Young modulus of healthy and cancerous epithelial tissues from indirect measurements

We propose a new method to estimate the ratio between the Young modulus of a healthy epithelial tissue and a cancerous tissue. Our method is based on a mechanistic approach. We regard the epithelium as a thin layer made of an isotropic hyperelastic material between two material surfaces endowed with surface tension. We derive a mechanical model which takes into account thickness change through a kinematical descriptor whose value, in the absence of mechanical loads, is determined by the competition between surface tension and bulk elasticity. Based on this model, we derive a relation between equilibrium thickness, surface tension, and bulk energy, along with a formula for the ratio between the Young modulus of the healthy and the cancerous tissue in terms of apico-basal pMLC2 intensity and tissue thickness, which are accessible to direct observation at the tissue-wide level through recently-developed experimental techniques. When assessed on the basis of our result, available experimental data confirm that cancerous epithelial tissues are softer than healthy tissues.