Quantitative ultrasound assessment of the influence of roughness and healing time on osseointegration phenomena.

The evolution of bone tissue quantity and quality in contact with the surface of orthopedic and dental implants is a strong determinant of the surgical outcome but remains difficult to be assessed quantitatively. The aim of this study was to investigate the performance of a quantitative ultrasound (QUS) method to measure bone-implant interface (BII) properties. A dedicated animal model considering coin-shaped titanium implants with two levels of surface roughness (smooth, Sa = 0.49 µm and rough, Sa = 3.5 µm) allowed to work with a reproducible geometry and a planar interface. The implants were inserted in rabbit femurs and tibiae for 7 or 13 weeks. The ultrasonic response of the BII was measured ex vivo, leading to the determination of the 2-D spatial variations of bone in contact with the implant surface. Histological analysis was carried out to determine the bone-implant contact (BIC) ratio. The amplitude of the echo was significantly higher after 7 weeks of healing time compared to 13 weeks, for both smooth (p < 0.01) and rough (p < 0.05) implants. A negative correlation (R = - 0.63) was obtained between the ultrasonic response and the BIC. This QUS technique is more sensitive to changes of BII morphology compared to histological analyses.

Modeling ultrasonic wave propagation in a dental implant - Bone system.

The evolution of the bone-implant interface reflects the implant osseointegration and bond strength, thereby determining the overall implant stability in the jawbone. Quantitative ultrasound represents a promising alternative technique to characterize the interfacial integrity, precisely due to the fact that those waves propagate essentially along the bone-implant interface, and are therefore influenced by its state. This study reports a numerical investigation of ultrasonic wave propagation for a commercial implant-jawbone system in which the thickness and mechanical properties of the interfacial layer (corresponding to the interphase) are systematically varied through the application of a rule of mixtures, in order to mimic the evolution from a dominantly soft tissue - like medium up to a fully healed bone. A simple figure of merit is devised in terms of an RMS-like (root mean square) factor based on the implant displacements, that evolves continuously and significantly with the bone "healing" process, thereby providing unequivocal information on the nature of the investigated bone-implant interface. The results show that the wave propagation pattern is primarily dictated by the impedance mismatch rather than by the interface thickness. This study validates the concept of quantitative ultrasonic testing as a sensitive alternative to the widespread resonant frequency analysis, thereby opening the way for future sensitivity analyses that will address more refined bone-implant interface pathologies such as those observed in the clinical realm.

Resonant frequency analysis of dental implants.

Dental implant stability influences the decision on the determination of the duration between implant insertion and loading. This work investigates the resonant frequency analysis by means of a numerical model. The investigation is done numerically through the determination of the eigenfrequencies and performing steady state response analyses using a commercial finite element package. A peri-implant interface, of simultaneously varying stiffness, density and layer thickness is introduced in the numerical 3D model in order to probe the sensitivity of the eigenfrequencies and steady state response to an evolving weakened layer, in an attempt to identify the bone reconstruction around the implant. For the first two modes, the resonant frequency is somewhat insensitive to the healing process, unless the weakened layer is rather large and compliant, like in the very early stages of the implantation. A "Normalized Healing Factor" is devised in the spirit of the Implant Stability Quotient, which can identify the healing process especially at the early stages after implantation. The sensitivity of the resonant frequency analysis to changes of mechanical properties of periprosthetic bone tissue seems relatively weak. Another indicator considering the amplitude as well as the resonance frequency might be more adapted to bone healing estimations. However, these results need to be verified experimentally as well as clinically.

Anatomical distribution of the degree of mineralization of bone tissue in human femoral neck: impact on biomechanical properties.

Osteoporotic hip fractures represent a major public health problem associated with high human and economic costs. The anatomical variation of the tissue mineral density (TMD) and of the elastic constants in femoral neck cortical bone specimens is an important determinant of bone fragility. The purpose of this study was to show that a Synchrotron radiation microcomputed tomography system coupled with a multiscale biomechanical model allows the determination of the 3-D anatomical dependence of TMD and of the elastic constants (i.e. the mechanical properties of an anisotropic material) in human femoral neck. Bone specimens from the inferior femoral neck were obtained from 18 patients undergoing standard hemiarthroplasty. The specimens were imaged using 3-D synchrotron micro-computed tomography with a voxel size of 10.13 µm, leading to the determination of the anatomical distributions of porosity and TMD. The elastic properties of bone tissue were computed using a multiscale model. The model uses the experimental data obtained at the scale of several micrometers to estimate the components of the elastic tensor of bone at the scale of the organ. Statistical analysis (ANOVA) revealed a significant effect of the radial position on porosity and TMD and a significant effect of axial position on TMD only. Porosity was found to increase in the radial direction moving from the periosteum inwards (p<10(-5)). At any given distance from the periosteum, porosity does not vary noticeably along the bone axis. TMD was found to be significantly higher (p<10(-5)) in the periosteal region than in other bone locations and decreases from the periosteal to the endosteal region with an average slope of 10.05 g.cm(-3).m(-1), the decrease being faster in the porous part of the samples (average slope equal of 30.04 g.cm(-3).m(-1)) than in dense cortical bone. TMD was found to decrease from the distal to the proximal part of the femur neck (average slope of 6.5 g.cm(-3).m(-1)). Considering TMD variations in the radial direction induces weak changes of bone properties compared to constant TMD. TMD variations in the axial direction are responsible for a significant variation of elastic constants. These results demonstrate that the anatomical variations of TMD affect the bone elastic properties, which could be explained by the complex stress field in bone affecting bone remodeling. TMD spatial variations should be taken into account to properly describe the spatial heterogeneity of elastic coefficients of bone tissue at the organ scale.

