Analyzing force measurements of multi-cellular clusters comprising indeterminate geometries

This study presents a new analytical approach for interpreting force–displacement data from parallel compression measurements of tumor spheroids. Traditional linear regression often underestimates elastic moduli due to assumptions of planar geometry, which are inappropriate for irregular or concave cellular aggregates. The authors propose the Integrated Elasticity (IE) regression, derived from extrapolating established contact mechanics theories between planar and spherical boundary conditions. Using melanoma spheroids (A375 and WM-266-4), the IE model produced more accurate and physically meaningful elastic modulus values than conventional linear fits. The results demonstrate that geometric variability among 3D tumor spheroids significantly impacts measured mechanical properties, and that IE regression provides a robust, geometry-independent means of quantifying spheroid stiffness.