Fetal Echocardiography & Ultrasound Physics Review

The Basic Concepts in Fetal Ultrasound Physics

This note compiles key ideas from the transcript covering ultrasound physics, units, waves, and pulsed ultrasound parameters.
It emphasizes concepts, definitions, relationships, and typical values used in diagnostic ultrasound.

Units, prefixes, and conversions

Unit systems provide context for numbers across length, time, mass, area, and volume.
- Length: meter (m), inch, kilometer (km)
- Time: second (s), minute (min)
- Mass: kilogram (kg)
- Area: square centimeter (cm²), square foot (ft²), square yard (yd²)
- Volume: cubic centimeter (cm³), cubic foot (ft³), etc.
Common unit conversions (example): 12 inches = 1 foot. Conversions do not change the total quantity, only the unit used.
Prefixes (order-of-magnitude):
- tera (T) = 10^12
- giga (G) = 10^9
- mega (M) = 10^6
- kilo (k) = 10^3
- hecto (h) = 10^2
- deka (da) = 10^1
- deci (d) = 10^-1
- centi (C) = 10^-2
- milli (m) = 10^-3
- micro (µ) = 10^-6
- nano (n) = 10^-9
Takeaway: The “total picture” remains the same when converting units, but the numeric value changes with the unit.

Direct and inverse proportions

Direct proportionality: when one quantity increases, the other increases by the same factor.
Inverse proportionality: when one quantity increases, the other decreases by the same factor.
Reciprocal relationship: two numbers multiply to 1 (e.g., 2 × 1/2 = 1).
Examples mentioned:
- Period and frequency are inverses: f = rac{1}{T} or T = rac{1}{f}.
- Other reciprocal relationships appear in unit analysis (e.g., Hz and seconds).

Acoustic waves: basics and terminology

Sound waves are mechanical, longitudinal waves that require a medium and travel in a straight line.
Wave types:
- Longitudinal waves: particle motion is parallel to the direction of wave propagation.
- Transverse waves: particle motion is perpendicular to the direction of wave propagation.
Acoustic variables identify the instantaneous state of a sound wave:
- Pressure (P): units: Pascals (Pa); description: concentration of force within an area.
- Density (ρ): units: kg/cm³ (typical in older notes; SI is kg/m³); description: concentration of mass within a volume.
- Distance (x): displacement or particle motion; units: cm, ft, etc.
Acoustic variables vs acoustic parameters:
- Acoustic variables describe instantaneous quantities (e.g., instantaneous pressure, density).
- Acoustic parameters describe features of the wave (e.g., period, frequency, amplitude, power, intensity, speed, wavelength).
Key statements:
- Sound pulses are created by a vibrating object (transducer) and travel through media.
- Reflections arise from interfaces within media and return to the transducer for imaging.
- Acoustic propagation properties describe how media affect the sound wave; biologic effects describe how sound interacts with tissue.

Interference and phase relationships

Wave interference can be constructive or destructive:
- In phase (phase difference ≈ 0): constructive interference.
- Out of phase (phase difference ≈ 180°): destructive interference.
Phase angle: when peaks align (in phase) interference is constructive; when peaks align out of alignment (out of phase) interference is destructive.
Notation examples in the transcript show multiple scenarios of in-phase vs out-of-phase interactions among pairs of waves.

Period, frequency, wavelength, and speed

Period (T): the time required to complete one cycle of a wave.
- Units: seconds (s), microseconds (µs), etc.
- Relationship: f = rac{1}{T} and T = rac{1}{f}.
Frequency (f): number of cycles per unit time.
- Units: Hz (s⁻¹).
Wavelength (λ): distance of one complete cycle.
- Relationship with speed: v = f imes BBlambda
- In a medium, BBlambda = rac{v}{f} where v is the propagation speed in that medium.
Propagation speed (v): speed at which the wave travels through a medium.
- In homogeneous media, all frequencies travel at the same speed in that medium.
- Typical values (soft tissue ≈ 1540 m/s).
- Medium-dependent: speeds in air, fat, bone, lung vary widely.
Soft tissue quick reference:
- v \,\approx \,1.54\ \text{mm/µs} = 1540\ \text{m/s}
- Wavelength example in soft tissue: for 3 MHz, \lambda \approx \frac{v}{f} = \frac{1540\ \text{m/s}}{3\times10^6\ \text{Hz}} \approx 0.000513\ \text{m} = 0.513\ \text{mm}.
Practical rule: higher frequency yields shorter wavelength and better axial resolution but reduced penetration; frequency is inversely related to penetration in tissue.

