Modelling of pattern formation and growth driven by reaction-diffusion equations
The development of the vertebrate joint is punctuated by a series of coordinated events regulated by molecular markers called morphogens. Some morphogens can activate or inhibit proliferation and/or the cell differentiation process, which results in tissue growth. The way morphogens diffuse and inte...
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| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/380647 |
| Acceso en línea: | https://hdl.handle.net/2117/380647 |
| Access Level: | acceso abierto |
| Palabra clave: | Reaction-diffusion equations Equacions de reacció-difusió Classificació AMS::35 Partial differential equations::35K Parabolic equations and systems Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals |
| Sumario: | The development of the vertebrate joint is punctuated by a series of coordinated events regulated by molecular markers called morphogens. Some morphogens can activate or inhibit proliferation and/or the cell differentiation process, which results in tissue growth. The way morphogens diffuse and interact is still not well understood. The reaction-diffusion equations have been used to model the patterning of morphogens in limb development. This work aims at studying how pattern may develop and influence the formation of a limb joint during embryo morphogenesis using the Schnakenberg reaction system. Our study focuses on identifying the conditions for the appearance of Turing patterns by studying the reaction-diffusion equations analytically and using finite element analysis. We show that the model parameters, the initial conditions, the boundary conditions and growth of the domain impact the evolution of pattern. Because non-linearities play a strong role in the pattern production, final patterns are difficult to predict especially in the growth process |
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