Effect of bone marrow on acoustic properties of trabecular bone--3D finite difference modeling study

Radiation Characteristics of Cranial Leaky Lamb Waves

We numerically and experimentally investigate the dispersion properties of leaky Lamb waves in the cranial bone. Cranial Lamb waves leak energy from the skull into the brain when propagating at speeds higher than the speed of sound in the surrounding fluid. The understanding of their radiation mechanism is significantly complicated by the geometric and mechanical characteristics of the cortical tables and the trabecular bone (diploë). Toward such understanding, we here analyze the sub-1.0 MHz radiation angle dispersion spectrum of porous bone phantoms and parietal bone geometries obtained from μ CT scans. Our numerical results show that, when diploic pores are physically modeled, leakage angles computed from time transient finite-element analyses correspond to those predicted by an equivalent three-layered fluid-loaded waveguide model. For the bone geometries analyzed, two main leaky branches are observed in the near-field dispersion spectrum: a fast wave radiated at small angles, which is related to the fastest fundamental Lamb mode supported by the cranial bone, and a slower wave radiated at larger angles. This observation is also confirmed by experimental tests carried out on an immersed parietal bone.

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.

Three-dimensional Simulation of Quantitative Ultrasound in Cancellous Bone Using the Echographic Response of a Metallic Pin

Degenerative discopathy is a common pathology that may require spine surgery. A metallic cylindrical pin is inserted into the vertebral body to maintain soft tissues and may be used as a reflector of ultrasonic wave to estimate bone density. The first aim of this paper is to validate a three-dimensional (3-D) model to simulate the ultrasonic propagation in a trabecular bone sample in which a metallic pin has been inserted. We also aim at determining the effect of changes of bone volume fraction (BV/TV) and of positioning errors on the quantitative ultrasound (QUS) parameters in this specific configuration. The approach consists in coupling finite-difference time-domain simulation with X-ray microcomputed tomography. The correlation coefficient between experimental and simulated speed of sound (SOS)-respectively, broadband ultrasonic attenuation (BUA)-was equal to 0.90 (respectively, 0.55). The results show a significant correlation of SOS with BV/TV ( R = 0.82), while BUA values exhibit a nonlinear behavior versus BV/TV. The orientation of the pin should be controlled with an accuracy of around 1° to obtain accurate results. The results indicate that using the ultrasonic wave reflected by a pin has a potential to estimate the bone density. SOS is more reliable than BUA due to its lower sensitivity to the tilt angle.

Micro-scale finite element modeling of ultrasound propagation in aluminum trabecular bone-mimicking phantoms: A comparison between numerical simulation and experimental results

The present study investigated the accuracy of micro-scale finite element modeling for simulating broadband ultrasound propagation in water-saturated trabecular bone-mimicking phantoms. To this end, five commercially manufactured aluminum foam samples as trabecular bone-mimicking phantoms were utilized for ultrasonic immersion through-transmission experiments. Based on micro-computed tomography images of the same physical samples, three-dimensional high-resolution computational samples were generated to be implemented in the micro-scale finite element models. The finite element models employed the standard Galerkin finite element method (FEM) in time domain to simulate the ultrasonic experiments. The numerical simulations did not include energy dissipative mechanisms of ultrasonic attenuation; however, they expectedly simulated reflection, refraction, scattering, and wave mode conversion. The accuracy of the finite element simulations were evaluated by comparing the simulated ultrasonic attenuation and velocity with the experimental data. The maximum and the average relative errors between the experimental and simulated attenuation coefficients in the frequency range of 0.6-1.4 MHz were 17% and 6% respectively. Moreover, the simulations closely predicted the time-of-flight based velocities and the phase velocities of ultrasound with maximum relative errors of 20 m/s and 11 m/s respectively. The results of this study strongly suggest that micro-scale finite element modeling can effectively simulate broadband ultrasound propagation in water-saturated trabecular bone-mimicking structures.

The finite element method for micro-scale modeling of ultrasound propagation in cancellous bone

Quantitative ultrasound for bone assessment is based on the correlations between ultrasonic parameters and the properties (mechanical and physical) of cancellous bone. To elucidate the correlations, understanding the physics of ultrasound in cancellous bone is demanded. Micro-scale modeling of ultrasound propagation in cancellous bone using the finite-difference time-domain (FDTD) method has been so far utilized as one of the approaches in this regard. However, the FDTD method accompanies two disadvantages: staircase sampling of cancellous bone by finite difference grids leads to generation of wave artifacts at the solid-fluid interface inside the bone; additionally, this method cannot explicitly satisfy the needed perfect-slip conditions at the interface. To overcome these disadvantages, the finite element method (FEM) is proposed in this study. Three-dimensional finite element models of six water-saturated cancellous bone samples with different bone volume were created. The values of speed of sound (SOS) and broadband ultrasound attenuation (BUA) were calculated through the finite element simulations of ultrasound propagation in each sample. Comparing the results with other experimental and simulation studies demonstrated the capabilities of the FEM for micro-scale modeling of ultrasound in water-saturated cancellous bone.

