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

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.

On the characteristics of natural hydraulic dampers: An image-based approach to study the fluid flow behaviour inside the human meniscal tissue

The meniscal tissue is a layered material with varying properties influenced by collagen content and arrangement. Understanding the relationship between structure and properties is crucial for disease management, treatment development, and biomaterial design. The internal layer of the meniscus is softer and more deformable than the outer layers, thanks to interconnected collagen channels that guide fluid flow. To investigate these relationships, we propose an integrated approach that combines Computational Fluid Dynamics (CFD) with Image Analysis (CFD-IA). We analyze fluid flow in the internal architecture of the human meniscus across a range of inlet velocities (0.1 mm/s to 1.6 m/s) using high-resolution 3D micro-computed tomography scans. Statistical correlations are observed between architectural parameters (tortuosity, connectivity, porosity, pore size) and fluid flow parameters (Re number distribution, permeability). Some channels exhibit Re values of 1400 at an inlet velocity of 1.6 m/s, and a transition from Darcy's regime to a non-Darcian regime occurs around an inlet velocity of 0.02 m/s. Location-dependent permeability ranges from 20-32 Darcy. Regression modelling reveals a strong correlation between fluid velocity and tortuosity at high inlet velocities, as well as with channel diameter at low inlet velocities. At higher inlet velocities, flow paths deviate more from the preferential direction, resulting in a decrease in the concentration parameter by an average of 0.4. This research provides valuable insights into the fluid flow behaviour within the meniscus and its structural influences. 3D models and image stack are available to download at https://doi.org/10.5281/zenodo.10401592. STATEMENT OF SIGNIFICANCE: The meniscus is a highly porous soft tissue with remarkable properties of load transfer and energy absorption. We give insight on the mechanism of energy absorption from high resolution uCT scans, never presented before, and a new method which combine CFD and image. The structure is similar to a sandwich structure with a stiff outside layer and a soft internal layer made of collagen channels oriented in a preferential direction guiding the fluid flow, enabling it to accommodate deformation and dissipate energy, making it a potentially optimized damping system. We investigate architectural/ fluid flow parameters- fluid regimes relationship, which is of interest of the readers working on designing suitable biomimetic systems that can be adopted for replacement.

The impact of vascular volume fraction and compressibility of the interstitial matrix on vascularised poroelastic tissues

In this work we address the role of the microstructural properties of a vascularised poroelastic material, characterised by the coupling between a poroelastic matrix and a viscous fluid vessels network, on its overall response in terms of pressures, velocities and stress maps. We embrace the recently developed model (Penta and Merodio in Meccanica 52(14):3321-3343, 2017) as a theoretical starting point and present the results obtained by solving the full interplay between the microscale, represented by the intervessels' distance, and the macroscale, representing the size of the overall tissue. We encode the influence of the vessels' density and the poroelastic matrix compressibility in the poroelastic coefficients of the model, which are obtained by solving appropriate periodic cell problem at the microscale. The double-poroelastic model (Penta and Merodio 2017) is then solved at the macroscale in the context of vascular tumours, for different values of vessels' walls permeability. The results clearly indicate that improving the compressibility of the matrix and decreasing the vessels' density enhances the transvascular pressure difference and hence transport of fluid and drug within a tumour mass after a transient time. Our results suggest to combine vessel and interstitial normalization in tumours to allow for better drug delivery into the lesions.

Combined computational analysis and cytology show limited depth osteogenic effect on bone defects in negative pressure wound therapy