Amplitude, power, and intensity

Amplitude (A): strength or maximum variation of an acoustic variable.
- It is the difference between maximum and minimum values of the acoustic variable; can be expressed in units of the variable (pressure, density, particle motion) or in decibels (dB).
- Amplitude is determined by the sound source and can be altered by the sonographer in some systems.
- As sound propagates through tissue, amplitude generally decreases (attenuation).
Power (P): rate at which work is performed or energy is transferred.
- Units: Watts (W).
- Relationship: typically P ∝ A² (amplitude squared).
Intensity (I): concentration of energy in a beam; power per unit cross-sectional area.
- Formula: I = rac{P}{A{ ext{beam}}} where Abeam is the cross-sectional area of the beam.
- Units: W/cm² (or W/m²).
- Intensity decreases with propagation through tissue due to attenuation.
Key relationships:
- Power is proportional to the square of the amplitude: P \propto A^2
- Intensity is proportional to the square of the amplitude: I \propto A^2
- For a fixed beam area, increasing power increases intensity; conversely, increasing beam area with the same power reduces intensity.
Practical significance: Intensity is a critical parameter for bioeffects and safety in diagnostic ultrasound.

Wavelength and speed: practical equations

Wavelength in a medium: \lambda = \frac{v}{f}
Soft-tissue rule of thumb: in soft tissue, approximately \lambda\, (\text{mm}) a0\approx\u00a0\frac{1.54}{f(\text{MHz})}
Propagation speed in a medium depends on medium properties only (not on the wave frequency) and is given by the properties of the medium (density, stiffness).
General speed relationships:
- Speed is higher in stiffer media and typically lower in less dense media; density and speed are inversely related, while stiffness (bulk modulus) and speed are directly related.
- A simple intuition: gas < liquid < solid for speed, with speed increasing as stiffness increases and density decreases (roughly).

Propagation speed in common media

Typical speeds (approximate):
- Air: ~330 m/s
- Lung: ~300–1,200 m/s (depending on air–tissue content)
- Fat: ~1,450 m/s
- Soft tissue: ~1,540 m/s
- Bone: ~2,000–4,000 m/s
Important takeaway: The speed of sound is determined by the medium, not by the transmitted frequency; all frequencies travel at the same speed in a given medium.

Pulsed ultrasound: key parameters

Pulsed sound (PW) consists of a transmit/on time followed by a receive/off time.
Key pulsed-wave (PW) parameters:
- Pulse Duration (PD): the actual time the pulse is on, from start to end. Units: time (s or µs). Symbol: PD. Formula: PD = n imes T = rac{n}{f} where n is the number of cycles in the pulse and T is the period.
- Pulse Repetition Period (PRP): time from the start of one pulse to the start of the next pulse. Units: time. Symbol: PRP. Relationship: PRP = rac{1}{PRF} where PRF is the-Pulse Repetition Frequency.
- Pulse Repetition Frequency (PRF): number of pulses transmitted per second. Units: Hz. Symbol: PRF. Relationship: PRF = rac{1}{PRP}. Also: PRF \times PRP = 1.
- Duty Factor (DF): fraction of time that the system transmits the pulse. DF = \frac{PD}{PRP}; often expressed as a percentage: DF(\%) = 100 \times \frac{PD}{PRP}.
- Spatial Pulse Length (SPL): physical length of the transmitted pulse in space. Units: mm. Symbol: SPL. Formula: SPL = n \times \lambda where n is the number of cycles in the pulse and λ is the wavelength.
Depth of View (DOF): the maximum imaging depth; affects PRP, PRF, and DF. Deep imaging → longer PRP and lower PRF; shallow imaging → shorter PRP and higher PRF.
Important: PD and SPL are intrinsic to the transducer and its pulse, and are not directly adjustable by depth alone; PRP, PRF, and DF are adjustable via imaging depth and system settings.
Typical relationships:
- Decreasing depth shortens PRP, increases PRF, and increases DF.
- Increasing depth lengthens PRP, decreases PRF, and decreases DF.
Practical implication: Shorter PD and SPL favor higher axial resolution; however, SPL depends on both the pulse and the medium.

