Permeability analysis of scaffolds for bone tissue engineering

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

3-D computational modeling of media flow through scaffolds in a perfusion bioreactor

Media perfusion bioreactor systems have been developed to improve mass transport throughout three-dimensional (3-D) tissue-engineered constructs cultured in vitro. In addition to enhancing the exchange of nutrients and wastes, these systems simultaneously deliver flow-mediated shear stresses to cells seeded within the constructs. Local shear stresses are a function of media flow rate and dynamic viscosity, bioreactor configuration, and porous scaffold microarchitecture. We have used the Lattice-Boltzmann method to simulate the flow conditions within perfused cell-seeded cylindrical scaffolds. Microcomputed tomography imaging was used to define the scaffold microarchitecture for the simulations, which produce a 3-D fluid velocity field throughout the scaffold porosity. Shear stresses were estimated at various media flow rates by multiplying the symmetric part of the gradient of the velocity field by the dynamic viscosity of the cell culture media. The shear stress algorithm was validated by modeling flow between infinite parallel plates and comparing the calculated shear stress distribution to the analytical solution. Relating the simulation results to perfusion experiments, an average surface shear stress of 5x10(-5)Pa was found to correspond to increased cell proliferation, while higher shear stresses were associated with upregulation of bone marker genes. This modeling approach can be used to compare results obtained for different perfusion bioreactor systems or different scaffold microarchitectures and may allow specific shear stresses to be determined that optimize the amount, type, or distribution of in vitro tissue growth.     

Predicting the stress distribution within scaffolds with ordered architecture

Current tissue engineering technologies involve the seeding of cells on porous scaffolds, within which the cells can proliferate and differentiate, when cultured in bioreactors. The flow of culture media through the scaffolds generates stresses that are important for both cell differentiation and cell growth. A recent study [Appl. Phys. Lett. 97 (2010), 024101] showed that flow-induced stresses inside highly porous and randomly structured scaffolds follow a three-point gamma probability density function (p.d.f.). The goal of the present study is to further investigate whether the same p.d.f. can also describe the distribution of stresses in structured porous scaffolds, what is the range of scaffold porosity for which the distribution is valid, and what is the physical reason for such behavior. To do that, the p.d.f. of flow-induced stresses in different scaffold geometries were calculated via flow dynamics simulations. It was found that the direction of flow relative to the internal architecture of the scaffolds is important for stress distributions. The stress distributions follow a common distribution within statistically acceptable accuracy, when the flow direction does not coincide with the direction of internal structural elements of the scaffold.     

Micropatterned biopolymer 3D scaffold for static and dynamic culture of human fibroblasts

During in vivo tissue regeneration, cell behavior is highly influenced by the surrounding environment. Thus, the choice of scaffold material and its microstructure is one of the fundamental steps for a successful in vitro culture. An efficacious method for scaffold fabrication should prove its versatility and the possibility of controlling micro- and nanostructure. In this paper, hyaluronic acid 3D scaffolds were developed through lamination of micropatterned membranes, fabricated after optimization of a soft-lithography method. The scaffold presented here is characterized by a homogeneous hexagonal lattice with porosity of 69%, specific surface area of 287 cm-1, and permeability of 18.9 microm2. The control over the geometry was achieved with an accuracy of 20 mum. This technique allowed not only fabrication of planar 3D scaffolds but also production of thin wall tubular constructs. Mechanical tests, performed on dry tubular scaffolds, show high rupture tensile strength. This construct could be promising not only as engineered vascular grafts but also for regeneration of skin, urethra, and intestinal walls. The biocompatibility of a 3D planar scaffold was tested by seeding human fibroblasts. The cells were cultured in both static and dynamic conditions, in a perfusion bioreactor at different flow rates. Microscope analysis and MTT test showed cell proliferation and viability and a uniform cell distribution likely due to an appropriate lattice structure.     

Development of biodegradable scaffolds based on magnetically guided assembly of magnetic sugar particles

Biodegradable scaffolds with controlled pore layout and porosity have great significance in tissue engineering for cell penetration, tissue ingrowth, vascularization, and nutrient delivery. Porogen leaching has been commonly used to control pore size, pore structure and porosity in the scaffold. In this paper we focus on the use/development of two magnetically guided porogen assembly methods using magnetic sugar particles (MSPs) for scaffold fabrication. First, a patterning device is utilized to align MSPs following designed templates. Then a magnetic sheet film is fabricated by mixing poly(vinyl alcohol, PVA) and NdFeB powder for steering the MSPs. After poly(l-lactide-co-?-caprolactone) (PLCL) casting and removal of the sugar template, a scaffold with spherical pores is obtained. The surface and the inner structure of the scaffolds are evaluated using light and electron micrographs showing their interconnection of pores, pore wall morphology and porosity. Single layer scaffolds with the size of 8mm in width and 10mm in length were constructed with controllable pore diameters in the ranges of 105-150 μm, 250-300 μm and 425-500 μm.     