Independent scattering model and velocity dispersion in trabecular bone: comparison with a multiple scattering model.

Speed of sound measurements are used clinically to assess bone strength. Trabecular bone is an attenuating composite material in which negative values of velocity dispersion have been measured; this behavior remaining poorly explained physically. The aim of this work is to describe the ultrasonic propagation in trabecular bone modeled by infinite cylinders immersed in a saturating matrix and to derive the physical determinants of velocity dispersion. An original homogenization model accounting for the coupling of independent scattering and absorption phenomena allows the computation of phase velocity and of dispersion while varying bone properties. The first step of the model consists in the computation of the attenuation coefficient at all frequencies. The second step of the model corresponds to the application of the general Kramers-Krönig relationship to derive the frequency dependence of phase velocity. The model predicts negative values of velocity dispersion in agreement with experimental results obtained in phantoms mimicking trabecular bone. In trabecular bone, only negative values of velocity dispersion are predicted by the model, which span within the range of values measured experimentally. However, the comparison of the present results with results obtained in Haiat et al. (J Acoust Soc Am 124:4047-4058, 2008) assuming multiple scattering indicates that accounting for multiple scattering phenomena leads to a better prediction of velocity dispersion in trabecular bone.

Determination of the heterogeneous anisotropic elastic properties of human femoral bone: from nanoscopic to organ scale.

Cortical bone is a multiscale composite material. Its elastic properties are anisotropic and heterogeneous across its cross-section, due to endosteal bone resorption which might affect bone strength. The aim of this paper was to describe a homogenization method leading to the estimation of the variation of the elastic coefficients across the bone cross-section and along the bone longitudinal axis. The method uses the spatial variations of bone porosity and of the degree of mineralization of the bone matrix (DMB) obtained from the analysis of 3-D synchrotron micro-computed tomography images. For all three scales considered (the foam (100 nm), the ultrastructure (5 microm) and the mesoscale (500 microm)), the elastic coefficients were determined using the Eshelby's inclusion problem. DMB values were used at the scale of the foam. Collagen was introduced at the scale of the ultrastructure and bone porosity was introduced at the mesoscale. The pores were considered as parallel cylinders oriented along the bone axis. Each elastic coefficient was computed for different regions of interest, allowing an estimation of its variations across the bone cross-section and along the bone longitudinal axis. The method was applied to a human femoral neck bone specimen, which is a site of osteoporotic fracture. The computed elastic coefficients for cortical bone were in good agreement with experimental results, but some discrepancies were obtained in the endosteal part (trabecular bone). These results highlight the importance of accounting for the heterogeneity of cortical bone properties across bone cross-section and along bone longitudinal axis.

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.

Sensitivity of qus parameters to controlled variations of bone strength assessed with a cellular model.

The physical principles underlying quantitative ultrasound (QUS) measurements are not fully understood yet. Therefore, the translation of QUS results into bone strength remains elusive. In the present study, we derive the sensitivity of broadband ultrasonic attenuation (BUA) and speed of sound (SOS) to variations of bone strength. For this purpose, a mechanical cellular model is combined to a multiple regression resulting from the analysis of finite-difference time domain (FDTD) simulations. Specifically, we investigate how QUS variables respond to a variation in strength of 10%, realized either by a change in material properties or a change in bone volume fraction (BV/TV). The results show that except when BV/TV is high, the variations of BUA in response to a variation in strength realized by a pure change of BV/TV exceeds the technique imprecision and thus can be detected. When the variation of strength is realized by changes of compressive or shear stiffness, the response in QUS properties is dominated by the variation in C(11), whereas changes in C(44), remaining below the precision error, cannot be detected. The interpretation of these data, however, is not straightforward due to sparse description of elastic properties at the tissue level. To overcome the limitation of the cellular model, more realistic computational models such as micro- finite element analysis have to be considered.

