Geometry Design Optimization of Functionally Graded Scaffolds for Bone Tissue Engineering: A Mechanobiological Approach

Functionally Graded Scaffolds (FGSs) are porous biomaterials where porosity changes in space with a specific gradient. In spite of their wide use in bone tissue engineering, possible models that relate the scaffold gradient to the mechanical and biological requirements for the regeneration of the bony tissue are currently missing. In this study we attempt to bridge the gap by developing a mechanobiology-based optimization algorithm aimed to determine the optimal graded porosity distribution in FGSs. The algorithm combines the parametric finite element model of a FGS, a computational mechano-regulation model and a numerical optimization routine. For assigned boundary and loading conditions, the algorithm builds iteratively different scaffold geometry configurations with different porosity distributions until the best microstructure geometry is reached, i.e. the geometry that allows the amount of bone formation to be maximized. We tested different porosity distribution laws, loading conditions and scaffold Young’s modulus values. For each combination of these variables, the explicit equation of the porosity distribution law–i.e the law that describes the pore dimensions in function of the spatial coordinates–was determined that allows the highest amounts of bone to be generated. The results show that the loading conditions affect significantly the optimal porosity distribution. For a pure compression loading, it was found that the pore dimensions are almost constant throughout the entire scaffold and using a FGS allows the formation of amounts of bone slightly larger than those obtainable with a homogeneous porosity scaffold. For a pure shear loading, instead, FGSs allow to significantly increase the bone formation compared to a homogeneous porosity scaffolds. Although experimental data is still necessary to properly relate the mechanical/biological environment to the scaffold microstructure, this model represents an important step towards optimizing geometry of functionally graded scaffolds based on mechanobiological criteria.     

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%.     

Fabrication of a biomimetic spinal cord tissue construct with heterogenous mechanical properties using intrascaffold cell assembly

In tissue engineering studies, scaffolds play a very important role in offering both physical and chemical cues for cell growth and tissue regeneration. However, in some cases, tissue regeneration requires scaffolds with high mechanical properties (e.g., bone and cartilage), while cells need a soft mechanical microenvironment. In this study, to mimic the heterogenous mechanical properties of a spinal cord tissue, a biomimetic rat tissue construct is fabricated. A collagen-coated poly(lactic-co-glycolic acid) scaffold is manufactured using thermally induced phase separation casting. Primary rat neural cells (P01 Wistar rat cortex) with soft hydrogels are later printed within the scaffold using an image-guided intrascaffold cell assembly technique. The scaffolds have unidirectional microporous structure with parallel axial macrochannels (260 ± 4 µm in diameter). Scaffolds showed mechanical properties similar to rat spine (ultimate tensile strength: 0.085 MPa, Young's modulus [stretch]: 0.31 MPa). The bioink composed of gelatin/alginate/fibrinogen is precisely printed into the macrochannels and showed mechanical properties suitable for neural cells (Young's modulus [compressive]: 3.814 kPa). Scaffold interface, cell viability, and immunostaining analyses show uniform distribution of stable, healthy, and elongated neural cells and neurites over 14 culture days in vitro. The results demonstrated that this method can serve as a valuable tool to aid manufacturing of tissue constructs requiring heterogenous mechanical properties for complex cell and/or biomolecule assembly.     

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.

     

Biodegradable microfluidic scaffolds for tissue engineering from amino alcohol-based poly(ester amide) elastomers

Biodegradable polymers with high mechanical strength, flexibility and optical transparency, optimal degradation properties and biocompatibility are critical to the success of tissue engineered devices and drug delivery systems. Most biodegradable polymers suffer from a short half-life due to rapid degradation upon implantation, exceedingly high stiffness, and limited ability to functionalize the surface with chemical moieties. This work describes the fabrication of microfluidic networks from poly(ester amide), poly(1,3-diamino-2-hydroxypropane-co-polyol sebacate) (APS), a recently developed biodegradable elastomeric polymer. Microfluidic scaffolds constructed from APS exhibit a much lower Young''s modulus and a significantly longer degradation half-life than those of previously reported systems. The device is fabricated using a modified replica-molding technique, which is rapid, inexpensive, reproducible and scalable, making the approach ideal for both rapid prototyping and manufacturing of tissue engineering scaffolds.Key words: biodegradable, microfluidics, tissue engineering, elastomer, scaffold, polymer     

