Effect of collagen fibril orientation on the anisotropic properties of peri-implant bone.

In orthopedic and dental surgery, the implantation of biomaterials within the bone to restore the integrity of the treated organ has become a standard procedure. Their long-term stability relies on the osseointegration phenomena, where bone grows onto and around metallic implants, creating a bone-implant interface. Bone is a highly hierarchical material that evolves spatially and temporally during this healing phase. A deeper understanding of its biomechanical characteristics is needed, as they are determinants for surgical success. In this context, we propose a multiscale homogenization model to evaluate the effective elastic properties of bone as a function of the distance from the implant, based on the tissue's structure and composition at lower scales. The model considers three scales: hydroxyapatite foam (nanoscale), ultrastructure (microscale), and tissue (mesoscale). The elastic properties and the volume fraction of the elementary constituents of bone matrix (mineral, collagen, and water), the orientation of the collagen fibril relative to the implant surface, and the mesoscale porosity constitute the input data of the model. The effect of a spatiotemporal variation in the collagen fibrils' orientation on the bone anisotropic properties in the proximity of the implant was investigated. The findings revealed a strong variation of the components of the effective elasticity tensor of the bone as a function of the distance from the implant. The effective elasticity appears to be primarily sensitive to the porosity (mesoscale) rather than to the collagen fibrils' orientation (sub-micro scale). However, the orientation of the fibrils has a significant influence on the isotropy of the bone. When analyzing the symmetry properties of the effective elasticity tensor, the ratio between the isotropic and hexagonal components is determined by a combination of the porosity and the fibrils' orientation. A decrease in porosity leads to a decrease in bone isotropy and, in turn, an increase in the impact of the fibrils' orientation. These results demonstrate that the collagen fibril orientation should be taken into account to properly describe the effective elastic anisotropy of bone at the organ scale.

Ultrasonic bandgaps in viscoelastic 1D-periodic media: Mechanical modeling and experimental validation.

Multi-material additive manufacturing is receiving increasing attention in the field of acoustics, in particular towards the design of micro-architectured periodic media used to achieve programmable ultrasonic responses. To unravel the effect of the material properties and spatial arrangement of the printed constituents, there is an unmet need in developing wave propagation models for prediction and optimization purposes. In this study, we propose to investigate the transmission of longitudinal ultrasound waves through 1D-periodic biphasic media, whose constituent materials are viscoelastic. To this end, Bloch-Floquet analysis is applied in the frame of viscoelasticity, with the aim of disentangling the relative contributions of viscoelasticity and periodicity on ultrasound signatures, such as dispersion, attenuation, and bandgaps localization. The impact of the finite size nature of these structures is then assessed by using a modeling approach based on the transfer matrix formalism. Finally, the modeling outcomes, i.e., frequency-dependent phase velocity and attenuation, are confronted with experiments conducted on 3D-printed samples, which exhibit a 1D periodicity at length-scales of a few hundreds of micrometers. Altogether, the obtained results shed light on the modeling characteristics to be considered when predicting the complex acoustic behavior of periodic media in the ultrasonic regime.

Ultrasound characterization of the viscoelastic properties of additively manufactured photopolymer materials.

Photopolymer-based additive manufacturing has received increasing attention in the field of acoustics over the past decade, specifically towards the design of tissue-mimicking phantoms and passive components for ultrasound imaging and therapy. While these applications rely on an accurate characterization of the longitudinal bulk properties of the materials, emerging applications involving periodic micro-architectured media also require the knowledge of the transverse bulk properties to achieve the desired acoustic behavior. However, a robust knowledge of these properties is still lacking for such attenuating materials. Here, we report on the longitudinal and transverse bulk properties, i.e., frequency-dependent phase velocities and attenuations, of photopolymer materials, which were characterized in the MHz regime using a double through-transmission method in oblique incidence. Samples were fabricated using two different printing technologies (stereolithography and polyjet) to assess the impact of two important factors of the manufacturing process: curing and material mixing. Overall, the experimentally observed dispersion and attenuation could be satisfactorily modeled using a power law attenuation to identify a reduced number of intrinsic ultrasound parameters. As a result, these parameters, and especially those reflecting transverse bulk properties, were shown to be very sensitive to slight variations of the manufacturing process.

Ultrasound characterization of bioinspired functionally graded soft-to-hard composites: Experiment and modeling.

