| Summary: | <p>Hospitals sometimes experience shortages of donor blood platelet supplies, motivating research into in vitro production of platelets. We use mathematical modelling to study platelet production.</p>
<p>First, we model the flow in a novel platelet bioreactor described by our collaborators in Shepherd et al. The bioreactor consists of an upper channel, a lower channel, and a cell-seeded porous collagen scaffold situated between the two. Flow is driven by gravity, and controlled by valves on the four 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 in the channels coupled to Darcy flow in the scaffold.</p>
<p>We first consider the quasi-steady regime, with slowly-moving valves, before incorporating inertia in two regimes: one to study small amplitude valve oscillations, and one to study order one amplitude valve oscillations. The former is a systematic reduction; the latter incorporates a phenomenological approximation for the cross-sectional flow profile. To achieve clinically and commercially viable yields of platelets, our collaborators will need to be able to finely control the fluxes and shear stresses in the bioreactor. Thus we use our model to predict how fluxes and shear stresses may be controlled using bioreactor valve dynamics and geometrical parameters.</p>
<p>Next, we study platelet production at the cellular level, modelling an intermediate stage of proplatelet formation. During this stage, pseudopodia (called proplatelets) elongate from the body of the platelet-producing cell, and platelets form along the proplatelets. Shear stress from external flow enhances both the proplatelet elongation and platelet formation rates, though it is unknown whether this enhancement is due to purely mechanical effects, or whether mechanotransductive effects are involved. We construct two models to investigate the dynamics of proplatelet elongation and to compare these two possible mechanisms, by assessing their effects on the shape and elongation rate of a single proplatelet. The first model uses active gel theory to model the cytoskeleton-powered proplatelet elongation, and resistive force theory to model the drag between external flow and the proplatelet. The second model uses the method of regularised Stokeslets to characterise the flow around proplatelets tethered to a wall in a half-space, with each proplatelet described as an inextensible elastic rod. The models provide computationally-light bases into which future experimental hypotheses may be incorporated.</p>
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