Finite element modelling of polymethylmethacrylate flow through cancellous bone

Porosity and surface curvature effects on the permeability and wall shear stress of trabecular bone: Guidelines for biomimetic scaffolds for bone repair

Scaffolds are an essential component of bone tissue engineering to provide support and create a physiological environment for cells. Biomimetic scaffolds are a promising approach to fulfill the requirements. Bone allografts are widely used scaffolds due to their mechanical and structural characteristics. The scaffold geometry is well known to be an important determinant of induced mechanical stimulation felt by the cells. However, the impact of allograft geometry on permeability and wall shear stress distribution is not well understood. This information is essential for designing biomimetic scaffolds that provide a suitable environment for cells to proliferate and differentiate. The present study investigates the effect of geometry on the permeability and wall shear stress of bone allografts at both macroscopic and microscopic scales. Our results concluded that the wall shear stress was strongly correlated with the porosity of the allograft. The level of wall shear stress at a local scale was also determined by the surface curvature characteristics. The results of this study can serve as a guideline for future biomimetic scaffold designs that provide a mechanical environment favorable for osteogenesis and bone repair.

Functionally graded stem optimizes the fixed and sliding surface coupling mechanism

Whether the optimization of fixed surface and sliding surface coupling mechanism is related to the hierarchical level of functionally graded porous stem is unknown. The functionally graded porous finite element stem models were constructed using tetrahedral microstructure with the porosities of 47-95%. The stress distribution for femoral bone gradually strengthened, the stress shielding was decreased along the increase of hierarchical levels of the stem after implantation. The coupling mechanism of fixed and sliding surfaces can be optimized by the functional gradient porous stem, the performance advantages become more prominent with the increase of hierarchical levels of the structure.

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.

Development of bioinks for 3D printing microporous, sintered calcium phosphate scaffolds

Beta-tricalcium phosphate (β-TCP)-based bioinks were developed to support direct-ink 3D printing-based manufacturing of macroporous scaffolds. Binding of the gelatin:β-TCP ink compositions was optimized by adding carboxymethylcellulose (CMC) to maximize the β-TCP content while maintaining printability. Post-sintering, the gelatin:β-TCP:CMC inks resulted in uniform grain size, uniform shrinkage of the printed structure, and included microporosity within the ceramic. The mechanical properties of the inks improved with increasing β-TCP content. The gelatin:β-TCP:CMC ink (25:75 gelatin:β-TCP and 3% CMC) optimized for mechanical strength was used to 3D print several architectures of macroporous scaffolds by varying the print nozzle tip diameter and pore spacing during the 3D printing process (compressive strength of 13.1 ± 2.51 MPa and elastic modulus of 696 ± 108 MPa was achieved). The sintered, macroporous β-TCP scaffolds demonstrated both high porosity and pore size but retained mechanical strength and stiffness compared to macroporous, calcium phosphate ceramic scaffolds manufactured using alternative methods. The high interconnected porosity (45-60%) and fluid conductance (between 1.04 ×10^-9 and 2.27 × 10^-9 m⁴s/kg) of the β-TCP scaffolds tested, and the ability to finely tune the architecture using 3D printing, resulted in the development of novel bioink formulations and made available a versatile manufacturing process with broad applicability in producing substrates suitable for biomedical applications.

Additive Manufacturing of Bone Scaffolds Using PolyJet and Stereolithography Techniques

In this study, the printing capability of two different additive manufacturing (3D printing) techniques, namely PolyJet and micro-stereolithography (µSLA), are investigated regarding the fabrication of bone scaffolds. The 3D-printed scaffold structures are used as supports in replacing and repairing fractured bone tissue. Printed bone scaffolds with complex structures produced using additive manufacturing technology can mimic the mechanical properties of natural human bone, providing lightweight structures with modifiable porosity levels. In this study, 3D scaffold structures are designed with different combinations of architectural parameters. The dimensional accuracy, permeability, and mechanical properties of complex 3D-printed scaffold structures are analyzed to compare the advantages and drawbacks associated with the two techniques. The fluid flow rates through the 3D-printed scaffold structures are measured and Darcy’s law is applied to calculate the experimentally measured permeability. The Kozeny–Carman equation is applied for theoretical calculation of permeability. Compression tests were performed on the printed samples to observe the effects of the printing techniques on the mechanical properties of the 3D-printed scaffold structures. The effect of the printing direction on the mechanical properties of the 3D-printed scaffold structures is also analyzed. The scaffold structures printed with the µSLA printer demonstrate higher permeability and mechanical properties as compared to those printed using the PolyJet technique. It is demonstrated that both the µSLA and PolyJet printing techniques can be used to print 3D scaffold structures with controlled porosity levels, providing permeability in a similar range to human bone.

3D printed Ti6Al4V bone scaffolds with different pore structure effects on bone ingrowth

The microstructure of porous scaffolds plays a vital role in bone regeneration, but its optimal shape is still unclear. In this study, four kinds of porous titanium alloy scaffolds with similar porosities (65%) and pore sizes (650 μm) and different structures were prepared by selective laser melting. Four scaffolds were implanted into the distal femur of rabbits to evaluate bone tissue growth in vivo. Micro-CT and hard tissue section analyses were performed 6 and 12 weeks after the operation to reveal the bone growth of the porous scaffold. The results show that diamond lattice unit (DIA) bone growth is the best of the four topological scaffolds. Through computational fluid dynamics (CFD) analysis, the permeability, velocity and flow trajectory inside the scaffold structure were calculated. The internal fluid velocity difference of the DIA structure is the smallest, and the trajectory of fluid flow inside the scaffold is the longest, which is beneficial for blood vessel growth, nutrient transport and bone formation. In this study, the mechanism of bone growth in different structures was revealed by in vivo experiments combined with CFD, providing a new theoretical basis for the design of bone scaffolds in the future.