Functional grading is a distinctive feature adopted by nature to improve the transition between tissues that present a strong mismatch in mechanical properties, a relevant example being the tendon-to-bone attachment. Recent progress in multi-material additive manufacturing now allows for the design and fabrication of bioinspired functionally graded soft-to-hard composites. Nevertheless, this emerging technology depends on several design variables, including both material and mechanistic ingredients, that are likely to affect the mechanical performance of such composites. In this paper, a model-based approach is developed to describe the interaction of ultrasound waves with homogeneous and heterogeneous additively manufactured samples, which respectively display a variation either of the material ingredients (e.g., ratio of the elementary constituents) or of their spatial arrangement (e.g., functional gradients, damage). Measurements are performed using longitudinal bulk waves, which are launched and detected using a linear transducer array. First, model is calibrated by exploiting the signals measured on the homogeneous samples, which allow identifying relationships between the model parameters and the material composition. Second, the model is validated by comparing the signals measured on the heterogeneous samples with those predicted numerically. Overall, the reported results pave the way for characterizing and optimizing multi-material systems that display complex bioinspired features.

Interaction of ultrasound waves with bone remodelling: a multiscale computational study.

Ultrasound stimulation is thought to influence bone remodelling process. But recently, the efficiency of ultrasound therapy for bone healing has been questioned. Despite an extensive literature describing the positive effect of ultrasound on bone regeneration-cell cultures, animal models, clinical studies-there are more and more reviews denouncing the inefficiency of clinical devices based on low-intensity pulsed ultrasound stimulation (LIPUS) of the bone healing. One of the reasons to cause controversy comes from the persistent misunderstanding of the underlying physical and biological mechanisms of ultrasound stimulation of bone repair. As ultrasonic waves are mechanical waves, the process to be studied is the one of the mechanotransduction. Previous studies on the bone mechanotransduction have demonstrated the key role of the osteocytes in bone mechano-sensing. Osteocytes are bone cells ubiquitous inside the bone matrix; they are immersed in the interstitial fluid (IF) inside the lacuno-canalicular network (LCN). They are considered as particularly sensitive to a particular type of mechanical stress: wall shear stress on osteocytes due to the IF flow in the LCN. Inspired from these findings and observations, the present work investigates the effect of LIPUS on the cortical bone from the tissue to the osteocytes, considering that the impact of the ultrasound stimulation applied at the tissue scale is related to the mechanical stress experimented by the bone cells. To do that simulations based on the finite element method are carried out in the commercial software Comsol Multiphysics to assess the wall shear stress levels induced by the LIPUS on the osteocytes. Two formulations of the wall shear stress were investigated based on two IF flow models inside the LCN and associated with two different values of the LCN permeability. The wall shear stress estimate is very different depending on the assumption considered. One of these two models provides wall shear stress values in accordance with previous works published on bone mechanotransduction. This study presents the preliminary results of a computational model that could provide keys to understanding the underlying mechanisms of the LIPUS.

Influence of anisotropic bone properties on the biomechanical behavior of the acetabular cup implant: a multiscale finite element study.

Although the biomechanical behavior of the acetabular cup (AC) implant is determinant for the surgical success, it remains difficult to be assessed due to the multiscale and anisotropic nature of bone tissue. The aim of the present study was to investigate the influence of the anisotropic properties of peri-implant trabecular bone tissue on the biomechanical behavior of the AC implant at the macroscopic scale. Thirteen bovine trabecular bone samples were imaged using micro-computed tomography (µCT) with a resolution of 18 µm. The anisotropic biomechanical properties of each sample were determined at the scale of the centimeter based on a dedicated method using asymptotic homogenization. The material properties obtained with this multiscale approach were used as input data in a 3D finite element model to simulate the macroscopic mechanical behavior of the AC implant under different loading conditions. The largest stress and strain magnitudes were found around the equatorial rim and in the polar area of the AC implant. All macroscopic stiffness quantities were significantly correlated (R2 > 0.85, p < 6.5 e-6) with BV/TV (bone volume/total volume). Moreover, the maximum value of the von Mises stress field was significantly correlated with BV/TV (R2 > 0.61, p < 1.6 e-3) and was always found at the bone-implant interface. However, the mean value of the microscopic stress (at the scale of the trabeculae) decrease as a function of BV/TV for vertical and torsional loading and do not depend on BV/TV for horizontal loading. These results highlight the importance of the anisotropic properties of bone tissue.

Computing dispersion curves of elastic/viscoelastic transversely-isotropic bone plates coupled with soft tissue and marrow using semi-analytical finite element (SAFE) method.

