Biomechanical Heterogeneity of Living Cells: Comparison between Atomic Force Microscopy and Finite Element Simulation

Atomic force microscopy (AFM) indentation is a popular method for characterizing the micromechanical properties of soft materials such as living cells. However, the mechanical data obtained from deep indentation measurements can be difficult and problematic to interpret as a result of the complex geometry of a cell, the nonlinearity of indentation contact, and constitutive relations of heterogeneous hyperelastic soft components. Living MDA-MB-231 cells were indented by spherical probes to obtain morphological and mechanical data that were adopted to build an accurate finite element model (FEM) for a parametric study. Initially, a 2D-axisymmetric numerical model was constructed with the main purpose of understanding the effect of geometrical and mechanical properties of constitutive parts such as the cell body, nucleus, and lamellipodium. A series of FEM deformation fields were directly compared with atomic force spectroscopy in order to resolve the mechanical convolution of heterogeneous parts and quantify Young's modulus and the geometry of nuclei. Furthermore, a 3D finite element model was constructed to investigate indentation events located far from the axisymmetric geometry. In this framework, the joint FEM/AFM approach has provided a useful methodology and a comprehensive characterization of the heterogeneous structure of living cells, emphasizing the deconvolution of geometrical structure and the true elastic modulus of the cell nucleus.