Systematic investigation of porogen size and content on scaffold morphometric parameters and properties

A systematic investigation of tissue engineering scaffolds prepared by salt leaching of a photopolymerized dimethacrylate was performed to determine how the scaffold structure (porosity, pore size, etc.) can be controlled and also to determine how the scaffold structure and the mechanical properties are related. Two series of scaffolds were prepared with (1) the same polymer-to-salt ratio but different salt sizes (ranging from average size of 100 to 390 microm) and (2) the same salt size but different polymer-to-salt ratios (ranging from salt mass of 70 to 90%). These scaffolds were examined to determine how the fabrication parameters affected the scaffold morphometric parameters and corresponding mechanical properties. Combined techniques of X-ray microcomputed tomography (microCT), mercury porosimetry, and gravimetric analysis were used to determine the scaffold parameters, such as porosity, pore size, and strut thickness and their size distributions, and pore interconnectivity. Scaffolds with porosities ranging from 57% to 92% (by volume) with interconnected structures could be fabricated using the current technique. The porosity and strut thickness were subsequently related to the mechanical response of the scaffolds, both of which contribute to the compression modulus of the scaffold. The current study shows that the structure and properties of the scaffold could be tailored by the size and the amount of porogen used in the fabrication of the scaffold.     

A mathematical model for bone tissue regeneration inside a specific type of scaffold

Bone tissue regeneration using scaffolds is receiving an increasing interest in orthopedic surgery and tissue engineering applications. In this study, we present the geometrical characterization of a specific family of scaffolds based on a face cubic centered (FCC) arrangement of empty pores leading to analytical formulae of porosity and specific surface. The effective behavior of those scaffolds, in terms of mechanical properties and permeability, is evaluated through the asymptotic homogenization theory applied to a representative volume element identified with the unit cell FCC. Bone growth into the scaffold is estimated by means of a phenomenological model that considers a macroscopic effective stress as the mechanical stimulus that regulates bone formation. Cell migration within the scaffold is modeled as a diffusion process based on Fick's law which allows us to estimate the cell invasion into the scaffold microstructure. The proposed model considers that bone growth velocity is proportional to the concentration of cells and regulated by the mechanical stimulus. This model allows us to explore what happens within the scaffold, the surrounding bone and their interaction. The mathematical model has been numerically implemented and qualitatively compared with previous experimental results found in the literature for a scaffold implanted in the femoral condyle of a rabbit. Specifically, the model predicts around 19 and 23% of bone regeneration for non-grafted and grafted scaffolds, respectively, both with an initial porosity of 76%.     

The influence of fibrous elastomer structure and porosity on matrix organization

Fibrous scaffolds are finding wide use in the field of tissue engineering, as they can be designed to mimic many native tissue properties and structures (e.g., cardiac tissue, meniscus). The influence of fiber alignment and scaffold architecture on cellular interactions and matrix organization was the focus of this study. Three scaffolds were fabricated from the photocrosslinkable elastomer poly(glycerol sebacate) (PGS), with changes in fiber alignment (non-aligned (NA) versus aligned (AL)) and the introduction of a PEO sacrificial polymer population to the AL scaffold (composite (CO)). PEO removal led to an increase in scaffold porosity and maintenance of scaffold anisotropy, as evident through visualization, mechanical testing, and mass loss studies. Hydrated scaffolds possessed moduli that ranged between ～3-240 kPa, failing within the range of properties (<300 kPa) appropriate for soft tissue engineering. CO scaffolds were completely degraded as early as 16 days, whereas NA and AL scaffolds had ～90% mass loss after 21 days when monitored in vitro. Neonatal cardiomyocytes, used as a representative cell type, that were seeded onto the scaffolds maintained their viability and aligned along the surface of the AL and CO fibers. When implanted subcutaneously in rats, a model that is commonly used to investigate in vivo tissue responses to biomaterials, CO scaffolds were completely integrated at 2 weeks, whereas ～13% and ～16% of the NA and AL scaffolds, respectively remained acellular. However, all scaffolds were completely populated with cells at 4 weeks post-implantation. Polarized light microscopy was used to evaluate the collagen elaboration and orientation within the scaffold. An increase in the amount of collagen was observed for CO scaffolds and enhanced alignment of the nascent collagen was observed for AL and CO scaffolds compared to NA scaffolds. Thus, these results indicate that the scaffold architecture and porosity are important considerations in controlling tissue formation.     