Porous polylactic acid scaffolds for bone regeneration: A study of additively manufactured triply periodic minimal surfaces and their osteogenic potential

Three different triply periodic minimal surfaces (TPMS) with three levels of porosity within those of cancellous bone were investigated as potential bone scaffolds. TPMS have emerged as potential designs to resemble the complex mechanical and mass transport properties of bone. Diamond, Schwarz, and Gyroid structures were 3D printed in polylactic acid, a resorbable medical grade material. The 3D printed structures were investigated for printing feasibility, and assessed by morphometric studies. Mechanical properties and permeability investigations resulted in similar values to cancellous bone. The morphometric analyses showed three different patterns of pore distribution: mono-, bi-, and multimodal pores. Subsequently, biological activity investigated with pre-osteoblastic cell lines showed no signs of cytotoxicity, and the scaffolds supported cell proliferation up to 3 weeks. Cell differentiation investigated by alkaline phosphatase showed an improvement for higher porosities and multimodal pore distributions, suggesting a higher dependency on pore distribution and size than the level of interconnectivity.

Tailored mechanical response and mass transport characteristic of selective laser melted porous metallic biomaterials for bone scaffolds

Porous metallic biomaterials developed from pentamode metamaterials (PMs) were rationally designed to mimic the topological, mechanical, and mass transport properties of human bones. Here, a series of diamond-based PMs with different strut parameters were fabricated from a Ti-6Al-4V powder by selective laser melting (SLM) technique. The morphological features, mechanical properties and permeability of PM samples were then characterized. In terms of morphology, the as-built PMs were well consistent with the as-designed ones, although the slight surface deviations were presented in overhanging areas. The PM scaffolds showed a switchable deformation pattern controlled by the slenderness ratio of struts. The double-cone strut topology increases the tortuosity and thereby accelerates the nutrients supply, waste removal, and cell migration to the whole scaffold region and circumambient bone tissue. The measured mechanical properties (i.e., E: 0.59-2.90 GPa, σ_y: 20.59-112.63 MPa) and computational permeability values (k: 9.87-49.19 × 10^-9 m²) of PM scaffolds were all in accordance with those of trabecular bone. The experimental permeability values were linearly dependent on the results of simulations. This study showed the great potential of PMs as bone scaffolds. Moreover, we demonstrated that PM-based porous biomaterials can decouple the mass transport and mechanical properties of bone scaffolds, so as to achieve an unprecedented level of tailoring their multi-physics properties. STATEMENT OF SIGNIFICANCE: The topological diversity can significantly improve the adaptability of the implant to the primary bone tissue. Previous studies revealed that the mechanical and mass transport properties of porous biomaterials are correlated to the material types, porosities and lattice topologies but neglected effects of strut design. We show here the influence of strut morphology on the mechanical and mass transport properties which are independently tailored, that is, the mass transport properties can be markedly increased while maintaining the mechanical properties of mimicking specific bones, vice versa. This study emphasizes the importance of strut topological design in the development of AM porous biomaterials.

Relationships Among Bone Morphological Parameters and Mechanical Properties of Cadaveric Human Vertebral Cancellous Bone

Mechanical properties and morphological features of the vertebral cancellous bone are related to resistance to fracture and capability of withstanding surgical treatments. In particular, vertebral strength is related to its elastic properties, whereas the ease of fluid motion, related to the success of incorporation orthopedic materials (eg, bone cement), is regulated by the hydraulic permeability (K). It has been shown that both elastic modulus and permeability of a material are affected by its morphology. The objective of this study was to establish relations between local values of K and the aggregate modulus (H), and parameters descriptive of the bone morphology. We hypothesized that multivariate statistical models, by including the contribution of several morphology parameters at once, would provide a strong correlation with K and H of the vertebral cancellous bone. Hence, μCT scans of human lumbar vertebra were used to determine a set of bone morphology descriptors. Subsequently, indentation tests on the bone samples were conducted to determine local values of K and H. Finally, a multivariate approach supported by principal component analysis was adopted to develop predictive statistical models of bone permeability and aggregate modulus as a function of bone morphology descriptors. It was found that linear combinations of bone volume fraction, trabecular thickness, trabecular spacing, structure model index, connectivity density, and degree of anisotropy provide a strong correlation (R 2 ~ 76%) with K and a weaker correlation (R 2 ~ 47%) with H. The results of this study can be exploited in computational mechanics frameworks for investigating the potential mechanical behavior of human vertebra and to develop strategies to treat or prevent pathological conditions such as osteoporosis, age-related bone loss, and vertebral compression fractures. © 2020 The Authors. JBMR Plus published by Wiley Periodicals, Inc. on behalf of American Society for Bone and Mineral Research.

