Numerical investigation of ultrasonic attenuation through 2D trabecular bone structures reconstructed from CT scans and random realizations.

In this paper, we compare ultrasound interrogations of actual CT-scanned images of trabecular bone with artificial randomly constructed bone. Even though it is known that actual bone does not have randomly distributed trabeculae, we find that the ultrasound attenuations are close enough to cast doubt on any microstructural information, such as trabeculae width and distance between trabeculae, being gleaned from such experiments. More precisely, we perform numerical simulations of ultrasound interrogation on cancellous bone to investigate the phenomenon of ultrasound attenuation as a function of excitation frequency and bone porosity.

Modeling of the kinetics of vitamin D(3) in osteoblastic cells.

A one-dimensional model for the transport of vitamin D(3) in an osteoblast cell is proposed, from its entry through the membrane to its activation of RANKL synthesis in the nucleus. In the membrane and cytoplasm, the transport of D(3) and RANKL is described by a diffusion process, while their interaction in the nucleus is modeled by a reaction-diffusion process. For the latter, an integral equation involving the boundary conditions, as well as an asymptotic solution in the regime of small concentrations, are derived.