Computational modeling of flow-induced shear stresses within 3D salt-leached porous scaffolds imaged via micro-CT

Prediction of the aggregation rate of nanoparticles in porous media in the diffusion-controlled regime

The fate and aggregation of nanoparticles (NPs) in the subsurface are important due to potentially harmful impacts on the environment and human health. This study aims to investigate the effects of flow velocity, particle size, and particle concentration on the aggregation rate of NPs in a diffusion-limited regime and build an equation to predict the aggregation rate when NPs move in the pore space between randomly packed spheres (including mono-disperse, bi-disperse, and tri-disperse spheres). The flow of 0.2 M potassium chloride (KCl) through the random sphere packings was simulated by the lattice Boltzmann method (LBM). The movement and aggregation of cerium oxide (CeO2) particles were then examined by using a Lagrangian particle tracking method based on a force balance approach. This method relied on Newton's second law of motion and took the interaction forces among particles into account. The aggregation rate of NPs was found to depend linearly on time, and the slope of the line was a power function of the particle concentration, the Reynolds (Re) and Schmidt (Sc) numbers. The exponent for the Sc number was triple that of the Re number, which was evidence that the random movement of NPs has a much stronger effect on the rate of diffusion-controlled aggregation than the convection.

Aggregation of nanoparticles and morphology of aggregates in porous media with computations

HYPOTHESIS

The main hypothesis is that the aggregation process for nanoparticles (NPs) propagating in porous media is affected by the structure of the flow field as well as by the properties of the primary NPs. If this were true, then the aggregation could be predicted and controlled. However, to obtain reliable results from computations, one needs to account for the interactions between the NPs as well as the details of the fluid velocity, thus making advances over prior efforts that either ignored the aggregation of NPs, or used probabilistic methods to model aggregation.

EXPERIMENTS

Computational experiments were conducted using the lattice Boltzmann method in conjunction with Lagrangian particle tracking (LPT). The LPT accounted for the physicochemical interaction forces among NPs. Computationally obtained aggregation kinetics and fractal dimensions of Cerium oxide (CeO2) particles, suspended in potassium chloride (KCl) solutions with different concentration, were verified against experimental results. The model was then employed to investigate the effects of ionic strength, fluid velocity, and particle size on the aggregation kinetics and the aggregate morphology, as NPs propagated in the pore space between randomly packed spheres.

FINDINGS

The aim of this study was to develop a computational model to simulate the aggregation of NPs and obtain the morphology of aggregates in confined geometries, based on the physics of NP interactions and the flow field. The most important factor that impacted both the aggregation process and the aggregate structure was found to be the concentration of the electrolyte. The pore velocity influenced the aggregation kinetics and the NP fractal dimension, especially in diffusion-limited aggregation. The primary particle size affected the diffusion-limited aggregation kinetics and the fractal dimension of reaction-limited aggregates noticeably.

Perfusion of MC3T3E1 Preosteoblast Spheroids within Polysaccharide-Based Hydrogel Scaffolds: An Experimental and Numerical Study at the Bioreactor Scale

The traditional 3D culture systems in vitro lack the biological and mechanical spatiotemporal stimuli characteristic to native tissue development. In our study, we combined porous polysaccharide-based hydrogel scaffolds with a bioreactor-type perfusion device that generates favorable mechanical stresses while enhancing nutrient transfers. MC3T3E1 mouse osteoblasts were seeded in the scaffolds and cultivated for 3 weeks under dynamic conditions at a perfusion rate of 10 mL min^-1. The spatial distribution of the cells labeled with superparamagnetic iron oxide nanoparticles was visualized by MRI. Confocal microscopy was used to assess cell numbers, their distribution inside the scaffolds, cell viability, and proliferation. The oxygen diffusion coefficient in the hydrogel was measured experimentally. Numerical simulations of the flow and oxygen transport within the bioreactor were performed using a lattice Boltzmann method with a two-relaxation time scheme. Last, the influence of cell density and spheroid size on cell oxygenation was investigated. The cells spontaneously organized into spheroids with a diameter of 30-100 μm. Cell viability remained unchanged under dynamic conditions but decreased under static culture. The cell proliferation (Ki67 expression) in spheroids was not observed. The flow simulation showed that the local fluid velocity reached 27 mm s^-1 at the height where the cross-sectional area of the flow was the smallest. The shear stress exerted by the fluid on the scaffolds may locally rise to 100 mPa, compared with the average value of 25 mPa. The oxygen diffusion coefficient in the hydrogel was 1.6×10-9 m² s^-1. The simulation of oxygen transport and consumption confirmed that the cells in spheroids did not suffer from hypoxia when the bioreactor was perfused at 10 mL min^-1, and suggested the existence of optimal spheroid size and spacing for appropriate oxygenation. Collectively, these findings enabled us to define the optimal conditions inside the bioreactor for an efficient in vitro cell organization and survival in spheroids, which are paramount to future applications with organoids.

