Unconfined compression of white matter

The porous properties of brain tissue are important for understanding normal and abnormal cerebrospinal fluid flow in the brain. In this study, a poroviscoelastic model was fitted to the stress relaxation response of white matter in unconfined compression performed under a range of low strain rates. A set of experiments was also performed on the tissue samples using a no-slip boundary condition. Results from these experiments demonstrated that the rheological response of the white matter is primarily governed by the intrinsic viscoelastic properties of the solid phase. The permeability of white matter was found to be of the order of 10(-12) m4/Ns.     

Indentation of an osteochondral repair: sensitivity to experimental variables and boundary conditions

The sensitivity of the affects of indenter radius, defect depth, cartilage permeability and flow boundary conditions, on the indentation testing of a repairing osteochondral defect was investigated. Since the boundary condition on the flow across the cartilage repair-subchondral bone interface is not known, the effects of two different conditions were investigated: free-flow and no-flow. A poroelastic finite element model of an osteochondral defect at different stages of the repair process was developed using dimensions typical of the rabbit knee. Results showed when the radius of the indenter was much less than the thickness of the cartilage the sensitivity of the indentation displacement to flow boundary conditions decreased. Simulated indentation displacement was insensitive to bone regeneration up to 50% of the initial defect depth, which suggests that only the properties of the material in the upper-half of the defect are being evaluated. Small variations in permeability had little affect on the simulated indentation. In a fully repaired defect, the simulated indentation is independent of the boundary condition. However, while the defect is in the process of repair and the regenerated cartilage is deeper than the host, indentation is sensitive to the flow boundary condition. Based on these results, and feasible experimental conditions, we conclude that the boundary condition on the repair-subchondral bone interface must be known in all cases except when the defect approaches full repair, if accurate estimates of material properties are to be obtained from indentation.     

Bone ingrowth into a porous coated implant predicted by a mechano-regulatory tissue differentiation algorithm

Bone ingrowth into a porous surface is one of the primary methods for fixation of orthopaedic implants. Improved understanding of bone formation and fixation of these devices should improve their performance and longevity. In this study predictions of bone ingrowth into an implant porous coating were investigated using mechano-reculatory models. The mechano-regulatory tissue differentiation algorithm proposed by Lacroix et al., and a modified version that enforces a tissue differentiation pathway by transitioning from differentiation to bone adaptation were investigated. The modified algorithm resulted in nearly the same behavior as the original algorithm when applied to a fracture-healing model. The algorithms were further compared using micromechanical finite element model of a beaded porous scaffold. Predictions of bone and fibrous tissue formation were compared between the two algorithms and to clinically observed phenomena. Under loading conditions corresponding to a press-fit hip stem, the modified algorithm predicted bone ingrowth into approximately 25% of the pore space, which is similar to that reported in experimental studies, while the original algorithm was unstable. When micromotion at the bone-implant interface was simulated, 20 mum of transverse displacement resulted in soft tissue formation at the bone-implant interface and minimal bone ingrowth. In contrast, 10 and 5 mum of micromotion resulted in bone filling 40% of the pore space and a stable interface, again consistent with clinical and experimental observations.     

Influence of boundary conditions on computed apparent elastic properties of cancellous bone

High-resolution finite element models of trabecular bone can be used to study trabecular structure–function relationships, elasticity, multiaxial strength, and tissue remodelling in more detail than experiments. Beside effects of the model size, scan/analysis resolution, segmentation process, etc., the type of the applied boundary conditions (BCs) have a strong influence on the predicted elastic properties. Appropriate BCs have to be applied on hexahedral digital finite element models in order to obtain effective elastic properties. Homogeneous displacement BCs as proposed by Van Rietbergen et al. (J Biomech 29(12):1653–1657, 1996) lead to “apparent” rather than to “effective” elastic properties. This study provides some answers concerning such differences by comparing various BC types (uniform displacement, mixed BCs, periodic BCs), different volume element definitions (original and mirrored models), and several bone volume fractions (BVTV ranging from 6.5 to 37.6%). First, the mixed BCs formulated by Hazanov (Arch Appl Mech 68(6):385–394, 1998) are theoretically extended to shear loading of a porous media. Second, six human bone samples are analyzed, their orthotropic Young’s moduli, shear moduli, and Poisson’s ratios computed and compared. It is found that the proposed mixed BCs give exactly the same effective elastic properties as periodic BCs if a periodic and orthotropic micro-structured material is used and thus denoted as “periodicity compatible” mixed uniform BCs (PMUBCs). As bone samples were shown to be nearly orthotropic for volume element side lengths ≥5 mm the proposed mixed BCs turn out to be the best choice because they give again essentially the same overall elastic properties as periodic BCs. For bone samples of smaller dimensions ( < 5 mm) with a strong anisotropy (beyond orthotropy) uniform displacement BCs remain applicable but they can significantly overestimate the effective stiffness. In Memoriam, Prof. Christian Huet.     

