Modeling fluid flow through irregular scaffolds for perfusion bioreactors

Direct perfusion of 3D tissue engineered constructs is known to enhance osteogenesis, which can be partly attributed to enhanced nutrient and waste transport. In addition flow mediated shear stresses are known to upregulate osteogenic differentiation and mineralization. A quantification of the hydrodynamic environment is therefore crucial to interpret and compare results of in vitro bioreactor experiments. This study aims to deal with the pitfalls of numerical model preparation of highly complex 3D bone scaffold structures and aims to provide more accurate wall shear stress (WSS) estimates. µCT imaging techniques were used to reconstruct the geometry of both a titanium (Ti) and a hydroxyapatite scaffold, starting from 430 images with a resolution of 8 µm. To tackle the tradeoff between model size and mesh resolution we selected two concentric regions of interest (cubes with a volume of 1 and 3.375 mm³, respectively) for both scaffolds. A flow guidance in front of the real inlet surface of the scaffold was designed to mimic realistic inlet conditions. With a flow rate of 0.04 mL/min perfused through a 5 mm diameter scaffold at an inlet velocity of 33.95 µm/s we obtained average WSSs of 1.10 and 1.46 mPa for the 1 mm³ and the 3.375 mm³ model of the hydroxyapatite scaffold compared to 1.40 and 1.95 mPa for the 1 mm³ model and the 3.375 mm³ model of the Ti scaffold, showing the important influence of the scaffold micro‐architecture heterogeneity and the proximity of boundaries. To assess that influence we selected cubic portions, of which the WSS data were analyzed, with the same size and the same location within both 1 and 3.375 mm³ cubic models. Varying the size of the inner portions simultaneously in both model selections gives a quantification of the sensitivity to boundary neighborhood. This methodology allows to get more insight in the complex concept of tissue engineering and will likely help to understand and eventually improve the fluid‐mechanical aspects. Biotechnol. Bioeng. 2009;103: 621–630. © 2009 Wiley Periodicals, Inc.     

Prediction of the micro-fluid dynamic environment imposed to three-dimensional engineered cell systems in bioreactors

Bioreactors allowing culture medium perfusion overcome diffusion limitations associated with static culturing and provide flow-mediated mechanical stimuli. The hydrodynamic stress imposed to cells will depend not only on the culture medium flow rate, but also on the scaffold three-dimensional (3D) micro-architecture. We developed a CFD model of the flow of culture medium through a 3D scaffold of homogeneous geometry, with the aim of predicting the shear stress acting on cells as a function of parameters that can be controlled during the scaffold fabrication process, such as the scaffold porosity and the pore size, and during the cell culture, such as the medium flow rate and the diameter of the perfused scaffold section. We built three groups of models corresponding to three pore sizes: 50, 100 and 150 microm. Each group was made of four models corresponding to 59%, 65%, 77%, and 89% porosity. A commercial finite-element code was used to set up and solve the problem and to analyze the results. The mode value of shear stress varied between 2 and 5 mPa, and was obtained for a circular scaffold of 15.5 mm diameter, perfused by a flow rate of 0.5 ml/min. The simulations showed that the pore size is a variable strongly influencing the predicted shear stress level, whereas the porosity is a variable strongly affecting the statistical distribution of the shear stresses, but not their magnitude. Our results provide a basis for the completion of more exhaustive quantitative studies to further assess the relationship between perfusion, at known micro-fluid dynamic conditions, and tissue growth in vitro.     

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.     

Influence of flow rate and scaffold pore size on cell behavior during mechanical stimulation in a flow perfusion bioreactor

Mechanically stimulating cell-seeded scaffolds by flow-perfusion is one approach utilized for developing clinically applicable bone graft substitutes. A key challenge is determining the magnitude of stimuli to apply that enhances cell differentiation but minimizes cell detachment from the scaffold. In this study, we employed a combined computational modeling and experimental approach to examine how the scaffold mean pore size influences cell attachment morphology and subsequently impacts upon cell deformation and detachment when subjected to fluid-flow. Cell detachment from osteoblast-seeded collagen-GAG scaffolds was evaluated experimentally across a range of scaffold pore sizes subjected to different flow rates and exposure times in a perfusion bioreactor. Cell detachment was found to be proportional to flow rate and inversely proportional to pore size. Using this data, a theoretical model was derived that accurately predicted cell detachment as a function of mean shear stress, mean pore size, and time. Computational modeling of cell deformation in response to fluid flow showed the percentage of cells exceeding a critical threshold of deformation correlated with cell detachment experimentally and the majority of these cells were of a bridging morphology (cells stretched across pores). These findings will help researchers optimize the mean pore size of scaffolds and perfusion bioreactor operating conditions to manage cell detachment when mechanically simulating cells via flow perfusion.     