A tissue engineered 3D printed calcium alkali phosphate bioceramic bone graft enables vascularization and regeneration of critical-size discontinuity bony defects in vivo

Introduction: Recently, efforts towards the development of patient-specific 3D printed scaffolds for bone tissue engineering from bioactive ceramics have continuously intensified. For reconstruction of segmental defects after subtotal mandibulectomy a suitable tissue engineered bioceramic bone graft needs to be endowed with homogenously distributed osteoblasts in order to mimic the advantageous features of vascularized autologous fibula grafts, which represent the standard of care, contain osteogenic cells and are transplanted with the respective blood vessel. Consequently, inducing vascularization early on is pivotal for bone tissue engineering. The current study explored an advanced bone tissue engineering approach combining an advanced 3D printing technique for bioactive resorbable ceramic scaffolds with a perfusion cell culture technique for pre-colonization with mesenchymal stem cells, and with an intrinsic angiogenesis technique for regenerating critical size, segmental discontinuity defects in vivo applying a rat model. To this end, the effect of differing Si-CAOP (silica containing calcium alkali orthophosphate) scaffold microarchitecture arising from 3D powder bed printing (RP) or the Schwarzwalder Somers (SSM) replica fabrication technique on vascularization and bone regeneration was analyzed in vivo. In 80 rats 6-mm segmental discontinuity defects were created in the left femur. Methods: Embryonic mesenchymal stem cells were cultured on RP and SSM scaffolds for 7d under perfusion to create Si-CAOP grafts with terminally differentiated osteoblasts and mineralizing bone matrix. These scaffolds were implanted into the segmental defects in combination with an arteriovenous bundle (AVB). Native scaffolds without cells or AVB served as controls. After 3 and 6 months, femurs were processed for angio-µCT or hard tissue histology, histomorphometric and immunohistochemical analysis of angiogenic and osteogenic marker expression. Results: At 3 and 6 months, defects reconstructed with RP scaffolds, cells and AVB displayed a statistically significant higher bone area fraction, blood vessel volume%, blood vessel surface/volume, blood vessel thickness, density and linear density than defects treated with the other scaffold configurations. Discussion: Taken together, this study demonstrated that the AVB technique is well suited for inducing adequate vascularization of the tissue engineered scaffold graft in segmental defects after 3 and 6 months, and that our tissue engineering approach employing 3D powder bed printed scaffolds facilitated segmental defect repair.

Influence of the injection of densified polymer suspension on the efficiency of DNAPL displacement in contaminated saturated soils

Nowadays the remediation of DNAPL contaminated zones near groundwater has gained great prominence in environmental fields due to the high importance of water resources. In this work, we suggest injecting a densified polymer suspension by adding barite particles to displace DNAPL. To evaluate the efficiency of the densification of polymer suspensions on the displacement of DNAPL, various densities of barite-polymer suspension; lower, equal, and higher than the density of DNAPL were prepared and their rheological behavior was analyzed. Then flow experiments were performed using a decimetric-scale 2D tank. The displacement procedure was monitored with an imaging technique and the production and injection process data were recorded by mass balance interpretation. It was shown that the densification of the polymer suspension could improve the displacement efficiency of DNAPL up to four times. The clogging behavior of barite-polymer suspension was assessed in a 1D column. Generalized Darcy's law and the continuity equation were used to numerically simulate the experimental two-phase flow. To take into account the clogging behavior of the suspension, the transport equation of diluted species was implemented into the model. The simulation results show that the model can properly predicts the experimental consequences.

Numerical Modelling of Reactive Flows through Porous Media

We consider a lattice Boltzmann (LB) model to solve the coupled Navier–Stokes and advection–diffusion equation with reactive boundary conditions at the interface between fluid and solid domains. The reactive boundary condition results in the position of the boundary changing continuously, and so boundary nodes may be partially filled with fluid at any instant. We develop the LB boundary conditions for both the velocity and concentration fields in the presence of partially filled boundary nodes and then validate this algorithm on some test cases—the Stefan problem for diffusion-dominated dissolution and kinetic-dominated dissolution. It is shown that the developed model agrees well with analytic results, so that they can be used for more general boundaries of arbitrary shape. Numerical simulations in three dimensions are then carried out on demonstration problems at various Peclet numbers to elucidate the transport mechanisms and their influence on solid grain dissolution.

Investigating Cancerous Exosomes’ Effects on CD8+ T-Cell IL-2 Production in a 3D Unidirectional Flow Bioreactor Using 3D Printed, RGD-Functionalized PLLA Scaffolds

Exosomes from cancer cells are implicated in cancer progression and metastasis, carrying immunosuppressive factors that limit the antitumor abilities of immune cells. The development of a real-time, 3D cell/scaffold construct flow perfusion system has been explored as a novel tool in the study of T-cells and exosomes from cancer cells. Exosomes from human lung cancer (H1299 and A549) cells were co-cultured in a unidirectional flow bioreactor with CD8+ T-cells immobilized onto 3D-printed RGD-functionalized poly(L-lactic) acid (PLLA) scaffolds and assessed for IL-2 production. The IL-2 production was investigated for a wide range of T-cell to exosome ratios. With the successful incorporation of the RGD binding motif onto the PLLA surface at controllable densities, CD8+ T-cells were successfully attached onto 2D disks and 3D printed porous PLLA scaffolds. T-cell attachment increased with increasing RGD surface density. The diameter of the attached T-cells was 7.2 ± 0.2 µm for RGD densities below 0.5 nmoles/mm2 but dropped to 5.1 ± 0.3 µm when the RGD density was 2 nmoles/mm2 due to overcrowding. The higher the number of cancer exosomes, the less the IL-2 production by the surface-attached T-cells. In 2D disks, the IL-2 production was silenced for T-cell to exosome ratios higher than 1:10 in static conditions. IL-2 production silencing in static 3D porous scaffolds required ratios higher than 1:20. The incorporation of flow resulted in moderate to significant T-cell detachment. The portions of T-cells retained on the 3D scaffolds after exposure for 4 h to 0.15 or 1.5 mL/min of perfusion flow were 89 ± 11% and 30 ± 8%, respectively. On 3D scaffolds and in the presence of flow at 0.15 ml/min, both H1299 and A549 cancerous exosomes significantly suppressed IL-2 production for T-cell to exosome ratios of 1:1000. The much higher level of exosomes needed to silence the IL-2 production from T-cells cultured under unidirectional flow, compared to static conditions, denotes the importance of the culturing conditions and the hydrodynamic environment, on the interactions between CD8+ T-cells and cancer exosomes.

