Quantification of substrate and cellular strains in stretchable 3D cell cultures: an experimental and computational framework

The mechanical cell environment is a key regulator of biological processes . In living tissues, cells are embedded into the 3D extracellular matrix and permanently exposed to mechanical forces. Quantification of the cellular strain state in a 3D matrix is therefore the first step towards understanding how physical cues determine single cell and multicellular behaviour. The majority of cell assays are, however, based on 2D cell cultures that lack many essential features of the in vivo cellular environment. Furthermore, nondestructive measurement of substrate and cellular mechanics requires appropriate computational tools for microscopic image analysis and interpretation. Here, we present an experimental and computational framework for generation and quantification of the cellular strain state in 3D cell cultures using a combination of 3D substrate stretcher, multichannel microscopic imaging and computational image analysis. The 3D substrate stretcher enables deformation of living cells embedded in bead‐labelled 3D collagen hydrogels. Local substrate and cell deformations are determined by tracking displacement of fluorescent beads with subsequent finite element interpolation of cell strains over a tetrahedral tessellation. In this feasibility study, we debate diverse aspects of deformable 3D culture construction, quantification and evaluation, and present an example of its application for quantitative analysis of a cellular model system based on primary mouse hepatocytes undergoing transforming growth factor (TGF‐β) induced epithelial‐to‐mesenchymal transition.