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In this work, we consider a gradostat made up of several chemostats coupled by migrations of substrates and products between them. We seek maximum product synthesis or maximum sustainable yield by optimizing with the dilution rate. The mathematical study of the complete model is carried out by searching equilibrium points and stability. We compare the overall maximal synthesis of the system of coupled chemostats to the sum of the maximal syntheses of isolated chemostats. We show that in the homogeneous case where all the chemostats are identical, the difference between the maximum synthesis of the system of coupled chemostats and the sum of the maximum syntheses of the isolated chemostats or excess yield cannot be positive. We show that the excess yield can be positive only in the heterogeneous case. In these cases, under some conditions, the coupling of chemostats can make it possible to obtain a higher productivity compared to the case of isolated chemostats. We illustrate our theoretical results with numerical simulations with various examples corresponding to slow and fast migrations.

This work considers the momentum transport and mass transfer of O₂ in a novel aerial rotating disk bioreactor (RDB) for animal cell or tissue culture. Specifically, this design uses a rotating lid placed above the surface of the culture medium to provide a stirring mechanism, which has potential benefits of enhanced gas transfer, reducing possible contamination, and better access to the culture medium below. The aim of this study is to use CFD to characterize the flow field, shear stresses, and oxygen profiles at a range of Reynolds number that lies within the laminar flow regime. Ultimately, such data will aid the development of an aerial RDB for tumor progression. Numerical simulation is used whereby the two-phase flow, comprising air as the gaseous phase, and water as the aqueous phase, is obtained by solving the unsteady, axisymmetric, incompressible Navier Stokes equation. Having obtained an accurate flow field, a species transport equation is then used to predict the oxygen transfer from the gaseous phase to the aqueous phase. Results are presented for a rotation Reynolds number (Re) range that corresponds to the impeller speed range of 60 to 240 rpm. While the flow is primarily swirl-dominant, it is found that the secondary flow in the aqueous region consists of a single recirculation pattern. As the oxygen transfer in the aqueous phase is mainly driven by convection, there is a clear depletion of oxygen at the center of the recirculation region. Shear stress distributions along the bottom stationary wall indicate a shift in the peak towards the external cylinder wall with increasing Re.

Bioreactors allowing culture medium direct-perfusion overcome diffusion limitations associated with static culturing and provide flow-mediated mechanical stimuli. The hydrodynamic stress imposed on chondrocytes will depend not only on the culture medium flow rate, but also on the scaffold three-dimensional (3D) micro-architecture. We performed computational fluid-dynamic (CFD) simulations of the flow of culture medium through a 3D porous scaffold, with the aim of predicting the shear stress acting on the cells as a function of parameters that can be set in a tissue-engineering experiment, such as the medium flow rate and the diameter of the perfused scaffold section. We developed two CFD models: the first model (Model 1) was built from micro-computed tomography reconstruction of the actual scaffold geometry, while the second model (Model 2) was based on a simplification of the actual scaffold microstructure. The two models showed comparable results in terms of the distribution of the shear stresses acting on the inner surfaces of the scaffold walls. Models 1 and 2 gave a median shear stress of 3 mPa at a flow rate of 0.5 cm³ min^-1 through a 15 mm diameter scaffold. 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.

Hydrodynamic cellular environment plays an important role in translating engineered tissue constructs into clinically useful grafts. However, the cellular fluid dynamic environment inside bioreactor systems is highly complex and it is normally impractical to experimentally characterize the local flow patterns at the cellular scale. Computational fluid dynamics (CFD) has been recognized as an invaluable and reliable alternative to investigate the complex relationship between hydrodynamic environments and the regeneration of engineered tissues at both the macroscopic and microscopic scales. This review describes the applications of CFD simulations to probe the hydrodynamic environment parameters (e.g., flow rate, shear stress, etc.) and the corresponding experimental validations. We highlight the use of CFD to optimize bioreactor design and scaffold architectures for improved ex-vivo hydrodynamic environments. It is envisioned that CFD could be used to customize specific hydrodynamic cellular environments to meet the unique requirements of different cell types in combination with advanced manufacturing techniques and finally facilitate the maturation of tissue-engineered constructs.

When preparing tissue engineering and regenerative medicine constructs, a commonly encountered problem is the failure of seeded cells to infiltrate the scaffold. In an increasing number of cases, constructs are being mechanically preconditioned with the expectation that preconditioning will enhance the construct's maturation and effectiveness by pre-exposing seeded cells to stimuli the tissue of interest experiences in vivo. However, whether or not mechanostimulation of a scaffold actually results in transmission of stimuli to the seeded cells remains poorly understood. The purpose of this research was to develop a model that quantifies how strain is transmitted to cells layered on a scaffold's surface compared to cells embedded within a scaffold. Three-dimensional finite element models representative of these conditions were created. When 10% strain was applied to the construct, embedded cells received the full imposed strain. However, cells growing on top of the scaffold received 5% strain within the first layer of cells, and the strain transmitted to cells in subsequent layers decreased exponentially with increasing distance from the scaffold's surface. When experimentally testing the model, strain-induced biological responses were muted in conditions where cell to scaffold contact was reduced. This research illustrates the importance of achieving cellular penetration and cell-to-scaffold contacts when mechanically conditioning tissue engineering constructs.

