Ultrasound Characterization of Cortical Bone Using Shannon Entropy.

OBJECTIVE: Ultrasound backscattered signals encompass information on the microstructure of heterogeneous media such as cortical bone, in which pores act as scatterers and result in the scattering and multiple scattering of ultrasound waves. The objective of this study was to investigate whether Shannon entropy can be exploited to characterize cortical porosity. METHODS: In the study described here, to demonstrate proof of concept, Shannon entropy was used as a quantitative ultrasound parameter to experimentally evaluate microstructural changes in samples with controlled scatterer concentrations made of a highly absorbing polydimethylsiloxane matrix (PDMS). Similar assessment was then performed using numerical simulations on cortical bone structures with varying average pore diameter (Ct.Po.Dm.), density (Ct.Po.Dn.) and porosity (Ct.Po.). RESULTS: The results suggest that an increase in pore diameter and porosity lead to an increase in entropy, indicating increased levels of randomness in the signals as a result of increased scattering. The entropy-versus-scatterer volume fraction in PDMS samples indicates an initial increasing trend that slows down as the scatterer concentration increases. High levels of attenuation cause the signal amplitudes and corresponding entropy values to decrease drastically. The same trend is observed when porosity of the bone samples is increased above 15%. CONCLUSION: Sensitivity of entropy to microstructural changes in highly scattering and absorbing media can potentially be exploited to diagnose and monitor osteoporosis.

Does the bone mineral density measured on a preoperative CT scan before total hip arthroplasty reflect the bone's mechanical properties?

INTRODUCTION: No method exists to quantify the bone quality and factors that will ensure osteointegration of total hip arthroplasty (THA) implants. A preoperative CT scan can be used to evaluate the bone mineral density (BMD) when planning a THA procedure. The aim of this study was to validate BMD measurement as a marker of bone quality based on a preoperative CT scan. HYPOTHESIS: BMD reflects the bone's mechanical properties for the purposes of preoperative THA planning. METHODS: Patients who underwent primary THA for hip osteoarthritis or dysplasia with cementless implants and 3D preoperative plan were enrolled prospectively. The cortical BMD was calculated on CT scans used in the preoperative planning process. During the surgical procedure, the femoral head and neck were collected. These bone samples were subsequently scanned with a calibrated micro-CT scanner. The BMD was derived from the micro-CT scan and used as input for a finite element model to determine the bone's mechanical properties. Correlations between BMD, apparent moduli of elasticity and porosity were calculated. RESULTS: The values of cortical BMD measured on the micro-CT and CT scan were significantly correlated (cc=0.52). The mean angular cortical BMD measured with the micro-CT scan was 1472.33mg/cm3 (SD: 357.53mg/cm3, 980.64-2830.6mg/cm3). There was no significant correlation between cortical BMD and the various apparent moduli of elasticity, except for Eyy and Gzy. Cortical BMD and porosity were inversely correlated with a Spearman coefficient of -0.41 (CI95: [-0.71; -0.02], p=0.03). There was also an inverse correlation between the apparent moduli of elasticity (independent of their orientation) and porosity (p<0.01). DISCUSSION: BMD provides information about porosity, which is a major factor when evaluating the bone's mechanical properties before THA. LEVEL OF EVIDENCE: IV.

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.

Femoral neck phantom imaging using time-domain topological energy method.

Ultrasonic bone imaging is a complex task, primarily because of the low energy contained in the signals reflected from the internal bone structures. In this study, the reconstruction of a bone-mimicking phantom echographic image using time-domain topological energy (TDTE) is proposed. A TDTE image results from a combination of forward and adjoint fields. The first is a solution of a numerical model that reproduces the setup of the experimental data acquisition to the best extent possible. The second has similar characteristics, but the source term is the time-reversed residue between the forward field and signals obtained from the experiment. The acquisition-reconstruction system used a linear phased-array transducer with a 5 MHz center frequency to acquire the signals and was coupled with a k-wave toolbox to implement the numerical models and perform the image reconstruction. The results showed good agreement between the geometry of the real phantom and the ultrasonic images. However, thickness evaluation errors were observed, which may be due to incorrect assumptions about the velocity models throughout the medium, a priori assumed to be known. Thus, this method has shown promising results and should be applied to the real femoral neck as a long-term objective.

Introduction.

