MORPHOELASTICITY

Morphoelasticity: The Mathematics and Mechanics of Biological Growth

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 Obiettivo del progetto (Objective)

'This proposal concerns the mathematical study of growth, structure, and function in physiological and biological systems. The aim is to provide a rigorous mathematical framework for the study of different growth processes in biological systems and to model specific biological systems. The research is divided into interconnected themes with perspectives in pure mechanics, applied mathematics, and theoretical biology. At the foundational level, the development of a mathematical theory for biological growth is particularly difficult, as it must describe nonlinear biological materials evolving in time, and operating in large deformations. My goal is to study the foundations of the theory, which requires the generality of differential geometry, exact elasticity, and nonlinear thermodynamics. At the methodology level, I will develop mathematical tools to explore the consequences of growth processes in many systems, such as the dynamics of growth; the nonlinear stability analysis of growing systems with application to morphogenesis and pattern formation; and the study of reduced theories for rods and shells. The goal here is to gain insight into the fundamental coupling between growth, geometry, and stress in many biological systems. The driving force behind a theory of growth is the analysis and modelling of specific systems in collaboration with life scientists. Various applications in biology and physiology will be considered such bacterial and fungal systems, stems and leaves, solid tumours, arteries, brain morphology, and blood vessels. I have established such collaborations and I will expand their scope while at Oxford. Another goal of this work is to help bridge the gap between scientists from different communities such as plant biologists, biomedical engineers, and bio-physicists. Applied mathematics has a unique opportunity to offer a unified theory of biological growth and I intend to play a leading role in establishing this new field of study.'

Introduzione (Teaser)

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.

Descrizione progetto (Article)

Members of the EU-funded project 'The mathematics and mechanics of biological growth' (MORPHOELASTICITY) 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.

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.