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.

Investigation of the influence of reflection on the attenuation of cancellous bone.

The model proposed in this paper is based on the fact that the reflection might have a significant contribution to the attenuation of the acoustic waves propagating through the cancellous bone. The numerical implementation of the mentioned effect is realized by the development of a new representative volume element that includes an infinitesimally thin 'transient' layer on the contact surface of the bone and the marrow. This layer serves to model the amplitude transformation of the incident wave by the transition through media with different acoustic impedances and to take into account the energy loss due to the reflection.

Wavelet decomposition of transmitted ultrasound wave through a 1-D muscle-bone system.

In the attempt for using ultrasound as a diagnostic device for osteoporosis, several authors have described the result of the in vitro experiment in which ultrasound is passed through a cancellous bone specimen placed in a water tank. However, in the in vivo setting, a patient's cancellous bone is surrounded by cortical and muscle layers. This paper considers in the one-dimensional case (1) what effect the cortical bone segments surrounding the cancellous segment would have on the received signal and (2) what the received signal would be when a source and receiver are placed on opposite sides of a structure consisting of a cancellous segment surrounded by cortical and muscle layers.