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.     

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.     

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.     

Macro-scale topology optimization for controlling internal shear stress in a porous scaffold bioreactor

Shear stress is an important physical factor that regulates proliferation, migration, and morphogenesis. In particular, the homeostasis of blood vessels is dependent on shear stress. To mimic this process ex vivo, efforts have been made to seed scaffolds with vascular and other cell types in the presence of growth factors and under pulsatile flow conditions. However, the resulting bioreactors lack information on shear stress and flow distributions within the scaffold. Consequently, it is difficult to interpret the effects of shear stress on cell function. Such knowledge would enable researchers to improve upon cell culture protocols. Recent work has focused on optimizing the microstructural parameters of the scaffold to fine tune the shear stress. In this study, we have adopted a different approach whereby flows are redirected throughout the bioreactor along channels patterned in the porous scaffold to yield shear stress distributions that are optimized for uniformity centered on a target value. A topology optimization algorithm coupled to computational fluid dynamics simulations was devised to this end. The channel topology in the porous scaffold was varied using a combination of genetic algorithm and fuzzy logic. The method is validated by experiments using magnetic resonance imaging readouts of the flow field.     

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.     

A finite element study of mechanical stimuli in scaffolds for bone tissue engineering

Mechanical stimuli are one of the factors that affect cell proliferation and differentiation in the process of bone tissue regeneration. Knowledge on the specific deformation sensed by cells at a microscopic level when mechanical loads are applied is still missing in the development of biomaterials for bone tissue engineering. The objective of this study was to analyze the behavior of the mechanical stimuli within some calcium phosphate-based scaffolds in terms of stress and strain distributions in the solid material phase and fluid velocity, fluid pressure and fluid shear stress distributions in the pores filled of fluid, by means of micro computed tomographed (CT)-based finite element (FE) models. Two samples of porous materials, one of calcium phosphate-based cement and another of biodegradable glass, were used. Compressive loads equivalent to 0.5% of compression applied to the solid material phase and interstitial fluid flows with inlet velocities of 1, 10 and 100 microm/s applied to the interconnected pores were simulated, changing also the inlet side and the viscosity of the medium. Similar strain distributions for both materials were found, with compressive and tensile strain maximal values of 1.6% and 0.6%, respectively. Mean values were consistent with the applied deformation. When 10 microm/s of inlet fluid velocity and 1.45 Pas viscosity, maximal values of fluid velocity were 12.76 mm/s for CaP cement and 14.87 mm/s for glass. Mean values were consistent with the inlet ones applied, and mean values of shear stress were around 5 x 10(-5)Pa. Variations on inlet fluid velocity and fluid viscosity produce proportional and independent changes in fluid velocity, fluid shear stress and fluid pressure. This study has shown how mechanical loads and fluid flow applied on the scaffolds cause different levels of mechanical stimuli within the samples according to the morphology of the materials.     

可控多孔结构支架制备及灌注式体外培养

利用CAD和快速成形技术设计制造具有可控多孔结构的支架。构建灌注式生物反应器系统,实现氧气和营养物质的大量输送,同时产生一定流体剪应力,调节细胞功能的发挥。根据支架负型结构制造出相应的树脂原型,用磷酸钙骨水泥进行填充烧结,得到与设计相符的多孔支架。接种兔成骨细胞,分别采用静态和灌注式三维动态培养方法,观察不同培养条件下细胞在支架表面以及所构造微管道内的生长情况。试验结果表明,灌注式体外培养方法更有利于细胞在支架微管道内的存活和功能的发挥,此灌注式系统能够改善支架微管道内细胞生存的微环境,增强黏附在支架微管道内细胞的活性,促进细胞进一步的增殖和矿化基质的产生。     

Fabrication of individual scaffolds based on a patient-specific alveolar bone defect model

Fabricating individualized tissue engineering scaffolds based on the three-dimensional shape of patient bone defects is required for the successful clinical application of bone tissue engineering. However, there are currently no reported studies of individualized bone tissue engineering scaffolds that truly reproduce a patient-specific bone defect. We fabricated individualized tissue engineering scaffolds based on alveolar bone defects. The individualized poly(lactide-co-glycolide) and tricalcium phosphate composite scaffolds were custom-made by acquiring the three-dimensional model through computed tomography, which was input into the computer-aided low-temperature deposition manufacturing system. The three-dimensional shape of the fabricated scaffold was identical to the patient-specific alveolar bone defects, with an average macropore diameter of 380 μm, micropore diameters ranging from 3 to 5 μm, and an average porosity of 87.4%. The mechanical properties of the scaffold were similar to adult cancellous bone. Scaffold biocompatibility was confirmed by attachment and proliferation of human bone marrow mesenchymal stem cells. Successful realization of individualized scaffold fabrication will enable clinical application of tissue-engineered bone at an early date.     

