Strain rate dependent poroelastic behavior of bovine vertebral trabecular bone

It is widely accepted that the pressure variation of interstitial fluid is one of the most important factors in bone physiology. In order to understand the role of interstitial fluid on porous bony structure, a consideration for the biomechanical interactions between fluid and solid constituents within bone is required. In this study, a poroelastic theory was applied to investigate the elastic behavior of calf vertebral trabecular bone composed of the porous solid trabeculae and the viscous bone marrow. The poroelastic behavior of trabecular bone in a uniaxial stress condition was simulated using a commercial finite difference analysis software (FLAC, Itasca Consulting Group, USA), and tested for 5 different strain rates, i. e., 0.001, 0.01, 0.1, and 10 per second. The material properties of the calf vertebral trabecular bone were utilized from the previous experimental study. Two asymptotic poroelastic responses, the drained and undrained deformations, were predicted. From the predicted results for the simulated five strain rates, it was found that the pore pressure generation has a linearly increasing behavior when the strain rate is the highest at 10 per second, otherwise it showed a nonlinear behavior. The pore pressure generation with respect to the strain was found to be increased as the strain rate increased. The elastic moduli predicted at each strain were 208.3, 212.2, 337.6, 593.1, and 602.2 MPa, respectively. Based on the results of the present study, it was suggested that the calf vertebral trabecular bone could be modeled as a poroelastic material and its strain rate dependent material behavior could be predicted.     

Recovery of airflow resistivity of poroelastic beams submitted to transient mechanical stress

The airflow resistivities of air-saturated poroelastic slender beams submitted to transient mechanical stress are recovered using fluid and solid borne compressional mode phase velocity expressions drawn from a modified Biot theory. A point where the two dilatational modes intersect and their phase velocities equal is first sought. This point also corresponds to the Biot transitional frequency indicating the frequency at which the solid and the pore fluid start disassociating due to the weakening of the viscous forces by the thinning of the viscous boundary layer in the pores. A bilinear time–frequency (TF) distribution is used to represent on the time–frequency plane, the captured transient mechanical stress waves from which the point of intersection/separation of the two modes is located. The projection of the Eigenfrequencies obtained from a simple 3D finite element modeling of the thin poroelastic beam, on a (TF) diagram, facilitates the identification of the modes. The transition frequencies for the poroelastic beams thus retrieved are verified through the use of variable frequency, single cycle sine wave bursts. The anisotropy of the foams are also revealed by analyzing the transient responses of the poroelastic beam specimens cut from the same panel but in two perpendicular directions in orientation to each other.     

Analysis of the impact responses in a degenerated spinal motion segment FE model

A three-dimensional non-linear poroelastic finite element model of an L3/L4 motion segment was used to analyze the biomechanical effects of degeneration under impact loading on the spinal segment. A previously developed degeneration algorithm was applied to generate a degenerated disc model. Regional variation in intact vertebral body bone morphology was simulated by assigning different void ratios of 4.0–5.02, which were assessed for 27 regions of vertebral cancellous bone. For the osteoporotic structure of the vertebral body, the body was divided into 5 regions with 10–24 void ratios. Different material properties were assigned to the annulus fibers; hereupon our annulus model reflected variation in tensile behavior of multiple layer annulus samples. The impact load applied to the top of the L3 vertebral body was assumed to be a triangular impulsive force with a maximum compressive impact load of 3 kN and 20ms impact duration time. Calculated results indicated that the effect of the degeneration was predominant at the center of the vertebral body. The maximum von Mises stress was found at the region of near the endplate. The degeneration increased the averaged stress at the center of the vertebral body of L3 from 1.54 MPa to 1.69 MPa, the stress remaining relatively small at L4. Decreased fluid volume ratio of the degenerated nucleus tended to increase pressure slightly at the nucleus, and the averaged stress at the nucleus was almost doubled compared to the intact case. The innermost layers of the anterior annulus showed the highest stress concentration, followed by outermost anterior and posterior regions, for both the degenerated and the intact models. Despite an irregular stress distribution in the degenerated model, pore pressure showed relatively uniform distribution. This paper was recommended for publication in revised form by Associate Editor Young Eun Kim YoungEun Kim received a B.S. degree in Mechanics and Design from Seoul National University in 1978. He then went on to receive his M.S. from KAIST in 1986 and Ph.D. degrees from U. of Iowa 1988. Dr. Kim is currently a Professor at the Dept. of Mechanical Engineering at Dankook University in Yongin, Korea. He is currently serving as an Editor of the Open Orthopedic Research Journal. He was also served as a division chair of KSPE. Dr. Kim’s research interests are in the area of biomechanics, and occupant dynamics.     

