Elastic force of red blood cell membrane during tank-treading motion: Consideration of the membrane's natural state

The elastic force of a red blood cell (RBC) membrane during its tank-treading motion was estimated using a three-dimensional spring network model. An RBC membrane was modelled by an assembly of triangular elements in which stretch/compression and bending springs were placed to express planar shear and out-of-plane bending deformations, respectively. An areal incompressibility of the membrane and a volumetric constraint on the entire RBC were taken into account. Different natural states of an RBC membrane were considered by adjusting reference lengths and angles of the stretch/compression and bending springs, respectively. An elastic motion simulation was conducted using the spring network model to reproduce a tank-treading motion of the membrane for a constant biconcave discoid RBC under a fluid shear force. Given the simulated tank-treading motion, an additional membrane elastic force due to the motion was determined from the elastic energy changes during the motion. It was confirmed that the natural state of the RBC membrane should be nonuniform to generate the additional elastic force. Greater spring constants and greater natural state nonuniformity induced a greater additional elastic force, and the elastic force was regarded as a resistance against the tank-treading motion. Additional elastic forces due to the membrane tank-treading motion for different sets of spring constants and natural state nonuniformity values were determined, and they were compared with fluid shear forces at shear rates within the range of which a transition between tank-treading and tumbling motions of an RBC occurs in experiments. The results suggested that for the experimentally measured elastic moduli, natural state nonuniformity in a physiological state is moderate between that for a spherical or flat shape and that for the biconcave shape. Moderate nonuniformity was also confirmed by a simulated RBC shape in a minimum state of elastic energy.