Photoinitiated cross-linking of the biodegradable polyester poly(propylene fumarate). Part II. In vitro degradation

This study investigated the in vitro degradation of both solid PPF networks and porous PPF scaffolds formed by photoinitiated cross-linking of PPF polymer chains. Three formulations of scaffolds of differing porosity and pore size were constructed by varying porogen size and content. The effects of pore size and pore volume on scaffold mass, geometry, porosity, mechanical properties, and water absorption were then examined. Throughout the study, the solid networks and porous scaffolds exhibited continual mass loss and slight change in length. Porogen content appeared to have the greatest effect upon physical degradation. For example, scaffolds initially fabricated with 80 wt % porogen content lost approximately 30% of their initial PPF content after 32 weeks of degradation, whereas scaffolds fabricated with 70 wt % porogen content lost approximately 18% after 32 weeks of degradation. For all scaffold formulations, water absorption capacity, porosity, and compressive modulus were maintained at constant values following porogen leaching. These results indicate the potential of photo-cross-linked PPF scaffolds in tissue engineering applications which require maintenance of scaffold structure, strength, and porosity during the initial stages of degradation.     

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

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

Effects of gel concentration, human fibronectin, and cation supplement on the tissue-engineered cartilage

Cultivation of bovine knee chondrocytes (BKCs) in various cationic additives was studied using chitosan-gelatin scaffolds, whose surfaces were modified by human fibronectin (HFN). Here, the genipin-crosslinked scaffolds were fabricated by the freezing/lyophilization method with various concentrations of the precursory gels. The experimental results indicated that a lower freezing temperature led to higher moisture content, porosity, and specific surface area of a scaffold. The higher the precursor concentration, the larger the moisture content of a scaffold. A fast biodegradation of scaffold matrix was generated by a high porosity with BKCs. A higher concentration of HFN coated on scaffold surfaces yielded a faster rate of BKC attachment from the culture medium. The amounts of BKCs, glycosaminoglycans, and collagen over 28-day cultivation increased with the scaffold porosity, the coating concentration of HFN, the seeding density of BKCs, and the calcium concentration in medium.     

Three-dimensional cell seeding and growth in radial-flow perfusion bioreactor for in vitro tissue reconstruction

Radial-flow perfusion bioreactor systems have been designed and evaluated to enable direct cell seeding into a three-dimensional (3-D) porous scaffold and subsequent cell culture for in vitro tissue reconstruction. However, one of the limitations of in vitro regeneration is the tissue necrosis that occurs at the central part of the 3-D scaffold. In the present study, tubular poly-L-lactic acid (PLLA) porous scaffolds with an optimized pore size and porosity were prepared by the lyophilization method, and the effect of different perfusion conditions on cell seeding and growth were compared with those of the conventional static culture. The medium flowed radially from the lumen toward the periphery of the tubular scaffolds. It was found that cell seeding under a radial-flow perfusion condition of 1.1 mL/cm2 x min was effective, and that the optimal flow rate for cell growth was 4.0 mL/cm2 x min. At this optimal rate, the increase in seeded cells in the perfusion culture over a period of 5 days was 7.3-fold greater than that by static culture over the same period. The perfusion cell seeding resulted in a uniform distribution of cells throughout the scaffold. Subsequently, the perfusion of medium and hence the provision of nutrients and oxygen permitted growth and maintenance of the tissue throughout the scaffold. The perfusion seeding/culture system was a much more effective strategy than the conventional system in which cells are seeded under a static condition and cultured in a bioreactor such as a spinner flask.     