Permeability analysis of scaffolds for bone tissue engineering

Porous artificial bone substitutes, especially bone scaffolds coupled with osteobiologics, have been developed as an alternative to the traditional bone grafts. The bone scaffold should have a set of properties to provide mechanical support and simultaneously promote tissue regeneration. Among these properties, scaffold permeability is a determinant factor as it plays a major role in the ability for cells to penetrate the porous media and for nutrients to diffuse. Thus, the aim of this work is to characterize the permeability of the scaffold microstructure, using both computational and experimental methods. Computationally, permeability was estimated by homogenization methods applied to the problem of a fluid flow through a porous media. These homogenized permeability properties are compared with those obtained experimentally. For this purpose a simple experimental setup was used to test scaffolds built using Solid Free Form techniques. The obtained results show a linear correlation between the computational and the experimental permeability. Also, this study showed that permeability encompasses the influence of both porosity and pore size on mass transport, thus indicating its importance as a design parameter. This work indicates that the mathematical approach used to determine permeability may be useful as a scaffold design tool.     

Interstitial fluid flow in the osteon with spatial gradients of mechanical properties: a finite element study

Bone remodelling is the process that maintains bone structure and strength through adaptation of bone tissue mechanical properties to applied loads. Bone can be modelled as a porous deformable material whose pores are filled with cells, organic material and interstitial fluid. Fluid flow is believed to play a role in the mechanotransduction of signals for bone remodelling. In this work, an osteon, the elementary unit of cortical bone, is idealized as a hollow cylinder made of a deformable porous matrix saturated with an interstitial fluid. We use Biot’s poroelasticity theory to model the mechanical behaviour of bone tissue taking into account transverse isotropic mechanical properties. A finite element poroelastic model is developed in the COMSOL Multiphysics software. Elasticity equations and Darcy’s law are implemented in this software; they are coupled through the introduction of an interaction term to obtain poroelasticity equations. Using numerical simulations, the investigation of the effect of spatial gradients of permeability or Poisson’s ratio is performed. Results are discussed for their implication on fluid flow in osteons: (i) a permeability gradient affects more the fluid pressure than the velocity profile; (ii) focusing on the fluid flow, the key element of loading is the strain rate; (iii) a Poisson’s ratio gradient affects both fluid pressure and fluid velocity. The influence of textural and mechanical properties of bone on mechanotransduction signals for bone remodelling is also discussed.     

Permeability study of vertebral cancellous bone using micro-computational fluid dynamics

Understanding of cancellous bone permeability is lacking despite its importance in designing tissue engineering scaffolds for bone regeneration and orthopaedic surgery that relies on infiltration of bone cement into porous cancellous bone. We employed micro-computational fluid dynamics to investigate permeability for 37 cancellous bone specimens, eliminating stringent technical requirements of bench-top testing. Microarchitectural parameters were also determined for the specimens and correlated, using uni-variate and multi-variate regression analyses, against permeability. We determined that bone surface density, trabecular pattern factor, structure model index and trabecular number are other possible predictors of permeability (with R values of 0.47, 0.44, 0.40 and 0.33), in addition to the commonly used porosity parameter (R value of 0.38). Pooling these parameters and performing multi-variate linear regression analysis improved yield the R-value of 0.50, indicating that porosity alone is a poor predictor of cancellous bone permeability and, therefore, other parameters should be included for a better and improved linear model.     

A theoretical analysis for determining the nonlinear hydraulic permeability of a soft tissue from a permeation experiment

The nonlinear nature of the hydraulic permeability, as well as the corresponding pressure and displacement fields, in a soft tissue are studied for steady-state permeation. From a two-phase continuum model analytical expressions are derived that can be used with the results from a permeation experiment to determine the dependence of the permeability on the strain. In the process it is found that, because of the compaction of the tissue arising from fluid flow, it is necessary to distinguish between the apparent and intrinsic permeability. The former, which is an averaged quantity, is the permeability usually obtained in permeation studies. However, as shown from the analysis, it can differ substantially from the latter, which is the local permeability in the tissue.     

