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A low-dimensional parametric deformation model of a cancer cell under shear flow is developed. The model is built around an experiment in which MDA-MB-231 adherent cells are subjected to flow with increasing shear. The cell surface deformation is imaged using differential interference contrast microscopy imaging techniques until the cell releases into the flow. We post-process the time sequence of images using an active shape model from which we obtain the principal components of deformation. These principal components are then used to obtain the parameters in an empirical constitutive equation determining the cell deformations as a function of the fluid normal and shear forces imparted. The cell surface is modeled as a 2D Gaussian interface which can be deformed with three active parameters: H (height), σx (x-width), and σy (y-width). Fluid forces are calculated on the cell surface by discretizing the surface with regularized Stokeslets, and the flow is driven by a stochastically fluctuating pressure gradient. The Stokeslet strengths are obtained so that viscous boundary conditions are enforced on the surface of the cell and the surrounding plate. We show that the low-dimensional model is able to capture the principal deformations of the cell reasonably well and argue that active shape models can be exploited further as a useful tool to bridge the gap between experiments, models, and numerical simulations in this biological setting. [ABSTRACT FROM AUTHOR]

Phoretic particles self-propel using self-generated physico-chemical gradients at their surface. Within a suspension, they interact hydrodynamically by setting the fluid around them into motion and chemically by modifying the chemical background seen by their neighbours. While most phoretic systems evolve in confined environments due to buoyancy effects, most models focus on their interactions in unbounded flows. Here, we propose a first model for the interaction of phoretic particles in Hele-Shaw confinement and show that in this limit, hydrodynamic and phoretic interactions share not only the same scaling but also the same form, albeit in opposite directions. In essence, we show that phoretic interactions effectively reverse the sign of the interactions that would be obtained for swimmers interacting purely hydrodynamically. Yet, hydrodynamic interactions cannot be neglected as they significantly impact the magnitude of the interactions. This model is then used to analyse the behavior of a suspension. The suspension exhibits swirling and clustering collective modes dictated by the orientational interactions between particles, similar to hydrodynamic swimmers, but here governed by the surface properties of the phoretic particle; the reversal in the sign of the interaction tends to slow down the swimming motion of the particles.