Effects of three-dimensional scaffolds on cell organization and tissue development

Tissue engineering scaffolds play a critical role in regulating the reconstructed human tissue development. Various types of scaffolds have been developed in recent years, including fibrous matrix and foam-like scaffolds. The design of scaffold materials has been investigated extensively. However, the design of physical structure of the scaffold, especially fibrous matrices, has not received much attention. This paper compares the different characteristics of fibrous and foam-like scaffolds, and reviews regulatory roles of important scaffold properties, including surface geometry, scaffold configuration, pore structure, mechanical property and bioactivity. Tissue regeneration, cell organization, proliferation and differentiation under different microstructures were evaluated. The importance of proper scaffold selection and design is further discussed with the examples of bone tissue engineering and stem cell tissue engineering. This review addresses the importance of scaffold microstructure and provides insights in designing appropriate scaffold structure for different applications of tissue engineering.     

Morphological characterization of a novel scaffold for anterior cruciate ligament tissue engineering

Tissue engineering offers an interesting alternative to current anterior cruciate ligament (ACL) surgeries. Indeed, a tissue-engineered solution could ideally overcome the long-term complications due to actual ACL reconstruction by being gradually replaced by biological tissue. Key requirements concerning the ideal scaffold for ligament tissue engineering are numerous and concern its mechanical properties, biochemical nature, and morphology. This study is aimed at predicting the morphology of a novel scaffold for ligament tissue engineering, based on multilayer braided biodegradable copoly(lactic acid-co-(e-caprolactone)) (PLCL) fibers The process used to create the scaffold is briefly presented, and the degradations of the material before and after the scaffold processing are compared. The process offers varying parameters, such as the number of layers in the scaffold, the pitch length of the braid, and the fibers' diameter. The prediction of the morphology in terms of pore size distribution and pores interconnectivity as a function of these parameters is performed numerically using an original method based on a virtual scaffold. The virtual scaffold geometry and the prediction of pore size distribution are evaluated by comparison with experimental results. The presented process permits creation of a tailorable scaffold for ligament tissue engineering using basic equipment and from minimum amounts of raw material. The virtual scaffold geometry closely mimics the geometry of real scaffolds, and the prediction of the pore size distribution is found to be in good accordance with measurements on real scaffolds. The scaffold offers an interconnected network of pores the sizes of which are adjustable by playing on the process parameters and are able to match the ideal pore size reported for tissue ingrowth. The adjustability of the presented scaffold could permit its application in both classical ACL reconstructions and anatomical double-bundle reconstructions. The precise knowledge of the scaffold morphology using the virtual scaffold will be useful to interpret the activity of cells once it will be seeded into the scaffold. An interesting perspective of the present work is to perform a similar study aiming at predicting the mechanical response of the scaffold according to the same process parameters, by implanting the virtual scaffold into a finite element algorithm.     

Understanding the effect of mean pore size on cell activity in collagen-glycosaminoglycan scaffolds

Mean pore size is an essential aspect of scaffolds for tissue-engineering. If pores are too small cells cannot migrate in towards the center of the construct limiting the diffusion of nutrients and removal of waste products. Conversely, if pores are too large there is a decrease in specific surface area available limiting cell attachment. However the relationship between scaffold pore size and cell activity is poorly understood and as a result there are conflicting reports within the literature on the optimal pore size required for successful tissue-engineering. Previous studies in bone tissue-engineering have indicated a range of mean pore sizes (96–150 µm) to facilitate optimal attachment. Other studies have shown a need for large pores (300–800 µm) for successful bone growth in scaffolds. These conflicting results indicate that a balance must be established between obtaining optimal cell attachment and facilitating bone growth. In this commentary we discuss our recent investigations into the effect of mean pore size in collagen-glycosaminoglycan (CG) scaffolds with pore sizes ranging from 85–325 μm and how it has provided an insight into the divergence within the literature.     

