A three-dimensional computational fluid dynamics- (CFD-) model based on a differential pressure laminar flow bioreactor prototype was developed to further examine performance under changing culture conditions. Cell growth inside scaffolds was simulated by decreasing intrinsic permeability values and led to pressure build-up in the upper culture chamber. Pressure release by an integrated bypass system allowed continuation of culture. The specific shape of the bioreactor culture vessel supported a homogenous flow profile and mass flux at the scaffold level at various scaffold permeabilities. Experimental data showed an increase in oxygen concentration measured inside a collagen scaffold seeded with human mesenchymal stem cells when cultured in the perfusion bioreactor after 24 h compared to static culture in a Petri dish (dynamic: 11% O2 versus static: 3% O2). Computational fluid simulation can support design of bioreactor systems for tissue engineering application.
Bioreactor designs for bone tissue engineering applications often use perfusion models where fluid shear stresses through porous scaffolds activate biological processes such as cell proliferation and differentiation [
Besides external forces such as shear stresses, pressure, and gravity, the concentration of oxygen is an important factor of the physiologic environment during bone growth and repair. Dissolved oxygen concentration has the unit mmol/L or mg/L, but, in the physiologic context, the unit is often expressed as % where 21% means that a solution is air-saturated, which corresponds to 6,7 mg/L oxygen at 37°C and 1013 hPa [
We have recently designed a differential pressure laminar flow bioreactor based on a two-dimensional CFD (computational fluid dynamics) model for flow and pressure control to support cell survival and tissue growth by prevention of high shear forces and pressure peaks [
Star-CCM+ program (version 8.04) from CD-Adapco was used for three-dimensional flow simulation. CAD data set from the bioreactor model was imported and converted, and a polyhedral prism mesh with 1.2° million cells and 6.9° million faces was created by the program-innate surface wrapper. To describe the flow inside the bioreactor, Reynolds-averaged Navier-Stokes equations were applied for liquid media. The inlet of the bioreactor was set as velocity with
The scaffold was simulated with a constant porous medium model using hybrid LSQ (least squares) Green-Gauss model. Parameters for modelling flow through porous media are summarized in Table
Scaffold | Darcian permeability |
Porous viscous resistance [kg/m3 |
Porous inertial resistance [kg/m4] |
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A |
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B |
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C |
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D |
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E |
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|
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For unit conversion, the porous viscous resistance [m−2] was multiplied by the viscosity of the fluid (water at 37°C, which is 6.915
The different permeabilities represent a collagen matrix (reported permeability in literature
For experimental testing in the bioreactor, we used MatriDerm (MedSkin Solution Suwelack, Billerbeck, Germany), which is a collagen-elastin matrix with a dense inner fiber structure and porous sizes between 20 and 50 and up to 100 and 150°
The momentum equations considered for the porous medium are described by Batchelor [
The stress tensor
For 3D geometries, conservation equations are given by
The porous media term is composed of two parts: Darcy’s, which contains the first part of the right-side equation, and a viscous loss term, which is defined by the second part of the right-side equation:
In Star-CCM+, the porous jump conditions are used to model a thin membrane that has known velocity (pressure drop) characteristics. It is essentially a 1D simplification of the porous media model available for cell zones.
The thin porous medium has a finite thickness over which the pressure change is defined as a combination of Darcy’s law and an additional inertial loss term:
The mass flux is the rate of mass flow per unit area [kg
For biological experiments, human adipose-derived mesenchymal stem cells were derived from fat tissue donors undergoing abdominoplasty after informed consent and in accordance with the guidelines of the Ethical Committee of Hannover Medical School. The full procedure followed standard protocols and has been described elsewhere [
The bioreactor was equipped with a laser-based oxygen measurement system called “OPAL,” which measures oxygen-dependent phosphorescence lifetime of microbeads (50
(a) Schematics of differential pressure laminar flow bioreactor system with integrated laser-based oxygen sensor system (from
For experiments, cylindrical collagen scaffolds were prepared with phosphorescent microbeads which were placed centrally inside the scaffolds and fixated with 20
The laminar flow bioreactor and the oxygen sensor system are being presented in Figure
Mesh of the bioreactor created with the Star-CCM+ program.
