Annual QA: Is the System or the Phantom Wrong?
During annual quality assurance, a curved array is tested on a tissue-equivalent phantom. The phantom's material has a measured speed of sound of 1520 m/s, while the scanner assumes 1540 m/s. Vertical pin targets are nominally at 2, 4, 6, and 8 cm and are measured at 2.05, 4.08, 6.11, and 8.15 cm. An axial resolution target of 1.0 mm separation measures 1.2 mm with electronic calipers. Department acceptance criteria are vertical distance accuracy within 2 percent or 2 mm, whichever is greater, and axial resolution of 1.5 mm or better. The service engineer proposes to recalibrate the system time base.
1. Compute the percent error at each pin and decide whether the system passes the vertical accuracy criterion.
Read the worked answer
Errors:
- 2 cm pin: 0.05 cm = 0.5 mm = 2.5 percent
- 4 cm pin: 0.08 cm = 0.8 mm = 2.0 percent
- 6 cm pin: 0.11 cm = 1.1 mm = 1.8 percent
- 8 cm pin: 0.15 cm = 1.5 mm = 1.9 percent
Against the criterion (2 percent or 2 mm, whichever is greater), the 8 cm and 6 cm points pass on both counts, the 4 cm point sits exactly at 2 percent but only 0.8 mm, and the 2 cm point is 2.5 percent but only 0.5 mm, inside the 2 mm allowance. All points pass as written.
More informative than pass/fail is the pattern: every error is a positive overshoot of roughly 1.7 to 2 percent, not a random scatter. That nearly constant multiplicative bias points to a propagation-speed mismatch, not a drifting clock.
2. Use the phantom's stated speed of sound to test the speed-mismatch hypothesis, and evaluate the engineer's proposal.
Read the worked answer
Displayed depth = true depth x (assumed speed / actual speed) = d x (1540/1520) = 1.0132 x d.
Predicted measurements: 2.03, 4.05, 6.08, 8.11 cm. Observed: 2.05, 4.08, 6.11, 8.15 cm.
Fitting a line to the observed data gives a slope of about 1.017 and an intercept of about 0.17 mm. A slope of 1.017 implies an actual speed of 1540/1.017 = about 1514 m/s, close to the phantom's 1520 m/s within caliper uncertainty. The small positive intercept is consistent with pin placement and caliper-placement error.
Conclusion: the depth errors are explained by the phantom material, not by a system fault. The axial resolution result of 1.2 mm also passes (criterion 1.5 mm), and correcting it for the same 1.7 percent bias gives about 1.18 mm. The engineer's recalibration would introduce a real error into a system that is currently correct, so it should be refused and the finding documented as a phantom-speed effect.
3. What single follow-up measurement would separate a system time-base error from a phantom-speed error?
Read the worked answer
Measure a horizontal (lateral) distance between pins of known separation, or between horizontal targets in the phantom.
Reasoning: displayed depth is derived from time of flight using the assumed speed, so it is speed-dependent. Lateral position is set by beam steering and geometry and is essentially speed-independent. If horizontal spacing is accurate while vertical spacing is off by a constant multiplicative factor, the time base is fine and the speed assumption is the culprit. If both axes are off, suspect the system, the scan converter, or the calipers.
Supporting options: repeat the vertical measurement on a second phantom with a documented 1540 m/s material, or repeat on a second scanner; if the same bias follows the phantom, the phantom is at fault. Either way, enter the discrepancy and the reasoning in the QA log rather than a bare pass mark, so next year's comparison is meaningful.