Determination of cancellous bone density using low frequency acoustic measurements

Abstract

In this article we offer a novel method for interrogating cancellous bone using ultra sound measurements. The problem is first modelled in terms of the acoustic pressure in the water bath surrounding the bone sample, the pore pressure and the displacement of the elastic matrix describing the cancellous bone specimen. The fluid pressure in the water tank is represented in terms of a boundary integral equation. Source points are placed on a parallel line on one side of the bone; whereas, receivers are placed on the other side of the bone. Sensitivity tests are run for two frequencies which show that the corresponding inverse problem leads to reasonable good results.

Keywords:

• inverse problems
• cancellous bone
• ultrasound

Acknowledgements

R.P. Gilbert was supported in part by the NSF through grant No. INT-0438765. P. Guyenne was supported in part by the University of Delaware Research Foundation and the NSF through grant No. DMS-0625931.