Surface refraction of sound waves affects calibration of three-dimensional ultrasound

Three-dimensional ultrasound (3D-US) is used in planning and treatment during external beam radiotherapy. The accuracy of the technique depends not only on the achievable image quality in clinical routine, but also on technical limitations of achievable precision during calibration. Refraction of ultrasound waves is a known source for geometric distortion, but such an effect was not expected in homogenous calibration phantoms. However, in this paper we demonstrate that the discontinuity of the refraction index at the phantom surface may affect the calibration unless the ultrasound probe is perfectly perpendicular to the phantom.

A calibration phantom was repeatedly scanned with a 3D-US system (Elekta Clarity) by three independent observers. The ultrasound probe was moved horizontally at a fixed angle in the sagittal plane. The resulting wedge shaped volume between probe and phantom was filled with water to couple in the ultrasound waves. Because the speed of sound in water was smaller than the speed of sound in Zerdine, the main component of the phantom, the angle of the ultrasound waves inside the phantom increased. This caused an apparent shift in the calibration features which was recorded as a function of the impeding angle. To confirm the magnitude and temperature dependence, the experiment was repeated by two of the observers with a mixture of ice and water at 0 °C and with thermalized tap water at 21 °C room temperature.

During the first series of measurements, a linear dependency of the displacements dx of the calibration features on the angle α of the ultrasound probe was observed. The three observers recorded significantly nonzero (p < 0.0001) and very consistent slopes of dx/dα of 0.12, 0.12, and 0.13 mm/°, respectively..

At 0 °C water temperature, the slope increased to 0.18 ± 0.04 mm/°. This matched the prediction of Snell’s law of 0.185 mm/° for a speed of sound of 1,402 m/s at the melting point of ice.

At 21 °C, slopes of 0.11 and 0.12 mm/° were recorded in agreement with the first experiment at about room temperature. The difference to the theoretical expectation of 0.07 mm/° was not significant (p = 0.09).

The surface refraction of sound waves my affect the calibration of three-dimensional ultrasound. The temperature dependence of the effect rules out alternative explanations for the observed shifts in calibration. At room temperature and for a structure that is 10 cm below the water-phantom interface, a tilt of the ultrasound probe of 10° may result in a position reading that is off by more than half a millimeter. Such errors are of the order of other relevant errors typically encountered during the calibration of a 3D-US system. Hence, care must be taken not to tilt the ultrasound probe during calibration.