Continuum- based computational models of biological living cell

Abstract

All living creatures, despite their profound diversity, share a common architectural building block: the cell. Cells are the basic functional units of life, yet are themselves comprised of numerous components with distinct mechanical characteristics. It is well established that cells have the ability to sense and respond to externally applied forces. However, the detailed mechanism of mechanosensation is still not clearly understood, and is an active area of research involving experimental and theoretical works. Mathematical modeling of the mechanical stimulus correlating to different experimental stimulation procedures forms the first step to understanding the mechanosensation in cellular system. In this thesis, a continuum -based computational model of living cells that explicitly incorporate the material properties of various cellular components are developed. In the constitutive modeling of cell, the continuum standard linear solid viscoelastic model (SLS), its natural extension for large scale deformation standard Neo-Hookean solid viscoelastic model (SnHS) as well as polymer mechanics- based dynamic shear modulus model was introduced. Finite element simulations of three widely used experiments- atomic force microscopy (AFM), magnetic twisting cytometry (MTC) and micropipette aspiration in the quantification of cell properties were carried out to verify the developed constitutive model. From the results of AFM finite element simulation, it was observed that the force-deformation and strain-relaxation curves obtained fit the experimental results very well. The influences of cytoplasm shear modulus which varies due to the formation of stress fiber, and cortex shear modulus which alters with the actin filament concentration factors and load frequency were systematically studied. Similarly, in magnetic twisting cytometry (MTC) simulation, the role of cytoplasm material properties, constant/sinusoidal forcing rates and various frequencies on the overall mechanical response of a cell was obtained. Numerical results are validated against experiments results. Micropipette aspiration simulation was also carried out in which the typical creep deformation test was carried out to study the viscoelastic behavior of the cell. Based on the results from finite element simulation, the effect of pipette radius, effect of cortex shear modulus and effect of pressure rate have been derived for the interpretation of the mechanical parameters from the micropipette aspiration.