Degradation of supercoiled plasmid DNA within a capillary device

Supercoiled plasmid DNA is susceptible to fluid stress in large-scale manufacturing processes. A capillary device was used to generate controlled shear conditions and the effects of different stresses on plasmid DNA structure were investigated. Computational fluid dynamics (CFD) analysis was employed to characterize the flow environment in the capillary device and different analytical techniques were used to quantify the DNA breakage. It was found that the degradation of plasmid DNA occurred at the entrance of the capillary and that the shear stress within the capillary did not affect the DNA structure. The degradation rate of plasmids was well correlated with the average elongational strain rate or the pressure drop at the entrance region. The conclusion may also be drawn that laminar shear stress does not play a significant role in plasmid DNA degradation.     

Fabrication of a Bioactive,PCL-based "Self-fitting" Shape Memory Polymer Scaffold

Tissue engineering has been explored as an alternative strategy for the treatment of critical-sized cranio-maxillofacial (CMF) bone defects. Essential to the success of this approach is a scaffold that is able to conformally fit within an irregular defect while also having the requisite biodegradability, pore interconnectivity and bioactivity. By nature of their shape recovery and fixity properties, shape memory polymer (SMP) scaffolds could achieve defect “self-fitting.” In this way, following exposure to warm saline (~60 ºC), the SMP scaffold would become malleable, permitting it to be hand-pressed into an irregular defect. Subsequent cooling (~37 ºC) would return the scaffold to its relatively rigid state within the defect. To meet these requirements, this protocol describes the preparation of SMP scaffolds prepared via the photochemical cure of biodegradable polycaprolactone diacrylate (PCL-DA) using a solvent-casting particulate-leaching (SCPL) method. A fused salt template is utilized to achieve pore interconnectivity. To realize bioactivity, a polydopamine coating is applied to the surface of the scaffold pore walls. Characterization of self-fitting and shape memory behaviors, pore interconnectivity and in vitro bioactivity are also described.     

Modeling of flow‐induced shear stress applied on 3D cellular scaffolds: Implications for vascular tissue engineering

Novel tissue‐culture bioreactors employ flow‐induced shear stress as a means of mechanical stimulation of cells. We developed a computational fluid dynamics model of the complex three‐dimensional (3D) microstructure of a porous scaffold incubated in a direct perfusion bioreactor. Our model was designed to predict high shear‐stress values within the physiological range of those naturally sensed by vascular cells (1–10 dyne/cm²), and will thereby provide suitable conditions for vascular tissue‐engineering experiments. The model also accounts for cellular growth, which was designed as an added cell layer grown on all scaffold walls. Five model variants were designed, with geometric differences corresponding to cell‐layer thicknesses of 0, 50, 75, 100, and 125 µm. Four inlet velocities (0.5, 1, 1.5, and 2 cm/s) were applied to each model. Wall shear‐stress distribution and overall pressure drop calculations were then used to characterize the relation between flow rate, shear stress, cell‐layer thickness, and pressure drop. The simulations showed that cellular growth within 3D scaffolds exposes cells to elevated shear stress, with considerably increasing average values in correlation to cell growth and inflow velocity. Our results provide in‐depth analysis of the microdynamic environment of cells cultured within 3D environments, and thus provide advanced control over tissue development in vitro. Biotechnol. Bioeng. 2010; 105: 645–654. © 2009 Wiley Periodicals, Inc.     

Biomechanical study on the edge shapes for penetrating keratoplasty

A parametric study to investigate the compressive and the shear stress distributions for various edge shapes created during penetrating keratoplasty (PK) using femtosecond laser is reported. The finite element analysis has been implemented using ABAQUS to study the cornea with various edge shapes, namely the standard edge shape, the zigzag edge shape, the top hat edge shape and the mushroom edge shape for PK. The ratio of maximum compressive stress to maximum shear stress is used as the main factor to assess the relative merits of wound healing rate for different edge shapes. For the typical values of tissue mechanical properties, the zigzag edge shape has the highest ratio of maximum compressive stress to maximum shear stress (11.1 in the xy-direction and 3.7 in the yz-direction), followed by the mushroom edge shape (7.7 in the xy-direction and 3.2 in the yz-direction). The ratios for the top hat and the standard edge shapes are even lower in both directions. A sensitivity analysis of the model has been done to demonstrate that the zigzag edge shape always results in the highest ratios of stresses regardless of the difference in the tissue mechanical properties. The zigzag edge shape also gives the lowest dioptric power D?=?45.4. The present results imply that the zigzag edge shape provides the best wound healing rate and optical outcome among the four edge shapes models for PK.     