Computational Simulation of Exosome Transport in Tumor Microenvironment

Cellular exosome-mediated crosstalk in tumor microenvironment (TME) is a critical component of anti-tumor immune responses. In addition to particle size, exosome transport and uptake by target cells is influenced by physical and physiological factors, including interstitial fluid pressure, and exosome concentration. These variables differ under both normal and pathological conditions, including cancer. The transport of exosomes in TME is governed by interstitial flow and diffusion. Based on these determinants, mathematical models were adapted to simulate the transport of exosomes in the TME with specified exosome release rates from the tumor cells. In this study, the significance of spatial relationship in exosome-mediated intercellular communication was established by treating their movement in the TME as a continuum using a transport equation, with advection due to interstitial flow and diffusion due to concentration gradients. To quantify the rate of release of exosomes by biomechanical forces acting on the tumor cells, we used a transwell platform with confluent triple negative breast cancer cells 4T1.2 seeded in BioFlex plates exposed to an oscillatory force. Exosome release rates were quantified from 4T1.2 cells seeded at the bottom of the well following the application of either no force or an oscillatory force, and these rates were used to model exosome transport in the transwell. The simulations predicted that a larger number of exosomes reached the membrane of the transwell for 4T1.2 cells exposed to the oscillatory force when compared to controls. Additionally, we simulated the interstitial fluid flow and exosome transport in a 2-dimensional TME with macrophages, T cells, and mixtures of these two populations at two different stages of a tumor growth. Computational simulations were carried out using the commercial computational simulation package, ANSYS/Fluent. The results of this study indicated higher exosome concentrations and larger interstitial fluid pressure at the later stages of the tumor growth. Quantifying the release of exosomes by cancer cells, their transport through the TME, and their concentration in TME will afford a deeper understanding of the mechanisms of these interactions and aid in deriving predictive models for therapeutic intervention.

Inlet flow rate of perfusion bioreactors affects fluid flow dynamics, but not oxygen concentration in 3D-printed scaffolds for bone tissue engineering: Computational analysis and experimental validation

Fluid flow dynamics and oxygen-concentration in 3D-printed scaffolds within perfusion bioreactors are sensitive to controllable bioreactor parameters such as inlet flow rate. Here we aimed to determine fluid flow dynamics, oxygen-concentration, and cell proliferation and distribution in 3D-printed scaffolds as a result of different inlet flow rates of perfusion bioreactors using experiments and finite element modeling. Pre-osteoblasts were treated with 1 h pulsating fluid flow with low (0.8 Pa; PFF^low) or high peak shear stress (6.5 Pa; PFF^high), and nitric oxide (NO) production was measured to validate shear stress sensitivity. Computational analysis was performed to determine fluid flow between 3D-scaffold-strands at three inlet flow rates (0.02, 0.1, 0.5 ml/min) during 5 days. MC3T3-E1 pre-osteoblast proliferation, matrix production, and oxygen-consumption in response to fluid flow in 3D-printed scaffolds inside a perfusion bioreactor were experimentally assessed. PFF^high more strongly stimulated NO production by pre-osteoblasts than PFF^low. 3D-simulation demonstrated that dependent on inlet flow rate, fluid velocity reached a maximum (50-1200 μm/s) between scaffold-strands, and fluid shear stress (0.5-4 mPa) and wall shear stress (0.5-20 mPa) on scaffold-strands surfaces. At all inlet flow rates, gauge fluid pressure and oxygen-concentration were similar. The simulated cell proliferation and distribution, and oxygen-concentration data were in good agreement with the experimental results. In conclusion, varying a perfusion bioreactor's inlet flow rate locally affects fluid velocity, fluid shear stress, and wall shear stress inside 3D-printed scaffolds, but not gauge fluid pressure, and oxygen-concentration, which seems crucial for optimized bone tissue engineering strategies using bioreactors, scaffolds, and cells.

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.

Hydrodynamic Dispersion in Porous Media and the Significance of Lagrangian Time and Space Scales

Transport in porous media is critical for many applications in the environment and in the chemical process industry. A key parameter for modeling this transport is the hydrodynamic dispersion coefficient for particles and scalars in a porous medium, which has been found to depend on properties of the medium structure, on the dispersing compound, and on the flow field characteristics. Previous studies have resulted in suggestions of different equation forms, showing the relationship between the hydrodynamic dispersion coefficient for various types of porous media in various flow regimes and the Peclet number. The Peclet number is calculated based on a Eulerian length scale, such as the diameter of the spheres in packed beds, or the pore diameter. However, the nature of hydrodynamic dispersion is Lagrangian, and it should take the molecular diffusion effects, as well as the convection effects, into account. This work shifts attention to the Lagrangian time and length scales for the definition of the Peclet number. It is focused on the dependence of the longitudinal hydrodynamic dispersion coefficient on the effective Lagrangian Peclet number by using a Lagrangian length scale and the effective molecular diffusivity. The lattice Boltzmann method (LBM) was employed to simulate flow in porous media that were constituted by packed spheres, and Lagrangian particle tracking (LPT) was used to track the movement of individual dispersing particles. It was found that the hydrodynamic dispersion coefficient linearly depends on the effective Lagrangian Peclet number for packed beds with different types of packing. This linear equation describing the dependence of the dispersion coefficient on the effective Lagrangian Peclet number is both simpler and more accurate than the one formed using the effective Eulerian Peclet number. In addition, the slope of the line is a characteristic coefficient for a given medium.

