# Principles and Physics of Ultrasound

Sound wave is a form of mechanical energy that travels through a conducting medium (e.g., body tissue) as a longitudinal wave producing alternating compression (high pressure) and rarefaction (low pressure) (Figs. 1.1 and 1.2). Sound propagation can be represented in a sinusoidal waveform with a characteristic pressure (P), wavelength (λ), frequency (f), period (T), and velocity. See Table 1.1 for details.

Table 1.1

Basic terminology

Terminology

Definition

Wavelength (λ)

The spatial period of the wave, and is determined by measuring the distance between two consecutive corresponding points of the same phase. It is expressed in meters (m)

Amplitude (A)

A measure of the height of the wave, i.e., maximal particle displacement. It is expressed in meters (m)

Period (Т)

The time taken for one complete wave cycle to occur. The unit of period is seconds (s)

Frequency (f)

The number of completed cycles per second. Thus, it is the inverse of the period (T) of a wave. The unit of frequency is hertz (Hz). Medical imaging uses high-frequency waves (1–20 MHz)

Velocity (c)

The speed of propagation of a sound wave through a medium (m/s). It is the product of its frequency (f) and wavelength (λ)

Energy (E)

The energy of a sound wave is proportional to the square of its amplitude (A). This means that as the amplitude of a wave decreases (such as with deeper penetration), the energy carried by the wave reduces drastically

Power (P)

Defines as the energy (E) delivered per unit time (t)

The speed of sound varies for different biological media, but the average value is assumed to be 1540 m/s for most human soft tissues. It can vary greatly, being as low as 330 m/s in air and as high as 4000 m/s through bone.

The wavelength (λ) is inversely related to the frequency (f). Thus, sound with a high frequency has a short wavelength and vice versa.

### Generation of an Ultrasound Wave

An ultrasound wave is generated when an electric field is applied to an array of piezoelectric crystals located on the transducer surface. Electrical stimulation causes mechanical distortion of the crystals resulting in vibration and production of sound waves (i.e., mechanical energy). The conversion of electrical to mechanical (sound) energy is called the converse piezoelectric effect. Each piezoelectric crystal produces an ultrasound wave. The summation of all waves generated by the piezoelectric crystals forms the ultrasound beam. Ultrasound waves are generated in pulses (intermittent trains of pressure waves), and each pulse commonly consists of two or three sound cycles of the same frequency.

The pulse length (PL) is the distance traveled per pulse. Waves of short pulse lengths improve axial resolution for ultrasound imaging. The PL cannot be reduced to less than 2 or 3 sound cycles by the damping materials within the transducer.

Pulse repetition frequency (PRF) is the rate of pulses emitted by the transducer (number of pulses per unit time) (Fig. 1.3). Ultrasound pulses must be spaced with enough time between pulses to permit the sound to reach the target of interest and return to the transducer before the next pulse is generated. The PRF for medical imaging ranges from 1 to 10 kHz. For example, if the PRF = 5 kHz and the time between pulses is 0.2 ms, it will take 0.1 ms to reach the target and 0.1 ms to return to the transducer. This means the pulse will travel 15.4 cm before the next pulse is emitted (1540 m/s × 0.1 ms = 0.154 m in 0.1 ms = 15.4 cm).

### Generation of an Ultrasound Image

An ultrasound image is generated when the pulse wave emitted from the transducer is transmitted into the body, reflected off the tissue interface, and returned to the transducer. The schematic diagram above showed the transducer waits to receive the returning wave (i.e., echo) after each pulsed wave (Fig. 1.4). The transducer transforms the echo (mechanical energy) into an electrical signal which is processed and displayed as an image on the screen. The conversion of sound to electrical energy is called the piezoelectric effect.

The image can be displayed in a number of modes (Fig. 1.5):

• Amplitude (A) mode is the display of amplitude spikes in the vertical axis and the time required for the return of the echo in the horizontal axis.

• Brightness (B) displays a two-dimensional map of the data acquired and is most commonly used for ultrasound guided intervention.

• Motion (M) mode, also called time motion or TM mode, displays a one-dimensional image usually used for analyzing moving body parts. This mode records the amplitude and rate of motion in real time and is commonly used in cardiovascular imaging.

### Ultrasound Tissue Interaction

As the ultrasound beam travels through tissue layers, the amplitude of the original signal becomes attenuated as the depth of penetration increases (Fig. 1.6).

Attenuation (energy loss) is due to:

1. 1.

Absorption (conversion of acoustic energy to heat)

2. 2.

Reflection

3. 3.

Scattering at interfaces

In soft tissue, 80% of the attenuation of the sound wave is caused by absorption resulting in heat production. Attenuation is measured in decibels per centimeter of tissue and is represented by the attenuation coefficient of the specific tissue type. The higher the attenuation coefficient, the more attenuated the ultrasound wave is by the specified tissue.

#### Absorption

Absorption is the process of transfer of the ultrasound beam’s energy to the medium through which it travels through heat generation and it accounts for most of the wave attenuation. The quality of the returning sound waves depends on the attenuation coefficient of different tissue.

