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We present a computational approach for solving reaction-diffusion equationson evolving surfaces which have been obtained from cell image data. It is basedon finite element spaces defined on surface triangulations extracted from timeseries of 3D images. A model for the transport of material between thesubsequent surfaces is required where we postulate a velocity in normaldirection. We apply the technique to image data obtained from a spreadingneutrophil cell. By simulating FRAP experiments we investigate the impact ofthe evolving geometry on the recovery. We find that for idealised FRAPconditions, changes in membrane geometry, easily account for differences of$\times 10$ in recovery half-times, which shows that experimentalists must takegreat care when interpreting membrane photobleaching results. We alsonumerically solve an activator -- depleted substrate system and report on theeffect of the membrane movement on the pattern evolution.

Solving reaction-diffusion equations on evolving surfaces defined by biological image data