3 Ultrasound Acoustic Parameters – Comprehensive Notes

Describing Sound Waves: Source vs Medium

• The source of the sound wave is the ultrasound (U/S) system and the transducer.
• Some parameters are determined by the U/S system; the sonographer can adjust the level of some of these.
• Other parameters are determined by the tissue (the medium) through which the sound travels.

The Seven Acoustic Parameters

• Acoustic parameters describe the nature of the sound/beam.
• There are seven: Period, Frequency, Amplitude, Power, Intensity, Wavelength, Propagation Speed.

Period (P)

• Definition: The time it takes a wave to vibrate a single cycle; equivalently, the time from the start of one cycle to the start of the next cycle.
• Units:
  • Time units: microseconds, seconds, hours, days
• Determined by: SOURCE (the U/S system); Sonographer CANNOT change it.
• Relationship to frequency: Frequency and period are reciprocal.
  • Primary relations:
    $F \times P = 1$
    $F = \frac{1}{P},\quad P = \frac{1}{F}$
• Conceptual view: Period is one of the two reciprocal descriptors of the wave cycle; changing it requires changing the source, not the tissue.

Frequency (F)

• Definition: The number of cycles per second.
• Units: Hz (per/second); also kHz, MHz.
• Determined by: SOURCE (the U/S system); Sonographer CANNOT change it.
• Relationship to period: see above (reciprocal relationship).
• Conceptual view: Frequency and period are reciprocal descriptions of the same time parameter.

Wavelength (\lambda)

• Definition: The distance covered by one complete cycle.
• Units: mm, cm, km, etc. (any unit of distance).
• Determined by: SOURCE and MEDIUM (the only ultrasound parameter that depends on both).
• Can be changed by the sonographer? NO (wavelength cannot be changed directly by the sonographer; it depends on the medium and the transmitted frequency).
• Relationship with speed and frequency:
  • Speed and wavelength are tied to frequency by the relation:
    $\lambda = \frac{C}{F}$
  • Consequently, the propagation speed is also related by:
    $C = \lambda F$
• Inverse relationship with frequency: as frequency increases, wavelength decreases (\lambda ↑ F ↓ and \lambda ↓ F ↑).
• Soft-tissue example (specific numerical rule):
  • In soft tissue, the approximate relationship is
    $\lambda \approx \frac{1.54\text{ mm}}{F}$
    where F is in MHz.
• Important example values in soft tissue:
  • 1 MHz → $\lambda \approx 1.54\text{ mm}$
  • 2 MHz → $\lambda \approx 0.77\text{ mm}$
  • In general, higher frequency yields shorter wavelength in the same medium.
• Reminder: This soft-tissue relationship is a common practical rule of thumb; it specifically assumes soft tissue medium.

Propagation Speed (C)

• Definition: The rate at which a sound wave travels through a medium.
• Units: m/s, mm/µs (or any distance divided by time).
• Determined by: MEDIUM (the tissue); Sonographer CANNOT change it directly.
• Relationship to wavelength and frequency:
  $C = \lambda F$
  which implies $\lambda = \frac{C}{F}$ and $F = \frac{C}{\lambda}$
• Typical values and notes:
  • Average speed of ultrasound in soft tissues: $C \approx 1.54\ \text{km/s} = 1540\ \text{m/s} = 1.54\ \text{mm}/\mu\text{s}$
  • Sound travels fastest in solids, slower in liquids, slowest in gases.
• Determinants: Stiffness and density of the medium (rules of thumb):
  • Higher stiffness leads to higher speed: $\text{Stiffness} \uparrow \Rightarrow C \uparrow$
  • Higher density tends to lower speed: $\text{Density} \uparrow \Rightarrow C \downarrow$
• Practical takeaway: Any change in measured speed indicates a change in the medium (not a change by the operator).

Amplitude (A)

• Definition: Difference between the maximum value and the average value of the pressure or other acoustic quantity; describes the magnitude of the wave.
• Sign: Amplitude can be positive or negative depending on the reference orientation.
• Units: Can be any unit of an acoustic variable; there is also a unit called the decibel (dB) for amplitude levels.
• Determined by: SOURCE; Sonographer CAN adjust it.
• Relationship to power: Amplitude and power are directly related; Power is proportional to the square of amplitude:
  $P = A^2$
• Examples of change:
  • If amplitude is increased by a factor of 3, then $P \text{ becomes } 3^2 = 9 \text{ times greater}.$
  • If amplitude is halved, $P \text{ becomes } (1/2)^2 = 1/4 \text{ of original}.$
• Conceptual note: Larger amplitude means a stronger wave, but power is the rate of energy transfer which depends on amplitude squared.

