Abstract
We present a simplified two-dimensional model of fluid flow, nutrient transport and cell distribution in a hollow fibre membrane bioreactor, with the aim of exploring how fluid flow can be used to control the distribution and yield of a cell population which is sensitive to both fluid shear stress and nutrient concentration. The cells are seeded in a scaffold in a layer on top of the hollow fibre, only partially occupying the extracapillary space. Above this layer is a region of free-flowing fluid which we refer to as the upper fluid layer. The flow in the lumen and upper fluid layer is described by the Stokes equations, whilst the flow in the porous fibre membrane is assumed to follow Darcy’s law. Porous mixture theory is used to model the dynamics of and interactions between the cells, scaffold and fluid in the cell–scaffold construct. The concentration of a limiting nutrient (e.g. oxygen) is governed by an advection–reaction–diffusion equation in each region. Through exploitation of the small aspect ratio of each region and asymptotic analysis, we derive a coupled system of partial differential equations for the cell volume fraction and nutrient concentration. We use this model to investigate the effect of mechanotransduction on the distribution and yield of the cell population, by considering cases in which cell proliferation is either enhanced or limited by fluid shear stress and by varying experimentally controllable parameters such as flow rate and cell–scaffold construct thickness.
Highlights
The need for a reliable and sufficient source of replacement tissue and organs is constantly increasing, due to our ageing population and consistent lack of donors
Water variables in the lumen, membrane, cell layer and upper fluid layer are denoted by subscripts l, m, w and f, respectively, and cell phase variables by subscript n, with the velocities given by ui =, the water pressures by pi, and the solute concentrations per unit volume of water by ci (i = l, m, w, f)
We can compare this to the corresponding system from Pearson et al (2013): it is interesting to see that, despite the apparently more complex set-up here, we can reduce the governing equations to a system of two instead of three coupled PDEs. This is due to the addition of the upper fluid layer region which was not present in Pearson et al (2013), and in which we can explicitly solve for the reduced water pressure
Summary
The need for a reliable and sufficient source of replacement tissue and organs is constantly increasing, due to our ageing population and consistent lack of donors. In O’Dea et al (2008), the authors develop a two-phase model of tissue growth in a perfusion bioreactor They include dependence of cell proliferation, extracellular matrix (ECM) deposition and cell death on the local cell density and fluid pressure. As well as cell proliferation and death, mechanotransduction can affect cell differentiation This is the focus of a paper by Byrne et al (2007), in which finite element analysis is used to model a poroelastic tissue–scaffold construct for bone regeneration, with the objective of determining optimal scaffold porosity under different mechanical loading conditions. We consider various experimentally relevant case studies, motivated by specific cell types, to investigate the effect of fluid shear stress on the proliferation rate, and distribution, of cells in a hollow fibre membrane bioreactor (HFMB) (see Fig. 1). We determine the range of possible behaviours from this set-up and find optimal flow rates for which the fluid shear stress has an advantageous effect: that is, it enables a more spatially uniform cell population and/or a higher cell yield to be obtained
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