SEM and 3D synchrotron radiation micro-tomography in the study of bioceramic scaffolds for tissue-engineering applications

Different biomaterials have been proposed as scaffolds for the delivery of cells and/or biological molecules to repair or regenerate damaged or diseased bone tissues. Particular attention is being given to porous bioceramics that mimic trabecular bone chemistry and structure. Chemical composition, density, pore shape, pore size, and pore interconnection are elements that have to be considered to improve the efficiency of these biomaterials. Commonly, two-dimensional (2D) systems of analysis such as scanning electron microscope (SEM) are used for the characterization and comparison of the scaffolds. Unfortunately, these systems do not allow a complete investigation of the three-dimensional (3D) spatial structure of the scaffold. In this study, we have considered two different techniques, that is, SEM and 3D synchrotron radiation (SR) micro-CT to extract information on the geometry of two hydroxyapatite (HA) bioceramics with identical chemical composition but different micro-porosity, pore size distribution, and pore interconnection pathway. The two scaffolds were obtained with two different procedures: (a) sponge matrix embedding (scaffold FB), and (b) foaming (scaffold EP). Both scaffolds showed structures suitable for tissue-engineering applications, but scaffold EP appeared superior with regard to interconnection of pores, surface on which the new bone could be deposited, and percentage of volume available to bone deposition.     

Quantification of fluid shear stress in bone tissue engineering scaffolds with spherical and cubical pore architectures

Recent studies have shown that mechanical stimulation, in the form of fluid perfusion and mechanical compression, can enhance osteogenic differentiation of mesenchymal stem cells and bone cells within tissue engineering scaffolds in vitro. The precise nature of mechanical stimulation within tissue engineering scaffolds is not only dictated by the exogenously applied loading regime, but also depends on the geometric features of the scaffold, in particular architecture, pore size and porosity. However, the precise contribution of each geometric feature towards the resulting mechanical stimulation within a scaffold is difficult to characterise due to the wide range of interacting parameters. In this study, we have applied a fluid–structure interaction model to investigate the role of scaffold geometry (architecture, pore size and porosity) on pore wall shear stress (WSS) under a range of different loading scenarios: fluid perfusion, mechanical compression and a combination of perfusion and compression. It is found that scaffold geometry (spherical and cubical pores), in particular the pore size, has a significant influence on the stimulation within scaffolds. Furthermore, we observed an amplified WSS within scaffolds under a combination of fluid perfusion and mechanical compression, which exceeded that caused by individual fluid perfusion or mechanical compression approximately threefold. By conducting this comprehensive parametric variation study, an expression was generated to allow the design and optimisation of 3D TE scaffolds and inform experimental loading regimes so that a desired level of mechanical stimulation, in terms of WSS is generated within the scaffold.     

The microscopic biological response of human chondrocytes to bovine bone scaffold

This study was performed to determine the microscopic biological response of human nasal septum chondrocytes and human knee articular chondrocytes placed on a demineralized bovine bone scaffold. Both chondrocytes were cultured and seeded onto the bovine bone scaffold with seeding density of 1 × 105 cells per 100 μl/scaffold and incubated for 1, 2, 5 and 7 days. Proliferation and viability of the cells were measured by mitochondrial dehydrogenase activity (MTT assay), adhesion study was analyzed by scanning electron microscopy and differentiation study was analyzed by immunofluorescence staining and confocal laser scanning electron microscopy. The results showed good proliferation and viability of both chondrocytes on the scaffolds from day 1 to day 7. Both chondrocytes increased in number with time and readily grew on the surface and into the open pores of the scaffold. Immunofluorescence staining demonstrated collagen type II on the scaffolds for both chondrocytes. The results showed good cells proliferation, attachment and maturity of the chondrocytes on the demineralized bovine bone scaffold. The bovine bone being easily resourced, relatively inexpensive and non toxic has good potential for use as a three dimensional construct in cartilage tissue engineering.     

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.     