Simulation of the disc degeneration with a poroelastic finite element model

To predict the degeneration process in the intervertebral disc, a finite element model of the spinal motion segment model was developed. The relationship between the biomechanical characteristics of fluid and solid matrix of the disc and cancellous core of the vertebral body, modeled as 20 node poroelastic elements, during the degeneration process was investigated. Excess von Mises stress in the disc element was assumed to be a possible source of degeneration under compressive loading condition. Recursive calculation was continued until the desired convergence was attained by changing the permeability and void ratio of those elements. The degenerated disc model showed that relatively small compressive stresses were generated in the nucleus elements compared to normal disc. Its distribution along the sagittal plane was consistent with a previously reported experimental result. Contrasts to this result, pore pressures in the nucleus were higher than those in the normal disc. Total stress, sum of compressive stress and pore pressure, indicated similar values for two different models. This study presented a new approach to study the likely mechanism responsible for the initiation and progression of the degenerative process within the intervertebral disc.     

Micromechanics-based evaluation of the poroelastic effect and stress concentration in thermochemically-decomposed composites

The poroelastic effect and stress concentration of thermochemically decomposed composites are evaluated based on micromechanics. Considering the pore shapes and array patterns, representative volume elements (RVEs) of homogenized composites are modeled and analyzed using a finite element method. The effects of porosity and material anisotropy are carefully investigated. The poroelastic parameters are calculated based on the pore-pressure-induced strain and effective elastic moduli as well as on the differences between the elastic moduli of solid-skeleton composites and porous composites. The strain energy density is measured to evaluate the microstress concentration caused by pore pressure. Moreover, the effects of constituent phases on the poroelastic parameters and strain energy density are examined by improving the RVE models for heterogeneous composites. The usefulness of the calculation method for poroelastic parameters is investigated through numerical experiments.     

Investigation of couple stress effects on poroelastic squeeze film of parallel plates

The couple stress effects on hydrodynamic performances of poroelastic squeeze film in the case of infinitely long parallel plates are examined in this paper. The lower plate is a poroelastic matrix saturated by a Newtonian fluid. The poroelasticity is taken into account by the means of homogenisation method. The rheological behaviour of the lubricant is described by the Stokes couple stress fluid theory. The modified Reynolds equation accounting for the couple stress, the elasticity of the poroelastic plate and the slip velocity condition at the film–poroelastic plate interface is derived. The governing equations in the fluid film and poroelastic plate are discretised by finite difference method and solved iteratively by using Gauss–Seidel method. The fluid film and poroelastic plate coupling is managed by the iterative fixed point technique. A computer program is developed in this study. The result analysis shows that couple stress effects on poroelastic squeeze film performances are significant. Copyright © 2016 John Wiley & Sons, Ltd.     

Osteocyte pericellular and perilacunar matrices as markers of bone–implant mechanical integrity

To develop durable bone healing strategies through improved control of bone repair, it is of critical importance to understand the mechanisms of bone mechanical integrity when in contact with biomaterials and implants. Bone mechanical integrity is defined here as the adaptation of structural properties of remodeled bone in regard to an applied mechanical loading. Accordingly, the authors present why future investigations in bone repair and regeneration should emphasize on the matrix surrounding the osteocytes. Osteocytes are mechanosensitive cells considered as the orchestrators of bone remodeling, which is the biological process involved in bone homeostasis. These bone cells are trapped in an interconnected porous network, the lacunocanalicular network, which is embedded in a bone mineralized extracellular matrix. As a consequence of an applied mechanical loading, the bone deformation results in the deformation of this lacunocanalicular network inducing a shift in interstitial fluid pressure and velocity, thus resulting in osteocyte stimulation. The material environment surrounding each osteocyte, the so called perilacunar and pericellular matrices properties, define its mechanosensitivity. While this mechanical stimulation pathway is well known, the laws used to predict bone remodeling are based on strains developing at a tissue scale, suggesting that these strains are related to the shift in fluid pressure and velocity at the lacunocanalicular scale. While this relationship has been validated through observation in healthy bone, the fluid behavior at the bone-implant interface is more complex. The presence of the implant modifies fluid behavior, so that for the same strain at a tissue scale, the shift in fluid pressure and velocity will be different than in a healthy bone tissue. In that context, new markers for bone mechanical integrity, considering fluid behavior, have to be defined. The viewpoint exposed by the authors indicates that the properties of the pericellular and the perilacunar matrices have to be systematically investigated and used as structural markers of fluid behavior in the course of bone biomaterial development.     

