This thesis presents the findings of the investigation into the Monte Carlo simulation of superficial cancer treatments of the head and neck region. The EGSnrc system of codes for the Monte Carlo simulation of the transport of electrons and photons through a phantom representative of either a water phantom or treatment site in a patient is utilised. Two clinical treatment units are simulated using the BEAMnrc system of codes: the Varian Medical Systems Clinac® 2100C accelerator for 6MeV electron fields and the Pantak Therapax SXT 150 X-ray unit for 80kV and 100kV photon fields. Depth dose, profile and isodose curves are compared against those measured from a PTW MP3 water phantom with good agreement being achieved. Quantitative dose distributions are determined for both MeV electron and kV photon fields with treatment sites containing high atomic number materials, rapidly sloping surfaces and different density interfaces. This highlights the relatively high level of dose deposition of dose in tissue-bone and tissue-cartilage interfaces in the kV photon fields. From these dose distributions DVH and dose comparators are used to assess the simulated treatment fields.

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The thesis considers and examines methods of surface propagation, where the normal velocity of the surface depends on the local curvature and the gradient of the surface. Such fronts occur in many different physical situations from the growth of crystals to the spreading of flames. A number of different methods are considered to find solutions to these physical problems. First the motion is modelled by partial differential equations and numerical methods are developed for solving these equations. The numerical methods involve characteristic, finite differences and transformation of the equations. Stability of the solutions is also briefly considered. Secondly the fronts are modelled by using a cellular approach which subdivides space into regions of small cells. The fronts are assumed to propagate through the region according to stochastic rules. Monte-Carlo simulations are carried out using this approach. Results of the simulations are carried out in two-dimensions and three-dimensions for a number of interesting physical examples.