Computing bone fragility using transient ultrasonic waves.

Abstract

In this paper, we determine bone fragility of cancellous bone in vivo by using a simple one-dimensional model of a muscle-cortical bone-cancellous bone sample, by measuring the refracted sound when the sample is exposed to impulses from a transducer. From these data, the bone parameters can be determined. Such a procedure is referred to as solving an inverse problem. A transducer is placed on one side of the skin of the member to be interrogated and a receiver is place diametrically opposed in contact with the member. The muscle will be modeled as an elastic material, whereas the the corrical and cancellous bone may be modeled by modified Biot equations albeit with different porosities. However, because of the known frequency dependence of the viscous term, we propose that the standard Biot equations, which are not well posed, be replaced by adding a convolution term. The form of the kernel b(t) in the convolution integral is suggested by frequency domain representation of the dissipation term in the Biot–Johnson–Koplik–Dashen model.