Basic Ultrasound Physics - Comprehensive Notes (Bullet-Point Summary)

Terminology and Professional Language

• Ultrasound vs. Sonography terminology

  • These terms are still used interchangeably in practice, but this is incorrect as a strict matter of terminology.

  • Ultrasound: a sonographic physics term describing the type of energy used to produce an examination (e.g., a sonogram/echocardiogram).

  • Diagnostic Medical Sonography: the proper term for referring to the profession.

  • Example from slide: ultrasound energy used to drive a sonographic exam; professional title is Diagnostic Medical Sonography.

  • Source cues: slide titled “Ultrasound or Sonography?” and note on language consistency (9/26/2022).

• Referencing image vs. energy: analogy to photography

  • Sonography uses reflected ultrasound waves to create an image; referring to the image itself as an “ultrasound” is like saying you are going to take a light to make a photograph. A photo is made with reflected light, just as an image is formed from echoes in ultrasound.

  • Quotation: Terry Duboise (2004).

  • Practical takeaway: use correct terms (e.g., sonogram/echocardiogram describe images; ultrasound energy describes the modality).

• Professional vocabulary to avoid (examples)

  • The following colloquialisms should not be used:

  • That/these “thingy/thingies” for transducer or EKG leads

  • “watch-a-ma-call-it”

  • The “stuff” on the screen (echoes/reflections)

  • Take the “picture” (instead, say acquire/store image or clip)

  • It looks “ugly” (poor image resolution)

  • Ultrasound “machine” (instead: ultrasound imaging system)

  • Rationale: using proper terminology supports professionalism in the field.

  • Source: slide on professional terminology (9/26/2022).

What is ultrasound imaging and how images are produced

• Basic image formation concept

  • Ultrasound imaging uses short bursts (pulses) of high-frequency sound energy.

  • Pulses propagate into the body, reflect back (echoes) to the transducer and imaging system.

  • System processes echoes and displays multiple echoes on screen.

  • Echo brightness varies (brightness corresponds to echo amplitude) and together form a 2D anatomical slice.

  • Core idea: image is built from echoes, not from continuous light-like energy; echoes provide the map of tissue interfaces.

• Image depends on multiple factors

  • The structures being scanned

  • The time of echo arrival (round-trip travel time from source to reflectors and back)

  • The intensity (amplitude) of echoes

Sound, waves, and basic wave terminology

• Sound characteristics (sound as a wave)

  • Sound energy is a wave (a coordinated disturbance) that travels through a medium at a fixed speed.

  • Also described as a pressure wave, a mechanical wave, with associated vibration.

  • Example reference: tuning fork experiments to illustrate mechanical wave behavior.

• Media and vibration

  • Sound must travel through a medium (air, water, tissue, etc.); it cannot travel through a vacuum.

  • Sound travels in straight lines (geometric propagation).

  • The medium’s properties determine speed and wavelength (see propagation speed section).

• Representation in the book

  • The wave is often represented as a transverse-like depiction in textbooks to illustrate high and low-pressure regions during compressions and rarefactions, but the actual sound wave in tissue is longitudinal in nature.

Sound types, speeds, and media in the body

• Speed of sound is medium-dependent

  • The speed is a property of the medium (not the frequency) and does not change unless the wave enters a different medium.

  • Typical speeds in common media:

  • Air: $c \,=\, 330\ \text{m/s}$

  • Lung: $300-1200\ \text{m/s}$ (variable)

  • Fat: $1450\ \text{m/s}$

  • Water: $1480\ \text{m/s}$

  • Soft tissue: $1540\ \text{m/s}$ (AVE)

  • Liver: $1550\ \text{m/s}$

  • Kidney: $1560\ \text{m/s}$

  • Muscle: $1600\ \text{m/s}$

  • Tendon: ≈$1850\ \text{m/s}$

  • Bone: $2000-4000\ \text{m/s}$

  • Metals: $2000-7000\ \text{m/s}$

  • Rule of thumb (Edelman): stiffness and speed move in the same direction; density and speed move in opposite directions; compressibility/elasticity are opposite of stiffness; bulk modulus ≡ stiffness.