Pore-scale analysis of Newtonian flow in the explicit geometry of vertebral trabecular bones using lattice Boltzmann simulation

The geometric and transport properties of trabecular bone are of particular interest for medical engineers active in orthopaedic applications and more specifically in hard tissue implantations. This article resorts to computational methods to provide some understanding of the geometric and transport properties of vertebral trabecular bone. A fuzzy distance transform algorithm was used for geometric analysis on the pore scale, and a lattice Boltzmann method (LBM) for the simulation of flow on the same scale. The transport properties of bone including the pressure drop, elongation, and shear component of dissipated energy, and the tortuosity of the bone geometry were extracted from the results of the LBM flow simulations. Whenever suitable, dimensionless numbers were used for the analysis of the data. The average pore size and distribution of the bone were found to be 746 microm and between 75 and 2940 microm, respectively. The permeability of the flow in the cavities of the specific bone sample was found to be 5.05 x 10(-8) m2 for the superior-inferior direction which was by a factor of 1.5-1.7 higher than the permeability in the other two anatomical directions (anterior-posterior). These findings are consistent with experimental results found 3 years prior independently. Tortuosity values approached 1.05 for the superior-inferior direction, and 1.13 and 1.11 for the other two perpendicular directions. The low tortuosities result mainly from the large bone porosity of 0.92. The flow on the pore scale seems to be shear dominated but 30 per cent of the energy dissipation was because of elongational effects. The converging and diverging geometry of the bone explains the significant elongation and deformation of the fluid elements. The transition from creeping flow (the Darcy regime), which is of interest to vertebral augmentation and this study, to the laminar region with significant inertia effects took place at a Reynolds number of about 1-10, as usual for porous media. Finally, the authors wish to advise the readers on the significant computational requirements to be allocated to such a virtual test bench.     

激光加工多孔端面机械密封的参数研究

建立了激光加工多孔端面机械密封的流体动力学分析模型。根据基本假设,一个孔栏上的液膜压力分布可表征整个密封面上的液膜压力。将参数进行无量纲化,采用有限差分法对激光加工多孔端面机械密封进行了参数研究,并利用MATLAB计算机软件得到了无量纲液膜压力的三雏分布规律。由计算分析可知,液膜平均压力随着液体粘度和转速的增加、液膜厚度的减小而增大;随着流体压力的增大,微孔产生的动压效应减弱。另外,微孔密度和微孔深径比的对液膜平均压力有很大影响,对其进行优化,可使平均液膜压力达到最大。     

Stress relaxation modelling of polymethylmethacrylate bone cement

This paper describes tests that were carried out to model the stress relaxation behaviour of polymethylmethacrylate (PMMA) bone cement. Stress relaxation of bone cement is believed to be a significant factor in the mechanism of load transfer in the femoral stem of a polished, collarless taper-fit replacement hip joints. It is therefore important that this condition and its implications are understood. Stress relaxation was carried out on PMMA samples of varying age in four-point bending configuration. It was shown that the samples stiffened with age and that the amount of stress relaxation reduced as the samples aged. The experimental results of the stress relaxation were accurately modelled on the double exponential of the Maxwell model so that long-term predictions of the stress condition could be made from short-term mechanical tests.     

基于流-固耦合模型的人工骨力学数值仿真

根据力学平衡条件推出应力场方程,并建立孔隙率和渗透率的动态模型;依据流体力学连续性方程,考虑流-固耦合情形下多孔介质骨架变形特性和流体的可压缩性,得到了孔隙流体的连续性方程,即渗流场方程。在此基础上辅以定解条件,建立了人工骨完备的饱和多孔介质流-固全耦合渗流的数学模型,进而分析人工骨在承受各种载荷时,其骨质应力场、变形场以及孔间骨液压力场的分布规律。     

A biomechanical study of osteoporotic vertebral trabecular bone: The use of micro-CT and high-resolution finite element analysis