Synthetic open cell foams versus a healthy human vertebra: Anisotropy, fluid flow and μ-CT structural studies

Commercial synthetic open-cell foams are an alternative to human cadaveric bone to simulate in vitro different scenarios of bone infiltration properties. Unfortunately, these artificial foams do not reproduce the anisotropic microstructure of natural bone and, consequently, their suitability in these studies is highly questionable. In order to achieve scaffolds that successfully mimic human bone, microstructural studies of both natural porous media and current synthetic approaches are necessary at different length scales. In this line, the present research was conducted to improve the understanding of local anisotropy in natural vertebral bone and synthetic bone-like porous foams. To attain this objective, small volumes of interest within these materials were reconstructed via micro-computed tomography. The anisotropy of the microstructures was analysed by means of both their main local histomorphometric features and the behaviour of an internal flow computed via computational fluid dynamics. The results showed that the information obtained from each of the micro-volumes of interest could be scaled up to understand not only the macroscopic averaged isotropic and/or anisotropic behaviour of the samples studied, but also to improve the design of macroscopic porous implants better fitting specific local histomorphometric scenarios. The results also clarify the discrepancies in the permeability obtained in the different micro-volumes of interest analysed. STATEMENT OF SIGNIFICANCE: A deep insight comparative study between the porous microstructure of healthy vertebral bone and that of synthetic bone-like open-cell rigid foams used in in vitro permeability studies of bone cement has been performed. The results obtained are of fundamental relevance to computational studies because, in order to achieve convergence values, the computation process should be limited to small computation domains or micro-volumes of interest. This makes the results specific spatial dependent and for this reason computation studies cannot directly capture the macroscopic average behaviour of an anisotropic porous structure such as the one observed in natural bones. The results derived from this study are also important because we have been able to show that the specific spatial information contained in only one healthy vertebra is enough to capture, from a geometric point of view, the same information of "specific surface area vs. porosity" - in other words, the same basic law - that can also be found in other human bones for different patients, even at different biological ages. This is an important finding that, despite the efforts made and the controversies formulated by other authors, should be studied more thoroughly with other bone species and tissues (healthy and/or diseased). Moreover, our results should help to understand that, with the extensive capabilities of current 3D printing technologies, there is an enormous potential in the design of biomimetic porous bone-like scaffolds for bone tissue engineering applications.

Mechanical behaviours and mass transport properties of bone-mimicking scaffolds consisted of gyroid structures manufactured using selective laser melting

Bone scaffolds created in porous structures manufactured using selective laser melting (SLM) are widely used in tissue engineering, since the elastic moduli of the scaffolds are easily adjusted according to the moduli of the tissues, and the large surfaces the scaffolds provide are beneficial to cell growth. SLM-built gyroid structures composed of 316L stainless steel have demonstrated superior properties such as good corrosion resistance, strong biocompatibility, self-supported performance, and excellent mechanical properties. In this study, gyroid structures of different volume fraction were modelled and manufactured using SLM; the mechanical properties of the structures were then investigated under quasi-static compression loads. The elastic moduli and yield stresses of the structures were calculated from stress-strain diagrams, which were developed by conducting quasi-static compression tests. In order to estimate the discrepancies between the designed and as-produced gyroid structures, optical microscopy and micro-CT scanner were used to observe the structures' micromorphology. Since good fluidness is conducive to the transport of nutrients, computational fluid dynamics (CFD) values were used to investigate the pressure and flow velocity of the channel of the three kinds of gyroid structures. The results show that the sizes of the as-produced structures were larger than their computer aided design (CAD) sizes, but the manufacturing errors are within a relatively stable range. The elastic moduli and yield stresses of the structures improved as their volume fractions increased. Gyroid structure can match the mechanical properties of human bone by changing the porosity of scaffold. The process of compression failure showed that 316L gyroid structures manufactured using SLM demonstrated high degrees of toughness. The results obtained from CFD simulation showed that gyroid structures have good fluidity, which has an accelerated effect on the fluid in the middle of the channel, and it is suitable for transport nutrients. Therefore, we could predict the scaffold's permeability by conducting CFD simulation to ensure an appropriate permeability before the scaffold being manufactured. SLM-built gyroid structures that composed of 316L stainless steel were suitable to be designed as bone scaffolds in terms of mechanical properties and mass-transport properties, and had significant promise.

The implication of the osteolysis threshold and interfacial gaps on periprosthetic osteolysis in cementless total hip replacement

Osteolysis around joint replacements may develop due to migration of wear particles from the joint space into gaps between the interface bone and the implant where they can accumulate in high concentrations to cause tissue damage. Osteolysis may appear in various postoperative times and morphological shapes which can be generalized into linear and focal. However, there are no clear explanations on the causes of such variations. Patients' degree of sensitivity to polyethylene particles (osteolysis thresholds), the local particle concentration and the access route provided by the interface gaps have been described as determining factors. To study their effects, a 2D computational fluid dynamics model of the hip joint capsule in communication with an interfacial gap and the surrounding bone was employed. Particles were presented using a discrete phase model (DPM). High capsular fluid pressure was considered as the driving force for particle migration. Simulations were run for different osteolysis thresholds ranging from 5×10⁸ to 1×10¹² particle number per gram of tissue and fibrous tissue generation in osteolytic lesion due to particles was simulated for the equivalent of ten postoperative years. In patients less sensitive to polyethylene particles (higher threshold), osteolysis may be linear and occur along an interfacial gap in less than 5% of the interfacial tissue. Focal osteolysis is more likely to develop in patients with higher sensitivity to polyethylene particles at distal regions to an interfacial gaps where up to 80% of the interfacial tissue may be replaced by fibrous tissue. In these patients, signs of osteolysis may also develop earlier (third postoperative year) than those with less sensitivity who may show very minor signs even after ten years. This study shows the importance of patient sensitivity to wear particles, the role of interfacial gaps in relation to morphology and the onset of osteolysis. Consequently, it may explain the clinically observed variation in osteolysis development.