  • Important summary: “All sound, regardless of frequency, travels at the same speed through any specific medium.”

• General implications

  • Sound speeds are slower in gases, faster in liquids, fastest in solids.

  • This affects wave travel time, refraction, and penetration depth in imaging.

Wave frequency, periods, and wavelength

• Frequency vs period (inverse relationship)

  • Frequency and period are inversely related: $f \, T = 1\quad\Rightarrow\quad T = \frac{1}{f}$

  • Product rule: for a given wave, the product of frequency (in Hz) and period (in seconds) equals 1.

• Definitions and typical ranges

  • Frequency: number of events (cycles) per second.

  • Typical diagnostic ultrasound frequencies: approx. $2\ \text{MHz}$ to $15\ \text{MHz}$ within the board’s examples; typical clinical systems operate in this range.

  • Audible: $20\ \text{Hz} \text{ to } 20{,}000\ \text{Hz}$;

  • Infrasound: <20\ \text{Hz};

  • Ultrasound: >20{,}000\ \text{Hz}

• Wavelength in tissue

  • Wavelength in soft tissue: $\lambda = \dfrac{c}{f}$ with $c \approx 1.54\ \text{mm}/\mu s$ (soft tissue speed) and frequency in MHz.

  • Therefore, in soft tissue:

  • At $1\ \text{MHz}: \lambda \approx \frac{1.54}{1} = 1.54\ \text{mm}$

  • At $2\ \text{MHz}: \lambda \approx \frac{1.54}{2} = 0.77\ \text{mm}$

  • At $3\ \text{MHz}: \lambda \approx \frac{1.54}{3} ≈ 0.513\ \text{mm}$

  • General relation: $\lambda = \dfrac{c}{f}$ and $\lambda\text{(mm)} = \dfrac{1.54}{f\text{(MHz)}}$ (soft tissue)

• Pulse picture: longitudinal vs transverse in the context of sound depiction

  • The actual sound wave is longitudinal; a transverse representation is a schematic to show regions of compression and rarefaction, i.e., pressure differences.

  • The peak/trough depiction corresponds to high/low pressure zones during compression and rarefaction.

• Practical rule: frequency affects penetration and resolution

  • Higher frequency: better resolution but less penetration (deeper imaging may require lower frequency).

  • Lower frequency: greater penetration but lower resolution.

Pulsed versus continuous ultrasound and imaging needs

• Continuous wave (CW) vs pulsed wave (PW)

  • Continuous wave is not suitable for imaging because it does not provide “listening” time to receive echoes.

  • Pulsed ultrasound provides both transmit (talking) and receive (listening) phases, enabling image formation.

• Pulsed ultrasound components

  • Pulse: a collection of cycles that travels together; has a beginning and an end.

  • Two main components: the cycles (transmit/on time) and the dead time (receive/off time).

• Why pulsed imaging is essential for diagnostics

  • During the listening phase, echoes are received, processed, and displayed with brightness reflecting echo amplitude.

  • Continuous waves would be constantly transmitting and would not produce useful reflections for imaging.

• Short summary from slides

  • Pulsed imaging allows collection of time-gated echoes to form 2D images (brightness encodes echo strength).

  • The pulse itself does not change; only the system’s listening time changes with depth and PRP/PRF settings.

Pulse-specific parameters and how they relate to imaging

• Pulse Duration (PD)

  • Defined as the time from the start to the end of a pulse (the “on” time).

  • Units: microseconds (µs), milliseconds (ms), seconds (s).

  • Typical values: 0.5–3 µs; clinical pulses usually 2–4 cycles.

  • Relation: pulse duration (µs) = (# cycles) × period (µs) or equivalently PD = N / f.

