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.

Ultrasound-Based Estimates of Cortical Bone Thickness and Porosity Are Associated With Nontraumatic Fractures in Postmenopausal Women: A Pilot Study.

Recent ultrasound (US) axial transmission techniques exploit the multimode waveguide response of long bones to yield estimates of cortical bone structure characteristics. This pilot cross-sectional study aimed to evaluate the performance at the one-third distal radius of a bidirectional axial transmission technique (BDAT) to discriminate between fractured and nonfractured postmenopausal women. Cortical thickness (Ct.Th) and porosity (Ct.Po) estimates were obtained for 201 postmenopausal women: 109 were nonfractured (62.6 ± 7.8 years), 92 with one or more nontraumatic fractures (68.8 ± 9.2 years), 17 with hip fractures (66.1 ± 10.3 years), 32 with vertebral fractures (72.4 ± 7.9 years), and 17 with wrist fractures (67.8 ± 9.6 years). The areal bone mineral density (aBMD) was obtained using DXA at the femur and spine. Femoral aBMD correlated weakly, but significantly with Ct.Th (R = 0.23, p < 0.001) and Ct.Po (R = -0.15, p < 0.05). Femoral aBMD and both US parameters were significantly different between the subgroup of all nontraumatic fractures combined and the control group (p < 0.05). The main findings were that (1) Ct.Po was discriminant for all nontraumatic fractures combined (OR = 1.39; area under the receiver operating characteristic curve [AUC] equal to 0.71), for vertebral (OR = 1.96; AUC = 0.84) and wrist fractures (OR = 1.80; AUC = 0.71), whereas Ct.Th was discriminant for hip fractures only (OR = 2.01; AUC = 0.72); there was a significant association (2) between increased Ct.Po and vertebral and wrist fractures when these fractures were not associated with any measured aBMD variables; (3) between increased Ct.Po and all nontraumatic fractures combined independently of aBMD neck; and (4) between decreased Ct.Th and hip fractures independently of aBMD femur. BDAT variables showed comparable performance to that of aBMD neck with all types of fractures (OR = 1.48; AUC = 0.72) and that of aBMD femur with hip fractures (OR = 2.21; AUC = 0.70). If these results are confirmed in prospective studies, cortical BDAT measurements may be considered useful for assessing fracture risk in postmenopausal women. © 2019 American Society for Bone and Mineral Research.

Damage prediction via nonlinear ultrasound: A micro-mechanical approach.

Nonlinear constitutive mechanical parameters, predominantly governed by micro-damage, interact with ultrasound to generate harmonics that are not present in the excitation. In principle, this phenomenon therefore permits early stage damage identification if these higher harmonics can be measured. To understand the underlying mechanism of harmonic generation, a nonlinear micro-mechanical approach is proposed here, that relates a distribution of clapping micro-cracks to the measurable macroscopic acoustic nonlinearity by representing the crack as an effective inclusion with Landau type nonlinearity at small strain. The clapping mechanism inside each micro-crack is represented by a Taylor expansion of the stress-strain constitutive law, whereby nonlinear terms arise. The micro-cracks are considered distributed in a macroscopic medium and the effective nonlinearity parameter associated with compression is determined via a nonlinear Mori-Tanaka homogenization theory. Relationships are thus obtained between the measurable acoustic nonlinearity and the Landau-type nonlinearity. The framework developed therefore yields links with nonlinear ultrasound, where the dependency of measurable acoustic nonlinearity is, under certain hypotheses, formally related to the density of micro-cracks and the bulk material properties.

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.

Genetic algorithms-based inversion of multimode guided waves for cortical bone characterization.

Recent progress in quantitative ultrasound has exploited the multimode waveguide response of long bones. Measurements of the guided modes, along with suitable waveguide modeling, have the potential to infer strength-related factors such as stiffness (mainly determined by cortical porosity) and cortical thickness. However, the development of such model-based approaches is challenging, in particular because of the multiparametric nature of the inverse problem. Current estimation methods in the bone field rely on a number of assumptions for pairing the incomplete experimental data with the theoretical guided modes (e.g. semi-automatic selection and classification of the data). The availability of an alternative inversion scheme that is user-independent is highly desirable. Thus, this paper introduces an efficient inversion method based on genetic algorithms using multimode guided waves, in which the mode-order is kept blind. Prior to its evaluation on bone, our proposal is validated using laboratory-controlled measurements on isotropic plates and bone-mimicking phantoms. The results show that the model parameters (i.e. cortical thickness and porosity) estimated from measurements on a few ex vivo human radii are in good agreement with the reference values derived from x-ray micro-computed tomography. Further, the cortical thickness estimated from in vivo measurements at the third from the distal end of the radius is in good agreement with the values delivered by site-matched high-resolution x-ray peripheral computed tomography.

A sparse digital signal model for ultrasonic nondestructive evaluation of layered materials.

Signal modeling has been proven to be an useful tool to characterize damaged materials under ultrasonic nondestructive evaluation (NDE). In this paper, we introduce a novel digital signal model for ultrasonic NDE of multilayered materials. This model borrows concepts from lattice filter theory, and bridges them to the physics involved in the wave-material interactions. In particular, the proposed theoretical framework shows that any multilayered material can be characterized by a transfer function with sparse coefficients. The filter coefficients are linked to the physical properties of the material and are analytically obtained from them, whereas a sparse distribution naturally arises and does not rely on heuristic approaches. The developed model is first validated with experimental measurements obtained from multilayered media consisting of homogeneous solids. Then, the sparse structure of the obtained digital filter is exploited through a model-based inverse problem for damage identification in a carbon fiber-reinforced polymer (CFRP) plate.

Mechanical assessment of cervical remodelling in pregnancy: insight from a synthetic model.

During the gestation and the cervical remodelling, several changes occur progressively in the structure of the tissue. An increase in the hydration, disorganisation of collagen network and decrease in elasticity can be observed. The collagen structure disorganisation is particularly complex: collagen fibres turn thicker and more wavy as the gestation progresses in a transition from relatively straight fibres to wavy fibres, while pores between collagen fibres become larger and separated. Shear wave elastography is a promising but not yet fully understood tool to assess these structural changes and the cervix׳s ability to dilate. To this end, a numerical histo-mechanical model is proposed in the present study, which aims at linking variations in the microscopic histo-biomechanical processes with shear wave propagation characteristics. Parametric simulations are carried out for a broad range of mechanical and geometrical parameters. Results show a direct relationship between the histological and morphological changes during pregnancy and the viscoelastic behaviour of the tissue.

Assessing viscoelasticity of shear wave propagation in cervical tissue by multiscale computational simulation.

The viscoelastic properties are recently being reported to be particularly sensitive to the gestation process, and to be intimately related to the microstructure of the cervical tissue. However, this link is not fully understood yet. In this work, we explore the importance of the heterogeneous multi-scale nature of cervical tissue for quantifying both elasticity and viscosity from shear waves velocity. To this end, shear wave propagations are simulated in a microscopic cervical tissue model using the finite difference time domain technique, over a wide frequency range from 15 to 200 kHz. Three standard rheological models (Voigt, Maxwell and Zener) are evaluated regarding their ability to reproduce the simulated dispersion curves, and their plausibility to describe cervical tissue is ranked by a stochastic model-class selection formulation. It is shown that the simplest model, i.e. that with less parameters, which best describes the simulated dispersion curves in cervical tissue is the Maxwell model. Furthermore, results show that the excitation frequency determines which rheological model can be representative for the tissue. Typically, viscoelastic parameters tend to converge for excitation frequencies over 100 kHz.