A Mathematical Model of a Valve-Controlled Bioreactor for Platelet Production

As blood donor numbers decrease, while demand for platelets increases, hospitals worldwide are becoming increasingly vulnerable to critical platelet shortages. Alternative methods of supplying platelets are therefore required. One approach is to engineer platelets in vitro in a bioreactor. To characterise such a system, we develop a mathematical model of a novel platelet bioreactor described in Shepherd et al. (Biomaterials, 2018, 182, 135-144). The bioreactor consists of upper and lower tube systems, with a cell-seeded porous collagen scaffold situated between them. Flow through the system is driven by gravity, and controlled by valves on each of the inlets and outlets. The bioreactor is long relative to its width, a feature which we exploit to derive a lubrication reduction of the Navier-Stokes equations for flow in the tube systems, coupled to Darcy flow through the porous scaffold. Flow in the tube systems and scaffold are coupled to form a network model for the bioreactor flow. We characterise the effect of geometrical parameters and valve configuration and synchronisation, on the fluxes through the bioreactor and shear stress experienced by cells in the scaffold. The simplicity of the model means that parameter sweeps take only seconds or minutes to perform, making the model a convenient tool for future bioreactor design optimisation.