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.     

Modeling evaluation of the fluid-dynamic microenvironment in tissue-engineered constructs: a micro-CT based model

Natural cartilage remodels both in vivo and in vitro in response to mechanical stresses, hence mechanical stimulation is believed to be a potential tool to modulate extra-cellular matrix synthesis in tissue-engineered cartilage. Fluid-induced shear is known to enhance chondrogenesis in engineered cartilage constructs. The quantification of the hydrodynamic environment is a condition required to study the biochemical response to shear of 3D engineered cell systems. We developed a computational model of culture medium flow through the microstructure of a porous scaffold, during direct- perfused culture. The 3D solid model of the scaffold micro-geometry was reconstructed from 250 micro-computed tomography (micro-CT) images. The results of the fluid dynamic simulations were analyzed at the central portions of the fluid domain, to avoid boundary effects. The average, median and mode shear stress values calculated at the scaffold walls were 3.48, 2.90, and 2.45 mPa respectively, at a flow rate of 0.5 cm(3)/min, perfused through a 15 mm diameter scaffold, at an inlet fluid velocity of 53 microm/s. These results were compared to results estimated using a simplified micro-scale model and to results estimated using an analytical macro-scale porous model. The predictions given by the CT-based model are being used in conjunction with an experimental bioreactor model, in order to quantify the effects of fluid-dynamic shear on the growth modulation of tissue-engineered cartilage constructs, to potentially enhance tissue growth in vitro.     

A computational and cellular solids approach to the stiffness-based design of bone scaffolds

We derive a cellular solids approach to the design of bone scaffolds for stiffness and pore size. Specifically, we focus on scaffolds made of stacked, alternating, orthogonal layers of hydroxyapatite rods, such as those obtained via micro-robotic deposition, and aim to determine the rod diameter, spacing and overlap required to obtain specified elastic moduli and pore size. To validate and calibrate the cellular solids model, we employ a finite element model and determine the effective scaffold moduli via numerical homogenization. In order to perform an efficient, automated execution of the numerical studies, we employ a geometry projection method so that analyses corresponding to different scaffold dimensions can be performed on a fixed, non-conforming mesh. Based on the developed model, we provide design charts to aid in the selection of rod diameter, spacing and overlap to be used in the robotic deposition to attain desired elastic moduli and pore size.     

Non-Newtonian Blood Flow in Left Coronary Arteries with Varying Stenosis: A Comparative Study

This paper presents Computational fluid dynamic (CFD) analysis of blood flow in three different 3-D models of left coronary artery (LCA). A comparative study of flow parameters (pressure distribution, velocity distribution and wall shear stress) in each of the models is done for a non-Newtonian (Carreau) as well as the Newtonian nature of blood viscosity over a complete cardiac cycle. The difference between these two types of behavior of blood is studied for both transient and steady states of flow. Additionally, flow parameters are compared for steady and transient boundary conditions considering blood as non-Newtonian fluid. The study shows that the highest wall shear stress (WSS), velocity and pressure are found in artery having stenosis in all the three branches of LCA. The use of Newtonian blood model is a good approximation for steady as well as transient blood flow boundary conditions if shear rate is above 100 s-1. However, the assumption of steady blood flow results in underestimating the values of flow parameters such as wall shear stress, pressure and velocity.     