Simulation of circulating tumor cell transport and adhesion in cell suspensions in microfluidic devices

Understanding cell transport and adhesion dynamics under flow is important for many biotransport problems. We investigated the influence of cell size, ligand coating density, micropost size, and intercellular collisions on circulating tumor cell adhesion and transport in microfluidic devices. The cells were modeled as coarse-grained cell membranes and the adhesion was modeled as pairwise interacting potentials, while the fluid was solved using the lattice Boltzmann method. The coupling between the cell and the fluid was achieved through the immersed boundary method. The cell showed transient rolling adhesion in high shear regions and firm adhesion in low shear regions. The adhesive force for rolling cells on a micropost was increasing before the cell reached the crest of the post and then decreasing afterward. The adhesive strength for cells increases with ligand coating density. Cell trajectories in a microfluidic device with a shifted post design were studied as well. At low concentrations, the majority of the cells follow streamlines closely. However, the intercellular collision and collision from red blood cells impacted the cell trajectories. An L 2 norm of | e | was defined to characterize the difference between the cell trajectories and the associated streamlines. It was shown that | e | L 2 increases with micropost sizes and cell concentrations.

Strategy for achieving standardized bone models

Reliably producing functional in vitro organ models, such as organ-on-chip systems, has the potential to considerably advance biology research, drug development time, and resource efficiency. However, despite the ongoing major progress in the field, three-dimensional bone tissue models remain elusive. In this review, we specifically investigate the control of perfusion flow effects as the missing link between isolated culture systems and scientifically exploitable bone models and propose a roadmap toward this goal.

Continuum Modeling and Simulation in Bone Tissue Engineering

Bone tissue engineering is currently a mature methodology from a research perspective. Moreover, modeling and simulation of involved processes and phenomena in BTE have been proved in a number of papers to be an excellent assessment tool in the stages of design and proof of concept through in-vivo or in-vitro experimentation. In this paper, a review of the most relevant contributions in modeling and simulation, in silico, in BTE applications is conducted. The most popular in silico simulations in BTE are classified into: (i) Mechanics modeling and scaffold design, (ii) transport and flow modeling, and (iii) modeling of physical phenomena. The paper is restricted to the review of the numerical implementation and simulation of continuum theories applied to different processes in BTE, such that molecular dynamics or discrete approaches are out of the scope of the paper. Two main conclusions are drawn at the end of the paper: First, the great potential and advantages that in silico simulation offers in BTE, and second, the need for interdisciplinary collaboration to further validate numerical models developed in BTE.

Assessment of the interplay between scaffold geometry, induced shear stresses, and cell proliferation within a packed bed perfusion bioreactor

By favoring cell proliferation and differentiation, perfusion bioreactors proved efficient at optimizing cell culture. The aim of this study was to quantify cell proliferation within a perfusion bioreactor and correlate it to the wall shear stress (WSS) distribution by combining 3-D imaging and computational fluid dynamics simulations.NIH-3T3 fibroblasts were cultured onto a scaffold model made of impermeable polyacetal spheres or Polydimethylsiloxane cubes. After 1, 2, and 3 weeks of culture, constructs were analyzed by micro-computed tomography (μCT) and quantification of cell proliferation was assessed. After 3 weeks, the volume of cells was found four times higher in the stacking of spheres than in the stacking of cube.3D-μCT reconstruction of bioreactors was used as input for the numerical simulations. Using a lattice-Boltzmann method, we simulated the fluid flow within the bioreactors. We retrieved the WSS distribution (PDF) on the scaffolds surface at the beginning of cultivation and correlated this distribution to the local presence of cells after 3 weeks of cultivation. We found that the WSS distributions strongly differ between spheres and cubes even if the porosity and the specific wetted area of the stackings were very similar. The PDF is narrower and the mean WSS is lower for cubes (11 mPa) than for spheres (20 mPa). For the stacking of spheres, the relative occupancy of the surface sites by cells is maximal when WSS is greater than 20 mPa. For cubes, the relative occupancy is maximal when the WSS is lower than 10 mPa. The discrepancies between spheres and cubes are attributed to the more numerous sites in stacking of spheres that may induce 3-D (multi-layered) proliferation.

Scaffolds with a High Surface Area-to-Volume Ratio and Cultured Under Fast Flow Perfusion Result in Optimal O2 Delivery to the Cells in Artificial Bone Tissues

Tissue engineering has the potential for repairing large bone defects, which impose a heavy financial burden on the public health. However, difficulties with O2 delivery to the cells residing in the interior of tissue engineering scaffolds make it challenging to grow artificial tissues of clinically-relevant sizes. This study uses image-based simulation in order to provide insight into how to better optimize the scaffold manufacturing parameters, and the culturing conditions, in order to resolve the O2 bottleneck. To do this, high resolution 3D X-ray images of two common scaffold types (salt leached foam and non-woven fiber mesh) are fed into Lattice Boltzmann Method fluid dynamics and reactive Lagrangian Scalar Tracking mass transfer solvers. The obtained findings indicate that the scaffolds should have maximal surface area-to-solid volume ratios for higher chances of the molecular collisions with the cells. Furthermore, the cell culture media should be flown through the scaffold pores as fast as practically possible (without detaching or killing the cells). Finally, we have provided a parametric sweep that maps how the molecular transport within the scaffolds is affected by variations in rates of O2 consumption by the cells. Ultimately, the results of this study are expected to benefit the computer-assisted design of tissue engineering scaffolds and culturing experiments.

