Sampling Strategies in Evolving Cancer : From Mathematical Models to Clinical Application

Despite tremendous resource investment in the fight against cancer over the last 50 years, prognosis of the late-stage malignant disease is almost inevitably unfavourable as most cancers are resilient against treatment. The source of this cancer resilience lies in rapid somatic evolution and consequential extensive intra-tumour genetic heterogeneity. Unravelling this complex genetic landscape of cancer is thus mandatory if we are ever to overcome the emergence of resistance. However, current sampling procedures allow only to investigate a small subset of malignant cells. Drawing conclusions about characteristics of the entire cancer from this partial information inevitably introduces a bias. To counter this bias, this thesis investigates sampling strategies in cancer genomic profiling by combining mathematical and computational modelling, and validating the models with cancer genomic data. In the first chapter, I introduce a mathematical model for calculating the number of samples needed to successfully identify mutations present in every cancer cell from multi-region genomic profiling of solid tumours. The clonality inference procedure is further tested in a spatial model of intratumour heterogeneity. Moreover, I show how the size of individual samples affects the probability for correct clonality estimation and how an optimized sampling pattern can improve detection accuracy to a great extent. In the next chapter, presented theoretical model was applied to genomic data derived from patients with gastric adenocarcinoma. We find that in three out of nine patients, the existing number of samples is sufficient to infer the clonality of detected mutations with a high degree of certainty. Additionally, an attempt to characterise the mode of evolution in primary tumours of each patient revealed a diversity of patterns characteristic for different evolutionary trajectories. The third chapter is dedicated to modelling the process of cancer genetic profiling in solid tumours using liquid biopsies. Here, I present the extent of sampling bias encountered in this type of diagnostics and show how it can lead to a distorted view of the tumour sub-clonal composition. I estimate the amount of genomic material necessary for detection and quantification of both individual and sets of genetic alterations present range of frequencies. Finally, in the last chapter, I present a software package for simulating spatial tumours developed in Python that provides an easily accessible resource for studying the evolutionary processes of cancer progression. The work presented in this thesis demonstrates how mathematical and computational modelling, combined with clinical data, can be used to support cancer diagnostics and assist clinicians in making better informed treatment decisions.