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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

- 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

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