Modelling the invasion of solid tumours - the role of the extracellular matrix in invasion

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This project will focus on two types of solid tumours namely, musculoskeletal sarcomas and glioblastoma. Sarcomas are a type of malignant tumour that can be found in many locations within the body as they originate in supportive or connective tissue. A total of 15 people per day in the UK are diagnosed with a sarcoma. Lower grade sarcomas can be treated using one or a combination of, surgery, chemotherapy or radiotherapy. However, higher grade sarcomas are much more aggressive so can spread to other parts of the body and may not be able to be removed using surgery. Glioblastoma is the most common type of malignant brain tumour in adults and although its occurrence is rare in comparison to other forms of cancer, it has a poor prognosis of an average of only 15 months. A multidisciplinary approach is required to treat glioblastoma which involves a combination of surgery, chemotherapy and radiotherapy. During surgery, not all the glioblastoma tumour can be removed from the brain due to the risk of causing damage to healthy brain tissue. Therefore, due to the highly invasive nature of glioblastoma reoccurrence is inevitable. This highlights the importance of investigating the invasion process because if it is better understood then treatments to prevent recurrence or the cancer from spreading might be able to be developed. The main aim of this project is to develop mathematical models which investigate the role of the extracellular matrix (ECM) in the invasion processes of solid tumours including musculoskeletal sarcomas and glioblastoma. Abnormal ECM is a component of the tumour microenvironment and the ECM is also a constituent of healthy tissue that the cancer invades. It has roles of controlling transport mechanisms and metabolism as well as the growth and spread of tumours. Due to its complexity, treatments targeting the ECM are not yet practised on patients. Given the key role of the ECM in the invasion process, it is surprising that relatively little information about it is included in current mathematical models. It is hoped that if the role of the ECM in the invasion process is better understood then the differences in the compositions of younger and older patients' matrix can be accounted for in the invasion of tumours. The models developed in this project will take into account the unique composition and remodelling capability of the ECM. To achieve this, the invasion of musculoskeletal sarcomas and glioblastoma will be modelled using discrete and continuous mathematical models which contain biological and clinical data. These models will be developed further to include the interactions between the ECM and either the musculoskeletal sarcomas or glioblastoma cells. This is important because if it is known how the ECM composition affects invasion then it may be possible to predict the invasion pathway based on a patient's ECM composition. The models will also allow for a deeper understanding into how specific components of the ECM affect tumour invasion and this could lead to future therapeutic targets being identified. The intention is to develop a hybrid discrete-continuous mathematical model of the invasion of musculoskeletal sarcomas and glioblastoma tumours. Continuous models represent the tumour as a whole continuous medium so focus on the movement of the tumour as one body. Partial differential equations (PDEs) are usually used to represent the continuous components of a model. Discrete models consider the movement of the individual cells which make up the tumour. Using a hybrid model will allow a combination of being able to represent cells as discrete agents whilst also being able to use PDEs to model other components such as the ECM. This allows a clear understanding of the relationship between the cancer cells and their environment. The models will be developed using MATLAB which has the advantage of an inbuilt PDE solver and Python due to its wide range of libraries.