We present a semi-analytical finite element (SAFE) scheme for accurately computing the velocity dispersion and attenuation in a trilayered system consisting of a transversely-isotropic (TI) cortical bone plate sandwiched between the soft tissue and marrow layers. The soft tissue and marrow are mimicked by two fluid layers of finite thickness. A Kelvin-Voigt model accounts for the absorption of all three biological domains. The simulated dispersion curves are validated by the results from the commercial software DISPERSE and published literature. Finally, the algorithm is applied to a viscoelastic trilayered TI bone model to interpret the guided modes of an ex-vivo experimental data set from a bone phantom.

Tissue mineral density measured at the sub-millimetre scale can provide reliable statistics of elastic properties of bone matrix.

Reliability of multiscale models of bone is related to the accuracy of the experimental information available on bone microstructure. X-ray-based imaging techniques allow to inspect bone structure and mineralization in vitro at the micrometre scale. However, spatial resolution achievable in vivo is much coarser and can produce blurry, uncertain information on bone microstructure. Working with uncertain data calls for new modelling paradigms able to propagate uncertainty through the scales. In this paper we investigate the effects of uncertain bone mineralization on the elastic coefficients of the bone matrix. To this aim, some stochastic concepts were developed and compared with one another in order to identify the best way to account for uncertain input data. These concepts step from a deterministic micromechanical model of bone matrix which was extended in order to account for uncertain bone composition. Uncertainty was introduced by assuming to know only mean value and dispersion of the parameters describing bone composition. Thus, these parameters were modelled as random variables and their distribution functions were obtained using the maximum entropy principle. Either the tissue mineral density (TMD) or the ensuing volume fractions of collagen and mineral were used to describe uncertain bone composition. Moreover, mean value and dispersion were estimated at the scales of either 10 or a few 100 [Formula: see text]m, representative of standard in vitro and in vivo spatial resolutions, respectively. Analysis of these modelling concepts suggests that TMD measured at the sub-millimetre scale can be used to obtain reliable statistical information about the elastic coefficients of bone matrix.

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

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

Finite element model of the impaction of a press-fitted acetabular cup.

Press-fit surgical procedures aim at providing primary stability to acetabular cup (AC) implants. Impact analysis constitutes a powerful approach to retrieve the AC implant insertion properties. The aim of this numerical study was to investigate the dynamic interaction occurring between the hammer, the ancillary and bone tissue during the impact and to assess the potential of impact analysis to retrieve AC implant insertion conditions. A dynamic two-dimensional axisymmetric model was developed to simulate the impaction of the AC implant into bone tissue assuming friction at the bone-implant interface and large deformations. Different values of interference fit (from 0.5 to 2 mm) and impact velocities (from 1 to 2 m.s-1) were considered. For each configuration, the variation of the force applied between the hammer and the ancillary was analyzed and an indicator I was determined based on the impact momentum of the signal. The simulated results are compared to the experiments. The value of the polar gap decreases with the impact velocity and increases with the interference fit. The bone-implant contact area was significantly correlated with the resonance frequency (R 2 = 0.94) and the indicator (R 2 = 0.95). The results show the potential of impact analyses to retrieve the bone-implant contact properties.

Assessment of the biomechanical stability of a dental implant with quantitative ultrasound: A three-dimensional finite element study.

Dental implant stability is an important determinant of the surgical success. Quantitative ultrasound (QUS) techniques can be used to assess such properties using the implant acting as a waveguide. However, the interaction between an ultrasonic wave and the implant remains poorly understood. The aim of this study is to investigate the sensitivity of the ultrasonic response to the quality and quantity of bone tissue in contact with the implant surface. The 10 MHz ultrasonic response of an implant used in clinical practice was simulated using an axisymmetric three-dimensional finite element model, which was validated experimentally. The amplitude of the echographic response of the implant increases when the depth of a liquid layer located at the implant interface increases. The results show the sensitivity of the QUS technique to the amount of bone in contact with the implant. The quality of bone tissue around the implant is varied by modifying the bone biomechanical properties by 20%. The amplitude of the implant echographic response decreases when bone quality increases, which corresponds to bone healing. In all cases, the amplitude of the implant response decreased when the dental implant stability increased, which is consistent with the experimental results.

Stochastic multiscale modelling of cortical bone elasticity based on high-resolution imaging.

