Tissue Interaction Model for Skin Pattern Formation

A nonlinear analysis of a mechanical model for biological pattern formation, SIAM J. pattern selection in a mechanical model for morphogenesis, Mathematical modelling of the generation and onset of spatial patterns in the early stages of embryonic development — reaction-diffusion equations, chemotaxis equations, mechanochemical force balance equations. (1988): the communication between different groups of cell and tissue types plays a crucial role during morphogenesis. Most of the models are concerned only with very specific tissues; little attention to modelling tissue interaction. Focus: two aspects of tissue interaction – two different models for vertebrate skin pattern formulation: (i) model by Cruywagen–Murray (1992) [3, 10]: Patterns and structure observed in animals develop from a homogeneous mass of cells seen in the early embryo. This process-morphogenesis-consists of a complex interaction of chemical, mechanical, and electrical phenomena. Uniform skin tissue can only be excited into spatial structure in the presence of tissue interaction; (ii) model by Shaw–Murray (1990) [12]: the interaction mechanism is not crucial for simple pattern formulation, however it can excite the skin tissue into producing far more complex patterns normally exhibited by such models. II. Tissue interaction Vertebrate skin is composed two layers: the epidermis and the dermis. epidermis – a sheet of tightly packed epithelial cells exhibiting viscoelastic properties; dermis – mesenchymal cells which can move in the extracellular matrix, an array of fibres and collagen. These layers are separated by a thin sheet of tissue called basal lamina. Pattern formation – almost simultaneously in both layers and in both dermis and epidermis due to the active communication between the layers. Theoretical scenario of the dermal-epidermal communication based upon the experimental results due to Chuong–Edelman: The actual factors (chemicals) are produced by the cells in the respective layers and diffuse across the basal lamina, which are mechanical signals with active stresses → a major effect on cell behavior; electrical signals. The epidermis is modelled as a viscoelastic sheet by a mechanochemical system and by the conservation of the epithelial cell; The mechanochemical system = a force balance equation describing the passive vis-coelastic stresses present in the tissue and a traction term responsible for the active tissue stresses which depends on a chemical signal received from the dermis. The dermis is modelled as a cell chemotaxis since cells in the dermal layer are more loosely arranged and are motile and by the conservation of the dermal cell; The chemo-attractant is induced …