Computational Study of the Effect of Cortical Porosity on Ultrasound Wave Propagation in Healthy and Osteoporotic Long Bones

Estimation of Cortical Bone Microstructure From Ultrasound Backscatter

Multichannel pulse-echo ultrasound using linear arrays and single-channel data acquisition systems opens new perspectives for the evaluation of cortical bone. In combination with spectral backscatter analysis, it can provide quantitative information about cortical microstructural properties. We present a numerical study, based on the finite-difference time-domain method, to estimate the backscatter cross section of randomly distributed circular pores in a bone matrix. A model that predicts the backscatter coefficient using arbitrary pore diameter distributions was derived. In an ex vivo study on 19 human tibia bones (six males, 13 females, 83.7 ± 8.4 years), multidirectional ultrasound backscatter measurements were performed using an ultrasound scanner equipped with a 6-MHz 128-element linear array with sweep motor control. A normalized depth-dependent spectral analysis was performed to derive backscatter and attenuation coefficients. Site-matched reference values of tissue acoustic impedance Z , cortical thickness (Ct.Th), pore density (Ct.Po.Dn), porosity (Ct.Po), and characteristic parameters of the pore diameter (Ct.Po.Dm) distribution were obtained from 100-MHz scanning-acoustic microscopy images. Proximal femur areal bone mineral density (aBMD), stiffness S , and ultimate force Fu from the same donors were available from a previous study. All pore structure and material properties could be predicted using linear combinations of backscatter parameters with a median to high accuracy (0.28 ≤ adjusted R² ≤ 0.59). The combination of cortical thickness and backscatter parameter provided similar or better prediction accuracies than aBMD. For the first time, a method for the noninvasive assessment of the pore diameter distribution in cortical bone by ultrasound is proposed. The combined assessment of cortical thickness, sound velocity, and pore size distribution in a mobile, nonionizing measurement system could have a major impact on preventing osteoporotic fractures.

Numerical evaluation of the mechanical environment of a fractured long bone for osteoporotic and non-osteoporotic subjects

Competent fracture healing monitoring requires an extensive knowledge of the evolution of the mechanical environment of the healing bone during daily-life activities such as walking. Fractures are caused due to a traumatic incidence, while low trauma or fragility fractures can also occur due to osteoporosis. It is expected that the mechanical behavior of healing bones differs among osteoporotic and non-osteoporotic subjects. This work presents finite element simulations of gait analysis considering a fractured long bone at the hematoma stage. The aim is to investigate the evolution of the mechanical environment of the femur for an osteoporotic and a non-osteoporotic subject. This is the first computational study providing quantitative information for the impact of osteoporosis on the mechanical environment of the femur. It was shown, that higher deformation and equivalent stress values are calculated for osteoporotic bones during a gait cycle, while the highest values were observed in the femoral head.

Towards assessing cortical bone porosity using low-frequency quantitative acoustics: A phantom-based study

PURPOSE

Cortical porosity is a key characteristic governing the structural properties and mechanical behaviour of bone, and its quantification is therefore critical for understanding and monitoring the development of various bone pathologies such as osteoporosis. Axial transmission quantitative acoustics has shown to be a promising technique for assessing bone health in a fast, non-invasive, and radiation-free manner. One major hurdle in bringing this approach to clinical application is the entanglement of the effects of individual characteristics (e.g. geometry, porosity, anisotropy etc.) on the measured wave propagation. In order to address this entanglement problem, we therefore propose a systematic bottom-up approach, in which only one bone property is varied, before addressing interaction effects. This work therefore investigated the sensitivity of low-frequency quantitative acoustics to changes in porosity as well as individual pore characteristics using specifically designed cortical bone phantoms.

MATERIALS AND METHODS

14 bone phantoms were designed with varying pore size, axial-, and radial pore number, resulting in porosities (bone volume fraction) between 0% and 15%, similar to porosity values found in human cortical bone. All phantoms were manufactured using laser sintering, measured using axial-transmission acoustics and analysed using a full-wave approach. Experimental results were compared to theoretical predictions based on a modified Timoshenko theory.

RESULTS

A clear dependence of phase velocity on frequency and porosity produced by increasing pore size or radial pore number was demonstrated, with the velocity decreasing by between 2-5 m/s per percent of additional porosity, which corresponds to -0.5% to -1.0% of wave speed. While the change in phase velocity due to axial pore number was consistent with the results due to pore size and radial pore number, the relative uncertainties for the estimates were too high to draw any conclusions for this parameter.

CONCLUSIONS

This work has shown the capability of low-frequency quantitative acoustics to reflect changes in porosity and individual pore characteristics and demonstrated that additive manufacturing is an appropriate method that allows the influence of individual bone properties on the wave propagation to be systematically assessed. The results of this work opens perspectives for the efficient development of a multi-frequency, multi-mode approach to screen, diagnose, and monitor bone pathologies in individuals.

Evaluation of ultrasonic scattering for different cortical bone porosities and excitation frequencies: A numerical study

Quantitative ultrasound is a promising and relative recent method for the assessment of bone. In this work, the interaction of ultrasound with the porosity of cortical bone is investigated for different frequencies. Emphasis is given on the study of complex scattering effects induced by the propagation of an ultrasonic wave in osseous tissues. Numerical models of cortical bone are established with a porosity of 0, 5 and 10% corresponding to healthy homogeneous bone, healthy inhomogeneous bone and normal ageing, respectively. Different excitation frequencies are applied in the range 0.2-1 MHz. The scattering amplitude and the acoustic pressure are calculated for multiple angles and receiving positions focusing on the backward direction. The results indicate that the application of higher frequencies can better distinguish changes in the energy distribution in the backward direction due to alterations of the cortical porosity.