Effect of scaffold architecture on cell seeding efficiency: A discrete phase model CFD analysis

Within perfusion cell culture systems, scaffold architecture is able to control important biological parameters such as permeability and fluid flow-induced shear stress. As well, one of the main factors affecting the final fate of this process as well as optimal cell differentiation and proliferation in these systems is initial adhesion of cells to scaffolds. In this study, the effect of scaffold architecture on the adhesion of the cells was computationally investigated. For this purpose, four scaffold models including double-diamond, gyroid, FR-D, and Schwarz-primitive were designed using triply periodic minimal surface (TPMS) geometry with a constant porosity of 80%. As well, the inlet velocity of zero to simulate static cell culture and three different inlet velocities for modeling the dynamic cell culture conditions were also selected. The results showed that cell culture efficiency of scaffolds could be changed up to seven times from architecture to architecture under the same conditions. The efficiency of cell culture in scaffolds with tortuous architecture was also reported higher than those with relatively straight microchannels. In terms of culture methods, unlike dynamic cell culture model in which almost a homogeneous cell distribution was observed in static cell culture simulation, more cells adhered, but they had agglomerated in the scaffold entrance regions and had failed to reach all regions. The results of this study shed more light on the selection and design of scaffold architecture for optimal cell culture in tissue engineering.

Histological Method to Study the Effect of Shear Stress on Cell Proliferation and Tissue Morphology in a Bioreactor

Background

Tissue engineering represents a promising approach for the production of bone substitutes. The use of perfusion bioreactors for the culture of bone-forming cells on a three-dimensional porous scaffold resolves mass transport limitations and provides mechanical stimuli. Despite the recent and important development of bioreactors for tissue engineering, the underlying mechanisms leading to the production of bone substitutes remain poorly understood.

Methods

In order to study cell proliferation in a perfusion bioreactor, we propose a simplified experimental set-up using an impermeable scaffold model made of 2 mm diameter glass beads on which mechanosensitive cells, NIH-3T3 fibroblasts are cultured for up to 3 weeks under 10 mL/min culture medium flow. A methodology combining histological procedure, image analysis and analytical calculations allows the description and quantification of cell proliferation and tissue production in relation to the mean wall shear stress within the bioreactor.

Results

Results show a massive expansion of the cell phase after 3 weeks in bioreactor compared to static control. A scenario of cell proliferation within the three-dimensional bioreactor porosity over the 3 weeks of culture is proposed pointing out the essential role of the contact points between adjacent beads. Calculations indicate that the mean wall shear stress experienced by the cells changes with culture time, from about 50 mPa at the beginning of the experiment to about 100 mPa after 3 weeks.

Conclusion

We anticipate that our results will help the development and calibration of predictive models, which rely on estimates and morphological description of cell proliferation under shear stress.

Analysis of biomechanical behavior of 3D printed mandibular graft with porous scaffold structure designed by topological optimization

BACKGROUND

Our long-term goal is to design and manufacture a customized graft with porous scaffold structure for repairing large mandibular defects using topological optimization and 3D printing technology. The purpose of this study is to characterize the mechanical behavior of 3D printed anisotropic scaffolds as bone analogs by fused deposition modeling (FDM).

METHODS

Cone beam computed tomography (CBCT) images were used to reconstruct a 3D mandible and finite element models. A virtual sectioned-block of the mandible was used as the control group and the trabecular portion of the block was modified by topological optimization methods as experimental groups. FDM (FDM) printed samples at 0, 45 and 90 degrees with Poly-lactic acid (PLA) material under a three-point bending test. Finite element analysis was also used to validate the data obtained from the physical model tests.

RESULTS

The ultimate load, yield load, failure deflection, yield deflection, stress, strain distribution, and porosity of scaffold structures were compared. The results show that the topological optimized graft had the best mechanical properties.

CONCLUSIONS

The results from mechanical tests on physical models and numerical simulations from this study show a great potential for topological optimization and 3D printing technology to be served in design and rapidly manufacturing of artificial porous grafts.

In vivo measurement of blood clot mechanics from computational fluid dynamics based on intravital microscopy images

Ischemia which leads to heart attacks and strokes is one of the major causes of death in the world. Whether an occlusion occurs or not depends on the ability of a growing thrombus to resist flow forces exerted on its structure. This manuscript provides the first known in vivo measurement of how much stress a clot can withstand, before yielding to the surrounding blood flow. Namely, Lattice-Boltzmann Method flow simulations are performed based on 3D clot geometries, which are estimated from intravital microscopy images of laser-induced injuries in cremaster microvasculature of live mice. In addition to reporting the blood clot yield stresses, we also show that the thrombus "core" does not experience significant deformation, while its "shell" does. This indicates that the shell is more prone to embolization. Therefore, drugs should be designed to target the shell selectively, while leaving the core intact to minimize excessive bleeding. Finally, we laid down a foundation for a nondimensionalization procedure which unraveled a relationship between clot mechanics and biology. Hence, the proposed framework could ultimately lead to a unified theory of thrombogenesis, capable of explaining all clotting events. Thus, the findings presented herein will be beneficial to the understanding and treatment of heart attacks, strokes and hemophilia.

