Marianne J. Ellis

Mathematical modelling of fibre-enhanced perfusion inside a tissue-engineering bioreactor

We develop a simple mathematical model for forced flow of culture medium through a porous scaffold in a tissue-engineering bioreactor. Porous-walled hollow fibres penetrate the scaffold and act as additional sources of culture medium. The model, based on Darcys law, is used to examine the nutrient and shear-stress distributions throughout the scaffold. We consider several configurations of fibres and inlet and outlet pipes. Compared with a numerical solution of the full Navier-Stokes equations within the complex scaffold geometry, the modelling approach is cheap, and does not require knowledge of the detailed microstructure of the particular scaffold being used. The potential of this approach is demonstrated through quantification of the effect the additional flow from the fibres has on the nutrient and shear-stress distribution.

A strategy to determine operating parameters in tissue engineering hollow fiber bioreactors

The development of tissue engineering hollow fiber bioreactors (HFB) requires the optimal design of the geometry and operation parameters of the system. This article provides a strategy for specifying operating conditions for the system based on mathematical models of oxygen delivery to the cell population. Analytical and numerical solutions of these models are developed based on Michaelis–Menten kinetics. Depending on the minimum oxygen concentration required to culture a functional cell population, together with the oxygen uptake kinetics, the strategy dictates the model needed to describe mass transport so that the operating conditions can be defined. If cmin ≫ Km we capture oxygen uptake using zero‐order kinetics and proceed analytically. This enables operating equations to be developed that allow the user to choose the medium flow rate, lumen length, and ECS depth to provide a prescribed value of cmin. When

Hollow fibre membrane bioreactors for tissue engineering applications

c_{{\rm min}} {\not {\gg }}K_{m}

A theoretical approach to zonation in a bioartificial liver

, we use numerical techniques to solve full Michaelis–Menten kinetics and present operating data for the bioreactor. The strategy presented utilizes both analytical and numerical approaches and can be applied to any cell type with known oxygen transport properties and uptake kinetics. Biotechnol. Bioeng. 2011; 108:1450–1461.

Definition and validation of operating equations for poly(vinyl alcohol)‐poly(lactide‐co‐glycolide) microfiltration membrane‐scaffold bioreactors

Hollow fibre membrane bioreactors (HFB) provide a novel approach towards tissue engineering applications in the field of regenerative medicine. For adherent cell types, HFBs offer an in vivo-like microenvironment as each fibre replicates a blood capillary and the mass transfer rate across the wall is independent from the shear stresses experienced by the cell. HFB also possesses the highest surface area to volume ratio of all bioreactor configurations. In theory, these factors enable a high quantity of the desired cellular product with less population variation, and favourable operating costs. Experimental analyses of different cell types and bioreactor designs show encouraging steps towards producing a clinically relevant device. This review discusses the basic HFB design for cell expansion and in vitro models; compares data produced on commercially available systems and addresses the operational differences between theory and practice. HFBs are showing some potential for mammalian cell culture but further work is needed to fully understand the complexities of cell culture in HFBs and how best to achieve the high theoretical cell yields.

Human Bone Derived Cell Culture on PLGA Flat Sheet Membranes of Different Lactide:Glycolide Ratio

Bioartificial livers have yet to gain clinical acceptance. In a previous study, a theoretical model was utilized to create operating region charts that graphically illustrated viable bioartificial liver configurations. On this basis a rationale for the choice of operating and design parameters for the device was created. The concept is extended here to include aspects of liver zonation for further design optimization. In vivo, liver cells display heterogeneity with respect to metabolic activity according to their position in the liver lobule. It is thought that oxygen tension is a primary modulator of this heterogeneity and on this assumption a theoretical model to describe the metabolic zonation within an in vitro bioartificial liver device has been adopted. The distribution of the metabolic zones under varying design and operating parameters is examined. In addition, plasma flow rates are calculated that give rise to an equal distribution of the metabolic zones. The results show that when a clinically relevant number of cells are contained in the BAL (10 billion), it is possible to constrain each of the three metabolic zones to approximately one‐third of the cell volume. This is the case for a number of different bioreactor designs. These considerations allow bioartificial liver design to be optimized. Biotechnol. Bioeng. 2012;109: 234–243.

A theoretical method to improve and optimize the design of bioartificial livers

The aim of this work is to provide operating data for biodegradable hollow fiber membrane bioreactors. The physicochemical cell culture environment can be controlled with the permeate flowrate, so this aim necessitates the provision of operating equations that enable end‐users to set the pressures and feed flowrates to obtain their desired culture environment. In this paper, theoretical expressions for the pure water retentate and permeate flowrates, derived using lubrication theory, are compared against experimental data for a single fiber poly(vinyl alcohol)–poly(lactide‐co‐glycolide) crossflow module to give values for the membrane permeability and slip. Analysis of the width of the boundary layer region where slip effects are important, together with the sensitivity of the retentate and permeate equations to the slip parameter, show that slip is insignificant for these membranes, which have a mean pore diameter of 1.1 µm. The experimental data is used to determine a membrane permeability, of k = 1.86 × 10−16 m2, and to validate the model. It was concluded that the operating equation that relates the permeate to feed ratio, c, lumen inlet flowrate, Q l,in, lumen outlet pressure, P 1, and ECS outlet pressure, P 0, is 1

Optimising Cell Aggregate Expansion in a Perfused Hollow Fibre Bioreactor via Mathematical Modelling

P_{1} - P_{0} = Q_{l,{\rm in}} (Ac + B)