Transverse path of ultrasound waves in thick-walled cylinders

The path is examined of a beam of ultrasound through the wall and central cavity of a series of thick-walled cylinders made of polymethylmethacrylate (PMMA) and brass used to simulate the cross-section of the cortical shaft of a long long bone. Water is used as a coupling medium for the external ultrasound transducers and to fill the central cavity. Broadband pulse excitation is employed with two focused 2.5 MHz transducers mounted on a digital calliper. The transmission times of flight are measured on a 100 MHz digital cathode ray oscilloscope. Two distinct pulses of ultrasound were consistently observed at the receiver transducer, the first due to a nonlinear path only in the cylinder wall, and the second due to a linear path travelling directly between the transducers through the centre of the cylinder. The nonlinear path can be explained by refraction at the external surface of the cylinder and diffraction around the central cavity. The nonlinear path is influenced by the relative size of the central cavity. The proposed model for the ultrasound propagation in the cylinder wall gives an excellent correlation with the observed speed and attenuation. The technique can be applied to long bones and has considerable potential as a means of measuring bone quality in human and veterinary medicine.