Biot's parameters estimation in ultrasound propagation through cancellous bone
This work addresses the challenge of non-invasive bone characterization for medical diagnostics, but it is an incremental step with only 2D numerical results.
The authors propose a Bayesian approach to estimate Biot's parameters for cancellous bone characterization using ultrasound, showing that the Conditional Mean estimator outperforms classical PDE-constrained minimization in 2D signal recovery.
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.