Biomechanics of Heart and Plant Tissues: Multiscale Modelling, Analysis and Numerical Simulations of Biological Materials Comprising Fibrous Microstructures

Interactions between biochemical processes, complex microstructures, mechanical properties and fluid flow (water or blood flow) play an essential role in the development and proper function of biological tissues (especially plant and human tissues).

The main objective of this project is to derive and analyse novel multiscale mathematical models for heart and plant tissue biomechanics, especially to consider the impact of complex microstructures on mechanical properties of biological tissues.
In the proposed research we shall combine the design of new mathematical models, qualitative analysis and numerical simulations of the model equations. Microscopic modelling approach will allow us to consider the non-homogeneous distribution of structural elements of biological tissues and interactions between microstructure, biochemistry and mechanics. Systems of nonlinear ordinary and partial differential equations (equations of nonlinear elasticity and reaction-diffusion equations) will be considered for continuous description of the biomechanics of plant and heart tissues [1]. Mathematical analysis will involve extension of homogenization techniques for non-periodic microstructures [2], and rigorous derivation of macroscopic equations from microscopic description of chemical processes in and mechanical properties of biological tissues. Numerical analysis will comprise selection and design of suitable numerical schemes for multiscale numerical simulations of mathematical models and derivation of error estimates for numerical approximations of solutions of corresponding partial differential equations [3].

Mathematical modelling and numerical simulations will allow us to examine how cellular processes (e.g. cellular signalling processes, remodelling of extracellular matrix) affect stress and strain distribution within heart muscles, and, hence, support a better understanding of biomechanical changes in the heart tissue caused by diseases. Multiscale modelling and simulation of plant tissue biomechanics is important to better understand the influence of microscopic interactions on macroscopic properties, development and growth of plant.

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