Fabrication of Mechanically Tunable and Bioactive Metal Scaffolds for Biomedical Applications

Biometal systems have been widely used for biomedical applications, in particular, as load-bearing materials. However, major challenges are high stiffness and low bioactivity of metals. In this study, we have developed a new method towards fabricating a new type of bioactive and mechanically reliable porous metal scaffolds-densified porous Ti scaffolds. The method consists of two fabrication processes, 1) the fabrication of porous Ti scaffolds by dynamic freeze casting, and 2) coating and densification of the porous scaffolds. The dynamic freeze casting method to fabricate porous Ti scaffolds allowed the densification of porous scaffolds by minimizing the chemical contamination and structural defects. The densification process is distinctive for three reasons. First, the densification process is simple, because it requires a control of only one parameter (degree of densification). Second, it is effective, as it achieves mechanical enhancement and sustainable release of biomolecules from porous scaffolds. Third, it has broad applications, as it is also applicable to the fabrication of functionally graded porous scaffolds by spatially varied strain during densification.     

Tissue engineering scaffolds based on photocured dimethacrylate polymers for in vitro optical imaging

Model tissue engineering scaffolds based on photocurable resin mixtures with sodium chloride have been prepared for optical imaging studies of cell attachment. A photoactivated ethoxylated bisphenol A dimethacrylate was mixed with sieved sodium chloride (NaCl) crystals and photocured to form a cross-linked composite. Upon soaking in water, the NaCl dissolved to leave a porous scaffold with desirable optical properties, mechanical integrity, and controlled porosity. Scaffolds were prepared with salt crystals that had been sieved to average diameters of 390, 300, 200, and 100 microm, yielding porosities of approximately 75 vol %. Scanning electron microscopy and X-ray microcomputed tomography confirmed that the pore size distribution of the scaffolds could be controlled using this photocuring technique. Compression tests showed that for scaffolds with 84% (by mass fraction) salt, the larger pore size scaffolds were more rigid, while the smaller pore size scaffolds were softer and more readily compressible. The prepared scaffolds were seeded with osteoblasts, cultured between 3 and 18 d, and examined using confocal microscopy. Because the cross-linked polymer in the scaffolds is an amorphous glass, it was possible to optically image cells that were over 400 microm beneath the surface of the sample.     

Porous 3-D scaffolds from regenerated silk fibroin

Three fabrication techniques, freeze-drying, salt leaching and gas foaming, were used to form porous three-dimensional silk biomaterial matrixes. Matrixes were characterized for morphological and functional properties related to processing method and conditions. The porosity of the salt leached scaffolds varied between 84 and 98% with a compressive strength up to 175 +/- 3 KPa, and the gas foamed scaffolds had porosities of 87-97% and compressive strength up to 280 +/- 4 KPa. The freeze-dried scaffolds were prepared at different freezing temperatures (-80 and -20 degrees C) and subsequently treated with different concentrations (15 and 25%) and hydrophilicity alcohols. The porosity of these scaffolds was up to 99%, and the maximum compressive strength was 30 +/- 2 KPa. Changes in silk fibroin structure during processing to form the 3D matrixes were determined by FT-IR and XrD. The salt leached and gas foaming techniques produced scaffolds with a useful combination of high compressive strength, interconnected pores, and pore sizes greater than 100 microns in diameter. The results suggest that silk-based 3D matrixes can be formed for utility in biomaterial applications.     

Silk scaffolds connected with different naturally occurring biomaterials for prostate cancer cell cultivation in 3D

In the present work, different biopolymer blend scaffolds based on the silk protein fibroin from Bombyx mori (BM) were prepared via freeze‐drying method. The chemical, structural, and mechanical properties of the three dimensional (3D) porous silk fibroin (SF) composite scaffolds of gelatin, collagen, and chitosan as well as SF from Antheraea pernyi (AP) and the recombinant spider silk protein spidroin (SSP1) have been systematically investigated, followed by cell culture experiments with epithelial prostate cancer cells (LNCaP) up to 14 days. Compared to the pure SF scaffold of BM, the blend scaffolds differ in porous morphology, elasticity, swelling behavior, and biochemical composition. The new composite scaffold with SSP1 showed an increased swelling degree and soft tissue like elastic properties. Whereas, in vitro cultivation of LNCaP cells demonstrated an increased growth behavior and spheroid formation within chitosan blended scaffolds based on its remarkable porosity, which supports nutrient supply matrix. Results of this study suggest that silk fibroin matrices are sufficient and certain SF composite scaffolds even improve 3D cell cultivation for prostate cancer research compared to matrices based on pure biomaterials or synthetic polymers.     

