Elasticity–density and viscoelasticity–density relationships at the tibia mid-diaphysis assessed from resonant ultrasound spectroscopy measurements

Calcium Phosphate Cements as Carriers of Functional Substances for the Treatment of Bone Tissue

Interest in calcium phosphate cements as materials for the restoration and treatment of bone tissue defects is still high. Despite commercialization and use in the clinic, the calcium phosphate cements have great potential for development. Existing approaches to the production of calcium phosphate cements as drugs are analyzed. A description of the pathogenesis of the main diseases of bone tissue (trauma, osteomyelitis, osteoporosis and tumor) and effective common treatment strategies are presented in the review. An analysis of the modern understanding of the complex action of the cement matrix and the additives and drugs distributed in it in relation to the successful treatment of bone defects is given. The mechanisms of biological action of functional substances determine the effectiveness of use in certain clinical cases. An important direction of using calcium phosphate cements as a carrier of functional substances is the volumetric incorporation of anti-inflammatory, antitumor, antiresorptive and osteogenic functional substances. The main functionalization requirement for carrier materials is prolonged elution. Various release factors related to the matrix, functional substances and elution conditions are considered in the work. It is shown that cements are a complex system. Changing one of the many initial parameters in a wide range changes the final characteristics of the matrix and, accordingly, the kinetics. The main approaches to the effective functionalization of calcium phosphate cements are considered in the review.

Structure-mechanical analysis of various fixation constructs for basicervical fractures of the proximal femur and clinical implications; finite element analysis

OBJECTIVE

This present study was conducted to determine the structural-mechanical stability of various fixation constructs through finite element (FE) analysis following simulation of a basicervical fracture and to introduce the clinical implications.

MATERIALS AND METHODS

We simulated fracture models by using a right synthetic femur (SAWBONES®). We imported the implant models into ANSYS® for placement in an optimal position. Five assembly models were constructed: (1) multiple cancellous screws (MCS), (2) FNS (femoral neck system®), (3) dynamic hip screw (DHS), (4) DHS with anti-rotation 7.0 screw (DHS + screw), and PFNA-II (Proximal Femoral Nail Antirotation-II®). The femur model's distal end was completely fixed and 7° abducted. We set the force vector at a 3° angle laterally and 15° posteriorly from the vertical ground. Analysis was done using Ansys® software with von Mises stress (VMS) in megapascals (MPa) and displacement (mm) RESULTS: The displacements of the proximal femur were 10.25 mm for MCS, 9.66 mm for DHS, 9.44 mm for DHS + screw, 9.86 mm for FNS, and 9.31 mm for PFNA-II. The maximum implant VMS was 148.94 MPa for MCS, 414.66 MPa for DHS, 385.59 MPa for DSH + screw, 464.07 MPa for FNS, and 505.07 MPa for PFNA-II. The maximum VMS at the fracture site was 621.13 MPa for MCS, 464.14 MPa for DHS, 64.51 MPa for DHS + screw, 344.54 MPa for FNS, and 647.49 MPa for PFNA-II. The maximum VMS at the fracture site was in the superior area with the high point around the posterior screw in the MCS, anterosuperior corner in the DHS, the posteroinferior site of the FNS, and posterosuperior site around the entry point in the PFNA-II. In the DHS + screw, the stresses were distributed evenly and disappeared at the maximum VMS fracture site.

CONCLUSION

Based on the fracture site and implant's stress distribution, the model receiving the optimal load was a DHS + screw construct, and the FNS implant could be applied to anatomically reduced fractures without comminution. Considering the high-stress concentration around the entry point, a PFNA-II fixation has a high probability of head-neck fragment rotational instability.

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 E_yy and G_zy. 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.