Table 1.2

Attenuation coefficient of various tissues

Material

α (dB/cm)

Blood

0.18

Fat

0.6

Muscle (across fibers)

3.3

Muscle (along fibers)

1.2

Aqueous and vitreous humor of the eye

0.1

Lens of the eye

2.0

Skull bone

20

Lungs

40

Liver

0.9

Brain

0.85

Kidney

1.0

Spinal cord

1.0

Water

0.0022

Castor oil

0.95

Lucite

2.0

The degree of attenuation also varies directly with the frequency of the ultrasound wave and the distance traveled (Fig. 1.7 and Table 1.2). Generally speaking, a high-frequency wave is associated with high attenuation, thus limiting tissue penetration, whereas a low-frequency wave is associated with low tissue attenuation and deep tissue penetration.

To compensate for attenuation, it is possible to amplify the signal intensity of the returning echo. The degree of receiver amplification is called the gain. Increasing the gain will amplify only the returning signal and not the transmit signal. An increase in the overall gain will increase brightness of the entire image, including the background noise. Preferably, the time gain compensation (TGC) is adjusted to selectively amplify the weaker signals returning from deeper structures.

#### Reflection

Attenuation also results from reflection and scattering of the ultrasound wave. The extent of reflection is determined by the difference in acoustic impedances of the two tissues at the interface, i.e., the degree of impedance mismatch.

Table 1.3

Acoustic impendence of various tissues

Body tissue

Acoustic impedance (106 RayIs)

Air

0.0004

Lung

0.18

Fat

1.34

Liver

1.65

Blood

1.65

Kidney

1.63

Muscle

1.71

Bone

7.8

Acoustic impedance is the resistance of a tissue to the passage of ultrasound. The higher the degree of impedance mismatch, the greater the amount of reflection (Table 1.3). The degree of reflection is high for air because air has an extremely low acoustic impedance (0.0004) relative to other body tissues. The bone also produces a strong reflection because its acoustic impedance is extremely high (7.8) relative to other body tissues. For this reason, it is clinically important to apply sufficient conducting gel (an acoustic coupling medium) on the transducer surface to eliminate any air pockets between the transducer and skin surface. Otherwise, much of the ultrasound waves will be reflected limiting tissue penetration.

The angle of the incidence is also a major determinant of reflection. An ultrasound wave hitting a smooth mirror-like interface at a 90° angle will result in a perpendicular reflection. An incident wave hitting the interface at an angle <90° will result in the wave being deflected away from the transducer at an angle equal to the angle of incidence but in the opposite direction (angle of reflection). When this happens, the signal of the returning echo is weakened, and a darker image is displayed (Fig. 1.8). This explains why it is difficult to visualize a needle inserted at a steep angle (>45° to the skin surface).

Specular reflection occurs at flat, smooth interfaces where the transmitted wave is reflected in a single direction depending on the angle of incidence. Examples of specular reflectors are fascial sheaths, the diaphragm, and walls of major vessels (Fig. 1.9). Block needles are also strong specular reflectors. For specular reflection to occur, the wavelength of the ultrasound wave must be smaller than the reflective structure. Otherwise, scattering will occur.

#### Scattering

Reflection in biological tissues is not always specular. Scattering (diffuse reflection) occurs when the incident wave encounters an interface that is not perfectly smooth (e.g., surface of visceral organs). Echoes from diffuse reflectors are generally weaker than those returning from specular reflectors. Scattering also occurs when the wavelength of the ultrasound wave is larger than the dimensions of the reflective structure (e.g., red blood cells). The reflected echo scatters in many different directions resulting in echoes of similar weak amplitudes. Ultrasonic scattering gives rise to much of the diagnostic information we observe in medical ultrasound imaging.

#### Transmission

After reflection and scattering, the remainder of the incident beam is refracted with a change in the direction of the transmitted beam (Fig. 1.10). Refraction occurs only when the speeds of sound are different on each side of the tissue interface. The degree of beam change (bending) is dependent on the change in the speed of sound traveling from one medium on the incident side to another medium on the transmitted side (Snell’s Law). With medical imaging, fat causes considerable refraction and image distortion, which contributes to some of the difficulties encountered in obese patients. Refraction encountered with bone imaging is even more significant leading to a major change in the direction of the incident beam and image distortion.

The final image on the screen of an ultrasound machine is the result of the interaction of ultrasound waves with the tissues being examined. As the ultrasound wave travels through the tissues, it loses amplitude, and hence energy (attenuation), which is the summative effect of absorption, reflection, and refraction of ultrasound waves.

## Image Acquisition and Processing

### Transducer Basic

An ultrasound transducer has a dual functionality. It is responsible for both the production of ultrasound waves and, after a set period of time, the reception of waves reflected from the tissues. This is called pulsed ultrasound. The pulse repetition frequency (PRF) is the number of pulses emitted by the transducer per unit of time. The PRF for medical imaging devices ranges from 1 to 10 kHz

The ultrasound transducer has the following layers (Fig. 1.11):

1. (a)

Backing material: located behind the piezoelectric element, it serves to prevent excessive vibration. This causes the element to generate ultrasonic waves with a shorter pulse length, improving axial resolution in images.

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