Integrative modelling of angiogenesis in the bovine corpus luteum

The corpus luteum (CL) is a tissue formed from the remnants of an ovulated follicle in the ovary, and it produces the progesterone needed for a healthy pregnancy. CL growth is highly dependent on a growing nutrient supply, and can be compared with the most aggressive vascular tumours. Angiogenesis, the growth of new blood vessels from existing ones, plays a key role in the growth and function of the CL. Inadequate angiogenesis has been linked to infertility in cows. The CL is composed of several vascular(e.g. endothelial cells (ECs), pericytes (PCs)), and avascular (e.g. luteal cells (LCs), immune cells) cell types, and several pro-angiogenic factors (e.g. Fibroblast Growth Factor 2, FGF2) found to be important in the angiogenic process. The objective of this thesis is to shed light on the cellular and extracellular level determinants of angiogenesis in the bovine CL. We begin with the relevant biological and mathematical literature in Chapter 1. In Chapter 2, an ordinary differential equation model of CL growth is introduced. We assume that the CL volume is a continuum of three cell types, ECs, LCs, and stromal cells (such as PCs). The fourth variable in the model, FGF2, enhances the EC proliferation rate. The model is able, by varying parameters such as the maximal proliferation rate of the ECs, to distinguish cases where the CL shifts from a ‘normal’ to a ‘pathological’ growth. In Chapter 3, we present in vitro CL published and novel studies from Robinson’s Lab. Preliminary results demonstrate interesting endothelial and pericyte behaviours regarding cell aggregation and sprout formation, which are the motivation for the next two Chapters. In these experimental studies, all the CL cell types were incorporated in the same in vitro culture, hence providing a closer approximation to the in vivo environment compared to other in vitro cultures which use only a single cell type (mainly ECs). However, this complicates matters in terms of distinguishing cell behaviours and factors which contribute on the overall cell dynamics. Therefore, in the Chapters 4 and 5 we use data from literature. In Chapter 4, by using the Cellular Potts Model (CPM) framework, we focus on EC-PC interactions, and particularly on the mechanism which is responsible for the EC growth inhibition. Our model incorporates two possible mechanisms for inhibition. That is, the mechanical cell-cell contact inhibition, and the inhibition mediated from diffusive TGF-b secreted once the two cell types come in contact. Interestingly, our model results suggest that the effective range of TGF-b is a crucial determinant of the degree of EC growth inhibition. Chapter 5, by using a CPM, is devoted to sprouting angiogenesis (the formation of new blood vessel). The dynamic interchange between stalk and tip EC phenotype is incorporated through the Notch signalling pathway, with the leading tip cell moving up macrophage-mediated VEGFA gradients in a non-uniform matrix environment. The model reproduces phenomena in sprouting angiogenesis, including sprout morphology, tip competition, and explains knockout experiments on the Notch signalling pathway. Finally, we close with Chapter 6 where we summarise the ain results from each chapter and propose model extensions for future directions.