A vascular sonographer examines two vessels in one patient: a carotid artery about…
PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Radiation physics and diagnostic imaging · Radiation physics and diagnostic imaging
Life at Thermal Energy, Ch Echoes, precession and the therapeutic beam
Problem
A vascular sonographer examines two vessels in one patient: a carotid artery about 4cm below the skin and the abdominal aorta about 12cm down. The scanner tolerates at most 60dB of round-trip loss, soft tissue loses 0.5dBcm−1MHz−1, and cs=1540ms−1. The Doppler processor cannot tell a shift below 100Hz from the echoes of the slowly moving vessel walls, so it discards any such shift.
((a)) For each vessel, find the highest probe frequency whose echo from that depth stays within the loss budget, and the wavelength at that frequency.
((b)) Each vessel is scanned at the frequency found in (a), with the beam at 60∘ to the flow. Show that the smallest blood speed the scanner can then measure is proportional to the vessel's depth, and find it for each vessel.
((c)) Late in each heartbeat the flow in this aorta slows to about 0.025ms−1. Can that speed be measured at 60∘? If not, find the largest beam-to-flow angle at which it can, and say whether the speed read at that angle is more or less sensitive to a small error in the angle than it was at 60∘.