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%.     

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.     

A multiscale optimisation method for bone growth scaffolds based on triply periodic minimal surfaces

Tissue engineered bone scaffolds are potential alternatives to bone allografts and autografts. Porous scaffolds based on triply periodic minimal surfaces (TPMS) are good candidates for tissue growth because they offer high surface-to-volume ratio, have tailorable stiffness, and can be easily fabricated by additive manufacturing. However, the range of TPMS scaffold types is extensive, and it is not yet clear which type provides the fastest cell or tissue growth while being sufficiently stiff to act as a bone graft. Nor is there currently an established methodology for TPMS bone scaffold design which can be quickly adopted by medical designers or biologists designing implants. In this study, we examine six TPMS scaffold types for use as tissue growth scaffolds and propose a general methodology to optimise their geometry. At the macro-scale, the optimisation routine ensures a scaffold stiffness within suitable limits for bone, while at the micro-scale it maximises the cell growth rate. The optimisation procedure also ensures the scaffold pores are of sufficient diameter to allow oxygen and nutrient delivery via capillaries. Of the examined TPMS structures, the Lidinoid and Split P cell types provide the greatest cell growth rates and are therefore the best candidates for bone scaffolds.

     

Predicting permeability of regular tissue engineering scaffolds: scaling analysis of pore architecture,scaffold length,and fluid flow rate effects

The main aim of this research is to numerically obtain the permeability coefficient in the cylindrical scaffolds. For this purpose, a mathematical analysis was performed to derive an equation for desired porosity in terms of morphological parameters. Then, the considered cylindrical geometries were modeled and the permeability coefficient was calculated according to the velocity and pressure drop values based on the Darcy’s law. In order to validate the accuracy of the present numerical solution, the obtained permeability coefficient was compared with the published experimental data. It was observed that this model can predict permeability with the utmost accuracy. Then, the effect of geometrical parameters including porosity, scaffold pore structure, unit cell size, and length of the scaffolds as well as entrance mass flow rate on the permeability of porous structures was studied. Furthermore, a parametric study with scaling laws analysis of sample length and mass flow rate effects on the permeability showed good fit to the obtained data. It can be concluded that the sensitivity of permeability is more noticeable at higher porosities. The present approach can be used to characterize and optimize the scaffold microstructure due to the necessity of cell growth and transferring considerations.     

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.     

A multiscale computational fluid dynamics approach to simulate the micro-fluidic environment within a tissue engineering scaffold with highly irregular pore geometry

Mechanical stimulation can regulate cellular behavior, e.g., differentiation, proliferation, matrix production and mineralization. To apply fluid-induced wall shear stress (WSS) on cells, perfusion bioreactors have been commonly used in tissue engineering experiments. The WSS on cells depends on the nature of the micro-fluidic environment within scaffolds under medium perfusion. Simulating the fluidic environment within scaffolds will be important for gaining a better insight into the actual mechanical stimulation on cells in a tissue engineering experiment. However, biomaterial scaffolds used in tissue engineering experiments typically have highly irregular pore geometries. This complexity in scaffold geometry implies high computational costs for simulating the precise fluidic environment within the scaffolds. In this study, we propose a low-computational cost and feasible technique for quantifying the micro-fluidic environment within the scaffolds, which have highly irregular pore geometries. This technique is based on a multiscale computational fluid dynamics approach. It is demonstrated that this approach can capture the WSS distribution in most regions within the scaffold. Importantly, the central process unit time needed to run the model is considerably low.

     

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.     

A Mechanobiology-based Algorithm to Optimize the Microstructure Geometry of Bone Tissue Scaffolds

Complexity of scaffold geometries and biological mechanisms involved in the bone generation process make the design of scaffolds a quite challenging task. The most common approaches utilized in bone tissue engineering require costly protocols and time-consuming experiments. In this study we present an algorithm that, combining parametric finite element models of scaffolds with numerical optimization methods and a computational mechano-regulation model, is able to predict the optimal scaffold microstructure. The scaffold geometrical parameters are perturbed until the best geometry that allows the largest amounts of bone to be generated, is reached. We study the effects of the following factors: (1) the shape of the pores; (2) their spatial distribution; (3) the number of pores per unit area. The optimal dimensions of the pores have been determined for different values of scaffold Young''s modulus and compression loading acting on the scaffold upper surface.Pores with rectangular section were predicted to lead to the formation of larger amounts of bone compared to square section pores; similarly, elliptic pores were predicted to allow the generation of greater amounts of bone compared to circular pores. The number of pores per unit area appears to have rather negligible effects on the bone regeneration process. Finally, the algorithm predicts that for increasing loads, increasing values of the scaffold Young''s modulus are preferable.The results shown in the article represent a proof-of-principle demonstration of the possibility to optimize the scaffold microstructure geometry based on mechanobiological criteria.     

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.     

