Applied Mathematics Seminars: Multiscale modelling and analysis of plant tissue biomechanics
12 May 2017 14:00 in CM219
Analysis of interactions between mechanical properties and chemical processes, which influence the elasticity and extensibility of plant tissues, is important for better understanding of plant growth and development. Plant tissues are composed of cells surrounded by cell walls and connected to each other by a cross-linked pectin network of middle lamella. The main feature of plant cells are their walls, which must be strong to resist high internal hydrostatic pressure (turgor pressure) and flexible to permit growth. It is supposed that calcium-pectin cross-linking chemistry is one of the main regulators of plant cell wall elasticity and extension.
In the microscopic model for plant cell wall and tissue biomechanics we will consider the influence of the microscopic structure and chemical processes on the mechanical properties of plant tissues. The interplay between the mechanics and the chemistry will be defined by assuming that the elastic properties of the plant cell walls depend on the chemical processes (i.e. on the density of calcium-pectin cross-links) and chemical reactions depend on mechanical stresses within the cell walls, modelling the fact that the stress within the plant cell walls can break the load-bearing cross-links. The microscopic model will constitute a strongly coupled system of reaction-diffusion-convection equations for chemical processes in plant cells, the equations of poroelasticity for elastic deformations of plant cell walls and middle lamella, and Stokes equations for fluid flow inside the cells. To analyse the macroscopic behaviour of plant tissues, the macroscopic models for plant cell wall and tissue biomechanics will be derived using homogenization techniques. In the multiscale analysis we will distinguish between periodic and random distribution of cells in a plant tissue. Numerical solutions for the macroscopic model will demonstrate the patterns in the interactions between mechanical stresses and chemical processes.
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