Additively manufactured metallic porous biomaterials based on minimal surfaces: A unique combination of topological, mechanical, and mass transport properties

Porous biomaterials that simultaneously mimic the topological, mechanical, and mass transport properties of bone are in great demand but are rarely found in the literature. In this study, we rationally designed and additively manufactured (AM) porous metallic biomaterials based on four different types of triply periodic minimal surfaces (TPMS) that mimic the properties of bone to an unprecedented level of multi-physics detail. Sixteen different types of porous biomaterials were rationally designed and fabricated using selective laser melting (SLM) from a titanium alloy (Ti-6Al-4V). The topology, quasi-static mechanical properties, fatigue resistance, and permeability of the developed biomaterials were then characterized. In terms of topology, the biomaterials resembled the morphological properties of trabecular bone including mean surface curvatures close to zero. The biomaterials showed a favorable but rare combination of relatively low elastic properties in the range of those observed for trabecular bone and high yield strengths exceeding those reported for cortical bone. This combination allows for simultaneously avoiding stress shielding, while providing ample mechanical support for bone tissue regeneration and osseointegration. Furthermore, as opposed to other AM porous biomaterials developed to date for which the fatigue endurance limit has been found to be ≈20% of their yield (or plateau) stress, some of the biomaterials developed in the current study show extremely high fatigue resistance with endurance limits up to 60% of their yield stress. It was also found that the permeability values measured for the developed biomaterials were in the range of values reported for trabecular bone. In summary, the developed porous metallic biomaterials based on TPMS mimic the topological, mechanical, and physical properties of trabecular bone to a great degree. These properties make them potential candidates to be applied as parts of orthopedic implants and/or as bone-substituting biomaterials.

STATEMENT OF SIGNIFICANCE

Bone-substituting biomaterials aim to mimic bone properties. Although mimicking some of bone properties is feasible, biomaterials that could simultaneously mimic all or most of the relevant bone properties are rare. We used rational design and additive manufacturing to develop porous metallic biomaterials that exhibit an interesting combination of topological, mechanical, and mass transport properties. The topology of the developed biomaterials resembles that of trabecular bone including a mean curvature close to zero. Moreover, the developed biomaterials show an unusual combination of low elastic modulus to avoid stress shielding and high strength to provide mechanical support. The fatigue resistance of the developed biomaterials is also exceptionally high, while their permeability is in the range of values reported for bone.

Estimation of anisotropic permeability in trabecular bone based on microCT imaging and pore-scale fluid dynamics simulations

In this paper, a comprehensive framework is proposed to estimate the anisotropic permeability matrix in trabecular bone specimens based on micro-computed tomography (microCT) imaging combined with pore-scale fluid dynamics simulations. Two essential steps in the proposed methodology are the selection of (i) a representative volume element (RVE) for calculation of trabecular bone permeability and (ii) a converged mesh for accurate calculation of pore fluid flow properties. Accurate estimates of trabecular bone porosities are obtained using a microCT image resolution of approximately 10 μm. We show that a trabecular bone RVE in the order of 2 × 2 × 2 mm³ is most suitable. Mesh convergence studies show that accurate fluid flow properties are obtained for a mesh size above 125,000 elements. Volume averaging of the pore-scale fluid flow properties allows calculation of the apparent permeability matrix of trabecular bone specimens. For the four specimens chosen, our numerical results show that the so obtained permeability coefficients are in excellent agreement with previously reported experimental data for both human and bovine trabecular bone samples. We also identified that bone samples taken from long bones generally exhibit a larger permeability in the longitudinal direction. The fact that all coefficients of the permeability matrix were different from zero indicates that bone samples are generally not harvested in the principal flow directions. The full permeability matrix was diagonalized by calculating the eigenvalues, while the eigenvectors showed how strongly the bone sample's orientations deviated from the principal flow directions. Porosity values of the four bone specimens range from 0.83 to 0.86, with a low standard deviation of ± 0.016, principal permeability values range from 0.22 to 1.45 ⋅ 10 ^-8 m², with a high standard deviation of ± 0.33. Also, the anisotropic ratio ranged from 0.27 to 0.83, with high standard deviation. These results indicate that while the four specimens are quite similar in terms of average porosity, large variability exists with respect to permeability and specimen anisotropy. The utilized computational approach compares well with semi-analytical models based on homogenization theory. This methodology can be applied in bone tissue engineering applications for generating accurate pore morphologies of bone replacement materials and to consistently select similar bone specimens in bone bioreactor studies.

Multiphasic modelling of bone-cement injection into vertebral cancellous bone

Percutaneous vertebroplasty represents a current procedure to effectively reinforce osteoporotic bone via the injection of bone cement. This contribution considers a continuum-mechanically based modelling approach and simulation techniques to predict the cement distributions within a vertebra during injection. To do so, experimental investigations, imaging data and image processing techniques are combined and exploited to extract necessary data from high-resolution μCT image data. The multiphasic model is based on the Theory of Porous Media, providing the theoretical basis to describe within one set of coupled equations the interaction of an elastically deformable solid skeleton, of liquid bone cement and the displacement of liquid bone marrow. The simulation results are validated against an experiment, in which bone cement was injected into a human vertebra under realistic conditions. The major advantage of this comprehensive modelling approach is the fact that one can not only predict the complex cement flow within an entire vertebra but is also capable of taking into account solid deformations in a fully coupled manner. The presented work is the first step towards the ultimate and future goal of extending this framework to a clinical tool allowing for pre-operative cement distribution predictions by means of numerical simulations.

