Translation of a viscoelastic cell surrounded by a Newtonian fluid

Information on the effect of fluid stresses on cells is needed for progress in regenerative stem cell therapies, wherein stem cells are injected into the bloodstream with the aim of reaching a target damaged organ and subsequently repairing the organ. This is hoped to avoid organ transplants. The fluid stresses experienced by the cell on its journey are known to directly impact its biomechanical response at the target site and hence the success of the therapy. However, this is not currently well-understood. In this presentation, we introduce a new mathematical model to capture the response of a biological cell to the stresses exerted on it by a Newtonian fluid. The cell is modelled as a sac of viscoelastic fluid, obeying the Upper Convected Maxwell constitutive law. The surrounding fluid is a viscous Newtonian fluid, obeying the Stokes equations. Exploiting the larger viscosity of the cell compared with the surrounding fluid enables the cell constitutive law to be linearized. New leading-order solutions for the intracellular flow and stress distributions over time for given initial conditions can then be obtained by primarily analytical means.