Understanding the Outcomes of Experimental Cancer Therapies through Mathematical Modelling

Oncolytic virotherapy and immunotherapy are examples of reasonably new techniques that are often combined in the fight against cancer. For some types of cancers, leukemias and melanomas for example, results have been promising. Some other cancers are instead very hard to treat, like brain cancers or pancreatic carcinomas, and progress has been less encouraging with those cases. Overall, there is currently a considerable interest in the scientific community on the use of viruses combined with the stimulation of the immune system to mount ad-hoc responses that can infect and destroy tumour cells, while preserving healthy cells and the surrounding micro-environment. For instance, five oncolytic viruses are now approved for patients' use in tumours as different as glioblastoma, melanoma, head and neck carcinoma, combined with immunotherapies like checkpoint blockade inhibitors, CAR-T, interferon therapy and immune boosting to advance our fight against malignancies. In this project, the goal is to improve existing mathematical and computational models so that they can better approximate and explain existing clinical and laboratory data. To achieve this, we perform a multi-stage experimental and data analysis focused on the growth dynamics of untreated and treated tumour populations. We employ Maximum Likelihood Estimation (MLE) to fit typical solutions of Ordinary Differential Equation (ODE) for cancer growth - specifically Logistic, Gompertz, and Richards - to experimental datasets. We analyse several metrics, assuming a normal distribution for the experimental noise, and later compare it with an alternative log-normal one. A rigorous persistence analysis is also conducted by iteratively subsampling data points to evaluate model robustness and identify the threshold where structural complexity outweighs parsimony. Further, we assess the forecasting accuracy of these prototypical models, showing that Sigmoidal models possess a good balance between qualitative fitting capacity and complexity in high-density data, whilst still performing well for more sparse clinical observations. Finally, using this framework, we investigate when solutions of ODEs typically used in cancer therapy can predict long-term cyclical behaviour of tumours, with an accuracy that can be useful for clinicians and experimentalists.