Rare event modelling for the progression of cancer

Purpose
This project will apply cutting-edge mathematical modelling techniques to solve computational and modelling issues in predicting the evolution of cancerous tumours. The project will combine rare event modelling from the physical sciences and cellular-level models from mathematical biology. The aim is to produce new cancer models with improved biological detail that can be solved on clinically relevant timescales, which can be decades.

Background
A wide-spread problem in treating cancer is to distinguish indolent (benign) tumours from metastatic-capable primary tumours (tumours that can spread to other parts of the body). Although therapies for metastatic disease exist, metastatic disease is a significant cause of death in cancer patients. This problem can lead to misdiagnosis, unnecessary treatment and a lack of clarity on which treatments are most effective.

A predictive mathematical model of cancer development could assist with the above issues. However, as the progression of cancer to metastasis is a rare event, in a direct simulation, virtually all of the computational time is consumed in simulating the quasi-stable behaviour of the indolent tumour, revealing no information about progression. This generic problem of rare events is common in the physical sciences, where modern techniques have enabled rare events to be simulated and understood. This project will extend these techniques to cancer modelling. The project will build on a state-of-the-art spatiotemporal cancer model, which models individual cancer cells in a host tissue, vascular networks and angiogenesis. In this model cells can divide, migrate or die, in response to their microenvironment of cell crowding and cell signalling. To this framework the project will add transitions between cell types, driven by random mutation events and intravasation events.

The project will use a rare event algorithm, forward flux sampling (FFS), to create a statistical map of the transition from indolent cancer to metastatic cancer. In a typical rare event transition the system spends the overwhelming majority of the time close to the start. Consequently, the sampling of the trajectory space is very uneven. Thus, despite a very long simulation the statistical resolution of the mechanism and crossing rate are very poor. FFS solves this problem by dividing the phase space into a series of interfaces that represent sequential advancement towards the rare event. The algorithm logs forward crossings of these interfaces and a series of trajectories are begun at these crossing points. This produces a far more even sampling of the trajectory space and so better statistics of the whole mechanism from a shorter simulation.

Apply: This studentship is open now and will be available until it is filled. To apply please visit the University Of Nottingham application page: http://www.nottingham.ac.uk/pgstudy/apply/apply-online.aspx