Mathematical modelling of cardiovascular disease low dose ionising radiation data analyses

Abstract

Cardiovascular disease (CVD) is the major cause of morbidity and mortality in many developing and developed countries. This dissertation proposes a framework for gaining a greater understanding of the inflammatory process that is thought to result in the development of atherosclerosis and effects of radiation on the subsequent cardiovascular disease through statistical analysis and mathematical modelling of this process. The potential effect of low dose radiation in atherosclerotic initiation and progression is assessed utilising data on inflammatory markers and plaque development generated by European and Canadian researchers collected as part of the EU NOTE Project. Following suggestions from previous in vitro and in vivo experimental data, the hypothesis under consideration is that at low doses and dose rates there is a largely antiinflammatory response. Implications of this for induction of atherosclerosis after low dose and low dose-rate exposure are assessed. Two and three dimensional reaction-diffusion models of the cardiovascular system are constructed. These are used to assess perturbations of equilibrium and non-equilibrium states. Inferences for low dose mechanisms in the light of much biological and epidemiological data are considered. Chapter 1 serves as an introduction, describing the aetiology of atherosclerosis, a complex disease with many routes to initiation and progression, as well as environmental, biochemical, genetic and mechanical risk factors. This chapter surveys the extensive literature on the subject. Effects of radiation and mechanisms of cardiovascular injury are likewise assessed and the findings from various epidemiological and animal studies along with statistical considerations are discussed. Chapter 2 gives an overview of mathematical models of cardiovascular disease, and how they may illuminate the structure and evolution of CVD from various perspectives; this chapter outlines challenges in using mathematics as a tool for analysing this complex process. Chapter 3 proposes a spatial reaction diffusion model for atherosclerosis and provides a general framework for modelling early stage disease. Numerical implementation of the equations is performed based on parameter values derived from the biological and epidemiological literature. Chapter 4 considers the association between low dose radiation, inflammation and plaque development and progression by conducting statistical analysis utilising data on ApoE-null, ApoE-heterozygote and wild-type mice and discussing the biological pathways. Chapter 5 concludes. Certain auxiliary figures and tables (largely relating to chapters3 and 4) are presented in the appendix, while definitions for various biological and statistical terms utilized throughout are provided in the glossary at the end.