Ectopic Osteogenesis and Scaffold Biodegradation of Nano-Hydroxyapatite-Chitosan in a Rat Model

The bone-formation and scaffold-biodegradation processes have not been fully characterized. This study aimed to determine the osteogenic ability of nHA-CS osteo-induced bone marrow mesenchymal stem cell (BMSC) composites and to explore the relationship between bone formation and scaffold biodegradation. The nHA-CS osteo-induced BMSC composites (nHA-CS+cells group) and the nHA-CS scaffolds (nHA-CS group) were implanted into the femoral spatium intermusculare of SD rats. At 2, 4, 6, 8, and 12 weeks post-implantation, the rat femurs were scanned using computerized tomography (CT), and the CT values of the implants were measured and comparatively analyzed. The implants were then harvested and subjected to hematoxylin and eosin (HE) and Masson''s trichrome staining, and the percentages of bone area, scaffold area and collagen area were compared between the two groups. The CT values of the implants were higher in the nHA-CS+cells group than the nHA-CS group at the same time points (P < 0.05). Histological analysis revealed that de novo bone and collagen formation in the pores of the scaffolds gradually increased from 2 weeks post-implantation in both groups and that the scaffold gradually degraded as bone formation proceeded. However, more de novo bone and collagen formation and scaffold degradation occurred in the nHA-CS+cells group than in the nHA-CS group at the same time points (P < 0.05). In conclusion, nHA-CS osteo-induced BMSC composites are promising bone tissue engineering substitutes, and osteo-induced BMSCs can significantly enhance the osteogenic ability and play an active role in the degradation of nHA-CS scaffolds on par with bone formation.     

Subject-specific mechanical properties of vertebral cancellous bone assessed using a low-dose X-ray device

ObjectivesAccording to the inter-individual variability of bone mechanical properties, subject-specific evaluation of the cancellous bone Young's modulus is needed to build finite-element models predicting vertebral strength with accuracy. Relationships based on the density assessed by quantitative computed tomography were proposed. However, quantitative computed tomography is not always suited for the analysis of the whole spine for patients’ follow-up because of the high radiation dose. Hence, this study aims at evaluating the mechanical properties of the vertebral cancellous bone using a low-dose X-ray device.Material and methodsNineteen vertebrae were considered. Biplanar radiographs were made using the low-dose EOS^® system with a dual-energy modality to evaluate antero-posterior and lateral areal bone mineral densities. A cylindrical sample was extracted from each vertebral body and tested until failure to assess the Young's modulus and the ultimate stress of the vertebral cancellous bone.Results and discussionMechanical properties were significantly related to the EOS^® areal densities. On one hand, the relationships remained less predictive than those based on quantitative computed tomography, but on the other hand, they better predict mechanical properties than previous studies using dual X-ray absorptiometry (clinical gold standard system for density assessment).ConclusionThe study shows the feasibility to predict the Young's modulus of the vertebral cancellous bone from the whole vertebral areal bone mineral density (BMD). It gives promising prospects to build finite-element models, including both subject-specific geometry and subject-specific mechanical properties by using a low-dose X-ray device for regions where high radiation doses would limit tomography assessment possibilities.     

Chemotaxis of mesenchymal stem cells within 3D biomimetic scaffolds--a modeling approach

Bone tissue engineering is a promising strategy to repair local defects by implanting biodegradable scaffolds which undergo remodeling and are replaced completely by autologous bone tissue. Here, we consider a Keller-Segel model to describe the chemotaxis of bone marrow-derived mesenchymal stem cells (BMSCs) into a mineralized collagen scaffold. Following recent experimental results in bone healing, demonstrating that a sub-population of BMSCs can be guided into 3D scaffolds by gradients of signaling molecules such as SDF-1α, we consider a population of BMSCs on the surface of the pore structure of the scaffold and the chemoattractant SDF-1α within the pores. The resulting model is a coupled bulk/surface model which we reformulate following a diffuse-interface approach in which the geometry is implicitly described using a phase-field function. We explain how to obtain such an implicit representation and present numerical results on μCT-data for real scaffolds, assuming a diffusion of SDF-1α being coupled to diffusion and chemotaxis of the cells towards SDF-1α. We observe a slowing-down of BMSC ingrowth after the scaffold becomes saturated with SDF-1α, suggesting that a slow release of SDF-1α avoiding an early saturation is required to enable a complete colonization of the scaffold. The validation of our results is possible via SDF-1α release from injectable carrier materials, and an adaptation of our model to similar coupled bulk/surface problems such as remodeling processes seems attractive.     

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.     