Numerical accuracy comparison of two boundary conditions commonly used to approximate shear stress distributions in tissue engineering scaffolds cultured under flow perfusion

INTRODUCTION

Flow-induced shear stresses have been found to be a stimulatory factor in pre-osteoblastic cells seeded in 3D porous scaffolds and cultured under continuous flow perfusion. However, due to the complex internal structure of the scaffolds, whole scaffold calculations of the local shear forces are computationally intensive. Instead, representative volume elements (RVEs), which are obtained by extracting smaller portions of the scaffold, are commonly used in literature without a numerical accuracy standard.

OBJECTIVE

Hence, the goal of this study is to examine how closely the whole scaffold simulations are approximated by the two types of boundary conditions used to enable the RVEs: "wall boundary condition" (WBC) and "periodic boundary condition" (PBC).

METHOD

To that end, lattice Boltzmann method fluid dynamics simulations were used to model the surface shear stresses in 3D scaffold reconstructions, obtained from high-resolution microcomputed tomography images.

RESULTS

It was found that despite the RVEs being sufficiently larger than 6 times the scaffold pore size (which is the only accuracy guideline found in literature), the stresses were still significantly under-predicted by both types of boundary conditions: between 20% and 80% average error, depending on the scaffold's porosity. Moreover, it was found that the error grew with higher porosity. This is likely due to the small pores dominating the flow field, and thereby negating the effects of the unrealistic boundary conditions, when the scaffold porosity is small. Finally, it was found that the PBC was always more accurate and computationally efficient than the WBC. Therefore, it is the recommended type of RVE.

Micro and nanotechnologies in heart valve tissue engineering

Due to the increased morbidity and mortality resulting from heart valve diseases, there is a growing demand for off-the-shelf implantable tissue engineered heart valves (TEHVs). Despite the significant progress in recent years in improving the design and performance of TEHV constructs, viable and functional human implantable TEHV constructs have remained elusive. The recent advances in micro and nanoscale technologies including the microfabrication, nano-microfiber based scaffolds preparation, 3D cell encapsulated hydrogels preparation, microfluidic, micro-bioreactors, nano-microscale biosensors as well as the computational methods and models for simulation of biological tissues have increased the potential for realizing viable, functional and implantable TEHV constructs. In this review, we aim to present an overview of the importance and recent advances in micro and nano-scale technologies for the development of TEHV constructs.

A mathematical model and computational framework for three-dimensional chondrocyte cell growth in a porous tissue scaffold placed inside a bi-directional flow perfusion bioreactor

The in vitro chondrocyte cell culture for cartilage tissue regeneration in a perfusion bioreactor is a complex process. Mathematical modeling and computational simulation can provide important insights into the culture process, which would be helpful for selecting culture conditions to improve the quality of the developed tissue constructs. However, simulation of the cell culture process is a challenging task due to the complicated interaction between the cells and local fluid flow and nutrient transport inside the complex porous scaffolds. In this study, a mathematical model and computational framework has been developed to simulate the three-dimensional (3D) cell growth in a porous scaffold placed inside a bi-directional flow perfusion bioreactor. The model was developed by taking into account the two-way coupling between the cell growth and local flow field and associated glucose concentration, and then used to perform a resolved-scale simulation based on the lattice Boltzmann method (LBM). The simulation predicts the local shear stress, glucose concentration, and 3D cell growth inside the porous scaffold for a period of 30 days of cell culture. The predicted cell growth rate was in good overall agreement with the experimental results available in the literature. This study demonstrates that the bi-directional flow perfusion culture system can enhance the homogeneity of the cell growth inside the scaffold. The model and computational framework developed is capable of providing significant insight into the culture process, thus providing a powerful tool for the design and optimization of the cell culture process.

Design, materials, and mechanobiology of biodegradable scaffolds for bone tissue engineering

A review about design, manufacture, and mechanobiology of biodegradable scaffolds for bone tissue engineering is given. First, fundamental aspects about bone tissue engineering and considerations related to scaffold design are established. Second, issues related to scaffold biomaterials and manufacturing processes are discussed. Finally, mechanobiology of bone tissue and computational models developed for simulating how bone healing occurs inside a scaffold are described.

Computational modelling of the scaffold-free chondrocyte regeneration: a two-way coupling between the cell growth and local fluid flow and nutrient concentration

The in vitro chondrocyte cell culture process in a perfusion bioreactor provides enhanced nutrient supply as well as the flow-induced shear stress that may have a positive influence on the cell growth. Mathematical and computational modelling of such a culture process, by solving the coupled flow, mass transfer and cell growth equations simultaneously, can provide important insight into the biomechanical environment of a bioreactor and the related cell growth process. To do this, a two-way coupling between the local flow field and cell growth is required. Notably, most of the computational and mathematical models to date have not taken into account the influence of the cell growth on the local flow field and nutrient concentration. The present research aimed at developing a mathematical model and performing a numerical simulation using the lattice Boltzmann method to predict the chondrocyte cell growth without a scaffold on a flat plate placed inside a perfusion bioreactor. The model considers the two-way coupling between the cell growth and local flow field, and the simulation has been performed for 174 culture days. To incorporate the cell growth into the model, a control-volume-based surface growth modelling approach has been adopted. The simulation results show the variation of local fluid velocity, shear stress and concentration distribution during the culture period due to the growth of the cell phase and also illustrate that the shear stress can increase the cell volume fraction to a certain extent.