A rotating bed system bioreactor enables cultivation of primary osteoblasts on well‐characterized sponceram® regarding structural and flow properties

The development of bone tissue engineering depends on the availability of suitable biomaterials, a well‐defined and controlled bioreactor system, and on the use of adequate cells. The biomaterial must fulfill chemical, biological, and mechanical requirements. Besides biocompatibility, the structural and flow characteristics of the biomaterial are of utmost importance for a successful dynamic cultivation of osteoblasts, since fluid percolation within the microstructure must be assured to supply to cells nutrients and waste removal. Therefore, the biomaterial must consist of a three‐dimensional structure, exhibit high porosity and present an interconnected porous network. Sponceram®, a ZrO₂ based porous ceramic, is characterized in the presented work with regard to its microstructural design. Intrinsic permeability is obtained through a standard Darcy's experiment, while Young's modulus is derived from a two plates stress–strain test in the linear range. Furthermore, the material is applied for the dynamic cultivation of primary osteoblasts in a newly developed rotating bed bioreactor. © 2010 American Institute of Chemical Engineers Biotechnol. Prog., 2010     

Permeability study of vertebral cancellous bone using micro-computational fluid dynamics

Understanding of cancellous bone permeability is lacking despite its importance in designing tissue engineering scaffolds for bone regeneration and orthopaedic surgery that relies on infiltration of bone cement into porous cancellous bone. We employed micro-computational fluid dynamics to investigate permeability for 37 cancellous bone specimens, eliminating stringent technical requirements of bench-top testing. Microarchitectural parameters were also determined for the specimens and correlated, using uni-variate and multi-variate regression analyses, against permeability. We determined that bone surface density, trabecular pattern factor, structure model index and trabecular number are other possible predictors of permeability (with R values of 0.47, 0.44, 0.40 and 0.33), in addition to the commonly used porosity parameter (R value of 0.38). Pooling these parameters and performing multi-variate linear regression analysis improved yield the R-value of 0.50, indicating that porosity alone is a poor predictor of cancellous bone permeability and, therefore, other parameters should be included for a better and improved linear model.     

Cytoskeletal organization of a cloned hemopoietic stromal cell line during attachment and spreading

The cell membrane of a cloned murine bone marrow stromal cell line D2XRII was extracted in situ using Triton X-100 detergent and the cytoskeletal structure studied during the process of adherence and spreading. During this process, three zones can be identified in the cytoplasm: the perinuclear zone, which was the fixed part of the cell; the peripheral mixed filamentous zone, which formed the core of long cytoplasmic projections; and an outer zone, which formed the boundary of cytoplasmic projections and contained only intermediate filaments. The process of spreading appeared to originate from very long strips of microfilaments emanating from the second zone, crossing the width of the outer zone, and extending beyond for a long distance. The second and third zones then appeared to "stream out" around the axis of this strip, and in this fashion the cytoplasm spreads over the substratum.     

Fluid transport and mechanical properties of articular cartilage: a review

This review is aimed at unifying our understanding of cartilage viscoelastic properties in compression, in particular the role of compression-dependent permeability in controlling interstitial fluid flow and its contribution to the observed viscoelastic effects. During the previous decade, it was shown that compression causes the permeability of cartilage to drop in a functional manner described by k = ko exp (epsilon M) where ko and M were defined as intrinsic permeability parameters and epsilon is the dilatation of the solid matrix (epsilon = tr delta u). Since permeability is inversely related to the diffusive drag coefficient of relative fluid motion with respect to the porous solid matrix, the measured load-deformation response of the tissue must therefore also depend on the non-linearly permeable nature of the tissue. We have summarized in this review our understanding of this non-linear phenomenon. This understanding of these flow-dependent viscoelastic effects are put into the historical perspective of a comprehensive literature review of earlier attempts to model the compressive viscoelastic properties of articular cartilage.     

A Particle Model for Prediction of Cement Infiltration of Cancellous Bone in Osteoporotic Bone Augmentation

Femoroplasty is a potential preventive treatment for osteoporotic hip fractures. It involves augmenting mechanical properties of the femur by injecting Polymethylmethacrylate (PMMA) bone cement. To reduce the risks involved and maximize the outcome, however, the procedure needs to be carefully planned and executed. An important part of the planning system is predicting infiltration of cement into the porous medium of cancellous bone. We used the method of Smoothed Particle Hydrodynamics (SPH) to model the flow of PMMA inside porous media. We modified the standard formulation of SPH to incorporate the extreme viscosities associated with bone cement. Darcy creeping flow of fluids through isotropic porous media was simulated and the results were compared with those reported in the literature. Further validation involved injecting PMMA cement inside porous foam blocks — osteoporotic cancellous bone surrogates — and simulating the injections using our proposed SPH model. Millimeter accuracy was obtained in comparing the simulated and actual cement shapes. Also, strong correlations were found between the simulated and the experimental data of spreading distance (R² = 0.86) and normalized pressure (R² = 0.90). Results suggest that the proposed model is suitable for use in an osteoporotic femoral augmentation planning framework.     