Accurate and reliable assessment of bone quality requires predictive methods which could probe bone microstructure and provide information on bone mechanical properties. Multiscale modelling and simulation represent a fast and powerful way to predict bone mechanical properties based on experimental information on bone microstructure as obtained through X-ray-based methods. However, technical limitations of experimental devices used to inspect bone microstructure may produce blurry data, especially in in vivo conditions. Uncertainties affecting the experimental data (input) may question the reliability of the results predicted by the model (output). Since input data are uncertain, deterministic approaches are limited and new modelling paradigms are required. In this paper, a novel stochastic multiscale model is developed to estimate the elastic properties of bone while taking into account uncertainties on bone composition. Effective elastic properties of cortical bone tissue were computed using a multiscale model based on continuum micromechanics. Volume fractions of bone components (collagen, mineral, and water) were considered as random variables whose probabilistic description was built using the maximum entropy principle. The relevance of this approach was proved by analysing a human bone sample taken from the inferior femoral neck. The sample was imaged using synchrotron radiation micro-computed tomography. 3-D distributions of Haversian porosity and tissue mineral density extracted from these images supplied the experimental information needed to build the stochastic models of the volume fractions. Thus, the stochastic multiscale model provided reliable statistical information (such as mean values and confidence intervals) on bone elastic properties at the tissue scale. Moreover, the existence of a simpler "nominal model", accounting for the main features of the stochastic model, was investigated. It was shown that such a model does exist, and its relevance was discussed.

Modeling of transient wave propagation in a heterogeneous solid layer coupled with fluid: application to long bones.

The aim of this work is to evaluate the effects of the heterogeneity and anisotropy of material properties of cortical bone on its ultrasonic response obtained by using axial transmission method. The heterogeneity and anisotropy of material properties are introduced by using a parametric probabilistic model. The geometrical configuration of the tested sample is described by a tri-layer medium composed of a heterogeneous and anisotropic solid layer sandwiched between two acoustic fluid layers of which one of these layers is excited by an acoustic linear source. The numerical results focus on studying of an interest quantity, called velocity of the first arriving signal, showing that it strongly depends on the dispersion induced by statistical fluctuations of stochastic elasticity field.

Finite element simulation of ultrasonic wave propagation in a dental implant for biomechanical stability assessment.

Dental implant stability, which is an important parameter for the surgical outcome, can now be assessed using quantitative ultrasound. However, the acoustical propagation in dental implants remains poorly understood. The objective of this numerical study was to understand the propagation phenomena of ultrasonic waves in cylindrically shaped prototype dental implants and to investigate the sensitivity of the ultrasonic response to the surrounding bone quantity and quality. The 10-MHz ultrasonic response of the implant was calculated using an axisymetric 3D finite element model, which was validated by comparison with results obtained experimentally and using a 2D finite difference numerical model. The results show that the implant ultrasonic response changes significantly when a liquid layer is located at the implant interface compared to the case of an interface fully bounded with bone tissue. A dedicated model based on experimental measurements was developed in order to account for the evolution of the bone biomechanical properties at the implant interface. The effect of a gradient of material properties on the implant ultrasonic response is determined. Based on the reproducibility of the measurement, the results indicate that the device should be sensitive to the effects of a healing duration of less than one week. In all cases, the amplitude of the implant response is shown to decrease when the dental implant primary and secondary stability increase, which is consistent with the experimental results. This study paves the way for the development of a quantitative ultrasound method to evaluate dental implant stability.

Biomechanical determinants of the stability of dental implants: influence of the bone-implant interface properties.

Dental implants are now widely used for the replacement of missing teeth in fully or partially edentulous patients and for cranial reconstructions. However, risks of failure, which may have dramatic consequences, are still experienced and remain difficult to anticipate. The stability of biomaterials inserted in bone tissue depends on multiscale phenomena of biomechanical (bone-implant interlocking) and of biological (mechanotransduction) natures. The objective of this review is to provide an overview of the biomechanical behavior of the bone-dental implant interface as a function of its environment by considering in silico, ex vivo and in vivo studies including animal models as well as clinical studies. The biomechanical determinants of osseointegration phenomena are related to bone remodeling in the vicinity of the implants (adaptation of the bone structure to accommodate the presence of a biomaterial). Aspects related to the description of the interface and to its space-time multiscale nature will first be reviewed. Then, the various approaches used in the literature to measure implant stability and the bone-implant interface properties in vitro and in vivo will be described. Quantitative ultrasound methods are promising because they are cheap, non invasive and because of their lower spatial resolution around the implant compared to other biomechanical approaches.

