Abstract
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 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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abendschein, W., andHyatt, G. W. (1970): ‘Ultrasonics and selected physical properties of bone,’Clin. Orthop. Rel. Res.,69, pp. 294–301
Andre, M. P., Craven, J. D., andGreenfield, M. A. (1980): ‘Measurement of the velocity of ultrasound in the human femurin vivo,’Med. Phys.,7, pp. 324–30
Buckingham, S. H. W., McCarthy, R. N., Anderson, G. A., Jeffcott, L. B., andMcCartney, R. N. (1992): ‘Ultrasound speed in the metacarpal cortex: a survey of 347 thoroughbreds in training,’Equine Vet. J., 24, pp. 191–195
Carter, D. R., andHayes, W. C. (1977): ‘The compressive behaviour of bone as a two phase porous structure,’J. Bone Joint Surg.,59A, pp. 954–962
Del Grosso, V. A., andMader, C. W. (1972): ‘Speed of sound in pure water’,J. Acoust. Soc. Amer.,52 pp. 1442–1446
Evans, J. A., andTavakoli, M. B. (1990): ‘Ultrasonic attenuation and velocity in bone,’Phys. Med. Biol.,35, 1387–96
Greenfield, M. A., Craven, J. D., Huddleston, A., Kehren, M. L., Wishko, D. S. andStern, R. (1981): ‘Measurement of the velocity of ultrasound in cortical bonein vivo,’Radiology,138, pp. 701–10
Greenspan, M., andTschigg, C. E. (1959): ‘Table of the speed of sound in water,’J. Acoust. Soc. Amer.,31, pp. 75–76
Jeffcott, L. B., Buckingham, S. H. W., McCarthy, R. N., Cleeland, J. C., Scotti, E., andMcCartney, R. N. (1988): ‘Noninvasive measurement of bone: a review of clinical and research applications in the horse,’Eq. Vet. J. Supp.,6, pp. 71–79
Langton, C. M., Ali, A. V., Riggs, C. M., Evans, G. P., andBonfield, W. (1990): ‘Measurement of ultrasonic velocity and broadband attenuation in cortical and cancellous bone,’Clin. Phys. Physiol. Meas.,11, pp. 243–249
Langton, C. M., Riggs, C. M., andEvans, G. P. (1991): ‘Pathway of ultrasound waves in the equine third metacarpal bone,’J. Biomed. Eng.,13, pp 113–118
Lees, S. (1986): ‘Sonic properties of mieralised tissues’in Greenleaf, J. F. (Ed.): ‘Tissue characterisation with ultrasound’ (CRC Press, Boca Raton) pp. 208–226
McCarthy, R. N., Jeffcott, L. B., andMcCartney, R. N. (1990): ‘Ultrasound speed in equine cortial bone: effects of orientation, density, temperature and porosity,’J. Biomech.,23, pp. 1139–1143
McCarthy, R. N., Jeffcott, L. B., andMcCartney, R. N. (1991): ‘A method for determining the transmission speed of ultrasound in long bones’,J. Biomech., to be published.
McCartney, R. N., andJeffcott, L. B. (1987): ‘Combined 2·25 MHz ultrasound velocity and bone mineral density measurements in the equine metacarpus and theirin vivo applications,’Med. Biol. Eng. Comput.,25, pp. 620–626
McCarthy, R. N., Jeffcott, L. B., andMcCartney, R. N. (1988): ‘Ultrasonic transmission velocity and single photon absorptiometric measurement of metacarpal strength: anin vitro study in the horse,’Eq. Vet. J. Supp.,6, pp. 80–87
Pinkerton, J. M. M. (1947): ‘A pulse method for the measurement of ultrasonic absorption in liquids: results for water,’Nature,160, pp. 128–129
Rossman, P. J. (1987): ‘Measurement of ultrasonic velocity and attenuation in the human os calcis and their relationships to photon absorptiometry bone mineral measurements,’ Masters, thesis, University of Winsconsin at Madison
Rossman, P., Zagzebski, J., Mesina, C., Sorenson, J., andMazess, R. (1989): ‘Comparison of speed of sound and ultrasound attenuation in the os calcis to bone density of the radius, femur and lumbar spine,’Clin. Phys. Physiol. Meas.,10, pp. 353–360
Schaffler, M. B., andBurr, D. B. (1988): ‘Stiffness of compact bone: effects of porosity and density,’J. Biomech.,21, pp. 13–16
Author information
Authors and Affiliations
Additional information
Dr Rob McCarthy died in 1993
Rights and permissions
About this article
Cite this article
McCartney, R.N., Jeffcott, L.B. & McCarthy, R.N. Transverse path of ultrasound waves in thick-walled cylinders. Med. Biol. Eng. Comput. 33, 551–557 (1995). https://doi.org/10.1007/BF02522513
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02522513