A Mathematical and Engineering Approach to the Investigation of C-Reactive Protein as a Cancer Biomarker and the Evolution of Cancer Networks

Abstract

Although medical intervention has been successful at least for some pathologies, cancer remains one of the greatest killers in the world, mainly in western countries. As a valuable tool in the fight against cancer, mathematical modelling has recently been added to the research field. The mathematical modelling of cancer provides an exact framework for understanding cancer evolution and for testing biological hypotheses. By translating biological complexity and translating biological components of cancer development into mathematical terms, the modelling process describes cancer-related phenomena as a complex set of interactions with the emerging outcome predicted by mathematical investigation that defines the field of mathematical oncology. In fact, this field is characterized by two key features: i) that mathematical models can be applied to develop a quantitative understanding cancer, and ii) that biology proposes new mathematical challenges, which motivate enhanced mathematical tools. Therefore, this PhD thesis investigates a mathematical approach to cancer, and the research include a number of sub-projects. Specifically, investigations of the behaviour of Creactive protein (CRP) as a cancer biomarker and evolution of cancer vascular networks is carried out. The first part of this thesis considers the role of biomarkers such as CRP in cancer prognosis starting with a comprehensive literature review on CRP. We then provide a prescription for CRP data sampling in clinical trials. Also, we investigate CRP forecasting and prediction via deep learning and ARIMA approaches. The remainder of the thesis concerns the use of graph theory in cancer vascular networks. This can split into two types: angiogenesis and vascular mimicry. We first review mathematical and computational models for angiogenesis. Then, we investigate the networks formed by pancreatic and breast cancers and endothelial cells, by applying graph theory to experimental cell growth data.