[Ultrasound Physics] GENERAL TERMS

[Contents]

1. Amplitude, Power, and Intensity

2. Attenuation

3. Range Equation/13 Microsecond Rule/Time of Flight

4. Bandwidth and Quality Factor

1. Amplitude, Power, and Intensity: indicators of the strength of sound

 

1) Amplitude [★★]

- difference between average value and maximum value of acoustic variable

= maximum cyclical change in quantity

2) Power (P)

- The rate of energy transfer or the rate at which work is performed [mW,W]

- Determined by

- sound source

- rate of decrease depends on wave and medium

- Operator adjustable

- Relationships: Power is directly related to amplitude

3) Intensity (I) [★★]

- Intensity = Power/beam area (I=P/a)

- Relationships

- Intensity is proportional to power

- Intensity is proportional to amplitude²

- Intensity is inversely proportional to beam area

- strength of the beam over specific area [mW/cm²]

- the concentration of energy in a sound beam

- Important parameter of bioeffects

- Determined by

- sound source

- rate of decrease depends on wave and medium

- Operator adjustable

SPTP (spatial peak, temporal peak)	SATP (spatial average, temporal peak)
SPTA (spatial peak, temporal average)	SATA (spatial average, temporal average)
SPPA (spatial peak, pulse average)	SAPA (spatial average, pulse average)

- spatial: US beam does not have same intensity at different locations within a beam>

- temporal: pulsed US beam does not have same intensity at different time

- SPTP: greatest intensity

- SPTA: Tissue heating

            - highest SPTA: PW doppler

               - lowest SPTA: gray-scale imaging (ophthalmic)

- SATA: smallest intensity

- SPPA, SAPA: not applicable for continuous-wave US

 

* Decibel (dB)

- relative measurement of intensity or amplitude based on logarithmic scale

            : dB>0 = Larger than reference intensity

               : dB <0 = Smaller than reference intensity

 - Not an absolute value

 

- B (dB) = 10 x log[I/I₀]

: output power increased by 10 → signal intensity increased by a factor of 10

- Intensity x 2 → 3 dB, Intensity x 4 → 6 dB

- Intensity x ½ → -3 dB, Intensity x ¼ → -6 dB 

2. Attenuation [★★]

 

1) weakening of amplitude and intensity as sound travels through the medium

- image in the far field is less bright compared to the near field.

 

2) Attenuation Coefficient (a)

- rate at which the amplitude and Intensity decrease as sound moves through a medium; [dB/cm]

- Attenuation coefficient = ½ x frequency

 

3) Attenuation = attenuation coefficient x path length = ½ frequency x path length

 

4) Relationships: frequency, attenuation coefficient, and attenuation are directly related

- frequency ↑ → attenuation coefficient ↑, attenuation↑[★★★★★]

- pathlength↑ → attenuation↑

 

5) Contributions to Attenuation [★★★★★]

- Absorption

: dominant form of attenuation in soft tissue

: conversion of sound energy into heat.

: Not) redirection of sound energy

- Reflection

: travels in the opposite direction of the main beam. Back to the source.

- Refraction

: bending of the sound beam as it travels.

- Scattering

: Occurs when surface is rough. Redirection to all different directions.

 

6) Attenuation & Media

- Attenuation properties very with the medium through which it is traveling

 

- Attenuation is lowest in water, Highest in air

: Low in blood, urine, biologic tissue, and fat

: Intermediate in soft tissue

: High in muscle & bone, calcification

: Highest in lung

3. Range Equation/13 Microsecond Rule/Time of Flight

1) Range Equation (Echo ranging) [★★]

- Estimates the depth of a reflector

- Based on the Go-Return Time (Time-of-Flight, echo arrival time)

: Calculated using the average propagating speed of soft tissue, 1.54 mm/us or 1540 m/s

- D (mm) = V x T / 2

(D= depth; V= acoustic velocity; T= time)

 

2) 13 Microsecond Rule

- For every 13μs, a reflector is 1 cm deeper within the anatomy and on the display

: Ex) If a reflector is 2cm deep, the pulses time of flight is 26μs

4. Bandwidth and Quality Factor

1) Bandwidth [★]

- range (difference between the highest and the lowest frequencies) of frequencies in a pulse

: the frequency emitted is not uniform

- Long duration events are narrow bandwidth and short duration events are wide bandwidth.

            : axial resolution is improved with wide bandwidth (shorter pulse duration) transducers

               : axial resolution worse with narrow bandwidth (longer pulse duration) transducers

- wide bandwidth pulses (2-5Hz): echo signals will be shifted down in frequency

(due to increased attenuation of higher frequencies)

- Fractional bandwidth

: bandwidth divided by the operating frequency

: The strongest frequency within the bandwidth is the operational frequency.

 

2) Operating Frequency (=Resonance frequency)

- Operating frequency (Resonant frequency) is the frequency of choice.

- F_o =   C_t/ (2 x thickness)

(Thinner element = higher frequency) (Thicker element = lower frequency)

 

3) Quality Factor (QF)

- Imaging

: Short distinct pulses and length are needed: Improved Axial Resolution

               - Wide bandwidth, lower Q factor

: most energy is lost after first few vibrations

: Use backing material to reduce ringing

- QF = f_o/bandwidth

: Wide bandwidth (multifrequency selection) – low Q factor – short duration

               - used for diagnostic pulsed-wave ultrasound (Low QF is good quality)

: Narrow bandwidth – high Q factor – long duration

 

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Reference

 

* Davies Ultrasound Physics review

* https://sites.google.com/site/lindadmsportfolio/ultrasound-physics/

* https://sites.google.com/site/nataljasultrasoundphysics/

* https://sites.google.com/site/ektasphysicseportfolio/doppler