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

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

Mechanical interaction between cells and fluid for bone tissue engineering scaffold: Modulation of the interfacial shear stress

An analytical model of the fluid/cell mechanical interaction was developed. The interfacial shear stress, due to the coupling between the fluid and the cell deformation, was characterized by a new dimensionless number N_fs. For N_fs above a critical value, the fluid/cell interaction had a damping effect on the interfacial shear stress. Conversely, for N_fs below this critical value, interfacial shear stress was amplified. As illustration, the role of the dynamic fluid/cell mechanical coupling was studied in a specific biological situation involving cells seeded in a bone scaffold. For the particular bone scaffold chosen, the dimensionless number N_fs was higher than the critical value. In this case, the dynamic shear stress at the fluid/cell interface is damped for increasing excitation frequency. Interestingly, this damping effect is correlated to the pore diameter of the scaffold, furnishing thus target values in the design of the scaffold. Correspondingly, an efficient cell stimulation might be achieved with a scaffold of pore size larger than 300 μm as no dynamic damping effect is likely to take place. The analytical model proposed in this study, while being a simplification of a fluid/cell mechanical interaction, brings complementary insights to numerical studies by analyzing the effect of different physical parameters.     

Computational evaluation of oxygen and shear stress distributions in 3D perfusion culture systems: macro-scale and micro-structured models

We present a combined macro-scale/micro-scale computational approach to quantify oxygen transport and flow-mediated shear stress to human chondrocytes cultured in three-dimensional scaffolds in a perfusion bioreactor system. A macro-scale model was developed to assess the influence of the bioreactor design and to identify the proper boundary conditions for the micro-scale model. The micro-scale model based on a micro-computed tomography (microCT) reconstruction of a poly(ethylene glycol terephthalate)/poly(butylene terephthalate) (PEGT/PBT) foam scaffold, was developed to assess the influence of the scaffold micro-architecture on local shear stress and oxygen levels within the scaffold pores. Experiments were performed to derive specific oxygen consumption rates for constructs perfused under flow rates of 0.3 and 0.03 ml min(-1). While macro-scale and micro-scale models predicted similar average oxygen levels at different depths within the scaffold, microCT models revealed small local oxygen variations within the scaffold micro-architecture. The combined macro-scale/micro-scale approach indicated that 0.3 ml min(-1), which subjected 95% of the cells to less than 6.3 mPa shear, would maintain the oxygen supply throughout the scaffold above anoxic levels (>1%), with 99.5% of the scaffold supplied with 8-2% O(2). Alternatively, at 0.03 ml min(-1), the macro-scale model predicted 6% of the cells would be supplied with 0.5-1% O(2), although this region of cells was confined to the periphery of the scaffold. Together with local variations predicted by the micro-scale model, the simulations underline that in the current model system, reducing the flow below 0.03 ml min(-1) would likely have dire consequences on cell viability to pronounced regions within the engineered construct. The presented approach provides a sensitive tool to aid efficient bioreactor optimization and scaffold design.     

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.     

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.     

IQ Domain GTPase-Activating Protein 1 is Involved in Shear Stress-Induced Progenitor-Derived Endothelial Cell Alignment

Shear stress is one of mechanical constraints which are exerted by blood flow on endothelial cells (ECs). To adapt to shear stress, ECs align in the direction of flow through adherens junction (AJ) remodeling. However, mechanisms regulating ECs alignment under shear stress are poorly understood. The scaffold protein IQ domain GTPase activating protein 1 (IQGAP1) is a scaffold protein which couples cell signaling to the actin and microtubule cytoskeletons and is involved in cell migration and adhesion. IQGAP1 also plays a role in AJ organization in epithelial cells. In this study, we investigated the potential IQGAP1 involvement in the endothelial cells alignment under shear stress. Progenitor-derived endothelial cells (PDECs), transfected (or not) with IQGAP1 small interfering RNA, were exposed to a laminar shear stress (1.2 N/m²) and AJ proteins (VE-cadherin and β-catenin) and IQGAP1 were labeled by immunofluorescence. We show that IQGAP1 is essential for ECs alignment under shear stress. We studied the role of IQGAP1 in AJs remodeling of PDECs exposed to shear stress by studying cell localization and IQGAP1 interactions with VE-cadherin and β-catenin by immunofluorescence and Proximity Ligation Assays. In static conditions, IQGAP1 interacts with VE-cadherin but not with β-catenin at the cell membrane. Under shear stress, IQGAP1 lost its interaction from VE-cadherin to β-catenin. This “switch” was concomitant with the loss of β-catenin/VE-cadherin interaction at the cell membrane. This work shows that IQGAP1 is essential to ECs alignment under shear stress and that AJ remodeling represents one of the mechanisms involved. These results provide a new approach to understand ECs alignment under to shear stress.     

