Lumen pressure within obliquely insonated absorbent solid cylindrical shells with application to Doppler flow phantoms

Flow phantoms used in medical ultrasound usually employ a plastic tube as a blood vessel mimic. These tubes often have acoustic properties differing significantly from the tissue and blood-mimicking media, which results in distortion of the acoustic pressure field within the tubes and, hence, of the Doppler flow spectra. Previous analyses of this problem have used some form of the infinite plate transmission coefficient, although at least one ray-based analysis has considered a cylindrical interface but with zero wall thickness. In this paper, we compare these approximate pressure fields with the exact solution for oblique incidence on a viscoelastic cylindrical shell at 5 MHz to find for which materials the plate approximation is valid. The shell has water both inside and outside, but it can be modified to use a different fluid inside and also to include absorption in either fluid. We find the plate approximation is reasonable for soft tubes such as the copolymer Cflex (Cole-Palmer, Niles, IL) but much less so for hard tubes such as polymethylmethacrylate (PMMA).