Hybrid Computational Methods for Analysis of AFM Indentation on Mechanically Heterogeneous Samples

Micro-heterogeneity of biological tissue arises from the multiplicity of components that make up the extracellular matrix (ECM) and the constituent cells. Components that have distinct mechanical properties will fundamentally impact the distribution of mechanical stress in the local cellular environment, ultimately determining how physical forces are transferred between macro and micro scales [1]. Atomic force microscope (AFM) indentation is well suited for probing heterogeneities in cell and tissue micromechanics [2], though subsequent data analysis assumes a mechanically homogeneous substrate. While some constituents can be experimentally isolated before testing, reconstructing the equivalent properties of the composite material remains a challenge. When experimental deconstruction is not possible, computational methods can provide an alternative solution. Herein, we introduce a hybrid method of indentation analysis that utilizes Eshelby’s homogenization theory [3] in conjunction with finite element modeling, to computationally deconstruct the material properties of the underlying components within a mechanically heterogeneous sample.