Permeability study of cancellous bone and its idealised structures

Artificial bone is a suitable alternative to autografts and allografts, however their use is still limited. Though there were numerous reports on their structural properties, permeability studies of artificial bones were comparably scarce. This study focused on the development of idealised, structured models of artificial cancellous bone and compared their permeability values with bone surface area and porosity. Cancellous bones from fresh bovine femur were extracted and cleaned following an established protocol. The samples were scanned using micro-computed tomography (μCT) and three-dimensional models of the cancellous bones were reconstructed for morphology study. Seven idealised and structured cancellous bone models were then developed and fabricated via rapid prototyping technique. A test-rig was developed and permeability tests were performed on the artificial and real cancellous bones. The results showed a linear correlation between the permeability and the porosity as well as the bone surface area. The plate-like idealised structure showed a similar value of permeability to the real cancellous bones.

The role of endplate poromechanical properties on the nutrient availability in the intervertebral disc

OBJECTIVE

To investigate the relevance of the human vertebral endplate poromechanics on the fluid and metabolic transport from and to the intervertebral disc (IVD) based on educated estimations of the poromechanical parameter values of the bony endplate (BEP).

METHODS

50 micro-models of different BEP samples were generated from μCTs of lumbar vertebrae and allowed direct determination of porosity values. Permeability values were calculated by using the micro-models, through the simulation of permeation via computational fluid dynamics. These educated ranges of porosity and permeability values were used as inputs for mechano-transport simulations to assess their effect on both the distributions of metabolites within an IVD model and the poromechanical calculations within the cartilaginous part of the endplate i.e., the cartilage endplate (CEP).

RESULTS

BEP effective permeability was highly correlated to local variations of porosity (R(2) ≈ 0.88). Universal patterns between bone volume fraction and permeability arose from these results and from other experimental data in the literature. These variations in BEP permeability and porosity had negligible effects on the distributions of metabolites within the disc. In the CEP, the variability of the poromechanical properties of the BEP did not affect the predicted consolidation but induced higher fluid velocities.

CONCLUSIONS

The present paper provides the first sets of thoroughly identified BEP parameter values that can be further used in patient-specific poromechanical studies. Representing BEP structural changes through variations in poromechanical properties did not affect the diffusion of metabolites. However, attention might be paid to alterations in fluid velocities and cell mechano-sensing within the CEP.

Numerical description and experimental validation of a rheology model for non-Newtonian fluid flow in cancellous bone

Fluids present or used in biology, medicine and (biomedical) engineering are often significantly non-Newtonian. Furthermore, they are chemically complex and can interact with the porous matrix through which they flow. The porous structures themselves display complex morphological inhomogeneities on a wide range of length scales. In vertebroplasty, a shear-thinning fluid, e.g. poly(methyl methacrylate) (PMMA), is injected into the cavities of vertebral trabecular bone for the stabilization of fractures and metastatic lesions. The main objective of this study was therefore to provide a protocol for numerically investigating the rheological properties of PMMA-based bone cements to predict its spreading behavior while flowing through vertebral trabecular bone. A numerical upscaling scheme based on a dimensionless formulation of the Navier-Stokes equation is proposed in order to relate the pore-scale rheological properties of the PMMA that were experimentally estimated using a plate rheometer, to the continuum-scale. On the pore length scale, a viscosity change on the order of one magnitude was observed whilst the shear-thinning properties caused a viscosity change on the order of only 10% on the continuum length scale and in a flow regime that is relevant for vertebroplasty. An experimental validation, performed on human cadaveric vertebrae (n=9), showed a significant improvement of the cement spreading prediction accuracy with a non-Newtonian formulation. A root mean square cement surface prediction error of 1.53mm (assuming a Newtonian fluid) and 1.37mm (assuming a shear-thinning fluid) was found. Our findings highlight the importance of incorporating the non-Newtonian fluids properties in computational models of porous media at the appropriate length scale.

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.

Permeability of Rapid Prototyped Artificial Bone Scaffold Structures

Fluid flow through a bone scaffold structure is an important factor in its ability to build up a living tissue. Permeability is often used as a measure of a structure’s ability to allow for flow of nutrients and waste products related to the growth of new tissue. These structures also need to meet conflicting mechanical strength requirements to allow for load bearing. In this work, the effect of different bone structure morphologies on permeability were examined both numerically and experimentally. Cubic and hexagonal based three dimensional scaffold structures were produced via stereolithography and 3D printing techniques. In particular, porosity percentage, pore size, and pore geometry were examined. Porosity content was varied from 30% to 70% and pore size from 0.34 mm to 3 mm. An adapted Kozeny-Carmen numerical method was applied for calculation of permeability through these structures and an experimental validation of these results was performed via a standard permeability experimental testing set-up. From the results it was determined that increased permeability was provided with the cubic rather than hexagonal structure as well as by utilizing the larger pore size and higher levels of porosity. Stereolithography was found to be the better processing technique, not only for improved micrometer scale dimensional accuracy reasons, but also due to the increase wettability found on the produced surfaces. The appropriate model constants determined in this work will allow for analysis of new alternate structure designs on the permeability of rapid prototyped synthetic bone structures.