Osteoporosis is one of the most dangerous skeletal diseases in relation to the highest fracture risk in vertebral bones. A considerable amount of work has been done to investigate the biomechanical characteristics of osteoporotic vertebral trabecular bone. Previous researchers studied the elastic characteristics using a micro-finite element (micro-FE) model, used to analyze realistic trabecular architectures in full detail, based on micro-computed tomography (μCT). Since osteoporotic compression fracture is closely associated with the mechanical characteristics of the vertebral trabecular bone and there were few micro-FE models to account for all of the elastic and plastic characteristics in vertebral trabecular bone, this study analyzed the effect of voxel resolution on the plastic characteristics as well as the elastic characteristics of three-dimensional (3D) osteoporotic lumbar trabecular bone models. Also, we evaluated the effect of specimen geometry on this problem. It has been reported that a cubic specimen with side length 6.5mm was suggested as standard specimens for the experimental test of trabecular bone. Current study examined whether or not the effect of the specimen geometry on the experimental test may be also applied to the simulated compression test of trabecular bone specimens. The experimental test employing the rapid prototyping (RP) technique and INSTRON test machine is performed to indirectly validate the results of the simulated compression test by micro-FE analysis. The review finished with the verification about the effects of the simulated compression test.     

Experimental and numerical study of membrane properties and pore pressure transmission of Ghom shale

Serious wellbore instability frequently occurs during drilling operations in shale formations. Selection of safe mud parameters to alleviate shale instability problems during drilling operations can benefit from predictive models that consider fully coupled chemo-mechanical phenomena involved in shale-drilling fluid interactions. Although different chemo-poroelastic analyses on these interactions are presented in the literature, only a few experimental measurements and analysis of model predictions are available. In this paper, pore pressure transmission test on Ghom shale is conducted and pore pressure changes in the shale sample under hydraulic and chemical loading is measured. The main outcome of this experiment is the reflection coefficient which is usually used to quantify the osmotic characteristics of the chemically active shale in contact with a water-based fluid. The measured parameter together with other physico-chemical properties of Ghom shale are used to simulate time evolution of pore pressure and solute mass fraction distributions in the sample based on the chemo-poroelastic model of the test and the finite element solution in MATLAB. Comparison with experimental data shows that the simulation results are in good agreement with the actual pressure measurements in the test. This result provides further validation for the theoretical model.     

Mechanical behavior and sealing performance of metal sealing system in roller cone bits

Metal sealing system is used frequently in the dynamic rotary seal of downhole tools of petroleum, natural gas and mining. Mechanical behavior and sealing performance of the metal sealing system in roller cone bit were analyzed in this paper. Influences of pressure difference, compression ratio, fluid pressure, angle and thermal load on the metal sealing system’s mechanical behavior and seal performance were studied. The results show that the effect of pressure difference should be considered under fluid pressure. The von Mises stress concentrates on the inside of O-rings under the influence of compression ratio. The low-stress area appears on the inside of O-rings under the effect of fluid pressure. The high-stress concentration area of metal sealing surface appears on the surface of metal rings under different angles. Sealing performance, compression ratio, fluid pressure and angle have the same change trend. Thermal load is not a single impact on the stress distribution and deformation, but together with fluid pressure affects the sealing performance. The dynamic O-ring more easily fails than the static O-ring. Those results can provide a new direction for the structural optimization of metal sealing system in roller cone bits.

     

MicroCT examination of human bone specimens: effects of polymethylmethacrylate embedding on structural parameters

X‐ray microtomography permits the nondestructive investigation of trabecular and cortical bone specimens without special preparation of the sample. To do a quantitative characterization, the cross‐section images have to be binarized, separating bone from nonbone. For this purpose, a widely used method is uniform thresholding. However, for commonly available microtomography scanners which use a polychromatic X‐ray source, it is unclear what effect the surrounding medium (e.g. air, saline solution, polymethylmethacrylate) has on the threshold value used for the binarization. In the literature an easy procedure to find the optimal uniform threshold value for a given acquisition condition is reported. By applying this procedure, the present work investigated whether a microtomography scan of trabecular bone samples in air or embedded in polymethylmethacrylate gave the same results in terms of structural parameters. The gold standard, that is, histological sections, was used as a reference. Two fixed threshold values were found, one for the microtomography scans performed in air and one for the scans with the same samples embedded in polymethylmethacrylate. These were applied on the correspondent microtomography images for the estimation of structural parameters, such as bone volume fraction, direct trabecular thickness, direct trabecular separation and structure model index. Paired comparisons were made in bone volume fraction between histological sections and microtomography cross‐sections for the same bone samples scanned first in air and then embedded in polymethylmethacrylate, by which no significant differences were found. Paired comparisons were also made in bone volume fraction, direct trabecular thickness, direct trabecular separation and structure model index for the same samples over volumes of interest of 4 × 4 × 4 mm³ between microtomography scans in air and scans with the samples embedded in polymethylmethacrylate. Neither these comparisons showed significant differences. This leads to the conclusion that structural parameters estimated by microtomography for human trabecular bone samples scanned either in air or embedded in polymethylmethacrylate are not affected by the surrounding medium (i.e. presence or absence of polymethylmethacrylate), provided that the corresponding optimal threshold value is applied for each acquisition condition.     

