Papillary networks in the dermal–epidermal junction of skin: A biomechanical model

Complex networks of finger-like protrusions characterize the dermal–epidermal junction of human skin. Although formed during the foetal development, such dermal papillae evolve in adulthood, often in response to a pathological condition. The aim of this work is to investigate the emergence of biaxial papillary networks in skin from a mechanical perspective. For this purpose, we define a biomechanical model taking into account the volumetric growth and the microstructural properties of the dermis and the epidermis. A scalar stream function is introduced to generate incompressible transformations, and used to define a variational formulation of the boundary value elastic problem. We demonstrate that incompatible growth of the layers can induce a bifurcation of the elastic stability driving the formation of dermal papillae. Such an interfacial instability is found to depend both on the geometrical constraints and on the mechanical properties of the skin components. The results provide a mechanical interpretation of skin morphogenesis, with possible applications for micropattern fabrication in soft layered materials.