Information theory framework to reconstruct Biot constants of trabecular bone from ultrasound

Reliable quantification of mechanical constants of bone tissue is an open issue with relevance for the diagnostic of bone quality disorders, such as osteoporosis. Two open questions are addressed here: the suitability of Biot´s poroelasticity to explain the complex propagation patterns of ultrasound through trabecular bone, combined with a two-parameter homogeneization model, and to determine the confidence intervals of the reconstruction. An information-theory based probabilistic inversion framework is proposed for the first time to answer both questions. This work is aimed at (i) reconstructing the Biot-theory parameters that simulate the ultrasonic transmission through a set of trabecular bone samples, as well as their plausible ranges, (ii) evaluate which parameters are reconstructable and which not, as well as the degree of plausibility of Biot´s theory to explain the experimental measurements, (iii) merge information provided by a two-parameter constitutive model to add knowledge to the reconstruction process, and evaluate the plausibility of this new hypothesis, again through the information-theory framework, and (iv) validate the reconstruction against independent tests.