Squeeze fluid film of spherical hydrophobic surfaces with wall slip

Isothermal squeeze film flow of Newtonian fluid between spherical hydrophobic surfaces with wall slip is investigated using a limiting shear stress model and complementary algorithm. Wall slip velocity is controlled by the liquid–solid interface limiting shear stress. It is found that the wall slip dramatically decreases the hydrodynamic support force of the squeeze fluid film. In the case of large wall slip the hydrodynamic support force increases only slightly with the decrease in the film thickness. We find that wall slip decreases with increasing film thickness and limiting shear stress, but increases with increasing fluid viscosity and approaching velocity. An empirical equation is given for prediction of the fluid load support capacity. The possible effect of pressure on wall slip is also discussed. It is found that fluid pressure suppresses wall slip after the proportionality coefficient of limiting shear stress reaches a critical threshold. However, almost no effect is found when it is below this critical threshold. Good agreements exist between the present theoretical predictions and some existing experimental observations.     

Finite element prediction of endosteal and periosteal bone remodelling in the turkey ulna: effect of remodelling signal and dead-zone definition

Bone remodelling is the adaptation of bone mass in response to localized changes in loading conditions. The nature of the mechanical signal governing remodelling, however, remains the subject of continued investigation. The aims of this study were to use an iterative finite element (FE) bone remodelling technique to explore the effect of different remodelling signals in the prediction of bone remodelling behaviour. A finite element model of the turkey ulna, following that of Brown et al., was analysed using the ABAQUS package. The model was validated against the static predictions of the Brown et al. study. A bone remodelling technique, based on swelling algorithms given by Taylor and Clift, was then applied to predict the dramatic change in loading conditions imposed. The resulting changes in FE mid-shaft bone geometry were compared with the remodelling observed experimentally and showed good agreement. The tensile principal stress was found to be the best remodelling signal under the imposed conditions. Localized sensitivities in the remodelling patterns were found, however, and the definition of the dead zone was modified as a result. Remodelling with the new dead-zone definition showed that both the tensile principal stress and the tensile principal strain produced the remodelling patterns that agreed most closely with experiment.     

松质骨流-固-热多场耦合微流速渗流实验研究及数值分析

在达西定律基础上自主研制了松质骨流固热多场耦合微流速渗透率测量装置,利用该装置对猪股骨结节新鲜松质骨进行了渗透试验,得到了该材料在不同的压力和温度下的渗透率,并且和理论数据进行了对比.建立了松质骨在流-固-热多场耦合下孔隙度和渗透率随温度和压力变化的动态数学模型.分析了实验过程中温度和流体压力等因素对实验结果的影响,讨论了该试验装置的相关应用范围和发展前景.     

Investigating the effect of remodelling signal type on the finite element based predictions of bone remodelling around the thrust plate prosthesis: a patient-specific comparison

The resorption of bone in the human femur following total hip arthroplasty is recognized to be related to the loading in the bone surrounding the prosthesis. However, the precise nature of the mechanical signal that influences the biological remodelling activity of the bone is not completely understood. In this study, a validated finite element modelling methodology was combined with a numerical algorithm to simulate the biological changes over time. This was used to produce bone remodelling predictions for an implanted thrust plate prosthesis (Centerpulse Orthopedics Limited) in a patient specific bone model. The analysis was then repeated using different mechanical signals to drive the remodelling algorithm. The results of these simulations were then compared to the patient-specific clinical data, to distinguish which of the candidate signals produced predictions consistent with the clinical evidence. Good agreement was found for a range of strain energy based signals and also deviatoric remodelling signals. The results, however, did not support the use of compressive dilatational strain as a candidate remodelling signal.