Optimum Model Based Scheduling of Radiotherapy for Avascular Solid Homogenous Tumour

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Acknowledgement

I would take this opportunity to thank my research supervisor, family and friends for their support and guidance without which this research would not have been possible.

DECLARATION

I, [type your full first names and surname here], declare that the contents of this dissertation/thesis represent my own unaided work, and that the dissertation/thesis has not previously been submitted for academic examination towards any qualification. Furthermore, it represents my own opinions and not necessarily those of the University.

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ABSTRACT

We incorporate a previously validated mathematical model of a vascularized tumor into an optimal control problem to determine the temporal scheduling of radiotherapy and angiogenic inhibitors that maximizes the control of a primary tumor. Our results reveal that optimal antiangiogenic monotherapy gives a large initial injection to attain a 20: 1 ratio of tumor cell volume to supporting vasculature volume. It thereafter maintains this 20: 1 ratio via a continuous dose rate that is intensi?ed over time. The optimal radiation monotherapy schedule is characterized by a modest dose intensi?cation over time. The best performance is achieved by our optimal combination regimen, where the antiangiogenic treatment again maintains a constant tumor-to-vasculature ratio, but is administered in a dose-intensi?ed manner only during the latter portion of the radiation fractionation schedule.

Table of Contents

ABSTRACT1

CHAPTER 1: INTRODUCTION3

Background3

Aims and Objectives4

Structure of the report5

CHAPTER 2: LITERATURE REVIEW6

Radio Biology9

Role of Angiogenesis in Primary Tumor Growth and Metastasis10

Mathematical Oncology12

The drug-free model12

The Tumour Growth Algorithm14

The Radiotherapy Algorithm18

Hypoxia, angiogenesis and radio resistance20

REFERENCES22

CHAPTER 1: INTRODUCTION

Background

Multiple studies have shown that hypoxia decreases cellular sensitivity to ionising radiation in living tissue. Consequently, there is an increase in radioresistance of hypoxic tumour cells following single or multifraction radiotherapy compared to oxic cells. Approximately 70% of locally advanced head and neck squamous cell carcinomas (HNSCC) have been reported to exhibit hypoxic regions, with median oxygen levels having a significant influence patient prognosis. Reports from HNSCC clinical trials and experimental work commonly express hypoxia as the percentage of cells in the tumor having pO2 values less than 10, 5, or 2.5mmHg, which is often very high (>50%). In contrast, the average pO2 for healthy epithelial cells is approximately 40mmHg. Tumor hypoxia occurs when the diffusion of oxygen from the surrounding tissue becomes insufficient in a non-vascularised tumour mass. It has been shown that tumours can grow up to a diameter of 1 to 2mm without an independent blood supply, after which neo-vascularisation is necessary for sustained growth (Skehan, 1986, pp. 496).

However, the new blood vessels may be chaotic in nature and possess faults such as holes and shunts. Consequently, an unstable and insufficient oxygen supply may develop causing tumour hypoxia. However, when a tumor is treated with fractionated radiotherapy, oxygen levels may begin to increase again during the process of tumour shrinkage, a phenomenon named reoxygenation (ROx) (Spratt, 1996, pp. 68). In aggressive tumours of epithelial origin such as HNSCC, cellular repopulation after trauma such high-dose irradiation, occurs through cell division of the surviving cell ...