Association of a synthetic bone graft and bone marrow cells as a composite biomaterial

Porous calcium phosphates have osteoconductive properties. The aim of this study was to obtain synthetic calcium phosphate bone graft substitute. X-ray diffraction was employed to investigate the formation of the beta-tricalcium phosphate (β-TCP) phase. We evaluated the effects of bone marrow on the osteoconductivity and mechanical properties of synthetic bone graft (SG). SG cylinders loaded with bone marrow (SGBM) and SG alone were implanted into rabbits femoral condyle bone defects. Histological examinations revealed the resorption of the SG, trabecular bone with osteoblasts and osteoid substance around the implants, and colonization inside the porous β-TCP by newly formed bone. Histomorphometry conducted after three months revealed the osteoid surface to be higher in SGBM than SG (p < 0.05). The compressive strengths of SG and SGBM were significantly higher than the anatomic control at all time periods. The elastic modulus of SBG and SGBM became weaker after implantation. The present results indicate that gB-TCP is a good matrix for bone marrow, which contributes osteoinductive properties in an orthotopic. The composite biomaterial may be useful in reconstructive bone surgery.     

Hydro-mechanical coupling in the periodontal ligament: A porohyperelastic finite element model

Harmonic tension–compression tests at 0.1, 0.5 and 1 Hz on hydrated bovine periodontal ligament (PDL) were numerically simulated. The process was modeled by finite elements (FE) within the framework of poromechanics, with the objective of isolating the contributions of the solid- and fluid phases. The solid matrix was modeled as a porous hyperelastic material (hyperfoam) through which the incompressible fluid filling the pores flowed in accordance with the Darcy’s law. The hydro-mechanical coupling between the porous solid matrix and the fluid phase circulating through it provided an apparent time-dependent response to the PDL, whose rate of deformation depended on the permeability of the porous solid with respect to the interstitial fluid. Since the PDL was subjected to significant deformations, finite strains were taken into account and an exponential dependence of PDL permeability on void ratio – and therefore on the deformation state – was assumed. PDL constitutive parameters were identified by fitting the simulated response to the experimental data for the tests at 1 Hz. The values thus obtained were then used to simulate the tests at 0.1 and 0.5 Hz. The results of the present simulation demonstrate that a porohyperelastic model with variable permeability is able to describe the two main aspects of the PDL’s response: (1) the dependency on strain-rate—the saturated material can develop volumetric strains by only exchanging fluid and (2) the asymmetry between tension and compression, which is due to the effect of both the permeability and the elastic properties on deformation.     

Computational modeling of cell adhesion and movement using a continuum-kinetics approach

Adhesion of leukocytes to substrate involves the coupling of disparate length and timescales between molecular mechanics and macroscopic transport, and existing models of cell adhesion do not use full cellular information. To address these challenges, a multiscale computational approach for studying the adhesion of a cell on a substrate is developed and assessed. The cellular level model consists of a continuum representation of the field equations and a moving boundary tracking capability to allow the cell to change its shape continuously. At the receptor-ligand level, a bond molecule is mechanically represented by a spring. Communication between the macro/micro- and nanoscale models is facilitated interactively during the computation. The computational model is assessed using an adherent cell, rolling and deforming along the vessel wall under imposed shear flows. Using this approach, we first confirm existing numerical and experimental results. In this study, the intracellular viscosity and interfacial tension are found to directly affect the rolling of a cell. Our results also show that the presence of a nucleus increases the bond lifetime, and decreases the cell rolling velocity. Furthermore, it is found that a cell with a larger diameter rolls faster, and decreases the bond lifetime. This study shows that cell rheological properties have significant effects on the adhesion process contrary to what has been hypothesized in most literature.     

