Biot's parameters estimation in ultrasound propagation through cancellous bone

TL;DR

This paper presents a Bayesian approach to estimate Biot's parameters in ultrasound propagation through cancellous bone, demonstrating improved signal recovery over classical methods using finite volume simulations.

Contribution

It introduces a Bayesian parameter estimation framework for Biot's model applied to cancellous bone ultrasound data, with numerical validation in 2D.

Findings

Conditional Mean estimator outperforms PDE-constrained minimization

Finite Volume Method effectively solves coupled Biot's equations

Numerical results demonstrate accurate parameter recovery

Abstract

Of interest is the characterization of a cancellous bone immersed in an acoustic fluid. The bone is placed between an ultrasonic point source and a receiver. Cancellous bone is regarded as a porous medium saturated with fluid according to Biot's theory. This model is coupled with the fluid in an open pore configuration and solved by means of the Finite Volume Method. Characterization is posed as a Bayesian parameter estimation problem in Biot's model given pressure data collected at the receiver. As a first step we present numerical results in 2D for signal recovery. It is shown that as point estimators, the Conditional Mean outperforms the classical PDE-constrained minimization solution.