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Getting Started
Ultrasound Physics and Image Formation

Sevan Harput1, Xiaowei Zhou2, and Meng-Xing Tang3

1 Division of Electrical and Electronic Engineering, London South Bank University, London, UK

2 State Key Laboratory of Ultrasound Engineering in Medicine, College of Biomedical Engineering, Chongqing Medical University, Chongqing, China

3 Department of Bioengineering, Imperial College London, UK

What Is Ultrasound?

Ultrasound refers to an acoustic wave whose frequency is greater than the upper limit of human hearing, which is usually considered to be 20?kHz. Medical ultrasound operates at a much higher frequency range (generally 1-15?MHz) and it is inaudible. Medical ultrasound images are produced based on the interaction between the ultrasound waves with the human body. For this reason, producing and interpreting an ultrasound image require an understanding of the ultrasound waves, their transmission and reception by sensors, and the mechanisms by which they interact with biological tissues.

Ultrasound Waves

Unlike electromagnetic waves used in optical imaging, X-ray, and computed tomography (CT), ultrasound waves are mechanical waves that require a physical medium to propagate through. For example, ultrasound waves can travel in water or human tissue, but not in a vacuum. Ultrasound waves transport mechanical energy through the local vibration of particles. In other terms, an ultrasound wave propagates by the backwards and forwards movement of the particles in the medium. It is important to note that while the wave travels, the particles themselves are merely displaced locally, with no net transport of the particles themselves. For example, if a lighted candle is placed in front of a loudspeaker, the flame may flicker due to local vibrations, but the flame would not be extinguished since there is no net flow of air, even though the sound can travel far away from the speaker [1]. While propagating in a medium, both the physical characteristics of the ultrasound wave and the medium are important for understanding the wave behaviour. Therefore, this section will first introduce the relevant physical processes and parameters that affect ultrasound wave propagation.

Ultrasound Wave Propagation

There are many types of acoustic waves, such as longitudinal, shear, torsional, and surface waves. The mechanical energy contained in one form of an acoustic wave can be converted to another, so most of the time these waves do not exist in isolation. However, for the sake of simplicity we will only describe the longitudinal or compressional waves, which are most commonly used in B-mode and Doppler imaging.

The propagation of longitudinal ultrasound waves is illustrated in Figure 1.1 using discrete particles. As we know, human tissue is not made up of discrete particles, but rather a continuous medium with a more complicated structure. This is merely a simplified physical model to explain wave propagation. During the wave propagation, particles are displaced due to the acoustic pressure in parallel to the direction of motion of the longitudinal wave, as illustrated in Figure 1.1a-c. When the pressure of the medium is increased by the wave, which is called the compression phase, particles in adjacent regions move towards each other. During the reduced pressure phase (rarefaction), particles move apart from each other. During these two phases, the change in the concentration of particles changes the local density, shown in Figure 1.1d as the higher-density regions with darker colours. This change in local density can be related to the change in acoustic pressure, which is also proportional to the velocity of the particles, Figure 1.1e. Particle velocity should not be confused with the speed of sound. The ultrasound wave travels, while the particles oscillate around their original position. The particle velocity is relatively small in comparison to the speed of sound in the medium.

Figure 1.1 (a-e) Longitudinal wave propagation using a simplified physical model depicted graphically. A detailed explanation is in the text above.

Speed of Sound, Frequency, and Wavelength

A propagating ultrasound wave can be characterised by its speed, frequency, and wavelength. Similar to other types of waves, the speed of propagation of an ultrasound wave is determined by the medium it is travelling in. Propagation speed is usually referred to as the speed of sound, denoted by 'c', and it is a function of the density, '?', and stiffness, 'k', of the medium, as shown in Equation 1.1:

Tissue with low density and high stiffness has a high speed of sound, whereas high density and low stiffness lead to low speed of sound. See Table 1.1 for speed of sound values in different tissue types and materials [2, 3].

In addition to speed of sound, the frequency, 'f', and the wavelength, '?', of the ultrasound wave are crucial parameters for medical ultrasound imaging. The frequency of a wave is the reciprocal of the time duration of a single oscillation cycle of the wave and carries a unit of Hz. The wavelength is the length of a single cycle of the wave and is linked to frequency and speed of sound, as in Equation 1.2:

In short, frequency has the timing information about the wave for a given space, and wavelength has the spatial (relating to physical space) information about the wave at a given time. Ultrasound image resolution is related to frequency/wavelength and is usually better at higher frequencies and shorter wavelengths. At a given ultrasound imaging frequency, the wavelength changes proportionally with the speed of sound. For medical ultrasound imaging, the speed of sound is usually assumed to be constant for the tissue and in order to change the image resolution, one needs to change the imaging frequency. For example, for an average speed of sound in soft tissues of 1540?m/s, the wavelength is 0.77?mm at 2?MHz and 0.154?mm at 10?MHz.

Table 1.1 Ultrasound properties of common materials and tissue.

Acoustic Impedance

Acoustic impedance is the effective resistance of a medium to the applied acoustic pressure. For example, the particle velocity in soft tissue will be higher than the particle velocity in bone for the same applied pressure due to the difference in their acoustic impedance (see Table 1.1). The acoustic impedance, 'Z', of a material is determined by its density and stiffness values, as shown in Equation 1.3:

Physical Processes That Affect Ultrasound Waves

Reflection

When an ultrasound wave travelling through a medium reaches an interface of another medium with a different acoustic impedance, some portion of the ultrasound wave is reflected, as shown in Figures 1.2 and 1.3. The amplitudes of the transmitted and reflected ultrasound waves depend on the difference between the acoustic impedances of both media, see Figure 1.3. This can be formulated as the reflection coefficient, shown in Equation 1.4:

The interfaces with higher reflection coefficients appear brighter on an ultrasound B-mode image, since a large portion of the ultrasound wave is reflected back. Reflection coefficients at some common interfaces are shown in Table 1.2.

It should be remembered that the underlying model for the equation of the reflection coefficient is based on specular reflection, which means a reflection from a perfectly flat surface or an interface.

In reality, the reflection of ultrasound waves can be considered either specular or diffuse (https://radiologykey.com/physics-of-ultrasound-2). When the ultrasound waves encounter a large smooth surface such as bone, the reflected echoes have relatively uniform direction. This is a type of specular reflection, as shown on the left of...