Vu-Hieu Nguyen

Poroelastic behaviour of cortical bone under harmonic axial loading: A finite element study at the osteonal scale

Bone fluid flow and its induced effects on the bone cells are important players in triggering and signalling bone formation and bone remodelling. This study aims to numerically investigate the behaviour of interstitial fluid flows in cortical bone under axial cyclic harmonic loads that mimics in vivo bone behaviour during daily activities like walking. Here, bone tissue is modelled as a fluid-saturated anisotropic poroelastic medium which consists of a periodic group of osteons. By using a frequency-domain finite element analysis, the fluid velocity field is quantified for various loading conditions and bone matrix parameters.

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.

Influence of interstitial bone microcracks on strain-induced fluid flow.

It is well known that microcracks act as a stimulus for bone remodelling, initiating resorption by osteoclasts and new bone formation by osteoblasts. Moreover, microcracks are likely to alter the fluid flow and convective transport through the bone tissue. This paper proposes a quantitative evaluation of the strain-induced interstitial fluid velocities developing in osteons in presence of a microcrack in the interstitial bone tissue. Based on Biot theory in the low-frequency range, a poroelastic model is carried out to study the hydro-mechanical behaviour of cracked osteonal tissue. The finite element results show that the presence of a microcrack in the interstitial osteonal tissue may drastically reduce the fluid velocity inside the neighbouring osteons. This fluid inactive zone inside osteons can cover up to 10% of their surface. Consequently, the fluid environment of bone mechano-sensitive cells is locally modified.

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.

Multichannel filtering and reconstruction of ultrasonic guided wave fields using time intercept-slowness transform.

Multichannel ultrasonic axial-transmission data are multimodal by nature. As guided waves are commonly used in nondestructive material testing, wave field filtering becomes important because the analysis is usually limited to a few lower-order modes and requires their extraction. An application of the Radon transform to enhance signal-to-noise ratio and separate wave fields in ultrasonic records is presented. The method considers guided wave fields as superpositions of plane waves defined by ray parameters (p) and time intercepts (τ) and stacks the amplitudes along linear trajectories, mapping time-offset (t - x) data to a τ - p or Radon panel. The transform is implemented using a least-squares strategy with Cauchy-norm regularization that serves to enhance the focusing power. The method was verified using simulated data and applied to an uneven spatially sampled bovine-bone-plate data set. The results demonstrate the Radon panels show isolated amplitude clusters and the Cauchy-norm constraint provides a more focused Radon image than the damped least-squares regularization. Wave field separation can be achieved by selectively windowing the τ - p signals and inverse transformation, which is illustrated by the successful extraction of the A0 mode in bone plate. In addition, the method effectively attenuates noise, enhances the coherency of the guided wave modes, and reconstructs the missing records. The proposed transform presents a powerful signal-enhancement tool to process guided waves for further analysis and inversion.

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 Biots 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.

Anisotropic Poroelastic Hollow Cylinders with Damaged Periphery under Harmonic Axial Loading: Relevance to Bone Remodelling

An anisotropic modelling of hollow porous cylinders under harmonic axial loading is proposed to simulate the in vivo behavior of structural elements of cortical bone called osteons. The peripheral surface of the medium is supposed to be impermeable, except on possible existing cracks. Numerical tests are performed by analytical and finite element methods based on the Biot poroelastic theory. The influence of microcracks on the fluid flow is numerically investigated. The findings show that the existence of peripheral cracks directly modifies the stimulation of the mechano‐sensitive network of the bone. Thus, this study attempts to propose a likely mechanism by which bone can sense changes of the surrounding mechanical environment.

Photo-induced SI-ATRP for the synthesis of photoclickable intercalated clay nanofillers

In situ photoinduced SI-ATRP is reported as a novel and efficient route for preparing intercalated nano-clay fillers bearing clickable functions. Poly(propargyl methacrylate) chains are grown inside the clay interlayer after silanisation and grafting of bromine ATRP initiator. The generic clickable character is demonstrated through grafting with azidomethyl benzene and mercaptosuccinic acid via photodriven 1,3-dipolar cycloaddition and thiol-yne click reactions, respectively.

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.

Numerical investigations of ultrasound wave propagating in long bones using a poroelastic model

Ultrasonic responses probed from an axial transmission test (ATT) may provide useful information about material and structural properties of cortical bone. For the mathematical modeling of ultrasonic wave propagation in long bones, most of studies assumed an (visco-)elastic behavior for cortical bone tissue by neglecting the interstitial pressure in the pores presented within this material. Here, a functionally graded anisotropic poroelastic model is proposed for describing the behavior of long bones in the ultrasonic frequency range. The simulation of time-domain wave propagation can efficiently be carried out by using a semi-analytical finite element method. The proposed model allows us investigate the influence of the presence of the pores, as well as their distribution in a bone layer on the speed of sound propagated in a cortical bone layer coupled with the marrow and the soft tissue. The effects of emitted signal’s frequency will also be examined.