Ultrasonic wave propagation in viscoelastic cortical bone plate coupled with fluids: a spectral finite element study.

This work deals with the ultrasonic wave propagation in the cortical layer of long bones which is known as being a functionally graded anisotropic material coupled with fluids. The viscous effects are taken into account. The geometrical configuration mimics the one of axial transmission technique used for evaluating the bone quality. We present a numerical procedure adapted for this purpose which is based on the spectral finite element method (FEM). By using a combined Laplace-Fourier transform, the vibroacoustic problem may be transformed into the frequency-wavenumber domain in which, as radiation conditions may be exactly introduced in the infinite fluid halfspaces, only the heterogeneous solid layer needs to be analysed using FEM. Several numerical tests are presented showing very good performance of the proposed approach. We present some results to study the influence of the frequency on the first arriving signal velocity in (visco)elastic bone plate.

Interstitial fluid flow within bone canaliculi and electro-chemo-mechanical features of the canalicular milieu: a multi-parametric sensitivity analysis.

Canalicular fluid flow is acknowledged to play a major role in bone functioning, allowing bone cells' metabolism and activity and providing an efficient way for cell-to-cell communication. Bone canaliculi are small canals running through the bone solid matrix, hosting osteocyte's dendrites, and saturated by an interstitial fluid rich in ions. Because of the small size of these canals (few hundred nanometers in diameter), fluid flow is coupled with electrochemical phenomena. In our previous works, we developed a multi-scale model accounting for coupled hydraulic and chemical transport in the canalicular network. Unfortunately, most of the physical and geometrical information required by the model is hardly accessible by nowadays experimental techniques. The goal of this study was to numerically assess the influence of the physical and material parameters involved in the canalicular fluid flow. The focus was set on the electro-chemo-mechanical features of the canalicular milieu, hopefully covering any in vivo scenario. Two main results were obtained. First, the most relevant parameters affecting the canalicular fluid flow were identified and their effects quantified. Second, these findings were given a larger scope to cover also scenarios not considered in this study. Therefore, this study gives insight into the potential interactions between electrochemistry and mechanics in bone and provides the rational for further theoretical and experimental investigations.

Possible role of calcium permselectivity in bone adaptation.

According to the core activity of calcium in the bone cellular expression, a new hypothesis linking calcium transport with the mechanical loading is proposed to explain the mechano-adaptation of bone tissue. Due to the piezoelectric coupling, the tensile and compressive areas of bone produce different electrical environments for the osteocytic cells that are embedded in the lacuno-canalicular porosity. This electrical asymmetry engenders a calcium enrichment-exclusion effect that strongly changes the calcium concentration in the lacuno-canalicular fluid and thus modifies the remodelling process. A bibliographic body of evidence supporting this idea is given and its experimental validation is suggested.

Simulation of ultrasonic wave propagation in anisotropic poroelastic bone plate using hybrid spectral/finite element method.

This paper deals with the modeling of guided waves propagation in in vivo cortical long bone, which is known to be anisotropic medium with functionally graded porosity. The bone is modeled as an anisotropic poroelastic material by using Biot's theory formulated in high frequency domain. A hybrid spectral/finite element formulation has been developed to find the time-domain solution of ultrasonic waves propagating in a poroelastic plate immersed in two fluid halfspaces. The numerical technique is based on a combined Laplace-Fourier transform, which allows to obtain a reduced dimension problem in the frequency-wavenumber domain. In the spectral domain, as radiation conditions representing infinite fluid halfspaces may be exactly introduced, only the heterogeneous solid layer needs to be analyzed by using finite element method. Several numerical tests are presented showing very good performance of the proposed procedure. A preliminary study on the first arrived signal velocities computed by using equivalent elastic and poroelastic models will be presented.

Equivalent contributing depth investigated by a lateral wave with axial transmission in viscoelastic cortical bone.

Cortical bone is a viscoelastic heterogeneous medium which may be assessed with axial transmission. This work aims at evaluating the average depth investigated by the lateral wave for radial variations of material properties in relatively thick cortical bone. The equivalent contributing depth (ECD) is derived from the finite element simulation results for spatial variations of a viscoelastic coefficient (η(11)) and of porosity. A value of ECD equal to around 1.6 mm is obtained for a spatial variation of η(11). The method fails to predict accurate values of the ECD for a spatial variation of porosity, because all parameters vary simultaneously.