Fabric dependence of quasi-waves in anisotropic porous media

Assessment of bone loss and osteoporosis by ultrasound systems is based on the speed of sound and broadband ultrasound attenuation of a single wave. However, the existence of a second wave in cancellous bone has been reported and its existence is an unequivocal signature of poroelastic media. To account for the fact that ultrasound is sensitive to microarchitecture as well as bone mineral density (BMD), a fabric-dependent anisotropic poroelastic wave propagation theory was recently developed for pure wave modes propagating along a plane of symmetry in an anisotropic medium. Key to this development was the inclusion of the fabric tensor--a quantitative stereological measure of the degree of structural anisotropy of bone--into the linear poroelasticity theory. In the present study, this framework is extended to the propagation of mixed wave modes along an arbitrary direction in anisotropic porous media called quasi-waves. It was found that differences between phase and group velocities are due to the anisotropy of the bone microarchitecture, and that the experimental wave velocities are more accurately predicted by the poroelastic model when the fabric tensor variable is taken into account. This poroelastic wave propagation theory represents an alternative for bone quality assessment beyond BMD.

A Mixed Boundary Representation to Simulate the Displacement of a Biofluid by a Biomaterial in Porous Media

Characterization of the biomaterial flow through porous bone is crucial for the success of the bone augmentation process in vertebroplasty. The biofluid, biomaterial, and local morphological bone characteristics determine the final shape of the filling, which is important both for the post-treatment mechanical loading and the risk of intraoperative extraosseous leakage. We have developed a computational model that describes the flow of biomaterials in porous bone structures by considering the material porosity, the region-dependent intrinsic permeability of the porous structure, the rheological properties of the biomaterial, and the boundary conditions of the filling process. To simulate the process of the substitution of a biofluid (bone marrow) by a biomaterial (bone cement), we developed a hybrid formulation to describe the evolution of the fluid boundary and properties and coupled it to a modified version of Darcy’s law. The apparent rheological properties are derived from a fluid-fluid interface tracking algorithm and a mixed boundary representation. The region- specific intrinsic permeability of the bone is governed by an empirical relationship resulting from a fitting process of experimental data. In a first step, we verified the model by studying the displacement process in spherical domains, where the spreading pattern is known in advance. The mixed boundary model demonstrated, as expected, that the determinants of the spreading pattern are the local intrinsic permeability of the porous matrix and the ratio of the viscosity of the fluids that are contributing to the displacement process. The simulations also illustrate the sensitivity of the mixed boundary representation to anisotropic permeability, which is related to the directional dependent microstructural properties of the porous medium. Furthermore, we compared the nonlinear finite element model to different published experimental studies and found a moderate to good agreement (R2=0.9895 for a one-dimensional bone core infiltration test and a 10.94–16.92% relative error for a three-dimensional spreading pattern study, respectively) between computational and experimental results.

Fabric dependence of wave propagation in anisotropic porous media

Current diagnosis of bone loss and osteoporosis is based on the measurement of the bone mineral density (BMD) or the apparent mass density. Unfortunately, in most clinical ultrasound densitometers: 1) measurements are often performed in a single anatomical direction, 2) only the first wave arriving to the ultrasound probe is characterized, and 3) the analysis of bone status is based on empirical relationships between measurable quantities such as speed of sound (SOS) and broadband ultrasound attenuation (BUA) and the density of the porous medium. However, the existence of a second wave in cancellous bone has been reported, which is an unequivocal signature of poroelastic media, as predicted by Biot's poroelastic wave propagation theory. In this paper, the governing equations for wave motion in the linear theory of anisotropic poroelastic materials are developed and extended to include the dependence of the constitutive relations upon fabric-a quantitative stereological measure of the degree of structural anisotropy in the pore architecture of a porous medium. This fabric-dependent anisotropic poroelastic approach is a theoretical framework to describe the microarchitectural-dependent relationship between measurable wave properties and the elastic constants of trabecular bone, and thus represents an alternative for bone quality assessment beyond BMD alone.

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 746μm and between 75 and 2940μm, respectively. The permeability of the flow in the cavities of the specific bone sample was found to be 5.05×10-8 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.

Rate dependence of hydraulic resistance in human lumbar vertebral bodies

STUDY DESIGN

Twenty-one intact human lumbar vertebral bodies (L3 and L4) were used to determine the changes in measured intraosseous pressure for 2 volumetric flow rates and to calculate hydraulic resistance in both cases.

OBJECTIVE

To evaluate changes in hydraulic resistance in intact vertebral bodies under different rates of flow.

SUMMARY OF BACKGROUND DATA

Hydraulic resistance has been implicated in the creation of high-speed vertebral injuries, such as burst fracture, but no previous study has measured hydraulic resistance under high-speed loading conditions. Previous work in whole bone preparations showed that hydraulic resistance was constant under low-speed conditions. The authors hypothesized that: (1) measured pressure would increase with increasing input flow rates, and (2) hydraulic resistance would remain constant at increased input flow rates.

METHODS

Using 2 input velocity conditions (10 mm/s and 2500 mm/s), resultant pressures were measured and hydraulic resistance calculated. Trabecular architecture was determined using micro-computerized tomography after testing.

RESULTS

Measured pressure increased with increasing input flow rates. However, average hydraulic resistance decreased significantly when comparing low-speed (3.40 +/- 1.58kPa*s/mL) and high-speed (0.16 +/- 0.08kPa*s/mL) groups.

CONCLUSIONS

Current hydraulic resistance results contradict previous findings. The observed decrease in hydraulic resistance suggests that, during high-speed injury events, marrow flow may damage the trabeculae and thereby weaken the vertebra.