Background: The treatment of bone defects remains a clinical challenge. The effect of negative pressure wound therapy (NPWT) on osteogenesis in bone defects has been recognized; however, bone marrow fluid dynamics under negative pressure (NP) remain unknown. In this study, we aimed to examine the marrow fluid mechanics within trabeculae by computational fluid dynamics (CFD), and to verify osteogenic gene expression, osteogenic differentiation to investigate the osteogenic depth under NP. Methods: The human femoral head is scanned using micro-CT to segment the volume of interest (VOI) trabeculae. The VOI trabeculae CFD model simulating the bone marrow cavity is developed by combining the Hypermesh and ANSYS software. The effect of trabecular anisotropy is investigated, and bone regeneration effects are simulated under NP scales of -80, -120, -160, and -200 mmHg. The working distance (WD) is proposed to describe the suction depth of the NP. Finally, gene sequence analysis, cytological experiments including bone mesenchymal stem cells (BMSCs) proliferation and osteogenic differentiation are conducted after the BMSCs are cultured under the same NP scale. Results: The pressure, shear stress on trabeculae, and marrow fluid velocity decrease exponentially with an increase in WD. The hydromechanics of fluid at any WD inside the marrow cavity can be theoretically quantified. The NP scale significantly affects the fluid properties, especially those fluid close to the NP source; however, the effect of the NP scale become marginal as WD deepens. Anisotropy of trabecular structure coupled with the anisotropic hydrodynamic behavior of bone marrow; An NP of -120 mmHg demonstrates the majority of bone formation-related genes, as well as the most effective proliferation and osteogenic differentiation of BMSCs compared to the other NP scales. Conclusion: An NP of -120 mmHg may have the optimal activated ability to promote osteogenesis, but the effective WD may be limited to a certain depth. These findings help improve the understanding of fluid mechanisms behind NPWT in treating bone defects.

A digital twin for simulating the vertebroplasty procedure and its impact on mechanical stability of vertebra in cancer patients

We present the application of ReconGAN, introduced in a previous study, for simulating the vertebroplasty (VP) operation and its impact on the fracture response of a vertebral body. ReconGAN consists of a Deep Convolutional Generative Adversarial Network (DCGAN) and a finite element based shape optimization algorithm to virtually reconstruct the trabecular bone microstructure. The VP procedure involves injecting shear-thinning liquid bone cement through a needle in the trabecular region to reinforce a diseased or fractured vertebra. To simulate this treatment modality, computational fluid dynamics (CFD) is employed to predict the morphology of the injected cement within the bone microstructure. A power-law equation is utilized to characterize the non-Newtonian shear-thinning behavior of the polymethyl methacrylate (PMMA) bone cement during injection simulations. The CFD model is coupled with the level-set method to simulate the motion of the interface separating bone cement and bone marrow. After predicting the cement morphology, a data co-registration algorithm is employed to transform the CFD model to a high-fidelity continuum damage mechanics (CDM) finite element model of the augmented vertebra for predicting the fracture response. A feasibility study is presented to demonstrate the ability of this CFD-CDM framework to investigate the effect of VP on the mechanical integrity of the vertebral body in a cancer patient with a lytic metastatic tumor.

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.

Cement augmentation of odontoid peg fractures: the effect of cement volume and distribution on construct stiffness

PURPOSE

The cement augmentation of a conventional anterior screw fixation in type II odontoid process fractures for elderly patients significantly increased stiffness and load to failure under anterior-posterior load in comparison with non-augmented fixation. The amount and quality of bone cement are usually taken ad hoc in clinical practise. In this study, we wanted to clarify the role of bone cement amount and its quality to the stiffness of odontoid and vertebrae body junction.

METHODS

Finite-element method was used to achieve different scenarios of cement augmentation. For all models, an initial stiffness was calculated. Model (1) the intact vertebrae were virtually potted into a polymethylmethacrylate base via the posterior vertebral arches. A V-shaped punch was used for loading the odontoid in an anterior-posterior direction. (2) The odontoid fracture type IIa (Anderson-D'Alonzo classification) was achieved by virtual transverse osteotomy. Anterior screw fixation was virtually performed by putting self-drilling titanium alloy 3.5 mm diameter anterior cannulated lag screw with a 12 mm thread into the inspected vertebrae. A V-shaped punch was used for loading the odontoid in an anterior-posterior direction. The vertebrae body was assumed to be non-cemented and cemented with different volume.

RESULTS

The mean cement volume was lowest for body base filling with 0.47 ± 0.03 ml. The standard body filling corresponds to 0.95 ± 0.15 ml. The largest volume corresponds to 1.62 ± 0.12 ml in the presence of cement leakage. The initial stiffness of the intact C2 vertebrae was taken as the reference value. The mean initial stiffness for non-porous cement (E = 3000 MPa) increased linearly (R2 = 0.98). The lowest stiffness (123.3 ± 5.8 N/mm) was measured in the intact C2 vertebrae. However, the highest stiffness (165.2 ± 5.2 N/mm) was measured when cement leakage out of the odontoid peg occurred. The mean initial stiffness of the base-only cemented group was 147.2 ± 8.4 N/mm compared with 157.9 ± 6.6 N/mm for the base and body cemented group. This difference was statistically significant (p < 0.0061). The mean initial stiffness for porous cement (E = 500 MPa) remains constant. Therefore, there is no difference between cemented and non-cemented junction. This difference was not statistically significant (p < 0.18).