Poroelastic analysis of interstitial fluid flow in a single lamellar trabecula subjected to cyclic loading

Trabecula, an anatomical unit of the cancellous bone, is a porous material that consists of a lamellar bone matrix and interstitial fluid in a lacuno-canalicular porosity. The flow of interstitial fluid caused by deformation of the bone matrix is believed to initiate a mechanical response in osteocytes for bone remodeling. In order to clarify the effect of the lamellar structure of the bone matrix—i.e., variations in material properties—on the fluid flow stimuli to osteocytes embedded in trabeculae, we investigated the mechanical behavior of an individual trabecula subjected to cyclic loading based on poroelasticity. We focused on variations in the trabecular permeability and developed an analytical solution containing both transient and steady-state responses for interstitial fluid pressure in a single trabecular model represented by a multilayered two-dimensional poroelastic slab. Based on the obtained solution, we calculated the pressure and seepage velocity of the interstitial fluid in lacuno-canalicular porosity, within the single trabecula, under various permeability distributions. Poroelastic analysis showed that a heterogeneous distribution of permeability produces remarkable variations in the fluid pressure and seepage velocity in the cross section of the individual trabecula, and suggests that fluid flow stimuli to osteocytes are mostly governed by the value of permeability in the neighborhood of the trabecular surfaces if there is no difference in the average permeability in a single trabecula.     

A continuum mechanical porous media model for vertebroplasty: Numerical simulations and experimental validation

The outcome of vertebroplasty is hard to predict due to its dependence on complex factors like bone cement and marrow rheologies. Cement leakage could occur if the procedure is done incorrectly, potentially causing adverse complications. A reliable simulation could predict the patient-specific outcome preoperatively and avoid the risk of cement leakage. Therefore, the aim of this work was to introduce a computationally feasible and experimentally validated model for simulating vertebroplasty. The developed model is a multiphase continuum-mechanical macro-scale model based on the Theory of Porous Media. The related governing equations were discretized using a combined finite element–finite volume approach by the so-called Box discretization. Three different rheological upscaling methods were used to compare and determine the most suitable approach for this application. For validation, a benchmark experiment was set up and simulated using the model. The influence of bone marrow and parameters like permeability, porosity, etc., was investigated to study the effect of varying conditions on vertebroplasty. The presented model could realistically simulate the injection of bone cement in porous materials when used with the correct rheological upscaling models, of which the semi-analytical averaging of the viscosity gave the best results. The marrow viscosity is identified as the crucial reference to categorize bone cements as ‘high- ’or ‘low-’ viscosity in the context of vertebroplasty. It is confirmed that a cement with higher viscosity than the marrow ensures stable development of the injection and a proper cement interdigitation inside the vertebra.

     

Use of high-resolution MRI for investigation of fluid flow and global permeability in a material with interconnected porosity

We present a multi-scale experimental approach designed to improve the investigation of both localized and global fluid flow in biomaterials with randomly interconnected porosity. Coralline hydroxyapatite (ProOsteon 500 from Interpore-Cross), having a relatively well-defined porosity, was used as an in vitro model of typical bone architecture. Axial fluid velocity profiles within the pores of a cylindrical hydroxyapatite sample were characterized using high-resolution MRI in conjunction with the measurement of global flow and associated permeability based on the Darcy-type relationship. Assuming Newtonian fluid behaviour, image analysis permitted computation of local porosity, intra-pore fluid shear, and visualization of flow heterogeneity within the sample. These results may benefit applications in biomaterials for the evaluation of factors influencing bony incorporation in porous scaffolds and on porous implant and bone surfaces. Normal and diseased biological tissues are also clinical relevant applications.     

Development and validation of a subject-specific finite element model of a human clavicle

This study aimed to develop and validate a finite element (FE) model of a human clavicle which can predict the structural response and bone fractures under both axial compression and anterior–posterior three-point bending loads. Quasi-static non-injurious axial compression and three-point bending tests were first conducted on a male clavicle followed by a dynamic three-point bending test to fracture. Then, two types of FE models of the clavicle were developed using bone material properties which were set to vary with the computed tomography image density of the bone. A volumetric solid FE model comprised solely of hexahedral elements was first developed. A solid-shell FE model was then created which modelled the trabecular bone as hexahedral elements and the cortical bone as quadrilateral shell elements. Finally, simulations were carried out using these models to evaluate the influence of variations in cortical thickness, mesh density, bone material properties and modelling approach on the biomechanical responses of the clavicle, compared with experimental data. The FE results indicate that the inclusion of density-based bone material properties can provide a more accurate reproduction of the force–displacement response and bone fracture timing than a model with uniform bone material properties. Inclusion of a variable cortical thickness distribution also slightly improves the ability of the model to predict the experimental response. The methods developed in this study will be useful for creating subject-specific FE models to better understand the biomechanics and injury mechanism of the clavicle.