The Effect of Range on the Ultrasonic Echo Amplitude from Cylindrical Biological Structures Normal to the Axis of a Circular Transceiver

It is shown that, biological structures like the tibia of a chicken and the thoracic descending aorta of a dog may behave (under certain circumstances) like non-biological reflecting cylinders w. r. t. the effect of range on the ultrasonic echo-amplitude. A rather-accurate mathematical expression giving the effect of range on the average pressure of the secondary wave on the surface of the transceiver (which is proportional to the echo-amplitude) is briefly derived here, for the case when the “cylindrical” reflector is situated normal to the central axis of the transceiver. Both radii of the biological structure and the transducer are assumed large compared with the wavelength and are small compared with the range. The mathematical expression obtained is compared with the already-known approximate expression as well as with the experimental responses. The resulting deviation is discussed.

It is also shown that, the theoretical response indicates – as expected – a “final” maximum of the echo at a certain distance between the biological reflector and the transceiver. The theoretical position of this maximum is checked experimentally and the deviation is determined. This maximum is of interest for some applications in the field of medical diagnosis as well as in other fields.