DATA: Hyperelasticity fitting for parallel plate compression of multicellular spheroids

Multicellular spheroids, widely used tissue building blocks in the emerging fields of bioprinting and biofabrication, are key prototypes to study tissue mechanics. Here, we present the characterization of a compressible hyperelasticity constitutive model developed by Giverso et al. based on Holmes-Mow type elasticity for multicellular spheroids. We implemented the constitutive model in a Finite Element (FE) piece of software, verified the FE implementation, and simulated the compression test of a spheroid between two parallel plates. We found dimensionless numbers—dimensionless load, lateral diameter stretch ratio, and compression ratio—associated with the constitutive model and the spheroid geometry. Using parametric sweeps in FE calculations, we were able to fit polynomial relationships for these dimensionless numbers. We experimentally performed parallel plate compression testing of human lung fibroblasts (HLF) spheroids, with a nominal size of 300 µm. We then fit the obtained polynomial relationship of dimensionless numbers to the experimental dataset to find material parameters of HLF spheroids associated with the proposed constitutive model. After fitting our model to the reported experiments, we performed a numerical simulation of micro-pipette aspiration of a spheroid to relate the aspiration pressure to the spheroid deformation. We highlighted the advantages of the parallel plate compression testing over a micro-pipette aspiration technique for mechanical characterization. The work we present herein provides a framework for the mechanical characterization of spheroids using parallel plate compression and the above-mentioned constitutive model.