Determination of the parameters of cancellous bone using high frequency acoustic measurements II: Inverse problems

In a precursor to this article the Biot model was used to model poroelastic media. The question this article addresses is whether the sort of experiments described by McKelvie and Palmer, Williams, and Hosokawa and Otani can be used to determine the parameters of the Biot model. A method of computing acoustic pressure in the low 100 kHz range was developed in Buchanan and Gilbert, "Determination of the parameters of cancellous bone using high frequency acoustic measurements," which appeared in Math. Comput. Modelling. In the present work a parameter recovery algorithm which uses parallel processing is developed and tested. It is found that when it is assumed that the agreement between calculated and measured data is about two digits, porosity can be determined to within about 1-2% and permeability, pore size and the bulk moduli to within about 40%, but in most cases less than 20%.