Diagnostic ultrasound imaging has gained wide acceptance for a broad range of clinical uses. In many cases, ultrasonography is the first-line imaging modality selected for its ease of access and absence of ionizing radiation. Over the last decades, ultrasonography has considerably evolved and is currently contributing to important improvements in patient diagnosis and treatment. Modern ultrasound imaging can provide soft tissue anatomical (shape, size…) and functional information (tissue movements, blood flow) in 3D and 4D, characterization and distinction among tissues (echostructure) and quantification of tissue properties (microstructure, tissue stiffness). Soft tissue quantitative ultrasound (QUS) refers to methods specifically developed to assess quantitative variables reflecting tissue physical properties, usually by analyzing the raw radiofrequency signals and/or its spectral characteristics.

Measurement of Cortical Bone Elasticity Tensor with Resonant Ultrasound Spectroscopy.

Resonant Ultrasound Spectroscopy estimates the stiffness coefficients of a material from the free resonant frequencies of a single specimen. It is particularly suitable for complete stiffness characterization of anisotropic materials available only as small samples (typically a few mm), and it does not suffer from some limitations associated to quasi-static mechanical test and ultrasound wave velocity measurements. RUS has been used for decades on geological samples and single crystals, but was until recently not applied to mineralized tissues such as bone. The reason is the significant mechanical damping presents in these materials, which causes the resonant peaks to overlap and prevent a direct measurement of the resonant frequencies. This chapter describes the use of RUS for the elastic characterization of mineralized tissues, cortical bone in particular. All steps are described, from sample preparation and measurement setup to signal processing and data analysis, including the developments and adaptions necessary to overcome the difficulties linked to damping. Viscoelastic characterization, from the width of the resonant peaks, is also presented. Mostly technical aspects are developed in this chapter, while the data obtained from RUS on several collections of mineralized tissues specimens are presented and discussed in Chap. 13.

Documenting the Anisotropic Stiffness of Hard Tissues with Resonant Ultrasound Spectroscopy.

Recent advances in resonant ultrasound spectroscopy (RUS) leverage accurate measurements of the anisotropic stiffness of hard tissues at millimeter scale. RUS is the only available technique to date to assess the entire stiffness tensor of bone from a unique rectangular parallelepiped specimen. Accurately measured stiffness constants are required for bone mechanics models and may provide information on some fundamental aspects of hard tissues biology such as regulation of bone mass, remodeling and healing. In this chapter, we review the anisotropic stiffness data of human hard tissues measured with RUS, mostly during the last decade. Hard tissues covered here include human enamel and dentin, cortical bone from the femur and tibia of human adults, and child cortical bone tissue, accounting for 288 specimens in total. Data was collected in the literature and from previous works of our group. We performed a comparative study to depict the differences in the elastic properties of these hard tissues. Our objectives were to: (1) document the range of anisotropic stiffness constants in human hard tissues (orthotropic or transverse isotropic symmetry); and (2) provide empirical laws between mass density and anisotropic stiffness of cortical bone at different skeletal sites. Finally, we discuss the challenges and perspectives to use RUS for large collections of specimens.

In vivopulse-echo measurement of apparent broadband attenuation andQfactor in cortical bone: a preliminary study.

Quantitative ultrasound (QUS) methods have been introduced to assess cortical bone health at the radius and tibia through the assessment of cortical thickness (Ct.Th), cortical porosity and bulk wave velocities. Ultrasonic attenuation is another QUS parameter which is not currently used. We assessed the feasibility ofin vivomeasurement of ultrasonic attenuation in cortical bone with a broadband transducer with 3.5 MHz center frequency. Echoes from the periosteal and endosteal interfaces were fitted with Gaussian pulses using sparse signal processing. Then, the slope of the broadband ultrasonic attenuation (Ct.nBUA) in cortical bone and quality factorQ11-1were calculated with a parametric approach based on the center-frequency shift. Five human subjects were measured at the one-third distal radius with pulse-echo ultrasound, and reference data was obtained with high-resolution x-ray peripheral computed tomography (Ct.Th and cortical volumetric bone mineral density (Ct.vBMD)). Ct.Th was used in the calculation of Ct.nBUA whileQ11-1is obtained solely from ultrasound data. The values of Ct.nBUA (6.7 ± 2.2 dB MHz-1.cm-1) andQ11-1(8.6 ± 3.1%) were consistent with the literature data and were correlated to Ct.vBMD (R2=0.92,p<0.01, RMSE = 0.56 dB.MHz-1.cm-1, andR2=0.93,p<0.01, RMSE = 0.76%). This preliminary study suggests that the attenuation of an ultrasound signal propagating in cortical bone can be measuredin vivoat the one-third distal radius and that it provides an information on bone quality as attenuation values were correlated to Ct.vBMD. It remains to ascertain that Ct.nBUA andQ11-1measured here exactly reflect the true (intrinsic) ultrasonic attenuation in cortical bone. Measurement of attenuation may be considered useful for assessing bone health combined with the measurement of Ct.Th, porosity and bulk wave velocities in multimodal cortical bone QUS methods.

