Numerical investigation of new rete ridge formation in a multi-layer model of skin subjected to tissue expansion.

The skin is a multilayered organ with microstructural and antomical heterogeneities that contribute to its unique mechanophysiology. Between the epidermis layer at the top and the dermis layer below, the basal keratinocytes form an interface with sinusoidal-like geometry termed rete ridges. In previous computational work we showed that the rete ridges contribute to lower delamination risk by increasing surface area and reducing the stress jump across the interface. Experimentally, we and others have shown that upon repeated tissue expansion and growth, physiological rete ridge frequency is preserved. Here we implement a 2D multilayered skin model where each layer is able to grow in response to applied loading toward recovering the layer-specific homeostatic stretch. Our simulations support the hypothesis that mechanics of growing tissue can explain secondary buckling and new rete ridge formation in tissue expansion. The process is robust with respect to parameters such as homeostatic stretch, layer thicknesses, and shear moduli of the different layers. Thicker epidermis suppresses higher frequency features, and so does a stiffer epidermis with respect to the basal layer. Interestingly, new rete ridge valleys are formed at locations that were originally peaks of the sine wave, whereas original valleys remain valleys. This pattern might have a connection to the localization of stem cell and transient amplifying cells in the epidermis. This study does not discard the role of cell-cell signaling dynamics, but rather emphasizes the possibility of achieving robust geometric patterns with simple rules of growing tissue, even in the absence of complex regulatory networks.