CFD simulations were performed for closed and open bypass systems and scaffolds with different permeability values representing different states of cell growth inside the scaffold as stated in Table
Results of the CFD simulation are presented in Figures
CFD simulation of pressure distribution inside the bioreactor with scaffold permeability of (a) 10−11 m2, (b) 10−12 m2, and (c) 10−13 m2 and closed bypass system demonstrates pressure build-up in the upper part of the culture vessel by decreasing scaffold permeability due to cell growth. Pressure can be released by opening the integrated bypass system (d) (here shown for permeability
CFD simulation of flow velocity with (a) closed and (b) open bypass system (permeability 10−12 m2). Closer view on velocity streamlines at the level of the scaffold holder for (c) closed and (d) open bypass configuration (permeability
Mass flux for (a) closed and (b) open bypass systems (scaffold permeability 10−12).
(a and b) Scanning electron microscopy shows the dense fiber network of the collagen matrix with mesenchymal stem cells after 10 days of dynamic culture in the bioreactor. (c) Cross-section of collagen matrix stained with DAPI fluorescence stain shows collagen fibrous network (in green) with adipose mesenchymal stem cells (blue: nuclei of MSC) cultured in the bioreactor after 14 days of culture. (d) Fluorescence microscopy shows vital mesenchymal cells longitudinally aligned after 1-week dynamic culture in perfusion bioreactor (cell vitality stain).
Results of flow velocity analysis are shown in Figure
Figure
Figure
Oxygen measurement centrally inside the cell-seeded collagen scaffolds demonstrated a significant difference between statically cultured scaffolds in a Petri dish compared to dynamically cultured scaffolds in the bioreactor as demonstrated in Figure
Oxygen concentration measured in statically cultured scaffolds in a Petri dish compared to dynamically cultured collagen scaffolds in a bioreactor after 24 h of seeding with adipose mesenchymal stem cells and further 24 h of static or dynamic culture (statistically significant difference with
In recent years, computational fluid dynamics has gained more and more interest in the development and optimization of systems for biotechnology such as bioreactors [
Results from our simulation underline the importance of pressure control in the system during cell growth inside the porous scaffold causing decrease in permeability. In our current operating prototype, the pressure control system is set up that a change in differential pressure of 1 mbar = 100 Pa activates the opening of the bypasses [
Our oxygen measurement data from the interior of the cell-seeded scaffold suggest an improvement of oxygen supply towards the cells during perfusion culture in the bioreactor. Further work is necessary in order to study oxygen distribution inside scaffolds during long-term perfusion cultures and determine its influence on cell growth and differentiation inside tissue-engineered constructs.
A three-dimensional computational model is presented to characterize flow and pressure distribution inside a perfusion bioreactor prototype. Simulation results underscore the importance of pressure control during changes in porous media permeability caused during cell growth and changes in internal scaffold architecture, which was solved by an internal bypass system for pressure release. Oxygen measurement data suggest an improved oxygen supply for the tissue-engineered constructs in the bioreactor during perfusion culture compared to static cultivation in a Petri dish.
The authors declare that there is no conflict of interests regarding the publication of this paper.
Birgit Weyand and Meir Israelowitz contributed equally to this work.
The authors thank Professor C. Kasper, BOKU, Vienna, for MatriDerm scaffold supplies, J. Zwicker, Zerspanung, and Metallbau Hannover for help with bioreactor modification, and G. Preiss, A. Lazarides, and S. Braun for technical support. This work was supported by a grant of Hannover Impuls Excellence Initiative, a State doctorate grant for female scientists for Birgit Weyand through Hannover Medical School and a medical student doctoral grant through the “Struc Med” program of Hannover Biomedical Research School for Mariel Noehre. In addition, this project received funding from the investment bank of the German federal state of Brandenburg, Grant no. 80149436 (FeLas3D).