 Ultrasound

# Ultrasound Physics

Main differences between Ultrasound and X-rays

 Diagnostic Ultrasound X-rays (radiology) wave type longitudinal mechanical waves electromagnetic waves transmission requirements elastic medium No medium generation stressing the medium accelerating electric charges velocity depends on the medium through which it propagates It is relatively constant: 299,792,456.2 m/s Carcinogenic No Yes * similar waves seismic, acoustic radio, light

## Velocity of sound in some Biological Materials

 Velocity of sound in some Biological Materials Material Velocity of Sound (m/s) Impedance (Rayl x 10 -6) Air 330 0.0004 Fat 1450 1.38 Water 1480 1.48 Average Human Soft Tissue 1540 1.63 Brain 1540 NA Liver 1550 1.65 Kidney 1560 1.62 Blood 1570 1.61 Muscle 1580 1.7 Lens of eye 1620 NA Skull Bone 4080 7.8

 Frequency and Resolution (axial resolution) This is for linear array transducers with parallel beams MHz Axial resolution Lateral resolution Resolution % 3.0 1.1 mm 2.8 mm 35.89% 4.0 0.8 mm 1.5 mm 60.86% 5.0 0.6 mm 1.2 mm 77.77% 7.5 0.4 mm 1.0 mm 100% 10.0 0.3 mm 1.0 mm 107.69% For harmonic imaging the input frequency doubles the output frequency (it works just for low frequencies)

### Some useful definitions in regard to Diagnostic Ultrasound Physics

This section provides some useful definitions or information in regard to important terms not easily found on the Internet:

• Absorption is the transfer of energy from the ultrasound beam to the tissue. It is proportional to frequency

• Apodization is a method for reducing side lobes in some arrays. It gradually decreases the vibration of the transducer surface with distance from its center. It is usually accomplished by using more power to excite the innermost elements.

• Axial resolution is the minimum separation between two interfaces located in a direction parallel to the beam so that they can be imaged as two different interfaces

• Decibel is a way to express the ratio of two sound intensities:  dB=10log10I1/I2 being I1 the reference. For instance: +3 dB = I multiplied by 2 and -3 db = I divided by 2

• Diffraction is the change in the directions and intensities of a group of waves after passing by an obstacle or through an aperture

• Duty factor is the lapse of time the transducer is actively transmitting sound

• Echo ranging is the relationship between transit time and reflector depth expressed as t = 2d/c

• Grating lobes as side lobes are secondary ultrasound beams projecting off-axis at predictable angles to the main beam. Side lobes are too small to produce important artifacts.

• Half Value Layer (HVL) is the distance the sound beam penetrates into a tissue when its intensity has been reduced to one half of its initial value

• Huygens' principle states that an expanding sphere of waves behaves as if each point on the wave front were a new source of radiation of the same frequency and phase

• Impedance is the product of the density of a material and the speed of sound in that material

• Pulse average intensity I(PA) is the average intensity during the pulse

• Lateral resolution is the minimum separation of two interfaces aligned along a direction perpendicular to the ultrasound beam. It depends on the beam width

• Partial Volume Artifact (slice thickness or volume averaging artifact), that occurs when the slice thickness is wider than the scanned structure

• Q-value means the degree that a transducer is finely tuned to specific narrow frequency range. For instance: Low Q means wide bandwitdh and High Q means narrow bandwidth

• Range resolution is the ability to determine the depth of reflectors

• Rayleigh scatterers are objects whose dimensions are much less than the ultrasound wavelength. Scattering increases with frequency raised to the 4th power and provides much of the diagnostic information from ultrasound

• Refraction is the bending of a wave beam when it crosses at an oblique angle the interface of two materials, through which the waves propagate at different velocities

• Snell's law governs the direction of the transmitted beam when refraction occurs:
sin qt = (c2/c1) x sin qi (qt and qi are transmit and incident angles respectively)

• Spatial Average Intensity (SA) is the acoustic power within the beam, divided by the beam area

• Spatial Peak Intensity (SP) is the point in the sound field with maximum intensity

• Side lobes are energy in the sound beam falling outside the main beam

• Spatial resolution means how closely two reflectors -or scattering regions, can be to one another while they can be identified as different reflectors

• Subdicing is a technique used to overcome grating lobes: each major transducer element is devided into smaller parts, each one being a half wave lenght

• Temporal (instantaneous) Peak Intensity I(TP) or I(IP) is the maximum intensity during the pulse

• Time Average Intensity I(TA): average intensity calculated over the time between pulses:
ITA= I(PA) x Duty factor

• Wavelength is l=c/f  (c = propagation speed; f = frequency)

## Doppler

• Aliasing is an artifact that lowers the frequency components when the PRF is less than 2 times the highest frequency of a Doppler signal

• Beat frequency, for CW Doppler, is the Doppler shift

• Doppler shift is the change in the perceived frequency relative to the transmitted frequency. Doppler shift frequency:  fD = fr - f0  = 2f0v/c

• Doppler shift frequency with incident angle: fD  = 2f0v/c cos q

• Ensemble length -packet size, shots per line- is the number of pulses per scan line. In color Doppler, each line of sight most be pulsed several times

• FFT. Fast Fourier Transform analyzer is a common device that performs spectral analysis in ultrasound instruments. In this case, it displays different quadrature Doppler frequencies, or reflector velocities when a sample volume cursor is used (Doppler frequency is proportional to reflector velocity) along time

• High pass filter is the wall filter

• Nyquist Frequency is the maximum frequency that can be sampled without aliasing. NF = PRF/2  (PRF stands for Pulse Repetition Frequency)

• Quadrature detection is a signal processing method for directional Doppler in which the signal reference frequency for two channels differ in phase by 1/4 period. The output Doppler signal phase for both channels also depends on the Doppler shift, whether positive or negative

• Spectral analysis is the quantitative analysis to display the distribution of frequencies

• Variance is the variation of Doppler frequencies within each pixel during a pulse packet, effective to detect turbulence with color Doppler