Spatial pulse length (SPL) and axial resolution

SPL is the distance from the start to the end of a single pulse. It is the spatial length of the pulse in tissue.
SPL formula: SPL = n \times \lambda where n is the number of cycles in the pulse and λ is the wavelength in the medium.
SPL is directly related to the number of cycles and to the wavelength; SPL is also indirectly related to frequency via λ.
Shorter SPL yields improved axial resolution; shorter SPL typically comes from fewer cycles per pulse or shorter wavelength (higher frequency).
Key practical note: SPL depends on both the transducer (source) and the medium; it is not adjustable independently by the sonographer.

Imaging depth, frequency, and resolution: practical trade-offs

Higher frequency → shorter wavelength → better axial resolution but reduced penetration depth.
Lower frequency → longer wavelength → deeper penetration but worse axial resolution.
For obstetric imaging and large patients, a compromise frequency may be selected (e.g., mid-range transducers).
The display quality and image resolution depend on the interplay of frequency, SPL, DF, PRP/PRF, and patient-specific factors.

Review: key formulas and relationships (summary)

Period and frequency: f = \frac{1}{T},\quad T = \frac{1}{f}
Speed, frequency, and wavelength: v = f \lambda,\quad \lambda = \frac{v}{f}
Soft-tissue wavelength rule: \lambda(\text{mm}) \approx \frac{1.54}{f(\text{MHz})}
Spatial pulse length: SPL = n\lambda
Pulse duration: PD = n \times T = \frac{n}{f}
Pulse repetition period and frequency: PRP = \frac{1}{PRF},\quad PRF = \frac{1}{PRP}
Duty factor: DF = \frac{PD}{PRP}
Intensity: I = \frac{P}{A_{beam}} = \text{W/cm}^2 with P \propto A^2,\quad I \propto A^2
Amplitude and power: P \propto A^2, I \propto A^2

Review: common exam-style questions (conceptual answers)

The speed of sound in a medium is determined by the medium’s properties (density and stiffness) and is not changed by frequency.
In diagnostic ultrasound, frequency is inversely related to penetration depth; higher frequency yields better axial resolution but less depth.
The spatial pulse length (SPL) determines axial resolution; shorter SPL improves axial resolution.
The Doppler/echo system adjusts depth of view by changing PRP and PRF; deeper imaging increases PRP and decreases PRF.
Acoustic power and ultrasound intensity are related to safety; intensity is a key safety parameter because it represents energy per unit area transported by the beam.
The units and prefixes section provides the basis for converting measurements (e.g., mm to cm, etc.) using the SI prefixes listed above.

Connections to foundational principles and real-world relevance

The inverse relationship between frequency and penetration explains why obstetric scans use higher frequency transducers in early gestation (good resolution) but may switch to lower frequencies for deeper structures or larger patients.
Axial resolution is primarily affected by SPL; thus, transducer choice, duty factor, and optimization of pulse length influence image clarity.
Understanding direct vs. inverse proportionality and reciprocal relationships helps in predicting how changing one parameter (e.g., frequency, depth) will impact others (e.g., wavelength, PRP, PRF, DF, SPL).
Safety considerations center on intensity and power; higher intensities can increase bioeffects, so reducing unnecessary exposure while maintaining image quality is essential in clinical practice.

Quick reference: sample numerical reminders

Conversion example: 12 inches = 1 foot; 1 foot = 12 inches.
Speed in soft tissue: v \approx 1.54\times10^3\ \text{m/s}
Wavelength in soft tissue: e.g., f = 3 MHz → \lambda \approx \frac{1.54\ \text{mm}/\mu\text{s}}{3\ \text{MHz}} \approx 0.513\ \text{mm}
SPL for a 4-cycle pulse with λ = 0.5 mm: SPL = n\lambda = 4 \times 0.5\ \text{mm} = 2.0\ \text{mm}
DF example: a pulse lasting 10 µs within a 100 µs PRP yields DF = \frac{PD}{PRP} = \frac{10}{100} = 0.10 = 10\%

Notation and terminology used in the transcript (glossary)

Acoustic variables: instantaneous pressure (P), density (ρ), particle motion (x).
Acoustic parameters: frequency (f), period (T), amplitude, power (P), intensity (I), speed (v), wavelength (λ), SPL, PD, PRP, PRF, and DF.
Media terms for propagation: density, stiffness, bulk modulus, attenuation/absorption, and biologic effects.
Visual vs numerical references: codes in the transcript’s review sections (e.g., relationships like increasing/decreasing order of prefixes) provide practice for exam-style problem solving.

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