ARDMS SPI Study Reference
ARDMS SPI Ultrasound Physics Formula Sheet
The ultimate equation guide for the ARDMS Sonography Principles & Instrumentation examination. Need to test calculations? Check our interactive physics calculators.
Pulsed Wave & Resolution
| Parameter | Formula | Key Clinical Concept |
|---|---|---|
| Axial Resolution | SPL / 2 | LARRD. Determined by spatial pulse length. Lower value = better resolution. |
| Spatial Pulse Length (SPL) | Number of Cycles × Wavelength (λ) | Determined by both sound source and medium. |
| Pulse Duration (PD) | Number of Cycles × Period (T) | Time from start of a pulse to end of that pulse. |
| Duty Factor (DF) | (Pulse Duration / PRP) × 100 | Typical clinical imaging range is 0.1% to 1.0%. |
Doppler & Hemodynamics
| Parameter | Formula | Key Clinical Concept |
|---|---|---|
| Doppler Equation | Fd = (2 × Fo × v × cos θ) / c | Maximum Doppler shift occurs at 0° when cos θ equals 1.0. |
| Nyquist Limit | PRF / 2 | Threshold above which spectral aliasing occurs. |
| Poiseuille's Law | ΔP = (8 × η × L × Q) / (π × r⁴) | A change in radius has an exponential effect on flow resistance. |
Time, Distance & Frame Rate
| Parameter | Formula | Key Clinical Concept |
|---|---|---|
| Period (T) | 1 / Frequency (f) | Period and frequency are reciprocals. Set by the sound source. |
| Wavelength (λ) | Propagation Speed (c) / Frequency (f) | In soft tissue (1540 m/s), λ in mm = 1.54 / frequency in MHz. |
| Pulse Repetition Period (PRP) | 1 / PRF | Time from the start of one pulse to the start of the next, including listening time. |
| Go-Return Time (Time of Flight) | 13 µs per cm of depth | Rule of thumb for soft tissue: an echo from 1 cm depth returns in about 13 µs. |
| Maximum PRF for a Depth | 77,000 / depth (cm) (Hz) | Equivalent to 77 / depth (cm) in kHz. Deeper imaging forces a lower PRF. |
| Frame Rate | PRF / Lines per Frame | More lines, deeper depth or multiple focal zones lower the frame rate. |
Decibels, Intensity & Reflection
| Parameter | Formula | Key Clinical Concept |
|---|---|---|
| Intensity | Power / Area | Doubling the power doubles the intensity; halving the beam area also doubles it. |
| Decibels (intensity or power) | dB = 10 × log₁₀(I₂ / I₁) | +3 dB ≈ ×2, −3 dB ≈ ×½, +10 dB = ×10. For amplitude or pressure the multiplier is 20 × log₁₀. |
| Total Attenuation | Attenuation Coefficient (dB/cm) × Path Length (cm) | Path length is the round-trip distance for an echo (2 × depth). |
| Half-Value Layer (HVL) | 3 dB / Attenuation Coefficient (dB/cm) | Depth at which intensity has fallen by 3 dB. Shallower for higher frequencies. |
| Intensity Reflection Coefficient (IRC) | [(Z₂ − Z₁) / (Z₂ + Z₁)]² | Normal incidence. Larger impedance mismatch means more reflection; equal impedances mean none. |
Beam Geometry & Hemodynamics
| Parameter | Formula | Key Clinical Concept |
|---|---|---|
| Near Zone Length (Focal Depth) | D² / (4 × λ) | D is the aperture (crystal) diameter. Larger aperture or higher frequency lengthens the near zone. |
| Continuity Equation | A₁ × v₁ = A₂ × v₂ | Velocity rises at a stenosis because the cross-sectional area falls. |
| Simplified Bernoulli | ΔP = 4 × v² | Pressure gradient in mmHg with velocity in m/s. |
| Reynolds Number | (ρ × v × D) / η | Values above roughly 2000 predict turbulent flow; below that flow tends to be laminar. |
| Resistive Index (RI) | (PSV − EDV) / PSV | Uses peak systolic and end-diastolic velocities. |
| Pulsatility Index (PI) | (PSV − EDV) / Mean Velocity | Uses the mean velocity over the cardiac cycle. |
Wave Properties & Attenuation
| Parameter | Formula | Key Clinical Concept |
|---|---|---|
| Acoustic Impedance (Z) | Density (ρ) × Propagation Speed (c) | Measured in Rayls. Determines boundary reflection magnitude. |
| Attenuation Coefficient | Frequency (MHz) / 2 | In soft tissue, approximately 0.5 dB/cm/MHz. |
| Snell's Law | sin(θt) / sin(θi) = c₂ / c₁ | Refraction requires oblique incidence and different propagation speeds. |