Modelling the mechanical behavior of red blood cells¹

Issue title: Dedicated to Professor A. L. Copley

Article type: Research Article

Authors: Skalak, Richard^{; *}

Affiliations: Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, New York 10027, U.S.A.

Note: [1] 1st International Congress of Biorheology, Lyon, France, 4–8 September 1972

Note: [*] Invited Lecturer.

Abstract: The human red blood cell is known to consist of a thin, flexible membrane filled with a concentrated solution of hemoglobin which has been shown to behave as a Newtonian fluid. The plasma in which red blood cells are suspended is also Newtonian. The properties of the red blood cell membrane are less well known and there are estimates of elastic moduli reported in the literature differing by as much as a factor of 103. The lowest elastic modulus appears in uniaxial tension tests in which one of the principal stresses in the membrane is zero. The largest moduli result from tests in which the tension in the membrane is isotropic, such as in sphering of red blood cells, near hemolysis. It is shown that these disparate moduli can be incorporated into a single description of the red blood cell membrane by use of the notion of the strain energy function. The derivatives of the strain energy function with respect to the Greens strain components yield the stress components. The expressions are valid for large strains such as occur in red cell membranes in sphering and sieving experiments. The main features of the red cell membrane that emerge are that it is much stiffer with respect to changes of areas than for strains in which the area is constant. The red blood cell membrane has also been shown to be viscoelastic to some extent and such behavior is incorporated by a modification of the stress-strain relations derived by use of the strain energy function. Applications of the proposed modelling of the red blood cell are discussed for sphering, sieving and pipette experiments and the flow of red blood cells in the microcirculation.

DOI: 10.3233/BIR-1973-10215

Journal: Biorheology, vol. 10, no. 2, pp. 229-238, 1973