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Mathematical modelling for biological systems

Technical difficulties plague implementation of highly accurate mathematical models of biological and physiological systems for studying growth, structure and function. The solution is a combination of differential geometry, exact elasticity and non-linear thermodynamics.
Mathematical modelling for biological systems
Members of the EU-funded project MORPHOELASTICITY (Morphoelasticity: The mathematics and mechanics of biological growth) successfully developed models to represent surface growth patterns in seashells, fungal growth, mucosal folding, airway remodelling and anisotropic fibre remodelling. Using these tools to represent growth and physical forces should elucidate normal versus pathological processes.

The growth and rotation model of the fungus Phycomyces blakesleeanus was modelled using a continuous mechanical model combining non-linearity, helical anisotropy and elasticity. Along with the surface growth model for seashell morphology, this has important implications for the study of fungal infection processes, plant growth and other wide-ranging applications.

Mucosal folding is a common occurrence in biological tissues where buckling occurs as a result of instability when differential growth competes with mechanical forces like pressure. Scientists also developed a model to describe mucosal folding that causes airway narrowing in chronic asthma patients on exposure to critical pressure.

Anisotropic fibre remodelling can describe morphogenesis in tissues and biological structures such as collagen and cellulose. Such tissues are composed of a soft matrix reinforced by fibres, and are an integral part of mammals, animals and plants. The study of growth patterns based on strength and direction of stress will elucidate their complex feedback dynamics.

Researchers developed a model simulating growth of a tumour and its interaction with the immune system that incorporated tumour-killing cells – regulatory T cells, helper T cells, and dendritic cells. The results suggest that for a given tumour growth rate, there is an optimal antigen action that maximises immune system response. For some tumours, there is an optimum dose of dendritic cells in this therapy.

MORPHOELASTICITY tools could find research applications in cancer, arterial aneurysm formation, and microbial growth and invasion, amongst other areas of research. These models will provide novel insight into several biological processes, enabling research in fields as diverse as plant biology, biomedicine, biophysics and zoology.

Related information

Keywords

Biological systems, mathematical models, MORPHOELASTICITY, surface growth, tumour
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