A training phantom gives the pairs (ultrasound frequency in MHz, maximum useful image depth in cm) (2, 14.0), (3, 10.0), (5, 6.5), (8, 4.0), (12, 2.8). A trainee claims useful depth is inversely proportional to frequency. (a) Describe the trend. [2] (b) Calculate frequency × depth for every pair and assess the claim using a ±10% consistency rule around the first product. [5] (c) Explain the physical trade-off between frequency, attenuation and image detail. [3] (d) Identify one limitation of transferring this phantom result to patients and one improvement. [2]

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Useful depth falls as frequency rises. Products are 28.0, 30.0, 32.5, 32.0 and 33.6 MHz·cm; the last exceeds ±10% of 28.0, so the complete dataset fails the stated consistency rule even though the inverse trend is approximate. (a) Maximum useful image depth decreases as frequency increases, with large losses at first and smaller absolute losses at the highest frequencies. The raw relationship is curved rather than linear. (b) The products frequency × depth are 2×14.0 = 28.0, 3×10.0 = 30.0, 5×6.5 = 32.5, 8×4.0 = 32.0 and 12×2.8 = 33.6 MHz·cm. (b) Ten percent of the first product is 2.8, so the allowed interval is 25.2–30.8. The 5, 8 and 12 MHz products lie above that interval; the full record does not meet the stated inverse-proportion rule. (c) Higher-frequency waves generally have shorter wavelength and can resolve smaller structures, but tissue attenuates them more strongly, reducing useful depth. The operator chooses a compromise for the target anatomy. (d) A uniform phantom cannot reproduce varied tissue, body size, bone, gas or operator technique. Repeat with tissue-equivalent phantoms of several compositions and blinded image-quality criteria before informing clinical practice.

Evaluate an ultrasound frequency–penetration claim

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Ultrasound frequency and useful image depth

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