Flow rates in perfusion bioreactors to maximise mineralisation in bone tissue engineering in vitro

In bone tissue engineering experiments, fluid-induced shear stress is able to stimulate cells to produce mineralised extracellular matrix (ECM). The application of shear stress on seeded cells can for example be achieved through bioreactors that perfuse medium through porous scaffolds. The generated mechanical environment (i.e. wall shear stress: WSS) within the scaffolds is complex due to the complexity of scaffold geometry. This complexity has so far prevented setting an optimal loading (i.e. flow rate) of the bioreactor to achieve an optimal distribution of WSS for stimulating cells to produce mineralised ECM. In this study, we demonstrate an approach combining computational fluid dynamics (CFD) and mechano-regulation theory to optimise flow rates of a perfusion bioreactor and various scaffold geometries (i.e. pore shape, porosity and pore diameter) in order to maximise shear stress induced mineralisation. The optimal flow rates, under which the highest fraction of scaffold surface area is subjected to a wall shear stress that induces mineralisation, are mainly dependent on the scaffold geometries. Nevertheless, the variation range of such optimal flow rates are within 0.5–5 mL/min (or in terms of fluid velocity: 0.166–1.66 mm/s), among different scaffolds. This approach can facilitate the determination of scaffold-dependent flow rates for bone tissue engineering experiments in vitro, avoiding performing a series of trial and error experiments.     

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.     

Electrospun poly(epsilon-caprolactone) microfiber and multilayer nanofiber/microfiber scaffolds: characterization of scaffolds and measurement of cellular infiltration

The physical and spatial architectural geometries of electrospun scaffolds are important to their application in tissue engineering strategies. In this work, poly(epsilon-caprolactone) microfiber scaffolds with average fiber diameters ranging from 2 to 10 microm were individually electrospun to determine the parameters required for reproducibly fabricating scaffolds. As fiber diameter increased, the average pore size of the scaffolds, as measured by mercury porosimetry, increased (values ranging from 20 to 45 microm), while a constant porosity was observed. To capitalize on both the larger pore sizes of the microfiber layers and the nanoscale dimensions of the nanofiber layers, layered scaffolds were fabricated by sequential electrospinning. These scaffolds consisted of alternating layers of poly(epsilon-caprolactone) microfibers and poly(epsilon-caprolactone) nanofibers. By electrospinning the nanofiber layers for different lengths of time, the thickness of the nanofiber layers could be modulated. Bilayered constructs consisting of microfiber scaffolds with varying thicknesses of nanofibers on top were generated and evaluated for their potential to affect rat marrow stromal cell attachment, spreading, and infiltration. Cell attachment after 24 h did not increase with increasing number of nanofibers, but the presence of nanofibers enhanced cell spreading as evidenced by stronger F-actin staining. Additionally, increasing the thickness of the nanofiber layer reduced the infiltration of cells into the scaffolds under both static and flow perfusion culture for the specific conditions tested. The scaffold design presented in this study allows for cellular infiltration into the scaffolds while at the same time providing nanofibers as a physical mimicry of extracellular matrix.     

Designing of PLA scaffolds for bone tissue replacement fabricated by ordinary commercial 3D printer

Background

The primary objective of Tissue engineering is a regeneration or replacement of tissues or organs damaged by disease, injury, or congenital anomalies. At present, Tissue engineering repairs damaged tissues and organs with artificial supporting structures called scaffolds. These are used for attachment and subsequent growth of appropriate cells. During the cell growth gradual biodegradation of the scaffold occurs and the final product is a new tissue with the desired shape and properties.In recent years, research workplaces are focused on developing scaffold by bio-fabrication techniques to achieve fast, precise and cheap automatic manufacturing of these structures. Most promising techniques seem to be Rapid prototyping due to its high level of precision and controlling. However, this technique is still to solve various issues before it is easily used for scaffold fabrication.In this article we tested printing of clinically applicable scaffolds with use of commercially available devices and materials. Research presented in this article is in general focused on “scaffolding” on a field of bone tissue replacement.

Results

Commercially available 3D printer and Polylactic acid were used to create originally designed and possibly suitable scaffold structures for bone tissue engineering. We tested printing of scaffolds with different geometrical structures. Based on the osteosarcoma cells proliferation experiment and mechanical testing of designed scaffold samples, it will be stated that it is likely not necessary to keep the recommended porosity of the scaffold for bone tissue replacement at about 90%, and it will also be clarified why this fact eliminates mechanical properties issue. Moreover, it is demonstrated that the size of an individual pore could be double the size of the recommended range between 0.2–0.35 mm without affecting the cell proliferation.

Conclusion

Rapid prototyping technique based on Fused deposition modelling was used for the fabrication of designed scaffold structures. All the experiments were performed in order to show how to possibly solve certain limitations and issues that are currently reported by research workplaces on the field of scaffold bio-fabrication. These results should provide new valuable knowledge for further research.