In the present study, a novel bioreactor for dynamic hydrostatic pressure loading that simultaneously permits medium perfusion was established. This bioreactor enables continuous cultivation without manual attendance. Additional emphasis was placed on a simple bioreactor design which was achieved by pressurizing the medium directly and by applying pressure loading and perfusion through the same piping. Straight forward pressure control and at the same time maintaining sterility were achieved by using a peristaltic pump including inlet and outlet magnetic pinch valves connected with a real-time control. Cell tests using chondrocytes were performed and similar cell proliferation rates in the bioreactor and in the incubator were found. We conclude that the novel bioreactor introduced here, has the potential to be easily applied for cartilage tissue engineering on a larger scale.

In clinical diabetic cardiomyopathy, hyperglycemia and dyslipidemia induce tissue injury, activation of cardiac fibroblasts and interstitial and perivascular fibrosis. Myofibroblasts repair the injured tissue by increasing collagen deposition in the cardiac interstitium and suppressing the activity of matrix metalloproteinases. The goal of this study was to find an ideal model to mimic the effect of high glucose concentration on human cardiac fibroblast activation. The profibrotic role of the transforming growth factor-$\beta$ (TGF-$\beta$) and the protective modulation of nitric oxide were examined in two-dimensional and three-dimensional cell culture models, as well as tissue engineering models, that involved the use of cardiac fibroblasts cultured within myocardial matrix scaffolds mounted in a bioreactor that delivered biochemical and mechanical stimuli. Results showed that high glucose levels were potent pro-fibrotic stimuli. In addition, high glucose levels in concert with TGF-$\beta$ constituted very strong signals that induced human cardiac fibroblast activation. Cardiac fibroblasts cultured within decellularized myocardial scaffolds and exposed to biochemical and mechanical stimuli represented an adequate model for this pathology. In conclusion, the bioreactor platform was instrumental in establishing an in vitro model of early fibrosis; this platform could be used to test the effects of various agents targeted to mitigate the fibrotic processes.

Whole organ engineering has emerged as a promising alternative avenue to fill the gap of donor organ shortage in organ transplantation. Recent breakthroughs in the decellularization of solid organs and repopulation with desired cell populations have generated neo-organ constructs with promising functional outcomes. The realization of this goal requires engineering advancement in the perfusion-based bioreactors to (i) efficiently deliver decellularization agents, followed by (ii) its reconstruction with relevant cell types and (iii) maintenance of viability and function of the repopulated organ. In this study, we report the development and assembly of a perfusion bioreactor with the potential to enable regenerative reconstruction of pancreas. The assembled bioreactor is versatile to efficiently decellularize multiple organs, as demonstrated by complete decellularization of pancreas, liver and heart in the same set-up. Further, the same system is amenable to support organ repopulation with diverse cell types. Using our in-house bioreactor system, we demonstrate pancreas repopulation with both immortalized MIN-6 beta cells and differentiating human pluripotent stem cells. Importantly, we show the significant advantage of perfusion culture over static culture in enhancing cell engraftment, viability and phenotypic maintenance of the repopulated pancreas. In addition, this study is a significant step forward for whole organ engineering as it will facilitate cost-effective and easy assembly of perfusion bioreactors to enable rapid advancement in regenerative organ reconstruction.

In vivo animal models are currently the gold standard for testing the capacity of stem/progenitor cells, smart biomaterials and novel growth factors for successful tissue engineering. In vitro models ultimately fail to provide the appropriate physiologically relevant microenvironment and hence animal models are an essential pre-requisite in the translation of any new therapy to the clinic. The aim of this chapter is to consider the available animal models commonly in use for tissue engineering, with a particular focus upon bone and cartilage research. Factors driving the choice of a given animal model are reviewed, according to the requirements of experimental design, hypothesis and the specific parameters to be tested. A number of animal models, together with their respective advantages and limitations are described, ranging from relatively simple experimental designs such as the subcutaneous implant and muscle pouch models, through to the diffusion chamber model and chorioallantoic membrane assay, to the more complex in vivo bioreactors and (arguably the most clinically relevant) bone and cartilage defect models. The need to consider the ethical issues of using animal models and the principles of reduction, replacement and refinement are emphasised in selecting the final experimental model of choice.

In this chapter, bone marrow harvest and isolation as well as mesenchymal stem cell (MSC) culture are described, including sources from human, rabbit, and rat. The biological activity changes of MSCs in the pathogenesis of bone disorders are exemplified by the steroid-associated osteonecrosis rabbit model. As a cell model, the value of MSCs in screening candidate agents against bone disorders is exemplified by icariin, a single-molecule component purified from epimedium, a famous bone-tonifying herb in traditional Chinese medicine. Besides their role as a cell model for the underlying mechanisms, exploration, and corresponding molecular drug screening of bone disorders, MSCs are also a very important source of cell seeds for bone-related tissue engineering repair, which needs a large scale of stem cells. We therefore introduce the concept of MSC in vitro expansion in microcarrier by bioreactor, and the magnetic resonance imaging (MRI) dynamic tracking technique after superparamagnetic iron oxide (SPIO) particle labeling after in vivo transplantation.

Most of fermentations processes are sensitive to the available oxygen in the culture media known as the oxygen transfer rate (OTR). On the present work we focused on the use of the experiment design with the "Face centered" model to characterize the Oxygen Transfer Coefficient (K_La) behavior in a New Brunswick bioreactor of 14L. We operated the agitation from 100 to 600 RPM and the aeration from 0.5 to 1 VVM because both factors are two of the most important and easy to manage factors to enhance the OTR. Several experiments were run to obtain data which was later analyzed with the MINITAB® Release 14.12.0.software to obtain a surface response model that predicted the K_La. Based on this, the biorreactor can be optimized in the use of energy from the impeller motor and compressor for aeration, resulting in cost saving and as scale up base with a minimum experiments required and with robust reproducible results.