Maximum effect of the heterogeneity of tissue mineralization on the effective cortical bone elastic properties.

The mineralization level is heterogeneous in cortical bone extracellular matrix as a consequence of remodeling. Models of the effective elastic properties at the millimeter scale have been developed based on idealizations of the vascular pore network and matrix properties. Some popular models do not take into account the heterogeneity of the matrix. However, the errors on the predicted elasticity when the difference in elastic properties between osteonal and interstitial tissues is not modeled have not been quantified. This work provides an estimation of the maximum error. We compare the effective elasticity of a representative volume element (RVE) assuming (1) different elastic properties in osteonal and interstitial tissues vs. (2) average matrix properties. In order to account for the variability of bone microstructure, we use a collection of high resolution images of the pore network to build RVEs. In each RVE we assumed a constant osteonal wall thickness and we artificially varied this thickness between 35 and 140 [Formula: see text]m to create RVEs with different amounts of osteonal tissue. The homogenization problem was solved with a fast Fourier transform (FFT)-based numerical scheme. We found that the error depends on pore volume fraction and varies on average from 1 to [Formula: see text] depending on the assumed diameter of the osteons. The results suggest that matrix heterogeneity may be disregarded in cortical bone models in most practical cases.

Cortical bone viscoelastic damping assessed with resonant ultrasound spectroscopy reflects porosity and mineral content.

Viscoelasticity is an essential property of bone related to fragility, which is altered in aging and bone disease. Bone viscoelastic behavior is attributed to several mechanisms involving collagen and mineral properties, porosities, and bone hierarchical tissue organization. We aimed to assess the relationships between cortical bone viscoelastic damping measured with Resonant Ultrasound Spectroscopy (RUS), microstructural and compositional characteristics. We measured 52 bone specimens from the femur of 26 elderly human donors. RUS provided a shear damping coefficient at a frequency of the order of 150 kHz. The characteristics of the structure of the vascular pore network and tissue mineral density were measured using synchrotron radiation high-resolution computed tomography (SR-µCT). Fourier transformed infrared microspectroscopy (FTIRM) was used to quantify mineral-to-organic phase ratio, mineral maturity, crystallinity, and collagen maturity. Cross-links were quantified from biochemistry. Viscoelastic damping was found to increase with vascular porosity (r=0.68), to decrease with the degree of mineralization of the extravascular matrix (r=-0.68), and was marginally affected by collagen. We built a multilinear model suggesting that when porosity is controlled, the variation of mineral content explains a small additional part of the variability of damping. The work supports the consideration of viscoelasticity measurement as a potential biomarker of fragility and provides a documentation of bone viscoelastic behavior and its determinants in a frequency range rarely investigated.

Bulk Wave Velocities in Cortical Bone Reflect Porosity and Compression Strength.

The goal of this study was to evaluate whether ultrasonic velocities in cortical bone can be considered as a proxy for mechanical quality of cortical bone tissue reflected by porosity and compression strength. Micro-computed tomography, compression mechanical testing and resonant ultrasound spectroscopy were used to assess, respectively, porosity, strength and velocity of bulk waves of both shear and longitudinal polarisations propagating along and perpendicular to osteons, in 92 cortical bone specimens from tibia and femur of elderly human donors. All velocities were significantly associated with strength (r = 0.65-0.83) and porosity (r = -0.64 to -0.77). Roughly, according to linear regression models, a decrease in velocity of 100 m/s corresponded to a loss of 20 MPa in strength (which is approximately 10% of the largest strength value) and to an increase in porosity of 5%. These results provide a rationale for the in vivo measurement of one or several velocities for the diagnosis of bone fragility.

Pre-operative bone mineral density is a predictive factor for excellent early patient-reported outcome measures in cementless total hip arthroplasty using a proximally fixed anatomic stem. A prospective study at two year minimum follow-up.

