Modelling perineural tumour invasion

Thesis

Perineural Tumour Invasion (PNI) describes a particularly aggressive mode of tumour spread where cells exhibit a propensity to infiltrate neural structures very rapidly. Clinical observations in the case of Non-Melanoma Skin Cancer (NMSC) suggest that cells of an epidermal tumour can invade the nerve endings lying in deeper tissue (up to 4mm) within, at most, six weeks. Various hypotheses exist regarding the mechanism behind PNI. One such hypothesis is that random motion alone may be sufficient to produce invasion within the observed time frame. Other hypotheses consider an up-regulated proliferation rate, a reduced apoptotic rate or the existence of a chemical gradient that attracts tumour cells towards the nerve sheath.

We explore simple models of cellular processes such as migration, proliferation, death in the absence (and presence) of spatial gradients from a discrete stochastic cell-based perspective. We then associate a continuum description at the collective (tissue) level via deterministic models. These are obtained analytically as mean-field approximations of the stochastic setting in the thermodynamic limit. This enables comparison of the mean time of invasion produced by stochastic simulations of simple position- and velocity-jump processes to corresponding analytical estimates derived from the deterministic models. We, thus, formulate an appropriate mathematical framework which is used to predict the rates of the aforementioned cellular processes required for such rapid invasion.

Our framework illustrates how analysis of the first moments of the distribution of first-passage times to an absorbing barrier by specific position- and velocity-jump processes enables a comparison between the different hypotheses. The setting is extended to include branching and annihilation processes. Finally, we use this ensemble of model mechanisms to compare both analytical and numerical predictions to biological observations so as to assess the validity of the different hypotheses. Testing each hypothesis using this framework shows that for realistic parameter values, derived from the biochemical literature, the existence of chemical or other spatial gradients is necessary to achieve sufficiently rapid invasion. All other hypotheses are rejected because they predict slower invasion by several orders of magnitude.

Authors: Sakellariou, K

• DOI: 10.5287/ora-kokn7bgrw
• Type of award: MSc by Research
• Level of award: Masters
• Awarding institution: University of Oxford