Geometric distortion of area in medical ultrasound images

Medical ultrasound scanners are typically calibrated to the soft tissue average of 1540 m s$^{-1}$. In regions of different sound speed, for example, organs and tumours, the $B$-scan image then becomes a distortion of the true tissue cross-section, due to the misrepresentation of length and refraction. To quantify this distortion we develop a general geometric ray model for an object with an atypical speed of sound embedded in an ambient medium. We analyse the ensuing area distortion for circular and elliptical objects, mapping it out as a function of the key parameters, including the speed of sound mismatch, the object size and its elongation. We find that the area distortion can become significant, even for small-scale speed of sound mismatches. Our findings are verified by ultrasound imaging of a test object.