PURPOSE: The goal of the study was to analyze the impact of the pre-operative bone mineral density on the patients' reported outcomes at two year minimum follow-up of cementless THA using a proximally fixed anatomic stem. METHODS: A prospective study included all patients who underwent a cementless THA using a specific proximally fixed anatomic stem and a 3D preoperative CT scan-based planning. The bone mineral density (BMD) of the metaphyseal cancellous bone was computed in a volume (of 1 mm thick and of 1 cm2 surface) at the level of the calcar 10 mm above the top of the lesser trochanter. Patients were assessed at two year follow-up using self-administered auto-questionnaires corresponding to the modified Harris (mHHS), the Oxford (OHS), and the Forgotten Hip (FHS) scores. A multiple linear regression statistical analysis was performed to assess the link between the mHHS, the age, body mass index (BMI), BMD, gender, and ASA grade. RESULTS: Fifty patients were included (29 men, 21 women), with an average age of 62 ± 12 years and an average BMI of 27 ± 5 kg/m2. At two year follow-up, on multivariate analysis, excellent mHHS (≥ 90%) was significantly associated with only two parameters: a BMI ≤ 25 kg /m2 with an odd ratio OR = 10 (CI95% [2.1-48.3], p = 0.004) and a BMD ≥ 72 mg/cm3 with an odd ratio OR = 4.87 (CI95% [1.2-18.6], p = 0.02). CONCLUSION: The short-term PROMs after cementless THA are impacted by pre-operative cancellous bone density. However, the BMI remains the most influential parameter on the clinical outcomes.

Modification of regional bone mineral density due to femoral rasping in cementless proximally fixed total hip arthroplasty.

BACKGROUND: Three-dimensional planning (3DP) in total hip arthroplasty using computed tomography (CT) to analyze bone mineral density (BMD) at the stem-femur interface has a high reported accuracy and excellent mid-term results in the literature. However, 3DP does not take into account the effect of femoral rasping on BMD distribution within the rasped cavity. Characterizing the impact of femoral rasping on BMD may help avoid mechanical failures, but this data is not accurately investigated. Therefore, we set out a cadaveric study to identify if: (1) Femoral rasping modified regional BMD in areas considered critical for bone anchorage of cementless metaphyseally fixed anatomic stems. (2) In areas of bone-implant contact with an initial high BMD, does femoral rasping increase BMD? HYPOTHESIS: Femoral rasping increases BMD in some zones considered critical for bone anchorage of cementless metaphyseally fixed anatomic stems within the rasped femoral cavity. METHODS: Four cadaveric femurs were selected to undergo a rasping procedure similar to surgical techniques used for metaphyseally fixed anatomic stems. Images of femurs before and after rasping were obtained with a micro-CT scanner (pixel size 35µm). BMD values before and after rasping were compared in a trabecular bone ring of 3mm thickness around the cavity created by the rasps, in a region extending 3cm above and 2cm below the middle of the lesser trochanter. RESULTS: Average BMD increased significantly after rasping in 3 of the 4 femurs (13% (0.27 to 0.30) (p=0.004)), 12% (0.32 to 0.36 (p=0.034)) and 15% (0.4 to 0.46 (p=0.001)), while there was no significant variation in the last femur (0.32 to 0.32 (p>0.05)). Increases in regional BMD were significantly higher in the lateral and medial areas, as well as in the most distal femoral regions. There were significantly lower variations of BMD in regions with initially higher BMD. DISCUSSION: Current opinion considers trabecular bone debris from femoral rasping to have an impact on final stem position and outcome. Our study has demonstrated an overall positive effect of femoral rasping on BMD in the rasped cavity. Understanding this in the context of 3DP may help avoid mechanical failures such as, suboptimal implant fit, fill, and stability as well as femoral fractures during stem implantation. LEVEL OF EVIDENCE: IV, Prospective in vitro study.

Artificial neural network to estimate micro-architectural properties of cortical bone using ultrasonic attenuation: A 2-D numerical study.

The goal of this study is to estimate micro-architectural parameters of cortical porosity such as pore diameter (φ), pore density (ρ) and porosity (ν) of cortical bone from ultrasound frequency dependent attenuation using an artificial neural network (ANN). First, heterogeneous structures with controlled pore diameters and pore densities (mono-disperse) were generated, to mimic simplified structure of cortical bone. Then, more realistic structures were obtained from high resolution CT scans of human cortical bone. 2-D finite-difference time-domain simulations were conducted to calculate the frequency-dependent attenuation in the 1-8 MHz range. An ANN was then trained with the ultrasonic attenuation at different frequencies as the input feature vectors while the output was set as the micro-architectural parameters (pore diameter, pore density and porosity). The ANN is composed of three fully connected dense layers with 24, 12 and 6 neurons, connected to the output layer. The dataset was trained over 6000 epochs with a batch size of 16. The trained ANN exhibits the ability to predict the micro-architectural parameters with high accuracy and low losses. ANN approaches could potentially be used as a tool to help inform physics-based modelling of ultrasound propagation in complex media such as cortical bone. This will lead to the solution of inverse-problems to retrieve bone micro-architectural parameters from ultrasound measurements for the non-invasive diagnosis and monitoring osteoporosis.