Curvature- and fluid-stress-driven tissue growth in a tissue-engineering scaffold pore

Cell proliferation within a fluid-filled porous tissue-engineering scaffold depends on a sensitive choice of pore geometry and flow rates: regions of high curvature encourage cell proliferation, while a critical flow rate is required to promote growth for certain cell types. When the flow rate is too slow, the nutrient supply is limited; when it is too fast, cells may be damaged by the high fluid shear stress. As a result, determining appropriate tissue-engineering-construct geometries and operating regimes poses a significant challenge that cannot be addressed by experimentation alone. In this paper, we present a mathematical theory for the fluid flow within a pore of a tissue-engineering scaffold, which is coupled to the growth of cells on the pore walls. We exploit the slenderness of a pore that is typical in such a scenario, to derive a reduced model that enables a comprehensive analysis of the system to be performed. We derive analytical solutions in a particular case of a nearly piecewise constant growth law and compare these with numerical solutions of the reduced model. Qualitative comparisons of tissue morphologies predicted by our model, with those observed experimentally, are also made. We demonstrate how the simplified system may be used to make predictions on the design of a tissue-engineering scaffold and the appropriate operating regime that ensures a desired level of tissue growth.

     

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

Flow-induced shear stresses have been found to be a stimulatory factor in pre-osteoblastic cells seeded in 3D porous scaffolds and cultured under continuous flow perfusion. However, due to the complex internal structure of porous scaffolds, analytical estimation of the local shear forces is impractical. The primary goal of this work is to investigate the shear stress distributions within Poly(l-lactic acid) scaffolds via computation. Scaffolds used in this study are prepared via salt leeching with various geometric characteristics (80–95% porosity and 215–402.5 μm average pore size). High resolution micro-computed tomography is used to obtain their 3D structure. Flow of osteogenic media through the scaffolds is modeled via lattice Boltzmann method. It is found that the surface stress distributions within the scaffolds are characterized by long tails to the right (a positive skewness). Their shape is not strongly dependent on the scaffold manufacturing parameters, but the magnitudes of the stresses are. Correlations are prepared for the estimation of the average surface shear stress experienced by the cells within the scaffolds and of the probability density function of the surface stresses. Though the manufacturing technique does not appear to affect the shape of the shear stress distributions, presence of manufacturing defects is found to be significant: defects create areas of high flow and high stress along their periphery. The results of this study are applicable to other polymer systems provided that they are manufactured by a similar salt leeching technique, while the imaging/modeling approach is applicable to all scaffolds relevant to tissue engineering.     

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.

     

A numerical study on hemodynamics in the left coronary bifurcation with normal and hypertension conditions

In this study, a three-dimensional analysis of the non-Newtonian blood flow was carried out in the left coronary bifurcation. The Casson model and hyperelastic and rigid models were used as the constitutive equation for blood flow and vessel wall model, respectively. Physiological conditions were considered first normal and then compliant with hypertension disease with the aim of evaluating hemodynamic parameters and a better understanding of the onset and progression of atherosclerosis plaques in the coronary artery bifurcation. Two-way fluid–structure interaction method applying a fully implicit second-order backward Euler differencing scheme has been used which is performed in the commercial code ANSYS and ANSYS CFX (version 15.0). When artery deformations and blood pressure are associated, arbitrary Lagrangian–Eulerian formulation is employed to calculate the artery domain response using the temporal blood response. As a result of bifurcation, noticeable velocity reduction and backflow formation decrease shear stress and made it oscillatory at the starting point of the LCx branch which caused the shear stress to be less than 1 and 2 Pa in the LCx and the LAD branches, respectively. Oscillatory shear index (OSI) as a hemodynamic parameter represents the increase in residence time and oscillatory wall shear stress. Because of using the ideal 3D geometry and realistic physiological conditions, the values obtained for shear stress are more accurate than the previous studies. Comparing the results of this study with previous clinical investigations shows that the regions with low wall shear stress less than 1.20 Pa and with high OSI value more than 0.3 are in more potential risk to the atherosclerosis plaque development, especially in the posterior after the bifurcation.     

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.