Improving Transcranial Acoustic Targeting: The Limits of CT-Based Velocity Estimates and the Role of MR

Transcranial magnetic resonance-guided focused ultrasound (tcMRgFUS) enables the noninvasive treatment of the deep brain. This capacity relies on the ability to focus acoustic energy through the in-tact skull, a feat that requires accurate estimates of the acoustic velocity in individual patient skulls. In current practice, these estimates are generated using a pretreatment computed tomography (CT) scan and then registered to a magnetic resonance (MR) dataset on the day of the treatment. Treatment safety and efficacy can be improved by eliminating the need to register the CT data to the MR images and by improving the accuracy of acoustic velocity measurements. In this study, we examine the capacity of MR to supplement or replace CT as a means of estimating velocity in the skull. We find that MR can predict velocity with less but comparable accuracy to CT. We then use micro-CT imaging to better understand the limitations of Hounsfield unit (HU)-based estimates of velocity, demonstrating that the macrostructure of pores in the skull contributes to the acoustic velocity of the bone. We find evidence that detailed T2 measurements provide information about pore macrostructure similar to the information obtained with micro-CT, offering a potential clinical mechanism for improving patient-specific estimates of acoustic velocity in the human skull.

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.

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.

Detection of Meniscal Tear Effects on Tibial Vibration Using Passive Knee Sound Measurements

OBJECTIVE

To evaluate whether non-invasive knee sound measurements can provide information related to the underlying structural changes in the knee following meniscal tear. These changes are explained using an equivalent vibrational model of the knee-tibia structure.

METHODS

First, we formed an analytical model by modeling the tibia as a cantilever beam with the fixed end being the knee. The knee end was supported by three lumped components with features corresponding with tibial stiffnesses, and meniscal damping effect. Second, we recorded knee sounds from 46 healthy legs and 9 legs with acute meniscal tears (n = 34 subjects). We developed an acoustic event ("click") detection algorithm to find patterns in the recordings, and used the instrumental variable continuous-time transfer function estimation algorithm to model them.

RESULTS

The knee sound measurements yielded consistently lower fundamental mode decay rate in legs with meniscal tears ( 16 ±13 s ^{- 1}) compared to healthy legs ( 182 ±128 s ^{- 1}), p < 0.05. When we performed an intra-subject analysis of the injured versus contralateral legs for the 9 subjects with meniscus tears, we observed significantly lower natural frequency and damping ratio (first mode results for healthy: [Formula: see text]injured: [Formula: see text]) for the first three vibration modes (p < 0.05). These results agreed with the theoretical expectations gleaned from the vibrational model.

SIGNIFICANCE

This combined analytical and experimental method improves our understanding of how vibrations can describe the underlying structural changes in the knee following meniscal tear, and supports their use as a tool for future efforts in non-invasively diagnosing meniscal tear injuries.

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.

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.

Assessing the effective elastic properties of the tendon-to-bone insertion: a multiscale modeling approach

The interphase joining tendon to bone plays the crucial role of integrating soft to hard tissues, by effectively transferring stresses across two tissues displaying a mismatch in mechanical properties of nearly two orders of magnitude. The outstanding mechanical properties of this interphase are attributed to its complex hierarchical structure, especially by means of competing gradients in mineral content and collagen fibers organization at different length scales. The goal of this study is to develop a multiscale model to describe how the tendon-to-bone insertion derives its overall mechanical behavior. To this end, the effective anisotropic stiffness tensor of the interphase is predicted by modeling its elastic response at different scales, spanning from the nanostructural to the mesostructural levels, using continuum micromechanics methods. The results obtained at a lower scale serve as inputs for the modeling at a higher scale. The obtained predictions are in good agreement with stochastic finite element simulations and experimental trends reported in literature. Such model has implication for the design of bioinspired bi-materials that display the functionally graded properties of the tendon-to-bone insertion.

Image-based finite-element modeling of the human femur

Fracture is considered a critical clinical endpoint in skeletal pathologies including osteoporosis and bone metastases. However, current clinical guidelines are limited with respect to identifying cases at high risk of fracture, as they do not account for many mechanical determinants that contribute to bone fracture. Improving fracture risk assessment is an important area of research with clear clinical relevance. Patient-specific numerical musculoskeletal models generated from diagnostic images are widely used in biomechanics research and may provide the foundation for clinical tools used to quantify fracture risk. However, prior to clinical translation, in vitro validation of predictions generated from such numerical models is necessary. Despite adopting radically different models, in vitro validation of image-based finite element (FE) models of the proximal femur (predicting strains and failure loads) have shown very similar, encouraging levels of accuracy. The accuracy of such in vitro models has motivated their application to clinical studies of osteoporotic and metastatic fractures. Such models have demonstrated promising but heterogeneous results, which may be explained by the lack of a uniform strategy with respect to FE modeling of the human femur. This review aims to critically discuss the state of the art of image-based femoral FE modeling strategies, highlighting principal features and differences among current approaches. Quantitative results are also reported with respect to the level of accuracy achieved from in vitro evaluations and clinical applications and are used to motivate the adoption of a standardized approach/workflow for image-based FE modeling of the femur.