Computed tomography porosity and spherical indentation for determining cortical bone millimetre-scale mechanical properties.

The cortex of the femoral neck is a key structural element of the human body, yet there is not a reliable metric for predicting the mechanical properties of the bone in this critical region. This study explored the use of a range of non-destructive metrics to measure femoral neck cortical bone stiffness at the millimetre length scale. A range of testing methods and imaging techniques were assessed for their ability to measure or predict the mechanical properties of cortical bone samples obtained from the femoral neck of hip replacement patients. Techniques that can potentially be applied in vivo to measure bone stiffness, including computed tomography (CT), bulk wave ultrasound (BWUS) and indentation, were compared against in vitro techniques, including compression testing, density measurements and resonant ultrasound spectroscopy. Porosity, as measured by micro-CT, correlated with femoral neck cortical bone's elastic modulus and ultimate compressive strength at the millimetre length scale. Large-tip spherical indentation also correlated with bone mechanical properties at this length scale but to a lesser extent. As the elastic mechanical properties of cortical bone correlated with porosity, we would recommend further development of technologies that can safely measure cortical porosity in vivo.

Trabecular architecture in the humeral metaphyses of non-avian reptiles (Crocodylia, Squamata and Testudines): Lifestyle, allometry and phylogeny.

The lifestyle of extinct tetrapods is often difficult to assess when clear morphological adaptations such as swimming paddles are absent. According to the hypothesis of bone functional adaptation, the architecture of trabecular bone adapts sensitively to physiological loadings. Previous studies have already shown a clear relation between trabecular architecture and locomotor behavior, mainly in mammals and birds. However, a link between trabecular architecture and lifestyle has rarely been examined. Here, we analyzed trabecular architecture of different clades of reptiles characterized by a wide range of lifestyles (aquatic, amphibious, generalist terrestrial, fossorial, and climbing). Humeri of squamates, turtles, and crocodylians have been scanned with microcomputed tomography. We selected spherical volumes of interest centered in the proximal metaphyses and measured trabecular spacing, thickness and number, degree of anisotropy, average branch length, bone volume fraction, bone surface density, and connectivity density. Only bone volume fraction showed a significant phylogenetic signal and its significant difference between squamates and other reptiles could be linked to their physiologies. We found negative allometric relationships for trabecular thickness and spacing, positive allometries for connectivity density and trabecular number and no dependence with size for degree of anisotropy and bone volume fraction. The different lifestyles are well separated in the morphological space using linear discriminant analyses, but a cross-validation procedure indicated a limited predictive ability of the model. The trabecular bone anisotropy has shown a gradient in turtles and in squamates: higher values in amphibious than terrestrial taxa. These allometric scalings, previously emphasized in mammals and birds, seem to be valid for all amniotes. Discriminant analysis has offered, to some extent, a distinction of lifestyles, which however remains difficult to strictly discriminate. Trabecular architecture seems to be a promising tool to infer lifestyle of extinct tetrapods, especially those involved in the terrestrialization.

Homogenization of cortical bone reveals that the organization and shape of pores marginally affect elasticity.

With ageing and various diseases, the vascular pore volume fraction (porosity) in cortical bone increases, and the morphology of the pore network is altered. Cortical bone elasticity is known to decrease with increasing porosity, but the effect of the microstructure is largely unknown, while it has been thoroughly studied for trabecular bone. Also, popular micromechanical models have disregarded several micro-architectural features, idealizing pores as cylinders aligned with the axis of the diaphysis. The aim of this paper is to quantify the relative effects on cortical bone anisotropic elasticity of porosity and other descriptors of the pore network micro-architecture associated with pore number, size and shape. The five stiffness constants of bone assumed to be a transversely isotropic material were measured with resonant ultrasound spectroscopy in 55 specimens from the femoral diaphysis of 29 donors. The pore network, imaged with synchrotron radiation X-ray micro-computed tomography, was used to derive the pore descriptors and to build a homogenization model using the fast Fourier transform (FFT) method. The model was calibrated using experimental elasticity. A detailed analysis of the computed effective elasticity revealed in particular that porosity explains most of the variations of the five stiffness constants and that the effects of other micro-architectural features are small compared to usual experimental errors. We also have evidence that modelling the pore network as an ensemble of cylinders yields biased elasticity values compared to predictions based on the real micro-architecture. The FFT homogenization method is shown to be particularly efficient to model cortical bone.

