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Biological systems are complex and inherently multiscale: processes at the subcellular, cellular and tissue scales are coupled via multiple interactions whose dysregulation contributes to the emergence of diseases such as cancer. Our lab is developing mathematical and computational models, which propose causal relationships between specific physical processes, in order to increase our understanding of the mechanisms that drive disease initiation, progression and treatment. Our lab is also developing statistical and mathematical methods to analyse complex, high dimensional biomedical datasets, with particular emphasis on characterising and quantifying spatial patterns in immunohistochemistry and multiplex immunofluorescence images.

Through the development of the above mathematical and computational tools, we aim to understand:

  • How interactions between tumour cells, immune cells and their microenvironment impact tumour growth and invasion;
  • How structural features of tumour vasculature impact blood flow, haematocrit distribution, and tissue oxygenation;
  • how cell genotype and phenotype are related in colorectal cancer stem cells and their progeny.

Snapshots from two simulations of a cell-based, multiscale model showing how the spatial patterns of immune cell infiltration (yellow) into multicellular tumour spheroids change over time and how they may differ between tumour spheroids.Snapshots from two simulations of a cell-based, multiscale model showing how the spatial patterns of immune cell infiltration (yellow) into multicellular tumour spheroids change over time and how they may differ between tumour spheroids.

 

In the future, we aim to extend our mechanistic models and data analysis methods, and to develop innovative ways to combine them with complex, multiscale biomedical datasets in order to learn more about disease initiation and progression. In the longer term, our goal is to provide an objective and rational basis to support decision-making in healthcare, particularly the increasing use of personalised medicine.

 

We are developing and applying techniques from topological data analysis to characterise and quantify the structure of biological tissues, including vascular networks, and how they change over time and in response to treatment. Data are filtered, for example by radial filtration, to produce a topological summary from which topological descriptors are derived.We are developing and applying techniques from topological data analysis to characterise and quantify the structure of biological tissues, including vascular networks, and how they change over time and in response to treatment. Data are filtered, for example by radial filtration, to produce a topological summary from which topological descriptors are derived.