Cortical bone mapping improves finite element strain prediction accuracy at the proximal femur

Despite evidence of the biomechanical role of cortical bone, current state of the art finite element models of the proximal femur built from clinical CT data lack a subject-specific representation of the bone cortex. Our main research hypothesis is that the subject-specific modelling of cortical bone layer from CT images, through a deconvolution procedure known as Cortical Bone Mapping (CBM, validated for cortical thickness and density estimates) can improve the accuracy of CT-based FE models of the proximal femur, currently limited by partial volume artefacts. Our secondary hypothesis is that a careful choice of cortical-specific density-elasticity relationship may improve model accuracy. We therefore: (i) implemented a procedure to include subject-specific CBM estimates of both cortical thickness and density in CT-based FE models. (ii) defined alternative models that included CBM estimates and featured a cortical-specific or an independently optimised density-elasticity relationship. (iii) tested our hypotheses in terms of elastic strain estimates and failure load and location prediction, by comparing with a published cohort of 14 femurs, where strain and strength in stance and fall loading configuration were experimentally measured, and estimated through reference FE models that did not explicitly model the cortical compartment. Our findings support the main hypothesis: an explicit modelling of the proximal femur cortical bone layer including CBM estimates of cortical bone thickness and density increased the FE strains prediction, mostly by reducing peak errors (average error reduced by 30%, maximum error and 95th percentile of error distribution halved) and especially when focusing on the femoral neck locations (all error metrics at least halved). We instead rejected the secondary hypothesis: changes in cortical density-elasticity relationship could not improve validation performances. From these improved baseline strain estimates, further work is needed to achieve accurate strength predictions, as models incorporating cortical thickness and density produced worse estimates of failure load and equivalent estimates of failure location when compared to reference models. In summary, we recommend including local estimates of cortical thickness and density in FE models to estimate bone strains in physiological conditions, and especially when designing exercise studies to promote bone strength.

Finite element study of the effects of fragment shape and screw configuration on the mechanical behavior of tibial tubercle osteotomy

PURPOSE

Tibial tubercle osteotomy (TTO) is a surgical technique used in the management of severe fractures of the knee joint and revision total knee arthroplasty. Limited research discusses the performance of the osteotomy and fixation of the TTO with screws. Therefore, this study investigated the effects of fragment shape and screw configuration on the mechanical behavior in the fixation of the TTO using the finite element (FE) method.

METHODS

FE TTO models with three fragment shapes and three screw configurations were developed. The three fragment shapes were a step cut, bevel cut, and straight cut. The screw configurations were two parallel horizontal and downward screws and two trapezoidal screws. A 1654-N upward tension force was applied on the tibia tubercle, and the distal end of the tibia was completely fixed.

RESULTS

The results indicated that the step cut resulted in higher stability than the bevel and straight cut, but the stress was higher as well. Among the screw configurations, two parallel downward screws resulted in the highest stability, given the same fragment shape. In the horizontal configuration, the step cut tibia developed the largest contact force to achieve stability of the bone fragment under loading.

CONCLUSION

The fragment shape with a step cut and fixation with two parallel horizontal or downward screws are suggested for TTO, while the trapezoidal screw configuration is not suggested. Furthermore, the downward screw configuration is a suitable strategy to reduce bone stress.

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.

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.

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.

Biomechanical investigation of tibial tubercle osteotomy fixed with various screw configurations

INTRODUCTION

To date, the effects of various screw configurations on the stability of tibial tubercle osteotomy (TTO) are not completely understood. Hence, the first aim of this study is to evaluate the stability of TTO under various screw configurations. The second aim is to evaluate the internal stresses in the bone and the contact forces on the bone fragment that are developed by the tibia and screws in response to the applied load after the equilibrant is revealed.