Anisotropic elastic properties of human femoral cortical bone and relationships with composition and microstructure in elderly.

The strong dependence between cortical bone elasticity at the millimetre-scale (mesoscale) and cortical porosity has been evidenced by previous studies. However, bone is an anisotropic composite material made by mineral, proteins and water assembled in a hierarchical structure. Whether the variations of structural and compositional properties of bone affect the different elastic coefficients at the mesoscale is not clear. Aiming to understand the relationships between bone elastic properties and compositions and microstructure, we applied state-of-the-art experimental modalities to assess these aspects of bone characteristics. All elastic coefficients (stiffness tensor of the transverse isotropic bone material), structure of the vascular pore network, collagen and mineral properties were measured in 52 specimens from the femoral diaphysis of 26 elderly donors. Statistical analyses and micromechanical modeling showed that vascular pore volume fraction and the degree of mineralization of bone are the most important determinants of cortical bone anisotropic mesoscopic elasticity. Though significant correlations were observed between collagen properties and elasticity, their effects in bone mesoscopic elasticity were minor in our data. This work also provides a unique set of data exhibiting a range of variations of compositional and microstructural cortical bone properties in the elderly and gives strong experimental evidence and basis for further development of biomechanical models for human cortical bone. STATEMENT OF SIGNIFICANCE: This study reports the relationships between microstructure, composition and the mesoscale anisotropic elastic properties of human femoral cortical bone in elderly. For the first time, we provide data covering the complete anisotropic elastic tensor, the microstructure of cortical vascular porosity, mineral and collagen characteristics obtained from the same or adjacent samples in each donor. The results revealed that cortical vascular porosity and degree of mineralization of bone are the most important determinants of bone anisotropic stiffness at the mesoscale. The presented data gives strong experimental evidence and basis for further development of biomechanical models for human cortical bone.

Ex vivo cortical porosity and thickness predictions at the tibia using full-spectrum ultrasonic guided-wave analysis.

The estimation of cortical thickness (Ct.Th) and porosity (Ct.Po) at the tibia using axial transmission ultrasound was successfully validated ex vivo against site-matched micro-computed tomography. The assessment of cortical parameters based on full-spectrum guided-wave analysis might improve the prediction of bone fractures in a cost-effective and radiation-free manner. PURPOSE: Cortical thickness (Ct.Th) and porosity (Ct.Po) are key parameters for the identification of patients with fragile bones. The main objective of this ex vivo study was to validate the measurement of Ct.Po and Ct.Th at the tibia using a non-ionizing, low-cost, and portable 500-kHz ultrasound axial transmission system. Additional ultrasonic velocities and site-matched reference parameters were included in the study to broaden the analysis. METHODS: Guided waves were successfully measured ex vivo in 17 human tibiae using a novel 500-kHz bi-directional axial transmission probe. Theoretical dispersion curves of a transverse isotropic free plate model with invariant matrix stiffness were fitted to the experimental dispersion curves in order to estimate Ct.Th and Ct.Po. In addition, the velocities of the first arriving signal (υFAS) and A0 mode (υA0) were measured. Reference Ct.Po, Ct.Th, and vBMD were obtained from site-matched micro-computed tomography. Scanning acoustic microscopy (SAM) provided the acoustic impedance of the axial cortical bone matrix. RESULTS: The best predictions of Ct.Po (R2 = 0.83, RMSE = 2.2%) and Ct.Th (R2 = 0.92, RMSE = 0.2 mm, one outlier excluded) were obtained from the plate model. The second best predictors of Ct.Po and Ct.Th were vBMD (R2 = 0.77, RMSE = 2.6%) and υA0 (R2 = 0.28, RMSE = 0.67 mm), respectively. CONCLUSIONS: Ct.Th and Ct.Po were accurately predicted at the human tibia ex vivo using a transverse isotropic free plate model with invariant matrix stiffness. The model-based predictions were not further enhanced when we accounted for variations in axial tissue stiffness as reflected by the acoustic impedance from SAM.