OPTIMIZATION MODEL OF THE ERYTHROCYTE STATIONARY SHAPE IN TWO-DIMENSIONAL APPROXIMATION

Author(s):  A.V. Golochalova, Belgorod National Research University, Belgorod , Russia

E.B. Kulumbaev, Dr., Prof., Belgorod State University, Belgorod, Russia, kulumbaev@bsu.edu.ru

Issue:  Volume 51, № 1

Rubric:  Physics. Mathematical modeling

Annotation:  A model of conditional nonlinear minimization of the erythrocyte membrane's elastic energy has been developed for the calculation its stationary shapes in the two-dimensional approximation in normal conditions and in the existence of external influences. The equilibrium shape was calculated for a given volume and surface area of a normal red blood cell, which qualitatively agrees with the experimentally observed and with the results of a two-dimensional dynamic description of the erythrocyte shape relaxation. The external effects of osmotic pressure or the capillary walls during a red blood cell aspiration are simulated by imposing additional conditions in the form of constraints on the vector-argument of the objective function. The results of the calculation of deformation under the action of osmotic pressure or capillary aspiration of a red blood cell qualitatively correspond to observational data.

Keywords:  erythrocyte, membrane shape, elastic energy, optimization model

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