NEUROIMAGING / NEUROSONOLOGY

# Physical principles of ultrasound

Created 28/03/2022, last revision 26/08/2023

The key physical principles needed to understand and optimize the ultrasound examination are included

## Basic ultrasound variables and parameters

• ultrasound = acoustic waves (pulses of sound) with a frequency of > 20 kHz
• the generator of ultrasound for medical applications are piezoelectric crystals
• crystals in a transducer (probe) are excited by electrical pulses (piezoelectric effect); one type of energy is converted into another (electrical  ⇒  mechanical)
• the probe (transducer) emits ultrasound pulses  that propagate through tissues and then return to the transducer as echoes (reflections)
• reflected echoes are converted back into electrical impulses by the transducer crystals and are transformed into the ultrasound image
• period of an ultrasound wave is the time that is required to capture one cycle; i.e., the time from the beginning of one cycle till the beginning of the next cycle (period = 1/frequency)
• frequency – the number of periods (oscillations) per second, measured in hertz (Hz)
• 1/sec = 1 Hertz (Hz)
• frequency is environmentally independent
• wavelength – describes the length of a single cycle or the distance that a wave travels in one period
• unlike frequency and period, it depends not only on the frequency but also on the speed of sound through the environment = it is determined by both the source and the medium
• it affects the longitudinal image resolution and, thus, image quality
• wavelength (mm) = propagation speed in tissue (mm/microsecond) / frequency (MHz) ⇒ high frequency means the short wavelength
• amplitude – refers to the strength of the sound wave, defined as the difference between the peak value and the average value of the waveform
• expressed in decibels or dB, which is a logarithmic scale
• can be changed by a sonographer
• amplitude decreases as the ultrasound move through tissue (attenuation)
• amplitude usually decreases by 1 dB per 1 MHz per 1 centimeter traveled (back and forth)
• with a 9 MHz probe examining the target at 4 cm (8 cm total distance), the amplitude attenuation will be 1 dB x 9 MHz x 8 cm = 72 dB
• power (W) – the total amount of energy in the ultrasound beam
• determined by the sound source
• decreases as the beam propagate through the tissues
• power and amplitude are closely related, with power being proportional to the square of the amplitude
• most of the energy carried by high-intensity ultrasound in tissue is converted to thermal energy
• intensity (W/cm2) of the ultrasound beam is defined as the concentration of energy in the beam; it decreases as the ultrasound propagates through tissue
• intensity = Power (W) / beam area (cm2)
• intensity is a key variable in ultrasound safety
• propagation speed  means how fast the ultrasound can travel through the tissue
• in the human soft tissue, the average speed is 1540 m/s
• speed is determined by the medium only; the denser is the medium, the slower is the speed of ultrasound
• speed enables to calculate the approximate distance of the examined object

## Tissue propagation

• as the ultrasound propagates through the tissue, its intensity (attenuation) decreases because of reflection, scattering, and absorption of ultrasound energy produced at the surfaces between the tissues of different density
• attenuation depends on frequency:  attenuation (dB)= 0.5 x propagation length x frequency
• reflection (the greater the difference between the impedances, the greater the amplitude of the reflected echo and the lower the intensity of the transmitted ultrasound)
• scattering (relatively small, uneven interface,  or particles in suspension)
• absorption
• there are two main effects of ultrasound on tissue
• thermal (caused by the friction of oscillating particles and the absorption of sound waves)
• non-thermal
• mechanical (e.g., cavitation)
• chemical
• biological

## Doppler effect

• describes the change in frequency and wavelength of the received versus transmitted signal caused by the non-zero mutual speed of the transmitter and receiver
• the frequency increases or decreases as the reflector approaches or moves away from the US transmitter
• ∆F=2 x v x frequency x cos α / propagation speed
• frequency shift – the difference between the transmitted and reflected frequency

#### Pulsed wave (PW) and continuous wave (CW) Doppler

• CW (continuous wave) Doppler transmits US waves and detects a frequency-shifted signal. CW Doppler probes contain two electroacoustic transducers – transmitter + receiver. The sampling volume is fixed by the overlap of the ultrasound beam emitted by the transmitter and the area from which the receiver can detect scattered or reflected waves. The main disadvantage is the existence of a relatively large fixed sampling volume, which makes it virtually impossible to choose the depth at which the velocity is measured
• PW (pulsed wave) Doppler system sends short pulses of US waves. By selecting the time for which the signal is then detected, both the depth and the size of the sampling volume can be adjusted
• the time between the transmission of the pulse and the start of reception determines the distance of the sampling volume from the probe
• the time for which the signal is received defines the size of the sampling volume
• a single electroacoustic transducer suffices to transmit and receive ultrasonic waves (PW alternates between transmitting and receiving data)
• the major disadvantage of PW Doppler is the aliasing  ⇒ change scale or select a lower frequency of the transducer

#### Pulse duration, Pulse Repetition Period (PRP), and Pulse Repetition Frequency (PRF)

• pulse duration – the time that the pulse is on; it is determined by the number of cycles and the period of each cycle
• Pulse Duration = (number of cycles x wavelength) / propagation speed
• Pulse Repetition Period (PRP) is the time between the onset of one pulse till the onset of the next one
• Pulse Repetition Frequency (PRF)the number of ultrasound pulses the device emits and receives per second (PRP/s)
• the limit of the highest measurable speed at a given PRF is often referred to as the Nyquist limit
• The Nyquist frequency corresponds to the value of the Doppler shift frequency (= speed) that is not yet distorted at a given PRF
• it is necessary to adjust the PRF in proportion to the velocity and depth of the vessel under examination
• a disproportionately high PRF rarely allows the display of slow flows, both in color and spectral recording
• the greater the depth of insonation, the lower the maximum PRF can be set

#### Insonation angel

• if the direction of the ultrasound beam and flow are identical, the angle is 0°, and the Doppler shift corresponds directly to the flow velocity
• the smaller the angle, the more accurate the actual velocity measurement
• with the angle of 90 degrees, the velocity cannot be measured
• when investigating extracranial arteries, an angle of < 60° is usually used