Liver cancer is a major cause of death worldwide and the impact that it has is set to increase in the coming decades. More than half a million cases are diagnosed each year and it is likely many more sufferers are dying unidentified in parts of the world with poor healthcare. Survival rates for untreated cases after diagnosis are low with few patients living beyond one year. A key cause for low survival rates being that the standard treatment is surgical resection; fewer than one quarter of patients are suitable for invasive surgery and five year survival rates rarely exceeds 66 %. RadioFrequency Ablation (RFA) is a minimally invasive technique which utilises the electrically resistive property of tissue to deposit heat energy locally in the vicinity of the tips of an RFA needle. Heat is transferred away through the tissue by conduction, convection of large blood vessels, and bulk flow of blood in smaller vessels. Liver cells, both cancerous and benign, when exposed to the resultant abnormally high temperatures die considerably more rapidly than in cases of natural hyperthermia. It is thus the radiotherapist’s objective to place the RFA needle in a position that maximises destruction of tumour cells, but minimises the collateral damage of surrounding healthy cells. The learning curve of this nontrivial task is reflected unfavourably in the statistics that relate patient survival rate to clinician experience. In this thesis two mathematical models are presented that could be combined into a ‘global’ model of the effects of RFA. To predict cell death in these conditions under RFA, the O’NeillModel is presented in which cells are accounted for by one of three states: alive, vulnerable, and dead. A mechanistic interpretation of the O’Neill Model is attained through comparison to a model from the literature. A known, but little investigated occurrence of tissue swelling in the annular region peripheral to the ablation volume is modelled in a novel way through equations from the literature that track ion transport across the cell membrane; the O’Neill Model for cell death is also incorporated into this model of oedema.