Fast wave ultrasonic propagation in trabecular bone: numerical study of the influence of porosity and structural anisotropy.

Our goal is to assess the potential of computational methods as an alternative to analytical models to predict the two longitudinal wave modes observed in cancellous bone and predicted by the Biot theory. A three-dimensional (3D) finite-difference time-domain method is coupled with 34 human femoral trabecular microstructures measured using microcomputed tomography. The main trabecular alignment (MTA) and the degree of anisotropy (DA) were assessed for all samples. DA values were comprised between 1.02 and 1.9. The influence of bone volume fraction (BV/TV) between 5% and 25% on the properties of the fast and slow waves was studied using a dedicated image processing algorithm to modify the initial 3D microstructures. A heuristic method was devised to determine when both wave modes are time separated. The simulations (performed in three perpendicular directions) predicted that both waves generally overlap in time for a direction of propagation perpendicular to the MTA. When these directions are parallel, both waves are separated in time for samples with high DA and BV/TV values. A relationship was found between the least bone volume fraction required for the observation of nonoverlapping waves and the degree of anisotropy: The higher the DA, the lower the least BV/TV.

Velocity dispersion in trabecular bone: influence of multiple scattering and of absorption.

Speed of sound measurements are widely used clinically to assess bone strength. Trabecular bone is an attenuating composite material in which negative values of velocity dispersion have been measured, this behavior remaining poorly explained physically. The aim of this work is to describe the ultrasonic propagation in trabecular bone modeled by infinite cylinders immersed in a saturating matrix, and to derive the physical determinants of velocity dispersion. A homogenization model accounting for the coupling of multiple scattering and absorption phenomena allows the computation of phase velocity and of dispersion while varying bone properties. The present model is adapted from the generalized self-consistent method developed in the work of Yang and Mal [(1994). "Multiple-scattering of elastic waves in a fiber-reinforced composite," J. Mech. Phys. Solids 42, 1945-1968]. It predicts negative values of velocity dispersion, in agreement with experimental results obtained in phantoms mimicking trabecular bone. In trabecular bone, mostly negative and also positive values of velocity dispersion are predicted by the model, which span within the range of values measured experimentally. Scattering effects are responsible for the negative values of dispersion, whereas the frequency dependence of the absorption coefficient in bone marrow and/or in the trabeculae results in an increase in dispersion, which may then become positive.

A method for the estimation of femoral bone mineral density from variables of ultrasound transmission through the human femur.

Quantitative ultrasound (QUS) measurements at peripheral sites can be used to estimate osteoporotic fracture risk. However, measurements at these sites are less suitable to predict bone mineral density (BMD) or fracture risk at the central skeleton. We investigated whether direct QUS measurements at the femur would allow to estimate dual X-ray absorptiometry (DXA) BMD of the total proximal femur with errors comparable to established DXA accuracy errors. Two independent sets of femora were measured in Kiel (6 f, 4 m, age: 55-90) and Paris (19 f, 20 m age: 45-95) using different benchtop systems in the two laboratories. The femora were scanned in transverse transmission mode using focused US transducers of 500 kHz center frequency. The QUS values were averaged over a region similar to the total hip region of dual X-ray absorptiometry (DXA) measurements. BMD was measured using DXA. SOS and BMD correlated significantly (p<0.0001) in both data sets (R2=0.81-0.93). Correlations between BUA and BMD were also significant at p<0.001, but correlation coefficients were lower (R2=0.61-0.75). Residual errors for the estimation of BMD were 8%-10% for SOS as predictor, and 14%-16% for BUA as predictor. The residual error of 8 to 10% for the estimation of BMD from SOS is comparable to variabilities among different DXA femur subregions and accuracy errors of femoral DXA measurements caused by the impact of soft tissue. It is substantially smaller than the errors of 13% for the estimation of total femur BMD from spine BMD, 14% for the estimation of total femur BMD from calcaneus SOS or 16% for the estimation of ash weight from DXA. The results of the study show that SOS is able to predict total BMD with adequate accuracy. If femoral BMD could be obtained in vivo with comparable accuracy, femoral QUS would be suited for the assessment of bone status at one of the main osteoporotic fracture sites.

Numerical simulation of wave propagation in cancellous bone.