  • In broader terms: higher frequency yields shorter pulse duration for a fixed number of cycles.

• Spatial Pulse Length (SPL)

  • SPL = distance spanned by one pulse in space.

  • Units: mm, meters, etc.

  • Determined by both the source and the medium; cannot be changed by the sonographer.

  • Typical range for diagnostic pulsed ultrasound: 0.1–1 mm.

  • Effect on image: SPL affects axial (along the beam) resolution; shorter SPL yields better axial resolution.

  • SPL relation: SPL (mm) = (# cycles) × (wavelength in mm).

• Pulse Repetition Period (PRP)

  • Time from the start of one pulse to the start of the next pulse.

  • Includes both on (transmit) and off (listening) times.

  • Units: µs (or any time unit).

  • Typical range: 100 µs to 1 ms.

  • PRP is approximately 100–1,000 times longer than the pulse duration.

  • Can be adjusted by changing imaging depth (via depth of field) by the operator; pulse duration remains fixed.

  • Change mechanism: adjusting imaging depth increases listening time (off time), thereby increasing PRP.

• Pulse Repetition Frequency (PRF)

  • The number of pulses that occur in one second.

  • Units: Hz (pulses per second).

  • Typically diagnostic imaging ranges: 1,000–10,000 Hz (1–10 kHz).

  • PRF is inversely related to PRP: $PRF = \dfrac{1}{PRP}$ and $PRP = \dfrac{1}{PRF}$

  • Shallow imaging yields higher PRF (more pulses per second) and shorter listening times; deep imaging yields lower PRF (fewer pulses per second) and longer listening times.

• Duty Factor (DF)

  • Percentage or fraction of time that the system transmits a pulse.

  • Units: unitless (percentage is DF as a percent).

  • Formula: $\text{DF} = \frac{\text{PD}}{\text{PRP}} \times 100\%$

  • Typical pulsed imaging ranges: 0.1% to 1% (0.001 to 0.01 in decimal form). A continuous-wave system would have DF = 100% (1.0).

  • DF is higher when imaging depth is shallower (more “talking” time relative to listening time) and lower when imaging depth is deeper.

• Important note on adjustments

  • Sonographer directly changes PRP and PRF via depth adjustments and system settings; the pulse duration is generally fixed by the system and cycle count per pulse.

  • When depth increases, listening time increases, PRP increases, PRF decreases, and DF decreases accordingly.

Relationship among pulse metrics and practical rules

• Inverse relationships and reciprocals

  • PRP and PRF are reciprocals: $PRP \cdot PRF = 1$

  • Period and frequency are reciprocals: $f \cdot T = 1$ and $T = \frac{1}{f}$.

• How depth influences PRP/PRF and duty factor

  • Shallow imaging: higher PRF, more “talking” time and less “listening” time; DF is higher.

  • Deep imaging: lower PRF, more listening, less talking; DF is lower.

• Equation forms to memorize

  • Pulse Duration: $PD = N \cdot \, \text{period} = \dfrac{N}{f}$

  • Spatial Pulse Length: $SPL = N \cdot \lambda$ and $\lambda = \dfrac{c}{f}$

  • Wavelength in tissue: $\lambda\text{(mm)} = \dfrac{1.54}{f\text{(MHz)}}$ (soft tissue, using $c\approx 1.54\ \text{mm}/\mu s$)

  • PRP and PRF: $PRP = \dfrac{1}{PRF}$ and $PRP\cdot PRF = 1\,.$

  • Duty Factor: $\text{DF} = \dfrac{PD}{PRP} \times 100\%$

• Practical numeric guidelines from slides

  • Typical PD values: 0.5–3 µs; commonly 2–4 cycles per pulse.

  • Typical SPL ranges: 0.1–1 mm for diagnostic pulsed ultrasound.

  • In soft tissue, a 1 MHz waveform corresponds to ~1.54 mm wavelength; higher frequencies reduce wavelength accordingly.