Singularity solution of Lanir's osmoelasticity: verification of discontinuity simulations in soft tissues

The literature characterizes cartilaginous tissues as osmoviscoelastic. Understanding the damage and failure of these tissues is essential for designing treatments. To determine tissue strength and local stresses, experimental studies—both clinical and animal—are generally supported by computational studies. Verification methods for computational studies of ionized porous media including cracks are hardly available. This study provides a method for verification and shows its performance. For this purpose, shear loading of a finite crack is addressed analytically and through a commercial finite element code. Impulsive shear loading by two-edge dislocation of a crack was considered in a 2D plane strain model for an ionized porous medium. To derive the analytical solution, the system of equation is decoupled by stress functions. The shear stress distribution at the plane of the crack is derived using Fourier and Laplace transformations. The analytical solution for the shear stress distribution is compared with computer simulations in ABAQUS version 6.4-5. Decoupling of the equations makes it possible to solve some boundary value problems in porous media taking chemical effects into account. The numerical calculations underestimate the shear stress at the crack-tips. Mesh refinement increases accuracy, but is still low in the neighborhood of the crack-tips.     

Use of porous pyrolytic carbon for analytical and microscale high-performance liquid chromatographic bioseparations

Porous carbonaceous adsorbent was prepared by carbonization of saccharose in silica gel pores followed by leeching out of the silica matrix. The product of pyrolysis was then deactivated by hydrogenation. The resulting adsorbent shows intermediate sorption properties between those of the highly polar pyrolytic glassy carbon and the hydrophobic graphitized carbon. The microparticulate mesoporous carbon was examined for its use in capillary HPLC separations. The separation of selected stereoisomers in a 320 μm I.D. capillary column packed with the porous carbon particles is described and discussed. Additionaly, the porous carbon filled with dextran gel was tested as a material for direct HPLC analysis of drugs in human serum.     

Cells in 3D matrices under interstitial flow: Effects of extracellular matrix alignment on cell shear stress and drag forces

Interstitial flow is an important regulator of various cell behaviors both in vitro and in vivo, yet the forces that fluid flow imposes on cells embedded in a 3D extracellular matrix (ECM), and the effects of matrix architecture on those forces, are not well understood. Here, we demonstrate how fiber alignment can affect the shear and pressure forces on the cell and ECM. Using computational fluid dynamics simulations, we show that while the solutions of the Brinkman equation accurately estimate the average fluid shear stress and the drag forces on a cell within a 3D fibrous medium, the distribution of shear stress on the cellular surface as well as the peak shear stresses remain intimately related to the pericellular fiber architecture and cannot be estimated using bulk-averaged properties. We demonstrate that perpendicular fiber alignment of the ECM yields lower shear stress and pressure forces on the cells and higher stresses on the ECM, leading to decreased permeability, while parallel fiber alignment leads to higher stresses on cells and increased permeability, as compared to a cubic lattice arrangement. The Spielman–Goren permeability relationships for fibrous media agreed well with CFD simulations of flow with explicitly considered fibers. These results suggest that the experimentally observed active remodeling of ECM fibers by fibroblasts under interstitial flow to a perpendicular alignment could serve to decrease the shear and drag forces on the cell.     

Interplay between Cytoskeletal Stresses and Cell Adaptation under Chronic Flow

Using stress sensitive FRET sensors we have measured cytoskeletal stresses in α-actinin and the associated reorganization of the actin cytoskeleton in cells subjected to chronic shear stress. We show that long-term shear stress reduces the average actinin stress and this effect is reversible with removal of flow. The flow-induced changes in cytoskeletal stresses are found to be dynamic, involving a transient decrease in stress (phase-I), a short-term increase (3–6 min) (Phase-II), followed by a longer-term decrease that reaches a minimum in ∼20 min (Phase-III), before saturating. These changes are accompanied by reorganization of the actin cytoskeleton from parallel F-actin bundles to peripheral bundles. Blocking mechanosensitive ion channels (MSCs) with Gd³⁺ and GsMTx4 (a specific inhibitor) eliminated the changes in cytoskeletal stress and the corresponding actin reorganization, indicating that Ca²⁺ permeable MSCs participate in the signaling cascades. This study shows that shear stress induced cell adaptation is mediated via MSCs.