Analyzing force measurements of multi-cellular clusters comprising indeterminate geometries

Multi-cellular biomimetic models often comprise heterogenic geometries. Therefore, quantification of their mechanical properties-which is crucial for various biomedical applications-is a challenge. Due to its simplicity, linear fitting is traditionally used in analyzing force-displacement data of parallel compression measurements of multi-cellular clusters, such as tumor spheroids. However, the linear assumption would be artificial when the contact geometry is not planar. We propose here the integrated elasticity (IE) regression, which is based on extrapolation of established elastic theories for well-defined geometries, and is free, extremely simple to apply, and optimal for analyzing coarsely concave multi-cellular clusters. We studied here the quality of the data analysis in force measurements of tumor spheroids comprising different types of melanoma cells, using either the IE or the traditional linear regressions. The IE regression maintained excellent precision also when the contact geometry deviated from planarity (as shown by our image analysis). While the quality of the linear fittings was relatively satisfying, these predicted smaller elastic moduli as compared to the IE regression. This was in accordance with previous studies, in which the elastic moduli predicted by linear fits were smaller compared to those obtained by well-established methods. This suggests that linear regressions underestimate the elastic constants of bio-samples even in cases where the fitting precision seems satisfying, and highlights the need in alternative methods as the IE scheme. For comparison between different types of spheroids we further recommend to increase the soundness by regarding relative moduli, using universal reference samples.