     

制备大孔径静电纺丝组织工程支架的研究进展

研究表明静电纺丝可以制备出模拟细胞外基质的三维结构,其中限制静电纺丝纤维支架应用的问题之一就是纤维排列紧密导致支架的孔径较小,从而阻碍了细胞的浸入,组织中血管化的形成以及支架与宿主细胞的融合。为了增大支架的孔径,提高孔隙率,许多研究者提出了相应的策略。本文综述了多种制备大孔径静电纺丝纤维支架的方法,主要包括不同接收装置控制电场分布、盐粒子/聚合物析出法、水浴接收、低温静电纺丝以及激光/紫外烧蚀法等,以上的方法都能够有效的增大静电纺丝三维支架的孔径,进而提高了细胞的浸润性、营养物质的传输以及废物的排出,为静电纺丝纤维支架在组织工程中的应用奠定了基础。     

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 multiscale investigation of mechanical properties of bio-inspired scaffolds

Abstract

Finding a structural design which allows the scaffold to have a high porosity and large pore size while retaining high strength is essential. Here, a bio-inspired scaffold is designed based on the observed geometrical pattern of the apatite atomic crystal structure, and mechanical properties are compared with other common scaffold geometries. The bio-inspired scaffold design is proven superior using a multiscale computational approach, which combines density functional theory and finite element analysis to predict the stress reaction and substitution effects on the scaffolds. This study provides insight into better scaffold design using bio-inspired structures and the effect of substitutions.     

Mesenchymal stem cell cultivation in electrospun scaffolds: mechanistic modeling for tissue engineering

Tissue engineering is a multidisciplinary field of research in which the cells, biomaterials, and processes can be optimized to develop a tissue substitute. Three-dimensional (3D) architectural features from electrospun scaffolds, such as porosity, tortuosity, fiber diameter, pore size, and interconnectivity have a great impact on cell behavior. Regarding tissue development in vitro, culture conditions such as pH, osmolality, temperature, nutrient, and metabolite concentrations dictate cell viability inside the constructs. The effect of different electrospun scaffold properties, bioreactor designs, mesenchymal stem cell culture parameters, and seeding techniques on cell behavior can be studied individually or combined with phenomenological modeling techniques. This work reviews the main culture and scaffold factors that affect tissue development in vitro regarding the culture of cells inside 3D matrices. The mathematical modeling of the relationship between these factors and cell behavior inside 3D constructs has also been critically reviewed, focusing on mesenchymal stem cell culture in electrospun scaffolds.     

Biomacromolecules electrostatic self-assembly on 3-dimensional tissue engineering scaffold

A poly(ethylenimine) (PEI) was employed to obtain a stable positively charged surface on a poly(D,L-lactide) (PDL-LA) tissue engineering scaffold. An extracellular matrix (ECM)-like biomacromolecule, gelatin, was selected as polyelectrolyte and deposit alternately with PEI on the activated PDL-LA scaffold via ESA technique. The zeta-potential result showed alternating charge of polyelectrolytes (PEI/gelatin) layering on PDL-LA microspheres. Quartz crystal microbalance (QCM) measurement further verified the gradual deposition of PEI/gelatin on the PDL-LA thin film. The combination of PEI aminolysis and the layer-by-layer technique was then explored to construct gelatin coating onto the 3-D porous PDL-LA scaffold. Scanning electronic microscopy showed that there is no notable difference between modified and unmodified PLA scaffolds, with regard to the porosity, pore diameter, and scaffold integration. The dual-tunnel confocal laser scanning microscopy indicated uniform gelatin distribution on the inner surface of the 3-D porous scaffold. The gradual build-up of protein layer on scaffold was investigated by radioiodination technique. Chondrocyte was chosen to test the cell behavior on modified and unmodified PDL-LA scaffolds. The results of the cell viability, total intracellular protein content, and cell morphology on the PEI/gelatin multilayers modified PDL-LA scaffold showed to promote chondrocyte growth. Comparing conventional coating methods, polyelectrolyte multilayers are easy and stable to prepare. It may be a promising choice for the surface modification of complex biomedical devices. These very flexible systems allow broad medical applications for drug delivery and tissue engineering.     

Optimization of cardiac cell seeding and distribution in 3D porous alginate scaffolds

Cardiac tissue engineering has evolved as a potential therapeutic approach to assist in cardiac regeneration. We have recently shown that tissue-engineered cardiac graft, constructed from cardiomyocytes seeded within an alginate scaffold, is capable of preventing the deterioration in cardiac function after myocardial infarction in rats. The present article addresses cell seeding within porous alginate scaffolds in an attempt to achieve 3D high-density cardiac constructs with a uniform cell distribution. Due to the hydrophilic nature of the alginate scaffold, its >90% porosity and interconnected pore structure, cell seeding onto the scaffold was efficient and short, up to 30 min. Application of a moderate centrifugal force during cell seeding resulted in a uniform cell distribution throughout the alginate scaffolds, consequently enabling the loading of a large number of cells onto the 3D scaffolds. The percent cell yield in the alginate scaffolds ranged between 60-90%, depending on cell density at seeding; it was 90% at seeding densities of up to 1 x 10(8) cells/cm(3) scaffold and decreased to 60% at higher densities. The highly dense cardiac constructs maintained high metabolic activity in culture. Scanning electron microscopy revealed that the cells aggregated within the scaffold pores. Some of the aggregates were contracting spontaneously within the matrix pores. Throughout the culture there was no indication of cardiomyocyte proliferation within the scaffolds, nor was it found in 3D cultures of cardiofibroblasts. This may enable the development of cardiac cocultures, without domination of cardiofibroblasts with time.