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Fabric dependent poroelasticity

The governing equations for wave motion in the linear theory of anisotropic poroelastic materials are extended to include the dependence of the constitutive relations upon the fabric tensor. This fabric-dependent anisotropic poroelastic approach is a theoretical framework to describe the microarchitectural-dependent relationship between measurable wave properties and the elastic constants of a porous material. We illustrate this theory by application to bone tissue. Current diagnosis of bone loss and osteoporosis is based on the measurement of the bone mineral density (BMD) or the apparent mass density. Unfortunately, in most clinical ultrasound densitometers: 1) measurements are often performed in a single anatomical direction, 2) only the first wave arriving to the ultrasound probe is characterized, and 3) the analysis of bone status is based on empirical relationships between measurable quantities such as speed of sound (SOS) and broadband ultrasound attenuation (BUA) and the density of the porous medium. However, the existence of a second wave in cancellous bone has been reported, which is an unequivocal signature of poroelastic media, as predicted by Biot’s poroelastic wave propagation theory.

Author(s):

Stephen Cowijn    
CCNY of CUNY
United States

Luis Cardoso    
CCNY of CUNY
United States