Effect of Cell Shape on Nanoindentation Measurements

The aim of this study is to understand if the shape of a cell can affect the characterization process of the mechanical properties via nanoindentation measurements. The characterization of the cell material by atomic force microscopy, in fact, traditionally implements the Hertz contact theory that is based on hypotheses not satisfied in the contact Atomic Force Microscope tip/cell and that do not take into account the actual cell morphology. In previous experimental studies, the mechanical properties of colorectal cancer cells differently shaped (rounded or elongated cells) and sized were determined via nanoindentation measurements. Implementing the Hertz theory, the authors found that differences in mechanical properties exist between the different cell lines with different shape. At this point, the question that can be raised is the following. Is it possible to state that this difference depends on the differences intrinsically existing between the mechanical properties of the investigated cells? Or, this difference can be justified with the difference in cells shape? In other words, the differences seen with the Hertz theory can depend on the fact that the cell shape was not taken into account. To respond to this question, the nanoindentation process of the different colorectal cancer cells was simulated via the finite element method. The finite element models reproducing the cells morphology were integrated into a numerical optimization algorithm that cyclically perturbs the cell mechanical properties until the difference between the force-indentation curve retrieved numerically and that obtained experimentally becomes smaller than an a priori fixed ε value. Once this occurs, the optimization algorithm stops and gives in output the optimal cell material properties. Interestingly, we found that the mechanical properties obtained via the Hertz contact theory are significantly different with respect to those computed with the proposed approach. Furthermore, we found that the material properties of the rounded cells are intrinsically different with respect to those of the elongated ones. The proposed approach provides new insights on the cell mechanobiology and on the effect of cell shape on the specific tasks in cancer growth and invasion.