Image- and Numerics-Based Analysis of Constitutive Properties of Cellular Structures

Abstract

External forces, cell adhesion and soluble signaling molecules influence fundamental functions of cells like shape, migration, proliferation or differentiation. Thus, investigating how mechanical forces affect 3D cell structure and function is of crucial significance in order to gain a better understanding healthy and malignant cell behavior during embryogenesis, regeneration or malignancy [1]. Micromanipulation of cells in a controlled environment is a widely used approach for understanding cellular responses with respect to external mechanical forces. While experimental data provide optical information about the overall cell shape, the 3D deformation state of intracellular structures is not accessible by direct observations and measurements. However, the continuous description of the intracellular deformation state can be calculated as a numerical solution of the boundary value problem given by the partial differential equations of structural mechanics, including a set of canonic material constants (stiffness, compressibility), and the boundary conditions derived from time series of images, e.g. change of visible cell contours. The main idea of our approach is to reformulate the problem of finding optimal modeling parameters as an image registration problem. That is the optimal set of modeling parameters corresponds to the minimum of a suitable similarity measure between computationally predicted and experimentally observed deformations. In this article, we focus on the numerical analysis of uniaxial stretching of a rat embryonic fibroblast 52 (REF 52) based on a series of 2D images reflecting the successive alteration of cell contours during deformation. The goal of this study consists in finding an optimal set of material constants within a non-linear hyperelastic material law, which is able to reproduce results of experimental observations.