Experimental estimation of stored stress within spherical microtissues

Biological tissues accumulate mechanical stress during their growth. The mere measurement of the stored stress is not an easy task. We address here the spherical case and our experiments consist in performing an incision of a spherical microtissue (tumor spheroid) grown in vitro. On the theoretical part we derive a compatibility condition on the stored stress in spherical symmetry, which imposes a relation between the circumferential and radial stored stress. The numerical implementation uses the hyperelastic model of Ciarlet and Geymonat. A parametric study is performed to assess the influence of each parameter on the shape of the domain after the incision. As a conclusion, the total radial stored stress can be confidently estimated from the measurement of the opening after incision. We validate the approach with experimental data.