Cement flow during impaction allografting: a finite element analysis

Cement intrusion into cancellous or impacted bone is not well understood. We adopted an engineering mechanics approach to predict the effect of surgical variables on the cement intrusion into impacted cancellous bone, used for the revision of failed total hip replacement with the impaction allografting technique. Specifically, a three-dimensional finite element model was used to determine the effects of cement viscosity, the magnitude and duration of pressurization, and the distribution of the porosity along the femur on cement intrusion. The overall averaged mean intrusion depth difference between the finite element model prediction and the cadaveric measurements was 1.1mm. The depth of penetration increased with higher pressurization pressure, duration of pressurization, and earlier stem insertion (lower viscosity), but maintained a similar profile. The distribution of the porosity along the femur determined the intrusion profile. Cement viscosity, the applied pressure or the duration of the pressurization can be adjusted to limit the cement volume injected into the medullary canal and therefore prevent the cement from reaching the endosteal surface.

A comparison of structural and mechanical properties in cancellous bone from the femoral head and acetabulum

Mechanical interlock obtained by penetration of bone cement into cancellous bone is critical to the success of cemented total hip replacement (THR). Although acetabular component loosening is an important mode of THR failure, the properties of acetabular cancellous bone relevant to cement penetration are not well characterized. Bone biopsies (9mm diameter, 10mm long) were taken from the articular surfaces of the acetabulum and femoral head during total hip replacement. After mechanical and chemical defatting the two groups of bone specimens were characterized using flow measurement, mechanical testing and finally serial sectioning and three-dimensional computer reconstruction. The mean permeabilities of the acetabular group (1.064 × 10−10 m2) and femoral group (1.155x 10−10m2) were calculated from the flow measurements, which used saline solution and a static pressure of 9.8 kPa. The mean Young's modulus, measured non-destructively, was 47.4 MPa for the femoral group and 116.4MPa for the acetabular group. Three-dimensional computer reconstruction of the specimens showed no significant differences in connectivity and porosity between the groups. Results obtained using femoral head cancellous bone to investigate bone cement penetration and fixation are directly relevant to fixation in the acetabulum.

A finite element rheological model for polymethylmethacrylate flow: analysis of the cement delivery in vertebroplasty

Polymethylmethacrylate (PMMA) is increasingly used in orthopaedics. Finite element (FE) modelling can play an important role in understanding the PMMA flow behaviour. However, FE models have not been used so far because conventional FE packages do not allow for the rheopectic and pseudoplastic behaviour of PMMA to be taken into consideration and because it requires multiple expertise to incorporate these behaviours into an FE package. The objectives of the present paper are to: (a) propose a rheological model that describes PMMA flow behaviour; (b) implement this model into ANSYS using FORTRAN; and (c) validate the implementation by comparing it with analytical solutions. After the validation showed good agreement, an FE model of PMMA delivery through an eight-gauge cannula was developed to examine the extra-vertebral flow conditions of vertebroplasty. The FE analysis showed a logarithmic increase of the injection pressure, where it almost doubled from 1.2 to 2.3 MPa over two minutes. This unanticipated non-linear increase is due to the highly non-uniform viscosity profile in the cannula. It can be concluded that: (a) the rheological model implemented in ANSYS can be used to analyse practical flow problems related to PMMA and (b) time and shear-rate effects of PMMA are crucial to estimate its flow behaviour accurately.

Experimental and theoretical investigation of directional permeability of human vertebral cancellous bone for cement infiltration

The use of acrylic polymers in infiltrating the porous bone structure is an emerging procedure for the augmentation of osteoporotic vertebrae. Although this procedure is employed frequently, it is performed based on empirical knowledge, and therefore, does not take into consideration the porosity-dependent permeability of human vertebral cancellous bone. The purpose of this study was to: (a). experimentally and theoretically investigate interdependence of the vertebral cancellous bone permeability and porosity, and (b). examine if the bone permeability of spinal cancellous bone can be predicted using bone mineral density measurements. If these relations can be established, they can be useful in optimizing the injection conditions for predicable cement infiltration. To determine the porosity-dependent and directional permeability, 34 bone cores-20 samples in the superior-inferior (SI) direction and 14 in the anterior-posterior (AP) direction-were cut from 20 lumbar vertebrae and infiltrated with silicone oil with a viscosity matching that of PMMA. The permeability of the cores was determined based on Darcy's law. The mean permeability of SI and AP cores was 4.45+/-1.72 x 10(-8) and 3.44+/-1.26 x 10(-8)m(2), respectively. An interesting finding of this study was that the permeability of the AP cores was approximately 78% of that of SI cores, though the porosity of the SI and AP cores taken from the same vertebra was approximately equal. In addition, we provided a theoretical model for the porosity-dependent permeability that accurately described non-linear dependency of the bone permeability and porosity in both directions. Although the relation of the bone permeability and porosity was established, bone mineral density was a weak predictor of the bone permeability. The experimental and theoretical results of this study can be used to understand polymer flow in cement infiltration procedures.

