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

et al. (2014) Optimising Cell Aggregate Expansion in a Perfused Hollow Fibre Bioreactor via Mathematical Modelling. PLoS ONE 9(8): e105813. doi:10.1371/journal.pone.0105813 Optimising Cell Aggregate Expansion in a Perfused Hollow Fibre Bioreactor via Mathematical Modelling Lloyd A. C. Chapman 0 Rebecca J. Shipley 0 Jonathan P. Whiteley 0 Marianne J. Ellis 0 Helen M. Byrne 0 Sarah L. Waters 0 Ben D. MacArthur, University of Southampton, United Kingdom 0 1 Mathematical Institute, University of Oxford , Oxford , United Kingdom , 2 Department of Mechanical Engineering, UCL , London , United Kingdom , 3 Department of Computer Science, University of Oxford , Oxford , United Kingdom , 4 Department of Chemical Engineering, University of Bath , Bath , United Kingdom The need for efficient and controlled expansion of cell populations is paramount in tissue engineering. Hollow fibre bioreactors (HFBs) have the potential to meet this need, but only with improved understanding of how operating conditions and cell seeding strategy affect cell proliferation in the bioreactor. This study is designed to assess the effects of two key operating parameters (the flow rate of culture medium into the fibre lumen and the fluid pressure imposed at the lumen outlet), together with the cell seeding distribution, on cell population growth in a single-fibre HFB. This is achieved using mathematical modelling and numerical methods to simulate the growth of cell aggregates along the outer surface of the fibre in response to the local oxygen concentration and fluid shear stress. The oxygen delivery to the cell aggregates and the fluid shear stress increase as the flow rate and pressure imposed at the lumen outlet are increased. Although the increased oxygen delivery promotes growth, the higher fluid shear stress can lead to cell death. For a given cell type and initial aggregate distribution, the operating parameters that give the most rapid overall growth can be identified from simulations. For example, when aggregates of rat cardiomyocytes that can tolerate shear stresses of up to 0:05 Pa are evenly distributed along the fibre, the inlet flow rate and outlet pressure that maximise the overall growth rate are predicted to be in the ranges 2:75|10{5 m2 s{1 to 3|10{5 m2 s{1 (equivalent to 2:07 ml min{1 to 2:26 ml min{1) and 1:077|105 Pa to 1:083|105 Pa (or 15.6 psi to 15.7 psi) respectively. The combined effects of the seeding distribution and flow on the growth are also investigated and the optimal conditions for growth found to depend on the shear tolerance and oxygen demands of the cells. - Funding: The work is primarily supported by an EPSRC Life Sciences Interface Doctoral Training Centre grant from the University of Oxford (EP/F500394/1). HMB is supported by King Abdullah University of Science and Technology, Saudi Arabia (Award No. KUK-C1-013-04). SLW is funded by the EPSRC through an Advanced Research Fellowship. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. In vitro tissue engineering that uses cells extracted from the patient to grow tissues in the laboratory offers a viable alternative to donor transplants for replacing tissue that has been damaged or lost. However, to grow substitutes of clinically relevant dimensions it is necessary first to expand the population of cells from the patient. Hollow fibre bioreactors (HFBs) are promising cell expansion devices: they consist of a glass module containing a single or multiple hollow porous biodegradable polymer fibre(s) onto (or around) which the cells are seeded. In this study, we consider the single-fibre HFB shown in Figure 1A. The outer surface of the fibre provides a large area (relative to the volume of the device) for cell proliferation. The flow rate of culture medium into the lumen, Qin, is prescribed and the relative fluid fluxes through the fibre wall (or membrane) and out of the lumen are controlled by a back pressure, Pl,out, applied at the lumen outlet. This enables the nutrient and fluid shear stress environment of the cell population to be controlled to encourage functional growth. Two outlets from the extra-capillary space (ECS), the space around the fibres, can be closed or opened to promote flow through the membrane and improve nutrient delivery to the cells and removal of waste products [1]. Despite these advantages, the combined effects of the flow conditions, nutrient transport and initial cell seeding distribution on cell population expansion are not well understood. Increasing the flow through the membrane improves nutrient delivery to the cells but also increases the fluid shear stress they experience. Whilst higher nutrient concentration promotes cell proliferation and higher shear stress can stimulate proliferation, excess shear stress can lead to cell death. Hence it is necessary to find the flow parameters and seeding distribution that give the optimal balance of nutrient delivery and shear stress for the given cell type. Cells are typically seeded onto the surface of the fibre by injecting an inoculum via the ECS outlets and fixing the module to a drum rotating at 6:6 rpm for 6 hrs [2]. This reduces cell damage and enhances cell adhesion compared to pumping the inoculum through the ECS. However, the cell distribution over the surface after culturing is often uneven (Figure 1B) and the yield poor compared with that achieved on flat tissue culture plastic [2]. During seeding, cells attach to the membrane individually or in small groups, but many cell populations grow predominantly as aggregates [25]. Experimental and modelling studies have sought to explain the interactions between the flow of culture medium, initial cell distribution and cell population growth in specific perfusion bioreactor systems (see [6] for a review). Although general relationships have been identified, they typically pertain to cells seeded in 3D scaffolds, so have limited applicability to the HFB. Indeed, no study has considered the effect of cell seeding on cell proliferation in a HFB. While it is possible to measure the nutrient concentration globally in HFB experiments, for example at the inlet and outlets, there is a lack of detailed spatial information on local nutrient levels, fluid shear stress and cell distribution inside the bioreactor. These issues motivate the development of the following mathematical model, in which we consider aggregates of cells that are a single cell thick growing along the outer surface of the fibre in a HFB. The growth rate of the aggregates depends on the local oxygen concentration (as oxygen is considered to be the growth-rate-limiting nutrient [1]) and the shear stress exerted on them by the flow (following [7,8]). We determine optimal operating conditions (lumen inlet flow rate and outlet pressure) for growth of the aggregates to con (...truncated)