Spatial pulse length and axial resolution

• SPL and axial resolution

  • Shorter SPL yields higher axial resolution because the system can distinguish closely spaced reflectors along the beam path.

  • SPL depends on both the number of cycles in a pulse and the wavelength: SPL = N × λ.

  • Since λ = c/f, increasing frequency (f) reduces λ and thus SPL for a fixed N, improving axial resolution up to system limits.

• Practical calculation

  • SPL (mm) = (# cycles) × (wavelength in mm) = N × λ.

  • If N is fixed, increasing frequency lowers λ and SPL, improving axial resolution; if N increases, SPL increases, potentially reducing axial resolution unless compensated by higher f.

Summary of image formation and board-oriented notes

• The SPI board terminology (education context)

  • ACOUSTIC PROPAGATION PROPERTIES: effects of the medium on the sound wave; what happens to sound when it enters the body.

  • BIOLOGIC EFFECTS: effects of the sound wave on tissue; what happens to tissue when sound enters the body.

• Key image formation concepts (recap)

  • Short pulses emit energy into tissue; echoes reflect back to transducer; the imaging system converts echo strength and timing into a 2D image.

  • Brightness encodes echo amplitude, not the mere presence of an echo; multiple echoes create composite tissue interfaces.

Practical exam references and resources

• Exam context and scoring references

  • A minimum score of 555 is a passing score for the SPI board; max score is 700.

• Reference works cited in the slides

  • Edelman, Sidney K. (2004), Understanding Ultrasound Physics, ESP, Inc.

  • Zagzebski, James A. (1996), Essentials of Ultrasound Physics, Mosby, Inc.

  • Online resource: Physics of Sound (external link)

• Additional notes

  • “Life, is the mirror image of Ultrasound Physics… it’s all about balance and reflections” (quote on slide).

  • YouTube and multimedia references used to illustrate concepts (e.g., tuning fork and wind-up music box examples) which aid intuition but are not examination material per se.

• Quick reference table: speed and tissue types (selected values)

  • Air: 330 m/s; Lung: 300–1200 m/s; Fat: 1450 m/s; Water: 1480 m/s; Soft tissue: 1540 m/s; Liver: 1550 m/s; Kidney: 1560 m/s; Muscle: 1600 m/s; Tendon: ~1850 m/s; Bone: 2000–4000 m/s; Metals: 2000–7000 m/s.

• Final takeaway

  • Ultrasound imaging relies on pulsed energy, time-gated echoes, and a set of interrelated parameters (PD, SPL, PRP, PRF, and DF) to form diagnostic images with appropriate resolution and penetration. Understanding the relationships among these quantities is essential for optimizing image quality and interpreting ultrasound physics on exams.

Key equations and constants to memorize

• Basic wave relationship

  • $f \cdot T = 1, \quad T = \dfrac{1}{f}$

• Wavelength in tissue

  • $\lambda = \dfrac{c}{f}, \quad c \approx 1.54\ \text{mm}/\mu\text{s}$

  • For soft tissue: $\lambda\text{(mm)} \approx \dfrac{1.54}{f\text{(MHz)}}$

• Spatial pulse length

  • $SPL = N \cdot \lambda$

• Pulse duration

  • $PD = N \cdot \text{period} = \dfrac{N}{f}$

• Pulse repetition period and frequency

  • $PRP = \dfrac{1}{PRF}, \quad PRF = \dfrac{1}{PRP}$

• Duty factor

  • $\text{DF} = \dfrac{PD}{PRP} \times 100\%$

• Power and amplitude relationships (qualitative)

  • Power is proportional to the square of amplitude: $P \propto A^2$

  • If amplitude doubles, power increases by a factor of 4.

• Speed of sound and tissue properties

  • $c = \text{speed of sound in medium}$ (depends on density and stiffness/density interactions; tissue speeds listed above).

• Interference basics (concept only)

  • Constructive interference occurs when waves are in phase; destructive interference occurs out of phase.