Rheological models of biological cells





Rheological model, Membrane, Erythrocyte, Deformation, Viscoelasticity


The most important experimental methods of studying the mechanical properties of cells, as well as the most common rheological models, among which the discrete models of the micro/nanostructure of the cell and continuous models that allow calculating the modulus of elasticity and viscosity of the cell in normal and pathological conditions are discussed. A review of continuous models is given with an indication of their features and differences. A new continuum model of the cell as a multi-layer shell filled with a viscoelastic fluid is proposed. Equations of the model and their solutions for cases of isotonic, isometric and dynamic experiments are obtained. Peculiarities of the mechanical behavior of the models depending on the identified parameters are investigated. A comparison with the data of experimental measurements is given. It is shown that the proposed multi-layer model allows evaluation of separate contribution of the mechanical properties of the cytoskeleton, membrane, adsorbed substances and the hydrated shell, which is important for clinical diagnosis of diseases by measuring the mechanical parameters of cells.

Pages of the article in the issue: 37 - 41

Language of the article: Ukrainian


FUNG Y.C. (1981) Biomechanics. Mechanical Properties of Living Tissues. Berlin: Springer-Verlag.

JEN C.J., JHIANG S.-J., CHEN H.-I. (2000) Cellular responses to mechanical stress. J. Appl. Physiol. 89 (4). р. 1657–1662.

KIZILOVA N.N., LOGVENKOV S.A., STEIN A.A. (2012) Mathematical modeling of transport-growth processes in multiphase biological continua. Fluid Dynamics. № 47(1). р. 1–9.

KIZILOVA N.M., SOLOVJOVA О.М. (2017) Analys of discrete rheological models of soft and liquid biological materials. Visnyk V.N. Karazin Kharkov National University, ser. «Mathematical modeling. Information technologies. Automated Control Systems». 35. p.21–30.

BARANETS V.A., KIZILOVA N.M. (2018) Discrete modeling of aggregation and sedimentation of micro- and nanoparticles in suspensions. Visnyk V.N. Karazin Kharkov National University, ser. «Mathematical modeling. Information technologies. Automated Control Systems». 40. p.4–14.




How to Cite

Batyuk, L. V., & Kizilova, N. M. (2022). Rheological models of biological cells. Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, (2), 37–41. https://doi.org/10.17721/1812-5409.2022/2.4



Differential equations, mathematical physics and mechanics