Effect of Layer Thickness and Printing Orientation on Mechanical Properties and Dimensional Accuracy of 3D Printed Porous Samples for Bone Tissue Engineering

Powder-based inkjet 3D printing method is one of the most attractive solid free form techniques. It involves a sequential layering process through which 3D porous scaffolds can be directly produced from computer-generated models. 3D printed products'' quality are controlled by the optimal build parameters. In this study, Calcium Sulfate based powders were used for porous scaffolds fabrication. The printed scaffolds of 0.8 mm pore size, with different layer thickness and printing orientation, were subjected to the depowdering step. The effects of four layer thicknesses and printing orientations, (parallel to X, Y and Z), on the physical and mechanical properties of printed scaffolds were investigated. It was observed that the compressive strength, toughness and Young''s modulus of samples with 0.1125 and 0.125 mm layer thickness were more than others. Furthermore, the results of SEM and μCT analyses showed that samples with 0.1125 mm layer thickness printed in X direction have more dimensional accuracy and significantly close to CAD software based designs with predefined pore size, porosity and pore interconnectivity.     

Rheology and synergy of κ-carrageenan/locust bean gum/konjac glucomannan gels

The rheology and melting of mixed polysaccharide gels containing konjac glucomannan (KGM), locust bean gum (LBG) and κ-carrageenan (KC) were studied. Synergy-type peaks in the Young's modulus at optimal mixing ratios were found for both KC/LBG and KC/KGM binary gels at a fixed total polysaccharide content (1:5.5 for LBG:KC and 1:7 for KGM:KC). The Young's modulus peak for KC/KGM was higher than for KC/LBG gels. The same stoichiometric mixing ratios were found when either LBG or KGM was added to KC at a fixed KC concentration, where the Young's modulus increased up to additions at the stoichiometric ratio, but leveled off at higher LBG or KGM additions. Addition of KGM or LBG to the 2-component gels beyond the stoichiometric (optimal) mixing ratio at a fixed total polysaccharide content led to a decrease in the Young's modulus and an increase in the rupture strain and stress in extension, and both trends were stronger for KGM than for LBG.     

Effect of rehabilitation exercise durations on the dynamic bone repair process by coupling polymer scaffold degradation and bone formation

Implantation of biodegradable scaffold is considered as a promising method to treat bone disorders, but knowledge of the dynamic bone repair process is extremely limited. In this study, based on the representative volume cell of a periodic scaffold, the influence of rehabilitation exercise duration per day on the bone repair was investigated by a computational framework. The framework coupled scaffold degradation and bone remodeling. The scaffold degradation was described by a function of stochastic hydrolysis independent of mechanical stimulation, and the bone formation was remodeled by a function of the mechanical stimulation, i.e., strain energy density. Then, numerical simulations were performed to study the dynamic bone repair process. The results showed that the scaffold degradation and the bone formation in the process were competitive. An optimal exercise duration per day emerged. All exercise durations promoted the bone maturation with a final Young’s modulus of 1.9 ± 0.3 GPa. The present study connects clinical rehabilitation and fundamental research, and is helpful to understand the bone repair process and further design bone scaffold for bone tissue engineering.     

A dynamical study of the mechanical stimuli and tissue differentiation within a CaP scaffold based on micro-CT finite element models

The control of the mechanical stimuli transmitted to the cells is critical for the design of functional scaffolds for tissue engineering. The objective of this study was to investigate the dynamics of the mechanical stimuli transmitted to the cells during tissue differentiation in an irregular morphology scaffold under compressive load and perfusion flow. A calcium phosphate-based glass porous scaffold was used. The solid phase and the fluid flow within the pores were modeled as linear elastic solid material and Newtonian fluid, respectively. In the fluid model, different levels of viscosity were used to simulate tissue differentiation. Compressive strain of 0.5% and fluid flow with constant inlet velocity of 10 μm/s or constant inlet pressure of 3 Pa were applied. Octahedral shear strain and fluid shear stress were used as mechano-regulatory stimuli. For constant inlet velocity, stimuli equivalent to bone were predicted in 80% of pore volume for the case of low tissue viscosity. For the cases of high viscosity, fluctuations between stimuli equivalent to tissue formation and cell death were predicted due to the increase in the fluid shear stress when tissue started to fill pores. When constant pressure was applied, stimuli equivalent to bone were predicted in 62% of pore volume when low tissue viscosity was used and 42% when high tissue viscosity was used. This study predicted critical variations of fluid shear stress when cells differentiated. If these variations are not controlled in vitro, they can impede the formation of new matured tissue.