ultrasound, Dept of Emergency Medicine, Icahn School of Medicine at Mount Sinai, New York, NY, USA. ²Dept of Radiology, Odense University Hospital, Odense, Denmark. ³Dept of Clinical Medicine, Odense University, Odense, Denmark. ⁴Dept of Clinical Medicine, Aarhus University, Aarhus, Denmark.

Correspondence: Bret P. Nelson, Division of Emergency Ultrasound, Dept of Emergency Medicine, Icahn School of Medicine at Mount Sinai, 1 Gustave L. Levy Place, New York, NY 10029, USA. E-mail: bretpnelson@gmail.com

Due to the poor penetration of US waves through air, LUS was traditionally considered a difficult modality to incorporate into practice. Eventually, it was realised that LUS is mostly a study of its artefacts. This concept laid the foundation for its use in diagnostic and procedural applications. Accordingly, the basic tenets of US physics must be understood in order to fully implement these techniques and interpret the acquired images. Moreover, since the structure of normal lung cannot be directly “seen” in a straightforward way as with other applications, educators must have a firm grasp on US artefacts in order to teach these concepts in a simple way that learners can appreciate. This chapter will describe several basic US concepts and principles that will be used throughout the rest of the book.

Basic physics, definitions and terminology

In order to understand how the energy of an US probe is ultimately translated into a discrete picture on the screen, the fundamental qualities of the science must first be understood. This science is best encapsulated by the piezoelectric effect, which describes the conversion of electrical energy into mechanical energy. First, applied electrical voltage from the machine deforms a crystal element in the transducer to generate the initial mechanical pressure wave. Upon the reflection and return of these echoes to the transducer, the crystal element is deformed once again. These deformations generate an electric current that the US machine converts into an image on the screen. The distance of a given structure on the screen from the US transducer is determined by the time required for the mechanical energy of its echo to return. The greyscale representation on the screen is determined by the intensity of that returning signal, with each echo corresponding to a point on the screen.

The sound waves described above consist of a series of repeating mechanical pressure waves propagating through a medium (figure 1). The peak pressure of a wave (its height when mapped out graphically) is defined as its amplitude and is measured in decibels (dB). This amplitude is a measurement of the strength of the echo returning to the US transducer as mechanical energy. The machine itself processes this information to determine the brightness of the structure on the screen. Stronger returning echoes (with higher amplitude) appear as bright white (or hyperechoic) areas on the screen, whereas weaker echoes (with lower amplitude) appear dark grey (hypoechoic) or black (anechoic) (figure 2). In between white and black, there exists a wide range on the continuum referred to as the greyscale.

Figure 1. Sound wave plotted as time versus pressure. Reproduced and modified from [1] with permission.

Figure 2. A midrange echotexture, like that of a solid organ, is shown on the left. On the right, the image of the thorax demonstrates areas that are hypoechoic (A), isoechoic (B) and hyperechoic (C) compared with the image on the left.

The velocity of the sound waves is also of critical importance for interpreting the screen images and teaching LUS. The velocity is defined as the speed of the US wave, measured in metres per second. Within any given medium through which the US wave passes, this velocity remains constant. Some media allow faster propagation than others; some examples are shown in table 1.

Generally speaking, waves propagate faster when molecules are closer in relation to one another, and they propagate more slowly with decreased density of molecules. The resistance to molecular movement in a particular tissue type is referred to as its acoustic impedance. The US machine uses these different propagation speeds to determine the distance of a structure from the transducer. It accomplishes this by measuring the time taken for the wave to reach that particular structure and be reflected back to the transducer.

Impedance is critically important in understanding LUS because the loss of US energy through tissue greatly determines how well it will form an image. Most structures that form good images with US have impedance values between 1.5 MRayl (water) and 1.7 MRayl (organs). In contrast, the acoustic impedance of air is 0.0004 MRayl, and for bone it is 6–8 MRayl. Since air and bone impede US wave transmission quite differently from water and organs, it is much more difficult to obtain accurate sonographic information from these structures. This will have an impact on the attenuation of US energy through these structures, as discussed later in this chapter.

Having described the elements determining the screen image’s characteristics (brightness, depth), we can now turn to the visual quality of this image. This resolution is determined by the frequency of the US wave, which is defined as the number of times per second that the wave repeats. It is measured in hertz (Hz), with 1 Hz being equal to one wave-cycle per second. US waves include any frequencies above audible sound (20–20 000 Hz). Diagnostic US uses frequencies ranging from 12 to 2 MHz, with 1 MHz being equal to 1 million Hz. Waves with high frequencies generate images with high resolution. They utilise more energy and create more waves per second. These waves thus lose energy more rapidly and have less energy available to penetrate to deeper distances. In contrast, waves with low frequencies utilise less energy and create fewer waves per second. Accordingly, the images produced are of lower resolution. Since these waves lose energy less rapidly, more energy remains available to penetrate more deeply. Frequency is thus directly correlated with image resolution and indirectly correlated with tissue penetration. The strength of the returning signal also depends on the surface structure of the organ. For instance, a linear surface structure of an organ will return much of the signal directly to the transducer and therefore have a higher signal (figure 3).

As described, resolution is defined as the ability of the US machine to differentiate between two closely located structures. Axial resolution refers to structures lying in a plane parallel to the US wave (directly along its path), while lateral resolution refers to structures lying in a perpendicular plane to the US beam. A beam is very thin and is created by tens to hundreds of scan lines. Lateral resolution will generally be inferior. Adjusting the depth of the view on the screen, as well as the width, will indirectly adjust the focal zone of the US beam.

Wavelength is defined as the distance a wave travels in a single cycle, as measured in micrometres. It fits within the following equation: velocity=frequency×wavelength. As described previously, the velocity of a wave remains constant as it propagates through a given tissue medium. Therefore, wavelength is inversely proportional to frequency. Accordingly, high-frequency waves (high-resolution images) correspond to lower wavelengths. These waves travel a shorter distance within a given cycle and thus demonstrate shallower penetration into tissue. In contrast, low-frequency waves (low-resolution images) correspond to higher wavelengths. These waves travel a greater distance within a given cycle and thus demonstrate deeper penetration into tissue. As a general rule, the depth of penetration of US in tissue is limited to 200 wavelengths. Thus, a high-frequency, short-wavelength 10 MHz transducer may penetrate only 3 cm into tissue, whereas a low-frequency 1 MHz transducer may penetrate 30 cm.

The velocity, and therefore the frequency and wavelength, can also be described by its property of attenuation. This is defined as the progressive weakness of a sound wave as it travels through a given medium. This loss of energy begins upon being emitted from the transducer, all the way through the return of the echo back to the transducer. Similar to velocity, each tissue medium has a corresponding attenuation coefficient. This value is determined by several factors including: the density of molecules of the medium, the number of different interfaces encountered by the wave and the wavelength (table 2).

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