METHODS

To calculate the biomechanical responses of the bone and screw under loading, finite element (FE) method was used in this study. Six types of screw configurations were studied in the simulation: two parallel horizontal screws placed at a 20 mm interval, two parallel horizontal screws placed at a 30 mm interval, two parallel upward screws, two parallel downward screws, two trapezoid screws, and two divergent screws. The displacement of the bone fragment, contact forces on the fragment, and the internal stress in the bone were used as indices for comparison.

RESULTS

Among all configurations, the configuration of two parallel downward screws yielded the highest stability with the lowest fragment displacement and gap opening. Although the maximum displacement of the TTO with the configuration of two parallel horizontal screws was slightly higher than that of the downward configuration, the difference was only 0.2 mm. The configuration of two upward screws resulted in the highest fragment displacement and gap deformation between the fragment and tibia. The stress of the osteotomized bone fragment was highest with the configuration of two upward screws.

CONCLUSION

Based on the present model, the current configuration of two parallel horizontal screws is recommended for TTO. If this is inappropriate in a specific clinical scenario, then the downward screw configuration may be used as an alternative. By contrast, the configuration of two parallel upward screws is least suggested for the fixation of TTO.

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 (υ_FAS) and A₀ mode (υ_A0) 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 υ_A0 (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.

Bone cortical thickness and porosity assessment using ultrasound guided waves: An ex vivo validation study

Several studies showed the ability of the cortex of long bones such as the radius and tibia to guide mechanical waves. Such experimental evidence has given rise to the emergence of a category of quantitative ultrasound techniques, referred to as the axial transmission, specifically developed to measure the propagation of ultrasound guided waves in the cortical shell along the axis of long bones. An ultrasound axial transmission technique, with an automated approach to quantify cortical thickness and porosity is described. The guided modes propagating in the cortex are recorded with a 1-MHz custom made linear transducer array. Measurement of the dispersion curves is achieved using a two-dimensional spatio-temporal Fourier transform combined with singular value decomposition. Automatic parameters identification is obtained through the solution of an inverse problem in which the dispersion curves are predicted with a two-dimensional transverse isotropic free plate model. Thirty-one radii and fifteen tibiae harvested from human cadavers underwent axial transmission measurements. Estimates of cortical thickness and porosity were obtained on 40 samples out of 46. The reproducibility, given by the root mean square error of the standard deviation of estimates, was 0.11 mm for thickness and 1.9% for porosity. To assess accuracy, site-matched micro-computed tomography images of the bone specimens imaged at 9 μm voxel size served as the gold standard. Agreement between micro-computed tomography and axial transmission for quantification of thickness and porosity at the radius and tibia ranged from R²=0.63 for porosity (root mean square error RMSE=1.8%) to 0.89 for thickness (RMSE=0.3 mm). Despite an overall good agreement for porosity, the method performs less well for porosities lower than 10%. The heterogeneity and general complexity of cortical bone structure, which are not fully accounted for by our model, are suspected to weaken the model approximation. This study presents the first validation study for assessing cortical thickness and porosity using the axial transmission technique. The automatic signal processing minimizes operator-dependent errors for parameters determination. Recovering the waveguide characteristics, that is to say cortical thickness and porosity, could provide reliable information about skeletal status and future fracture risk.

Assessment of elastic coefficients of child cortical bone using resonant ultrasound spectroscopy

The assessment of the anisotropic elastic properties of non-pathological child cortical bone remains a challenge for the biomechanical engineering community and an important clinical issue. Resonant ultrasound spectroscopy (RUS) can be used to determine bone stiffness coefficients from the mechanical resonances of bone specimens. Here, a RUS protocol was used on 7 fibula specimens from children (mean age 14 ± 3 years) to estimate the whole elastic stiffness tensor of non-pathological child cortical bone considered as orthotropic. Despite a small number of sample, results are consistent with this hypothesis, even if a trend towards transverse isotropy is discussed. Indeed, the average values of the 9 independent stiffness coefficients obtained in this study for child bone are: C₁₁ = 16.73 ± 0.19 GPa, C₂₂ = 16.19 ± 0.12 GPa, C₃₃ = 24.47 ± 0.30 GPa, C₄₄ = 4.14 ± 0.08 GPa, C₅₅ = 4.16 ± 0.07 GPa, C₆₆ = 3.13 ± 0.05 GPa, C₁₂ = 10.14 ± 0.20 GPa, C₁₃ = 10.67 ± 0.27 GPa, C₂₃ = 10.25 ± 0.14 GPa.