How to determine the permeability for cement infiltration of osteoporotic cancellous bone

Cement augmentation is an emerging surgical procedure in which bone cement is used to infiltrate and reinforce osteoporotic vertebrae. Although this infiltration procedure has been widely applied, it is performed empirically and little is known about the flow characteristics of cement during the injection process. We present a theoretical and experimental approach to investigate the intertrabecular bone permeability during the infiltration procedure. The cement permeability was considered to be dependent on time, bone porosity, and cement viscosity in our analysis. In order to determine the time-dependent permeability, ten cancellous bone cores were harvested from osteoporotic vertebrae, infiltrated with acrylic cement at a constant flow rate, and the pressure drop across the cores during the infiltration was measured. The viscosity dependence of the permeability was determined based on published experimental data. The theoretical model for the permeability as a function of bone porosity and time was then fit to the testing data. Our findings suggest that the intertrabecular bone permeability depends strongly on time. For instance, the initial permeability (60.89 mm(4)/N(*)s) reduced to approximately 63% of its original value within 18 seconds. This study is the first to analyze cement flow through osteoporotic bone. The theoretical and experimental models provided in this paper are generic. Thus, they can be used to systematically study and optimize the infiltration process for clinical practice.

Hydraulic resistance and permeability in human lumbar vertebral bodies

Hydraulic resistance (HR) was measured for ten intact human lumbar vertebrae to further understand the mechanisms of fluid flow through porous bone. Oil was forced through the vertebral bodies under various volumetric flow rates and the resultant pressure was measured The pressure-flow relationship for each specimen was linear. Therefore, HR was constant with a mean of 2.22 +/- 1.45 kPa*sec/ml. The mean permeability of the intact vertebral bodies was 4.90x10(-10) +/- 4.45x10(-10) m2. These results indicate that this methodology is valid for whole bone samples and enables the exploration of the effects of HR on the creation of high-speed fractures.

Direct perfusion measurements of cancellous bone anisotropic permeability

More extensive characterization of trabecular connectivity and intertrabecular space will be instrumental in understanding disease states and designing engineered bone. This project presents an experimental protocol to define the directional dependence of transport properties as measured from healthy cancellous bone when considered as a biologic, porous medium. In the initial design phases, mature bovine bone was harvested from the femoral neck (n=6 cylinders) and distal condyle (n=4 cubes) regions and used for "proof of concept" experimentation. A power study on those results led to the presented work on 20 cubic samples (mean volume=4.09cm(3)) harvested from a single bovine distal femur. Anisotropic intrinsic permeabilities (k(i)) were quantified along the orthogonal anatomic axes (i=medial-lateral, anterior-posterior, and superior-inferior) from each individual cubic bone sample. Using direct perfusion measurements, permeability was calculated based upon Darcy's Law describing flow through porous media. The maximum mean value was associated with the superior-inferior orientation (4.65x10(-10)m(2)) in comparison with the mean anterior-posterior (4.52x10(-10)m(2)) and medial-lateral (2.33x10(-10)m(2)) direction values. The results demonstrate the anisotropic (p=0.0143) and heterogeneous (p=0.0002) nature of the tissue and encourage the ongoing quantification of parameters within the established poroelastic models.

Finite element models in tissue mechanics and orthopaedic implant design

This article attempts to review the literature on finite element modelling in three areas of biomechanics: (i) analysis of the skeleton, (ii) analysis and design of orthopaedic devices and (iii) analysis of tissue growth, remodelling and degeneration. It is shown that the method applied to bone and soft tissue has allowed researchers to predict the deformations of musculoskeletal structures and to explore biophysical stimuli within tissues at the cellular level. Next, the contribution of finite element modelling to the scientific understanding of joint replacement is reviewed. Finally, it is shown that, by incorporating finite element models into iterative computer procedures, adaptive biological processes can be simulated opening an exciting field of research by allowing scientists to test proposed 'rules' or 'algorithms' for tissue growth, adaptation and degeneration. These algorithms have been used to explore the mechanical basis of processes such as bone remodelling, fracture healing and osteoporosis. RELEVANCE: With faster computers and more reliable software, computer simulation is becoming an important tool of orthopaedic research. Future research programmes will use computer simulation to reduce the reliance on animal experimentation, and to complement clinical trials.

Measurements of permeability in human calcaneal trabecular bone

2.36 cm diameter cores of trabecular bone (n = 22), oriented in the mediolateral direction, were obtained from fresh-frozen calcanei of 16 cadavers ranging in age from 32 to 89 yr. The cores were defatted and tested to determine values for permeability along the cylinder axis. Permeability values (0.4-11 x 10(-9)m2) were found to be strongly correlated with specimen porosity (78-92%) through a linear relationship (r2 = 0.91). These results provide essential information for the biphasic or poroelastic modeling of fluid-filled trabecular bone at this location.

Poroelastic creep response analysis of a lumbar motion segment in compression

The nonlinear three-dimensional poroelastic creep response of a lumbar motion segment under a constant axial compression (400, 1200, or 2000 N) is investigated for a period of 2 h. The role of facet joints, strain-dependent variable permeability, boundary pore pressure, and coupled sagittal rotation on response is studied. Biomechanics of annulus excision, nucleotomy, and facetectomy are also investigated. Both material and geometric nonlinearities are considered. The annulus bulk is modelled as a nonhomogeneous composite of collagenous fibers and annulus bulk. As time progresses, axial displacement increases, pore pressure decreases, annulus bulk undergoes larger compressive stresses, fiber layers become slack, and facets carry larger loads. Surgical alterations markedly soften the temporal response and increase facets forces. In contrast, the strain-dependent variable permeability and boundary pore pressure stiffen the response and decrease forces on the facets. Changes in the nucleus fluid content, facet joints, boundary pore pressure, and disc permeability markedly influence the lumbar biomechanics.