Simultaneous analysis of elastic and nonspecific adhesive properties of thin sample and biological cell considering bottom substrate effect

A new asymptotically correct contact model has been developed for conical tip based atomic force microscopy (AFM) nanoindentation. This new model provides both elastic and nonspecific adhesion properties of cells and soft gels by taking sample thickness at the point of indentation and its depth of indentation into consideration. The bottom substrate effect (BSE) is the most common source of error in the study of "AFM force maps" of the cellular sample. The present model incorporates an asymptotically correct correction term as a function of depth of indentation to eliminate the substrate effect in the analysis. Later, the model is extended to analyze the unloading portion of the indentation curve to extract the stiffness and adhesive properties simultaneously. A comparative study of the estimated material properties using other established contact models shows that the provided corrections effectively curb the errors coming from infinite thickness assumption. Nonspecific adhesive nature of a cell is represented in terms of adhesion parameter (ca) based on the "work of adhesion," this is an alternative to the peak value of tip-sample attractive (negative) force commonly used as representative adhesion measurement. The simple analytical expression of the model can help in estimating more realistic and accurate biomechanical properties of cells from atomic force microscopy based indentation technique.