A complete structural performance analysis and modelling of hydroxyapatite scaffolds with variable porosity

The use of hydroxyapatite (HA) scaffolds for bone regeneration is an alternative procedure to treat bone defects due to cancer, other diseases or traumas. Although the use of HA has been widely studied in the literature, there are still some disparities regarding its mechanical performance. This paper presents a complete analysis of the structural performance of porous HA scaffolds based on experimental tests, numerical simulations and theoretical studies. HA scaffolds with variable porosity were considered and fabricated by the water-soluble polymer method, using poly vinyl alcohol as pore former. These scaffolds were then characterised by scanning electron microscopy, stereo microscopy, X-ray diffraction, porosity analysis and mechanical tests. Different scaffold models were proposed and analysed by the finite element method to obtain numerical predictions of the mechanical properties. Also theoretical predictions based on the (Gibson LJ, Ashby MF. 1988. Cellular solids: structure and properties. Oxford: Pergamon Press) model were obtained. Finally the experimental, numerical and theoretical results were compared. From this comparison, it was observed that the proposed numerical and theoretical models can be used to predict, with adequate accuracy, the mechanical performance of HA scaffolds for different porosity values.     

Different Porosities of Chitosan Can Influence the Osteogenic Differentiation Potential of Stem Cells

Scaffolds porosity has an important role in in vitro and in vivo differentiation process of stem cells with given the amount of space available to the cells to proliferate and differentiate. In the present study, chitosan with three porosities including 10%, 15%, and 20% that created by gelatin were used for investigation of the proliferation and osteogenic differentiation potential of adipose‐derived stem cells (ADSCs). In order to be more like the scaffold to natural bone tissue, freeze‐drying method was used in the scaffold preparation. Scaffold morphology, cell attachment, and toxicity were evaluated using scanning electron microscopy and MTT assay. Then, osteogenic differentiation potential of ADSCs cultured on chitosan with different porosities was evaluated by common osteogenic markers such as Alizarin red staining, ALP activity, calcium content, and osteogenic‐related genes expression via real‐time RT‐PCR. Although all scaffolds supported the proliferation and differentiation of ADSCs, but 10% scaffold demonstrated higher amount of osteogenic markers in comparison with the other porosities and control groups. Taking together, it can be concluded that osteogenic differentiation well done in the scaffolds with lower porosity because density of the cells will increase by forcing resulted from the scaffold, so osteogenic differentiation of the stem cells have an inverse association with scaffold porosity. J. Cell. Biochem. 119: 625–633, 2018. © 2017 Wiley Periodicals, Inc.     

Simulated tissue growth for 3D printed scaffolds

Experiments have demonstrated biological tissues grow by mechanically sensing their localized curvature, therefore making geometry a key consideration for tissue scaffold design. We developed a simulation approach for modeling tissue growth on beam-based geometries of repeating unit cells, with four lattice topologies considered. In simulations, tissue was seeded on surfaces with new tissue growing in empty voxels with positive curvature. Growth was fastest on topologies with more beams per unit cell when unit cell volume/porosity was fixed, but fastest for topologies with fewer beams per unit cell when beam width/porosity was fixed. Tissue filled proportional to mean positive surface curvature per volume. Faster filling scaffolds had lower permeability, which is important to support nutrient transport, and highlights a need for tuning geometries appropriately for conflicting trade-offs. A balance among trade-offs was found for scaffolds with beam diameters of about \(300\,\upmu \hbox {m}\) and 50% porosity, therefore providing the opportunity for further optimization based on criteria such as mechanical factors. Overall, these findings provide insight into how curvature-based tissue growth progresses in complex scaffold geometries, and a foundation for developing optimized scaffolds for clinical applications.     

Darcian permeability constant as indicator for shear stresses in regular scaffold systems for tissue engineering

The shear stresses in printed scaffold systems for tissue engineering depend on the flow properties and void volume in the scaffold. In this work, computational fluid dynamics (CFD) is used to simulate flow fields within porous scaffolds used for cell growth. From these models the shear stresses acting on the scaffold fibres are calculated. The results led to the conclusion that the Darcian (k ₁) permeability constant is a good predictor for the shear stresses in scaffold systems for tissue engineering. This permeability constant is easy to calculate from the distance between and thickness of the fibres used in a 3D printed scaffold. As a consequence computational effort and specialists for CFD can be circumvented by using this permeability constant to predict the shear stresses. If the permeability constant is below a critical value, cell growth within the specific scaffold design may cause a significant increase in shear stress. Such a design should therefore be avoided when the shear stress experienced by the cells should remain in the same order of magnitude.     

