Detectability of blood vessels by means of the ultrasonic echo method using a focused ultrasonic beam

The detectability of a small, hypothetical cylinder-shaped blood vessel with a diameter of 0.1 mm has been considered analytically using the ultrasonic echo method. Soft tissues surrounding the vessel have been taken as homogeneous and not causing reflections of ultrasonic waves. They have been ascribed both with bulk and shear elasticity. A beam of longitudinal ultrasonic waves incident on the vessel has been taken in the form of a focused beam at the focus of which the blood vessel has been placed. It has been assumed that the reflection of ultrasonic waves from the blood vessel is caused by the difference between the velocity of waves in the tissue surrounding the vessel and that in blood.
Assuming a frequency of ultrasonic waves of 2.6 MHz, a diameter of the transmit-receive piezoelectric transducer of 2 cm, a focal length of this transducer of 10 or 8 cm, voltage of the transmitter of 250 V and sensitivity of the receiver of 10^{-5}V, the conditions of detectability have been determined.
It has been shown that the signal of an echo from the blood vessel assumed is potentially detectable. Its magnitude depends critically on the distance between the vessel and the surface of the body, resulting from the attenuation of waves in tissues penetrated.