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

Mechanisms of Interaction of Ultrasound With Cancellous Bone: A Review

Ultrasound is now a clinically accepted modality in the management of osteoporosis. The most common commercial clinical devices assess fracture risk from measurements of attenuation and sound speed in cancellous bone. This review discusses fundamental mechanisms underlying the interaction between ultrasound and cancellous bone. Because of its two-phase structure (mineralized trabecular network embedded in soft tissue-marrow), its anisotropy, and its inhomogeneity, cancellous bone is more difficult to characterize than most soft tissues. Experimental data for the dependencies of attenuation, sound speed, dispersion, and scattering on ultrasound frequency, bone mineral density, composition, microstructure, and mechanical properties are presented. The relative roles of absorption, scattering, and phase cancellation in determining attenuation measurements in vitro and in vivo are delineated. Common speed of sound metrics, which entail measurements of transit times of pulse leading edges (to avoid multipath interference), are greatly influenced by attenuation, dispersion, and system properties, including center frequency and bandwidth. However, a theoretical model has been shown to be effective for correction for these confounding factors in vitro and in vivo. Theoretical and phantom models are presented to elucidate why cancellous bone exhibits negative dispersion, unlike soft tissue, which exhibits positive dispersion. Signal processing methods are presented for separating "fast" and "slow" waves (predicted by poroelasticity theory and supported in cancellous bone) even when the two waves overlap in time and frequency domains. Models to explain dependencies of scattering on frequency and mean trabecular thickness are presented and compared with measurements. Anisotropy, the effect of the fluid filler medium (marrow in vivo or water in vitro), phantoms, computational modeling of ultrasound propagation, acoustic microscopy, and nonlinear properties in cancellous bone are also discussed.

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. The theoretical model is based on acoustic propagation equations for a composite fluid-solid material and is solved by a staggered-grid finite-difference scheme in the time domain. Numerical experiments are performed on two-dimensional bone samples reconstructed from CT-scanned images of real human calcaneus and from random distributions of fluid-solid particles generated via the turning bands method. A detailed comparison is performed on various parameters such as the attenuation rate and speed of sound through the bone samples as well as the normalized broadband ultrasound attenuation coefficient. Comparing results from these two types of bone samples allows us to assess the role of bone microstructure in ultrasound attenuation. It is found that the random model provides suitable bone samples for ultrasound interrogation in the transverse direction of the trabecular network.

The kinetics of vitamin D₃ in the osteoblastic cell

Experimental evidence is presented on the translocation of vitamin D metabolite, 1,25-(OH)₂D₃, from the membrane to the nucleus in osteoblast progenitor cells. A mathematical model permitting traversal of the cytoplasm at either a fixed velocity or by diffusion is formulated in order to determine whether transport along the cytoskeletal tracks is more consistent with the observed spatial-temporal distribution than diffusion, and it is so found. The model includes reactions in the nucleus involving D₃ to form other compounds, such as protegerin, and thus also makes predictions of the concentrations of these compounds in various regions of the cell.