CONCLUSION

The present study showed that the low porous cement was able to significantly influence the stiffness of the augmented odontoid screw fixation in vitro, although further in vivo clinical studies should be undertaken. Our results suggest that only a small amount of non-porous cement is needed to restore stiffness at least to its pre-fracture level and this can be achieved with the injection of 0.7-1.2 ml of cement. These slides can be retrieved under Electronic Supplementary Material.

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.

Computer Simulation and Analysis on Flow Characteristics and Distribution Patterns of Polymethylmethacrylate in Lumbar Vertebral Body and Vertebral Pedicle

This study was designed to analyze the flow and distribution of polymethylmethacrylate (PMMA) in vertebral body through computer simulation. Cadaveric lumbar vertebrae were scanned through electron beam tomography (EBT). The data was imported into Mimics software to build computational model. Vertebral body center and junction of pedicle and vertebral body were chosen as injection points. Silicone oil with viscosity of 100,000 cSt matching with PMMA bone cement was chosen for injection. The flow and distribution of silicone oil were analyzed using Fluent software. In vertebral body, silicone oil formed a circle-like shape centered by injection point on transverse and longitudinal sections, finally forming a sphere-like shape as a whole. Silicone oil diffused along lateral and posterior walls forming a circle-like shape on transverse section centered by injection point in pedicle, eventually forming a sphere-like shape as a whole. This study demonstrated that silicone oil flowed and diffused into a circle-like shape centered by injection point and finally formed a sphere-like shape as a whole in both vertebral body and pedicle. The flow and distribution of silicon oil in computational model could simulate PMMA distribution in vertebral body. It may provide theoretical evidence to reduce PMMA leakage risk during percutaneous vertebroplasty.

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.

Is trabecular bone permeability governed by molecular ordering-induced fluid viscosity gain? Arguments from re-evaluation of experimental data in the framework of homogenization theory

It is generally agreed on that trabecular bone permeability, a physiologically important quantity, is governed by the material׳s (vascular or intertrabecular) porosity as well as by the viscosity of the pore-filling fluids. Still, there is less agreement on how these two key factors govern bone permeability. In order to shed more light onto this somewhat open issue, we here develop a random homogenization scheme for upscaling Poiseuille flow in the vascular porosity, up to Darcy-type permeability of the overall porous medium "trabecular bone". The underlying representative volume element of the macroscopic bone material contains two types of phases: a spherical, impermeable extracellular bone matrix phase interacts with interpenetrating cylindrical pore channel phases that are oriented in all different space directions. This type of interaction is modeled by means of a self-consistent homogenization scheme. While the permeability of the bone matrix equals to zero, the permeability of the pore phase is found through expressing the classical Hagen-Poiseuille law for laminar flow in the format of a "micro-Darcy law". The upscaling scheme contains pore size and porosity as geometrical input variables; however, they can be related to each other, based on well-known relations between porosity and specific bone surface. As two key results, validated through comprehensive experimental data, it appears (i) that the famous Kozeny-Carman constant (which relates bone permeability to the cube of the porosity, the square of the specific surface, as well as to the bone fluid viscosity) needs to be replaced by an again porosity-dependent rational function, and (ii) that the overall bone permeability is strongly affected by the pore fluid viscosity, which, in case of polarized fluids, is strongly increased due to the presence of electrically charged pore walls.

Numerical model for intraosseous infusion of the human calvarium for hydrocephalus shunting

Hydrocephaly is the defective absorption of cerebrospinal fluid (CSF) into the blood stream. This work is an experimental and computational fluid dynamic modelling study to determine the permeability of the diploë as a potential receptor for CSF. Human calvariae were studied by micro-CT to measure their porosity, the area of flow and develop model geometry. Pressure-flow measurements were conducted on specimens to determine their permeability in the physiological and transverse flow directions to compare with numerical results. The overall porosity and permeability of the calvaria were spatially variable. Results suggest an order of magnitude increase in permeability for a 14% increase in overall porosity based on a small number of samples. Numerical results fell within the experimental infusion tests results. Due to the difficulty and ethical considerations in obtaining adolescent skull samples to perform large-scale testing, the developed model will be invaluable.