Synthesis and Mechanical Characterization of Binary and Ternary Intermetallic Alloys Based on Fe-Ti-Al by Resonant Ultrasound Vibrational Methods

Precise but simple experimental and inverse methods allowing the recovery of mechanical material parameters are necessary for the exploration of materials with novel crystallographic structures and elastic properties, particularly for new materials and those existing only in theory. The alloys studied herein are of new atomic compositions. This paper reports an experimental study involving the synthesis and development of methods for the determination of the elastic properties of binary (Fe-Al, Fe-Ti and Ti-Al) and ternary (Fe-Ti-Al) intermetallic alloys with different concentrations of their individual constituents. The alloys studied were synthesized from high purity metals using an arc furnace with argon flow to ensure their uniformity and homogeneity. Precise but simple methods for the recovery of the elastic constants of the isotropic metals from resonant ultrasound vibration data were developed. These methods allowed the fine analysis of the relationships between the atomic concentration of a given constituent and the Young&rsquo;s modulus or alloy density.

Quantification of stiffness measurement errors in resonant ultrasound spectroscopy of human cortical bone

Resonant ultrasound spectroscopy (RUS) is the state-of-the-art method used to investigate the elastic properties of anisotropic solids. Recently, RUS was applied to measure human cortical bone, an anisotropic material with low Q-factor (20), which is challenging due to the difficulty in retrieving resonant frequencies. Determining the precision of the estimated stiffness constants is not straightforward because RUS is an indirect method involving minimizing the distance between measured and calculated resonant frequencies using a model. This work was motivated by the need to quantify the errors on stiffness constants due to different error sources in RUS, including uncertainties on the resonant frequencies and specimen dimensions and imperfect rectangular parallelepiped (RP) specimen geometry. The errors were first investigated using Monte Carlo simulations with typical uncertainty values of experimentally measured resonant frequencies and dimensions assuming a perfect RP geometry. Second, the exact specimen geometry of a set of bone specimens were recorded by synchrotron radiation micro-computed tomography. Then, a "virtual" RUS experiment is proposed to quantify the errors induced by imperfect geometry. Results show that for a bone specimen of ∼1° perpendicularity and parallelism errors, an accuracy of a few percent ( <6.2%) for all the stiffness constants and engineering moduli is achievable.

In Vivo Characterization of Cortical Bone Using Guided Waves Measured by Axial Transmission

Cortical bone loss is not fully assessed by the current X-ray methods, and there is an unmet need in identifying women at risk of osteoporotic fracture, who should receive a treatment. The last decade has seen the emergence of the ultrasound (US) axial transmission (AT) techniques to assess a cortical bone. Recent AT techniques exploit the multimode waveguide response of the long bones such as the radius. A recent ex vivo study by our group evidenced that a multimode AT approach can yield simultaneous estimates of cortical thickness (Ct.Th) and stiffness. The aim of this paper is to move one step forward to evaluate the feasibility of measuring multimode guided waves (GW) in vivo and to infer from it cortical thickness. Measurements were taken on the forearm of 14 healthy subjects with the goal to test the accuracy of the estimated thickness using the bidirectional AT method implemented on a dedicated 1-MHz linear US array. This setup allows determining in vivo the dispersion curves of GW transmitted in the cortical layer of the radius. An inverse procedure based on the comparison between the measured and modeled dispersion curves predicted by a 2-D transverse isotropic free plate waveguide model allowed an estimation of cortical thickness, despite the presence of soft tissue. The Ct.Th values were validated by comparison with the site-matched estimates derived from X-ray high-resolution peripheral quantitative computed tomography. Results showed a significant correlation between both measurements ( r² = 0.7 , , and [Formula: see text] mm). This pilot study demonstrates the potential of bidirectional AT for the in vivo assessment of cortical thickness, a bone strength-related factor.