Circumferential guided wave measurements of a cylindrical fluid-filled bone-mimicking phantom

In the context of hip fracture risk prediction, measurement of guided waves could improve the assessment of cortical femoral neck properties. The decomposition of the time reversal operator (DORT) method was previously shown to be efficient to measure circumferential guided modes in an empty cortical bone-mimicking tube of circular cross section. In this study, an adaptation of the DORT method is proposed to probe the same bone-mimicking tube but filled with a marrow-mimicking fluid. The contributions to the backscattered field of waves multiply reflected in the cavity of the tube interfere with those of circumferential guided waves. The former contributions are eliminated in the backpropagation image using ad hoc criterion determined with simulation. Eight portions of different guided modes were observed from experimental and simulated data. They were identified by comparison with theoretical predictions. This work confirms the feasibility of measuring guided waves in a fluid-filled tube of bone-mimicking material with the DORT method.

Longitudinal elastic properties and porosity of cortical bone tissue vary with age in human proximal femur

Tissue level structural and mechanical properties are important determinants of bone strength. As an individual ages, microstructural changes occur in bone, e.g., trabeculae and cortex become thinner and porosity increases. However, it is not known how the elastic properties of bone change during aging. Bone tissue may lose its elasticity and become more brittle and prone to fractures as it ages. In the present study the age-dependent variation in the spatial distributions of microstructural and microelastic properties of the human femoral neck and shaft were evaluated by using acoustic microscopy. Although these properties may not be directly measured in vivo, there is a major interest to investigate their relationships with the linear elastic measurements obtained by diagnostic ultrasound at the most severe fracture sites, e.g., the femoral neck. However, before the validity of novel in vivo techniques can be established, it is essential to understand the age-dependent variation in tissue elastic properties and porosity at different skeletal sites. A total of 42 transverse cross-sectional bone samples were obtained from the femoral neck (Fn) and proximal femoral shaft (Ps) of 21 men (mean±SD age 47.1±17.8, range 17-82years). Samples were quantitatively imaged using a scanning acoustic microscope (SAM) equipped with a 50MHz ultrasound transducer. Distributions of the elastic coefficient (c33) of cortical (Ct) and trabecular (Tr) tissues and microstructure of cortex (cortical thickness Ct.Th and porosity Ct.Po) were determined. Variations in c33 were observed with respect to tissue type (c33Tr<c33Ct), location (c33(Ct.Ps)=37.7GPa>c33(Ct.Fn)=35.3GPa>c33(Tr.Ps)=33.8GPa>c33(Tr.Fn)=31.9GPa), and cadaver age (R(2)=0.28-0.46, p<0.05). Regional variations in porosity were found in the neck (superior 13.1%; inferior 6.1%; anterior 10.1%; posterior 8.6%) and in the shaft (medial 9.5%; lateral 7.7%; anterior 8.6%; posterior 12.0%). In conclusion, significant variations in elastic coefficients were detected between femoral neck and shaft as well as between the quadrants of the cross-sections of neck and shaft. Moreover, an age-related increase in cortical porosity and a stiffening of the bone tissue were observed. These findings may explain in part the increase in susceptibility to suffer low energy fractures during aging and highlight the potential of ultrasound in clinical osteoporosis diagnostics.

Multi-site bone ultrasound measurements in elderly women with and without previous hip fractures

About 75% of patients suffering from osteoporosis are not diagnosed. This study describes a multi-site bone ultrasound method for osteoporosis diagnostics. In comparison with axial dual energy X-ray absorptiometry (DXA), the ultrasound method showed good diagnostic performance and could discriminate fracture subjects among elderly females.

INTRODUCTION

Axial DXA, the gold standard diagnostic method for osteoporosis, predicts fractures only moderately. At present, no reliable diagnostic methods are available at the primary health care level. Here, a multi-site ultrasound method is proposed for osteoporosis diagnostics.

METHODS

Thirty elderly women were examined using the ultrasound backscatter measurements in proximal femur, proximal radius, proximal and distal tibia in vivo. First, we predicted the areal bone mineral density (BMD) at femoral neck by ultrasound measurements in tibia combined with specific subject characteristics (density index, DI) and, second, we tested the ability of ultrasound backscatter measurements at proximal femur to discriminate between individuals with previously fractured hips from those without fractures. Areal BMD was determined by axial DXA.