Numerical simulation of wave propagation is performed through 31 3D volumes of trabecular bone. These volumes were reconstructed from high synchrotron microtomography experiments and are used as the input geometry in a simulation software developed in our laboratory. The simulation algorithm accounts for propagation into both the saturating fluid and bone but absorption is not taken into account. We show that 3D simulation predicts phenomena observed experimentally in trabecular bones : linear frequency dependence of attenuation, increase of attenuation and speed of sound with the bone volume fraction, negative phase velocity dispersion in most of the specimens, propagation of fast and slow wave depending on the orientation of the trabecular network compared to the direction of propagation of the ultrasound. Moreover, the predicted attenuation is in very close agreement with the experimental one measured on the same specimens. Coupling numerical simulation with real bone architecture therefore provides a powerful tool to investigate the physics of ultrasound propagation in trabecular structures.

Numerical simulation of the dependence of quantitative ultrasonic parameters on trabecular bone microarchitecture and elastic constants.

Finite-difference numerical simulation of ultrasound propagation in complex media such as cancellous bone represents a fertile alternative to analytical approaches because it can manage the complex 3D bone structure by coupling the numerical computation with 3D numerical models of bone microarchitecture obtained from high-resolution imaging modalities. The objective of this work was to assess in silico the sensitivity of ultrasound parameters to controlled changes of microarchitecture and variation of elastic constants. The simulation software uses a finite-difference approach based on the Virieux numerical scheme. An incident plane wave was propagated through a volume of bone of approximately 5 x 5 x 8 mm(3). The volumes were reconstructed from high-resolution micro-computed tomography data. An iterative numerical scenario of "virtual osteoporosis" was implemented using a dedicated image processing algorithm in order to modify the initial 3D microstructures. Numerical computations of wave propagation were performed at each step of the process. The sensitivity to bone material properties was also tested by changing the elastic constants of bone tissue. Our results suggest that ultrasonic variables (slope of the frequency-dependent attenuation coefficient and speed of sound) are mostly influenced by bone volume fraction. However, material properties and structure also appear to play a role. The impact of modifications of the stiffness coefficients remained lower than the variability caused by structural variations. This study emphasizes the potential of numerical computations tools coupled to realistic 3D structures to elucidate the physical mechanisms of interaction between ultrasound and bone structure and to assess the sensitivity of ultrasound variables to different bone properties.

Optimal prediction of bone mineral density with ultrasonic measurements in excised human femur.

Bone mineral density (BMD) measured with dual energy X-ray absorptiometry (DXA) techniques is the current gold standard for osteoporotic fracture risk prediction. Quantitative ultrasound (QUS) techniques in transmission measurements are, however, increasingly recognized as an alternative approach. It is feasible to select different QUS methods, one type being optimized to assess microarchitectural properties of bone structure and another to assess BMD. Broadband ultrasonic attenuation (BUA) and ultrasonic velocity (UV) measured on the proximal human femur have been shown to be both significantly correlated with BMD. However, a great diversity of algorithms has been reported to measure the time-of-flight used to derive UV values. The purpose of this study was to determine which procedure results in the optimal BMD prediction at the proximal femur from ultrasound measurements. Thirty-eight excised human femurs were measured in transmission with a pair of focused 0.5-MHz central frequency transducers. Two-dimensional scans were performed and radiofrequency (RF) signals were recorded digitally at each scan position. BUA was estimated and eight different signal processing techniques were performed to estimate UV. For each signal-processing technique UV was compared to BMD. We show that the best prediction of BMD was obtained with signal-processing techniques taking into account only the first part of the transmitted signal (r2BMD-SOS = 0.86). Moreover, we show that a linear multiple regression using both BUA and speed of sound (SOS) and applied to site-matched regions of interest improved the accuracy of BMD predictions (r2BMD-SOS/BUA = 0.95). Our results demonstrate that selecting specific signal-processing methods for QUS variables allows optimal assessment of BMD. Correlation is sufficiently high that this specific QUS method can be considered as a good surrogate of BMD.

In vitro speed of sound measurement at intact human femur specimens.

Quantitative ultrasound has been recognized as a useful tool for fracture risk prediction. Current measurement techniques are limited to peripheral skeletal sites. Our objective was to demonstrate the in vitro feasibility of ultrasonic velocity measurements on human proximal femur and to investigate the relationship between velocity and bone mineral density (BMD). Sound velocity images were computed from 2-D scans performed on 38 excised human femurs in transmission at 0.5 MHz. Different regions-of-interest were investigated. Dual x-ray absorptiometry scans have been achieved for BMD measurements in site-matched regions. Our study demonstrates the feasibility of ultrasonic velocity measurements at the hip with reasonable precision (coefficient of variation of 0.3%). The best prediction of BMD was reached in the intertrochanter region (r(2) = 0.91, p < 10(-4)), with a residual error of 0.06 g/cm(2) (10%). Because BMD measured at the femur is the best predictor of hip fracture risk, the highly significant correlation and small residual error found in this study suggest that speed of sound measurement at the femur might be a good candidate for hip fracture risk prediction.