Ultrasonic wave properties of human bone marrow in the femur and tibia

The influence of intra-cortical microstructure on the contrast in ultrasound images of the cortex of long bones: A 2D simulation study

Decreased thickness of the bone cortex due to bone loss in the course of ageing and osteoporosis is associated with reduced bone strength. Cortical thickness measurement from ultrasound images was recently demonstrated in young adults. This requires the identification of both the outer (periosteum) and inner (endosteum) surfaces of the bone cortex. However, with bone loss, the cortical porosity and the size of the vascular pores increase resulting in enhanced ultrasound scattering which may prevent the detection of the endosteum. The aim of this work was to study the influence of cortical bone microstructure variables, such as porosity and pore size, on the contrast of the endosteum in ultrasound images. We wanted to estimate the range of these variables for which ultrasound imaging of the endosteum is feasible. We generated synthetic data using a two-dimensional time-domain code to simulate the propagation of elastodynamic waves. A synthetic aperture imaging sequence with an array transducer operating at a center frequency of 2.5 MHz was used. The numerical simulations were conducted for 105 cortical microstructures obtained from high resolution X-ray computed tomography images of ex vivo bone samples with a porosity ranging from 2% to 24 %. Images were reconstructed using a delay-and-sum (DAS) algorithm with optimized f-number, correction of refraction at the periosteum, and sample-specific wave-speed. We observed a range variation of 18 dB of endosteum contrast in our data set depending on the bone microstructure. We found that as porosity increases, speckle intensity inside the bone cortex increases whereas the intensity of the signal from the endosteum decreases. Also, a microstructure with large pores (diameter >250 μm) was associated with poor endosteum visibility, compared with a microstructure with equal porosity but a more narrow distribution of pore sizes. These findings suggest that ultrasound imaging of the bone cortex with a probe operating at a central frequency of 2.5 MHz using refraction-corrected DAS is capable of detecting the endosteum of a cortex with moderate porosity (less than about 10%) if the largest pores remain smaller than about 200 μm.

A simplified homogenization model applied to viscoelastic behavior of cortical bone at ultrasonic frequencies

Cortical bone is a complex multiscale medium and its study is of importance for clinical fracture prevention. In particular, cortical attenuation is known to be linked with shock energy absorption and ability to resist fracture. However, the links between cortical bone absorption and its multiscale structure are still not well understood. This work is about the use of homogenized tensors in order to characterize the viscoelastic behavior of cortical bone at ultrasonic frequencies, i.e., about 0.1 to 10 MHz. Such tensors are derived from the cell problem via two-scale homogenization theory for linear elastic and Kelvin-Voigt viscoelastic descriptions. The elliptic formulations obtained from the cell problems are implemented within the range of medically-observed porosities. Microstructure is assessed considering cubic cells with cylindrical inclusion and transverse isotropic assumption. A simplified model, adding one temporal parameter τ per phase, allows a good agreement with experimental data. The corresponding attenuation is proportional to the square of the frequency, in agreement with Kramer-Kronig relations. This development is proposed in the context of robust clinical inverse problem approaches using a restricted number of parameter. Two main properties for the material filling the pores are adjusted and discussed: absorption and shear contribution. Best agreement with experimental data is observed for material inside the pores being solid and highly attenuating.

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.

Velocity dispersion and backscatter in marrow-filled and water-filled trabecular bone samples in vitro

The phase velocity and the backscatter coefficient were measured in 28 bovine femoral trabecular bone samples filled with marrow and water in vitro from 0.2 to 0.6 MHz. The phase velocities decreased approximately linearly with increasing frequency and the average dispersion rate of -34 ms^-1MHz^-1 in the marrow-filled samples was higher than that of -42 ms^-1MHz^-1 in the water-filled samples. The backscatter coefficients exhibited nonlinear, monotonically increasing dependences on the frequency and the average value of the exponent n = 2.92 (frequency dependence) in the marrow-filled samples was higher than the value of n = 2.79 in the water-filled samples.