Modelling and simulation of the chondrocyte cell growth, glucose consumption and lactate production within a porous tissue scaffold inside a perfusion bioreactor

Mathematical and numerical modelling of the tissue culture process in a perfusion bioreactor is able to provide insight into the fluid flow, nutrients and wastes transport, dynamics of the pH value, and the cell growth rate. Knowing the complicated interdependence of these processes is essential for optimizing the culture process for cell growth. This paper presents a resolved scale numerical simulation, which allows one not only to characterize the supply of glucose inside a porous tissue scaffold in a perfusion bioreactor, but also to assess the overall culture condition and predict the cell growth rate. The simulation uses a simplified scaffold that consists of a repeatable unit composed of multiple strands. The simulation results explore some problematic regions inside the simplified scaffold where the concentration of glucose becomes lower than the critical value for the chondrocyte cell viability and the cell growth rate becomes significantly reduced.

Prediction of cell growth rate over scaffold strands inside a perfusion bioreactor

Mathematical and computational modeling of the dynamic process where tissue scaffolds are cultured in perfusion bioreactors is able to provide insight into the cell and tissue growth which can facilitate the design of tissue scaffolds and selection of optimal operating conditions. To date, a resolved-scale simulation of cell growth in the culture process, by taking account of the influences of the supply of nutrients and fluid shear stress on the cells, is not yet available in the literature. This paper presents such a simulation study specifically on cartilage tissue regeneration by numerically solving the momentum, scalar transport and cell growth equations, simultaneously, based on the lattice Boltzmann method. The simulation uses a simplified scaffold that consists of two circular strands placed in tandem inside a microchannel, with the object of identifying the effect of one strand on the other. The results indicate that the presence of the front strand can reduce the cell growth rate on the surface of the rear strand, depending on the distance between them. As such, the present study allows for investigation into the influence of the scaffold geometry on the cell growth rate within scaffolds, thus providing a means to improve the scaffold design and the culture process.

Spatial optimization in perfusion bioreactors improves bone tissue-engineered construct quality attributes

Perfusion bioreactors have shown great promise for tissue engineering applications providing a homogeneous and consistent distribution of nutrients and flow-induced shear stresses throughout tissue-engineered constructs. However, non-uniform fluid-flow profiles found in the perfusion chamber entrance region have been shown to affect tissue-engineered construct quality characteristics during culture. In this study a whole perfusion and construct, three dimensional (3D) computational fluid dynamics approach was used in order to optimize a critical design parameter such as the location of the regular pore scaffolds within the perfusion bioreactor chamber. Computational studies were coupled to bioreactor experiments for a case-study flow rate. Two cases were compared in the first instance seeded scaffolds were positioned immediately after the perfusion chamber inlet while a second group was positioned at the computationally determined optimum distance were a steady state flow profile had been reached. Experimental data showed that scaffold location affected significantly cell content and neo-tissue distribution, as determined and quantified by contrast enhanced nanoCT, within the constructs both at 14 and 21 days of culture. However, gene expression level of osteopontin and osteocalcin was not affected by the scaffold location. This study demonstrates that the bioreactor chamber environment, incorporating a scaffold and its location within it, affects the flow patterns within the pores throughout the scaffold requiring therefore dedicated optimization that can lead to bone tissue engineered constructs with improved quality attributes.

Investigation of the in vitro culture process for skeletal-tissue-engineered constructs using computational fluid dynamics and experimental methods

The in vitro culture process via bioreactors is critical to create tissue-engineered constructs (TECs) to repair or replace the damaged tissues/organs in various engineered applications. In the past, the TEC culture process was typically treated as a black box and performed on the basis of trial and error. Recently, computational fluid dynamics (CFD) has demonstrated its potential to analyze the fluid flow inside and around the TECs, therefore, being able to provide insight into the culture process, such as information on the velocity field and shear stress distribution that can significantly affect such cellular activities as cell viability and proliferation during the culture process. This paper briefly reviews the CFD and experimental methods used to investigate the in vitro culture process of skeletal-type TECs in bioreactors, where mechanical deformation of the TEC can be ignored. Specifically, this paper presents CFD modeling approaches for the analysis of the velocity and shear stress fields, mass transfer, and cell growth during the culture process and also describes various particle image velocimetry (PIV) based experimental methods to measure the velocity and shear stress in the in vitro culture process. Some key issues and challenges are also identified and discussed along with recommendations for future research.

Bulk stress distributions in the pore space of sphere-packed beds under Darcy flow conditions

In this paper, bulk stress distributions in the pore space of columns packed with spheres are numerically computed with lattice Boltzmann simulations. Three different ideally packed and one randomly packed configuration of the columns are considered under Darcy flow conditions. The stress distributions change when the packing type changes. In the Darcy regime, the normalized stress distribution for a particular packing type is independent of the pressure difference that drives the flow and presents a common pattern. The three parameter (3P) log-normal distribution is found to describe the stress distributions in the randomly packed beds within statistical accuracy. In addition, the 3P log-normal distribution is still valid when highly porous scaffold geometries rather than sphere beds are examined. It is also shown that the 3P log-normal distribution can describe the bulk stress distribution in consolidated reservoir rocks like Berea sandstone.