Power (P)

• Definition: Rate of energy transfer or the rate at which work is performed by the wave.
• Units: Watts (W).
• Determined by: SOURCE; Sonographer CAN change it.
• Behavior with propagation: Power tends to decrease as the beam propagates through the body (attenuation) due to interactions with the medium and scattering.
• Relationship to amplitude: $P = A^2$ (power is proportional to amplitude squared).

Intensity (I)

• Definition: Concentration of energy in a sound wave.
• Calculation:
  $I = \frac{P}{\text{Area}}$
  where Area is the beam’s cross-sectional area.
• Units: $\text{W}/\text{cm}^2$ (Power in watts, area in cm$^2$).
• Determined by: SOURCE; Sonographer CAN change it.
• Behavior with propagation: Intensity decreases as the beam travels through the medium (due to attenuation and geometric spreading).

Relationships and Summary of Parameter Roles

• Reciprocal relationship (period and frequency): $F \times P = 1,$ with equivalent forms $F = \frac{1}{P},\quad P = \frac{1}{F}.$
  • Both are determined by the SOURCE and cannot be independently altered by the sonographer.
• Wavelength and speed relationship: $\lambda = \frac{C}{F},\quad C = \lambda F.$
  • Wavelength is the distance of one cycle; speed depends on the medium; frequency is set by the source.
• Medium vs source determinants:
  • Speed (C) is determined by the medium (tissue characteristics).
  • Period and Frequency are determined by the source (ultrasound system) and generally cannot be changed by the operator.
  • Wavelength depends on both source and medium.
  • Amplitude, Power, and Intensity are adjustable by the operator (and depend on source settings and tissue interactions).
• Practical rule of thumb for soft tissue values:
  • The standard speed in soft tissue is approximately $C \approx 1.54\ \text{mm}/\mu\text{s} = 1540\ \text{m/s}.$
  • Frequency-to-wavelength relationship in soft tissue follows $\lambda \approx \frac{1.54\ \text{mm}}{F}\, (F\text{ in MHz}).$
• Three key magnitude descriptors (Three Bigness Parameters):
  • Amplitude (A)
  • Power (P)
  • Intensity (I)
  • These describe the size/strength of the wave and are respectively linked by the relationships above; note also that Intensity depends on Power and beam cross-sectional Area.
• Diagrammatic interpretation (conceptual):
  • Pressure distribution at an instant in time: $p(x)$ with amplitude Po and pressure at a point $p(t)$ over time; the figures illustrate how period, amplitude, and wavelength relate in space and time.
• Summary of determinism:
  • Period, Frequency: largely determined by the source; relatively fixed from frame to frame by the system settings.
  • Wavelength: determined by both source and medium; cannot be changed directly by the operator.
  • Speed: determined by medium characteristics; not adjustable by the operator.
  • Amplitude, Power, Intensity: adjustable by the operator; influence beam strength and energy deposition.

Quick Soft-Tissue Reference Values and Rules

• Propagation speed in soft tissue: $C \approx 1.54\ \text{mm}/\mu\text{s}$ (or $1540\ \text{m/s}$ or $1.54\ \text{km/s}$).
• Wavelength in soft tissue for a given frequency:
  • $\lambda \approx \frac{1.54\ \text{mm}}{F}$, with F in MHz.
  • Example: at 1 MHz, $\lambda \approx 1.54\ \text{mm}$; at 3 MHz, $\lambda \approx \frac{1.54}{3} \approx 0.513\ \text{mm}$ (in soft tissue).
• General speed rule: speed is highest in solids, lower in liquids, lowest in gases; changes in speed imply different tissue characteristics.

Notes on Figures and Notation from the Transcript

• p(x) and p(t) illustrate pressure distribution in space and time, respectively.
• The diagrams show the relationship among period, amplitude, and wavelength in a simplifying way to visualize how these parameters manifest in a beam.
• The material emphasizes that some parameters are sinked in the medical device’s control (source), others in the tissue (medium), and some can be adjusted by the operator (sonographer).

Practical Takeaways for Exam Preparation

• Know the seven acoustic parameters and their definitions, units, and whether they’re source-determined, medium-determined, or adjustable by the sonographer.
• Be able to state and use the core equations:
  • Frequency–Period reciprocity: $F = \frac{1}{P},\quad P = \frac{1}{F},\quad F\times P = 1$
  • Wavelength and speed: $\lambda = \frac{C}{F},\quad C = \lambda F$
  • Power and Amplitude: $P = A^2$
  • Intensity: $I = \frac{P}{A<em>{beam}}\quad\text{with}\; A</em>{beam} \approx \text{beam cross-sectional area}$
• Remember the soft-tissue practical values and relationships, especially the typical speed and the approximate wavelength rule of thumb.
• Distinguish which parameters you can change in real-time during imaging (Amplitude, Power, Intensity) versus those that are fixed by the system (Period, Frequency) or determined by tissue (Speed, with some wavelength dependence).