RESULTS

Combined ultrasound parameters, cortical thickness at distal and proximal tibia, with age and weight of the subject, provided a significant estimate of BMD(neck) (r = 0.86, p < 0.001, n = 30). When inserted into FRAX (World Health Organization fracture risk assessment tool), the DI indicated the same treatment proposal as the BMD(neck) with 86% sensitivity and 100% specificity. The receiver operating characteristic analyses, with a combination of ultrasound parameters and patient characteristics, discriminated fracture subjects from the controls similarly as the model combining BMD(neck) and patient characteristics.

CONCLUSIONS

For the first time, ultrasound backscatter measurements of proximal femur were conducted in vivo. The results indicate that ultrasound parameters, combined with patient characteristics, may provide a means for osteoporosis diagnostics.

2-D finite difference time domain model of ultrasound reflection from normal and osteoarthritic human articular cartilage surface

Quantitative high-frequency ultrasonic evaluation of articular cartilage has shown a potential for the diagnosis of osteoarthritis, where the roughness of the surface, collagen and proteoglycan contents, and the density and mechanical properties of cartilage change concurrently. Experimentally, these factors are difficult to investigate individually and thus a numerical model is needed. The present study is the first one to use finite difference time domain modeling of pulse-echo measurements of articular cartilage. Ultrasound reflection from the surface was investigated with varying surface roughness, material parameters (Young's modulus, density, longitudinal, and transversal velocities) and inclination of the samples. The 2-D simulation results were compared with the results from experimental measurements of the same samples in an identical geometry. Both the roughness and the material parameters contributed significantly to the ultrasound reflection. The angular dependence of the ultrasound reflection was strong for a smooth cartilage surface but disappeared for the samples with a rougher surface. These results support the findings of previous experimental studies and indicate that ultrasound detects changes in the cartilage that are characteristic of osteoarthritis. In the present study there are differences between the results of the simulations and the experimental measurements. However, the systematic patterns in the experimental behavior are correctly reproduced by the model. In the future, our goal is to develop more realistic acoustic models incorporating inhomogeneity and anisotropy of the cartilage.

Influence of the filling fluid on frequency-dependent velocity and attenuation in cancellous bones between 0.35 and 2.5 MHz

The paper is focused on experiments on human cancellous bones filled with different fluids with the goal of evaluating their contribution to velocity dispersion, absorption, and scattering mechanisms. The specimens were measured first filled with marrow and subsequently, after marrow removal, with water and alcohol. No significant influence of the fluids was evidenced on the attenuation coefficient. Given the absence of impact of viscosity of the saturating fluid, the authors hypothesized that the source of attenuation is associated with viscoelastic absorption in the solid trabeculae and with scattering. Alteration of scattering obtained by changing the acoustic impedance mismatch between the fluid (alcohol vs water) and the trabeculae was reflected neither in the attenuation nor in its slope. This led the authors to suggest that longitudinal-to-shear scattering together with absorption in the solid phase are candidates as main sources for the attenuation. The differences in velocity values indicate that the elastic properties of the fluid are main determinants of the phase velocity. This finding is particularly significant in the context of /in vivo/ measurements, because it demonstrates that the subject-dependent properties of marrow may partly explain the inter-subject variability of speed of sound values.

Relationship between ultrasonic parameters and apparent trabecular bone elastic modulus: a numerical approach

The physical principles underlying quantitative ultrasound (QUS) measurements in trabecular bone are not fully understood. The translation of QUS results into bone strength remains elusive. However, ultrasound being mechanical waves, it is likely to assess apparent bone elasticity. The aim of this study is to derive the sensitivity of QUS parameters to variations of apparent bone elasticity, a surrogate for strength. The geometry of 34 human trabecular bone samples cut in the great trochanter was reconstructed using 3-D synchrotron micro-computed tomography. Finite-difference time-domain simulations coupled to 3-D micro-structural models were performed in the three perpendicular directions for each sample and each direction. A voxel-based micro-finite element linear analysis was employed to compute the apparent Young's modulus (E) of each sample for each direction. For the antero-posterior direction, the predictive power of speed of sound and normalized broadband ultrasonic attenuation to assess E was equal to 0.9 and 0.87, respectively, which is better than what is obtained using bone density alone or coupled with micro-architectural parameters and of the same order of what can be achieved with the fabric tensor approach. When the direction of testing is parallel to the main trabecular orientation, the predictive power of QUS parameters decreases and the fabric tensor approach always gives the best results. This decrease can be explained by the presence of two longitudinal wave modes. Our results, which were obtained using two distinct simulation tools applied on the same set of samples, highlight the potential of QUS techniques to assess bone strength.