Micro-computed tomography based computational fluid dynamics for the determination of shear stresses in scaffolds within a perfusion bioreactor

Perfusion bioreactors are known to exert shear stresses on cultured cells, leading to cell differentiation and enhanced extracellular matrix deposition on scaffolds. The influence of the scaffold's porous microstructure is investigated for a polycaprolactone (PCL) scaffold with a regular microarchitecture and a silk fibroin (SF) scaffold with an irregular network of interconnected pores. Their complex 3D geometries are imaged by micro-computed tomography and used in direct pore-level simulations of the entire scaffold-bioreactor system to numerically solve the governing mass and momentum conservation equations for fluid flow through porous media. The velocity field and wall shear stress distribution are determined for both scaffolds. The PCL scaffold exhibited an asymmetric distribution with peak and plateau, while the SF scaffold exhibited a homogenous distribution and conditioned the flow more efficiently than the PCL scaffold. The methodology guides the design and optimization of the scaffold geometry.

Use of perfusion bioreactors and large animal models for long bone tissue engineering

Tissue engineering and regenerative medicine (TERM) strategies for generation of new bone tissue includes the combined use of autologous or heterologous mesenchymal stem cells (MSC) and three-dimensional (3D) scaffold materials serving as structural support for the cells, that develop into tissue-like substitutes under appropriate in vitro culture conditions. This approach is very important due to the limitations and risks associated with autologous, as well as allogenic bone grafiting procedures currently used. However, the cultivation of osteoprogenitor cells in 3D scaffolds presents several challenges, such as the efficient transport of nutrient and oxygen and removal of waste products from the cells in the interior of the scaffold. In this context, perfusion bioreactor systems are key components for bone TERM, as many recent studies have shown that such systems can provide dynamic environments with enhanced diffusion of nutrients and therefore, perfusion can be used to generate grafts of clinically relevant sizes and shapes. Nevertheless, to determine whether a developed tissue-like substitute conforms to the requirements of biocompatibility, mechanical stability and safety, it must undergo rigorous testing both in vitro and in vivo. Results from in vitro studies can be difficult to extrapolate to the in vivo situation, and for this reason, the use of animal models is often an essential step in the testing of orthopedic implants before clinical use in humans. This review provides an overview of the concepts, advantages, and challenges associated with different types of perfusion bioreactor systems, particularly focusing on systems that may enable the generation of critical size tissue engineered constructs. Furthermore, this review discusses some of the most frequently used animal models, such as sheep and goats, to study the in vivo functionality of bone implant materials, in critical size defects.

Imaging challenges in biomaterials and tissue engineering

Biomaterials are employed in the fields of tissue engineering and regenerative medicine (TERM) in order to enhance the regeneration or replacement of tissue function and/or structure. The unique environments resulting from the presence of biomaterials, cells, and tissues result in distinct challenges in regards to monitoring and assessing the results of these interventions. Imaging technologies for three-dimensional (3D) analysis have been identified as a strategic priority in TERM research. Traditionally, histological and immunohistochemical techniques have been used to evaluate engineered tissues. However, these methods do not allow for an accurate volume assessment, are invasive, and do not provide information on functional status. Imaging techniques are needed that enable non-destructive, longitudinal, quantitative, and three-dimensional analysis of TERM strategies. This review focuses on evaluating the application of available imaging modalities for assessment of biomaterials and tissue in TERM applications. Included is a discussion of limitations of these techniques and identification of areas for further development.

A survey of methods for the evaluation of tissue engineering scaffold permeability

The performance of porous scaffolds for tissue engineering (TE) applications is evaluated, in general, in terms of porosity, pore size and distribution, and pore tortuosity. These descriptors are often confounding when they are applied to characterize transport phenomena within porous scaffolds. On the contrary, permeability is a more effective parameter in (1) estimating mass and species transport through the scaffold and (2) describing its topological features, thus allowing a better evaluation of the overall scaffold performance. However, the evaluation of TE scaffold permeability suffers of a lack of uniformity and standards in measurement and testing procedures which makes the comparison of results obtained in different laboratories unfeasible. In this review paper we summarize the most important features influencing TE scaffold permeability, linking them to the theoretical background. An overview of methods applied for TE scaffold permeability evaluation is given, presenting experimental test benches and computational methods applied (1) to integrate experimental measurements and (2) to support the TE scaffold design process. Both experimental and computational limitations in the permeability evaluation process are also discussed.

A differential pressure laminar flow reactor supports osteogenic differentiation and extracellular matrix formation from adipose mesenchymal stem cells in a macroporous ceramic scaffold

We present a laminar flow reactor for bone tissue engineering that was developed based on a computational fluid dynamics model. The bioreactor design permits a laminar flow field through its specific internal shape. An integrated bypass system that prevents pressure build-up through bypass openings for pressure release allows for a constant pressure environment during the changing of permeability values that are caused by cellular growth within a porous scaffold. A macroporous ceramic scaffold, composed of zirconium dioxide, was used as a test biomaterial that studies adipose stem cell behavior within a controlled three-dimensional (3D) flow and pressure environment. The topographic structure of the material provided a basis for stem cell proliferation and differentiation toward the osteogenic lineage. Dynamic culture conditions in the bioreactor supported cell viability during long-term culture and induced cell cluster formation and extra-cellular matrix deposition within the porous scaffold, though no complete closure of the pores with new-formed tissue was observed. We postulate that our system is suitable for studying fluid shear stress effects on stem cell proliferation and differentiation toward bone formation in tissue-engineered 3D constructs.