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Stochastic patterns of tissue inclusions

Biological tissue growth involves the secretion of new tissue (extracellular matrix, collagen fibers) by cells. This secretion incorporates scattered inclusions such as proteins and minerals into the new tissue. During bone tissue growth, some of the tissue-secreting cells themselves become incorporated into the new tissue. The distribution of these tissue-embedded cells is believed to influence subsequent tissue growth processes.

Study level
PhD, Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

Collisions with evolving surfaces

The density of impacts of particles colliding with an evolving surface is of particular interest for several industrial and biological applications. These include etching and deposition processes [1], the incorporation of molecules in a tissue during its growth, budding cell membranes, and biological tissue growth [2]. Impacts on an evolving surface are generated unevenly depending on the relative velocity between the particles and the surface. The distribution of impacts further evolves in a curvature-dependent manner due to the local distortions …

Study level
PhD, Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

Creation of fibre meshworks at moving interfaces

Extracellular matrix (ECM) secreted by cells is composed of a meshwork of fibres infiltrated with proteins and/or minerals. This fibre meshwork often matures after its creation by rearranging its structure, e.g. according to local mechanical clues, or by the infiltration of new molecules [1]. In this project, the fibre meshwork will be represented by a continuous tensorial field [2].ReferencesBidan C et al. Gradual conversion of cellular stress patterns into pre-stressed matrix architecture during in vitro tissue growth, J R Soc …

Study level
Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

Size patterns in Turing patterns: how to grow body segments

Certain repeating elements of the body, such as teeth, fingers, limbs and vertebrae, follow the rule that the size of the middle element of a group of three is the average size of the three elements. This simple rule constrains how the relative sizes of segments develop in the embryo and evolve over long periods of time. The precise mechanisms that determine the number and size of repeating structures, such as fingers and teeth, remain largely unknown.

Study level
PhD, Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

Optimising bone shape with memory networks

Bone is a dynamic tissue that optimises its shape to the mechanical loads that it carries. Bone mass is accrued where loads are high, and reduced where loads are low. This adaptation of bone tissue to mechanical loads is well-known and observed in many instances. However, what serves as a reference mechanical state in this shape optimisation remains largely unknown.

Study level
PhD, Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

How do collisions control tissue growth?

Biological tissue growth occurs mostly at or near the tissue's surface, where spatial interactions between the tissue and its surroundings can have strong influences onto the local rate of growth.This project will investigate how collisions between molecules or cells with an evolving tissue are dependent on the tissue shape and how these collisions may control tissue growth rate and tissue composition.

Study level
PhD, Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

Creation of fibrous tissue at moving interfaces

The extracellular matrix (ECM) secreted by cells is composed of a meshwork of fibres infiltrated with proteins and/or minerals. This fibre meshwork often matures after its creation by rearranging its structure. In this project, the fibre meshwork will be represented by a continuous anisotropic field. …

Study level
PhD, Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

Stochastic patterns of inclusions during tissue growth

Biological tissue growth involves the secretion of new tissue (extracellular matrix, collagen fibers) by cells. This secretion incorporates scattered inclusions such as proteins and minerals into the new tissue. During bone tissue growth, some of the tissue-secreting cells themselves become incorporated into the new tissue. The distribution of these embedded cells is believed to influence subsequent tissue growth processes.

Study level
PhD, Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

Dynamical systems and theoretical biology

Numerous physical and biological systems involve processes of diffusive and/or advective transport (for example, pollutant dispersal, insect pest infestation, heat) and/or reaction (such as interaction, growth, decay) that vary over space and time. As such they can best be described by coupled systems of partial differential equations.Projects are available that focus on aspects of constructing and validating mathematical models and simulations of tissue growth and repair problems, such as epidermal and corneal wound healing, bone fracture healing and tumour growth.Mathematically, …

Study level
Honours
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

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