A multiscale model for red blood cell mechanics.

The objective of this article is the derivation of a continuum model for mechanics of red blood cells via multiscale analysis. On the microscopic level, we consider realistic discrete models in terms of energy functionals defined on networks/lattices. Using concepts of Gamma-convergence, convergence results as well as explicit homogenisation formulae are derived. Based on a characterisation via energy functionals, appropriate macroscopic stress-strain relationships (constitutive equations) can be determined. Further, mechanical moduli of the derived macroscopic continuum model are directly related to microscopic moduli. As a test case we consider optical tweezers experiments, one of the most common experiments to study mechanical properties of cells. Our simulations of the derived continuum model are based on finite element methods and account explicitly for membrane mechanics and its coupling with bulk mechanics. Since the discretisation of the continuum model can be chosen freely, rather than it is given by the topology of the microscopic cytoskeletal network, the approach allows a significant reduction of computational efforts. Our approach is highly flexible and can be generalised to many other cell models, also including biochemical control.