Dynamics of diffusivity and pressure drop in flow-through and parallel-flow bioreactors during tissue regeneration

In this study, transport characteristics in flow-through and parallel-flow bioreactors used in tissue engineering were simulated using computational fluid dynamics. To study nutrient distribution and consumption by smooth muscle cells colonizing the 100 mm diameter and 2-mm thick scaffold, effective diffusivity of glucose was experimentally determined using a two-chambered setup. Three different concentrations of chitosan-gelatin scaffolds were prepared by freezing at -80°C followed by lyophilization. Experiments were performed in both bioreactors to measure pressure drop at different flow rates. At low flow rates, experimental results were in agreement with the simulation results for both bioreactors. However, increase in flow rate beyond 5 mL/min in flow-through bioreactor showed channeling at the circumference resulting in lower pressure drop relative to simulation results. The Peclet number inside the scaffold indicated nutrient distribution within the flow-through bioreactor to be convection-dependent, whereas the parallel-flow bioreactor was diffusion-dependent. Three alternative design modifications to the parallel-flow were made by (i) introducing an additional inlet and an outlet, (ii) changing channel position, and (iii) changing the hold-up volume. Simulation studies were performed to assess the effect of scaffold thickness, cell densities, and permeability. These new designs improved nutrient distribution for 2 mm scaffolds; however, parallel-flow configuration was found to be unsuitable for scaffolds more than 4-mm thick, especially at low porosities as tissues regenerate. Furthermore, operable flow rate in flow-through bioreactors is constrained by the mechanical strength of the scaffold. In summary, this study showed limitations and differences between flow-through and parallel-flow bioreactors used in tissue engineering.     

Modeling,simulations, and optimization of smooth muscle cell tissue engineering for the production of vascular grafts

The paper presents a transient, continuum, two-phase model of the tissue engineering in fibrous scaffolds, including transport equations for the flowing culture medium, nutrient and cell concentration with transverse and in-plane diffusion and cell migration, a novel feature of local in-plane transport across a phenomenological pore and innovative layer-by-layer cell filling approach. The model is successfully validated for the smooth muscle cell tissue engineering of a vascular graft using crosslinked, electrospun gelatin fiber scaffolds for both static and dynamic cell culture, the latter in a dynamic bioreactor with a rotating shaft on which the tubular scaffold is attached. Parametric studies evaluate the impact of the scaffold microstructure, cell dynamics, oxygen transport, and static or dynamic conditions on the rate and extent of cell proliferation and depth of oxygen accessibility. An optimized scaffold of 75% dry porosity is proposed that can be tissue engineered into a viable and still fully oxygenated graft of the tunica media of the coronary artery within 2 days in the dynamic bioreactor. Such scaffold also matches the mechanical properties of the tunica media of the human coronary artery and the suture retention strength of a saphenous vein, often used as a coronary artery graft.     

A novel method for biomaterial scaffold internal architecture design to match bone elastic properties with desired porosity

An often-proposed tissue engineering design hypothesis is that the scaffold should provide a biomimetic mechanical environment for initial function and appropriate remodeling of regenerating tissue while concurrently providing sufficient porosity for cell migration and cell/gene delivery. To provide a systematic study of this hypothesis, the ability to precisely design and manufacture biomaterial scaffolds is needed. Traditional methods for scaffold design and fabrication cannot provide the control over scaffold architecture design to achieve specified properties within fixed limits on porosity. The purpose of this paper was to develop a general design optimization scheme for 3D internal scaffold architecture to match desired elastic properties and porosity simultaneously, by introducing the homogenization-based topology optimization algorithm (also known as general layout optimization). With an initial target for bone tissue engineering, we demonstrate that the method can produce highly porous structures that match human trabecular bone anisotropic stiffness using accepted biomaterials. In addition, we show that anisotropic bone stiffness may be matched with scaffolds of widely different porosity. Finally, we also demonstrate that prototypes of the designed structures can be fabricated using solid free-form fabrication (SFF) techniques.     

Permeability evaluation of 45S5 Bioglass®-based scaffolds for bone tissue engineering

Permeability is a key parameter for microstructural design of scaffolds, since it is related to their capability for waste removal and nutrients/oxygen supply. In this framework, Darcy's experiments were carried out in order to determine the relationship between the pressure drop gradient and the fluid flow velocity in Bioglass^®-based scaffolds to obtain the scaffold's permeability. Using deionised water as working fluid, the measured average permeability value on scaffolds of 90–95% porosity was 1.96×10^?9 m². This value lies in the published range of permeability values for trabecular bone.