John McLellan

Date of Award


Degree Type


Degree Name

Doctor of Philosophy


The finite range of electrons in tissue makes electron beams a useful radiation treatment modality for many tumour sites. However, the simplistic methods of dose calculation in current clinical use lack sufficient accuracy in many situations of clinical importance. This thesis rests on the premise that a more accurate dose calculation method must incorporate all the major physical processes which shape the dose distribution.;The thesis unites the important transport processes of electron energy loss and angular scattering in a single mathematical model known as the compound Poisson process (CPP). CPP-based calculations of energy-loss spectra for 10, 20 and 30 MeV electrons incident on graphite and aluminum absorbers agreed within 1% with Monte Carlo simulations for electrons travelling path lengths less than 0.5 g/cm{dollar}\sp2{dollar}. Similarly, calculations of angular distributions agreed with Monte Carlo simulations within 2% for 5 and 10 MeV electrons traversing water slabs up to 0.5 cm thick.;The evolution and Monte Carlo methods of dose calculation can both incorporate the CPP model into a complete transport calculation. An analysis of the convergence of the two methods reveals that: (i) the number of histories in a Monte Carlo simulation is analogous to the number of discrete bins in the evolution method, (ii) the convergence of the evolution method depends on the dimensionality of the problem while the convergence of the Monte Carlo method does not, and (iii) for the full six dimensional transport problem, the ratio of the error in the evolution method to that in the Monte Carlo method is proportional to N{dollar}\sp{lcub}1/6{rcub}{dollar} where N is the number of histories or bins.;Since the convergence of the evolution method improves with fewer dimensions, an approximate "dimensionally-reduced" evolution method is proposed. Preliminary calculations of dose distributions in a homogeneous water phantom achieved reasonable agreement with Monte Carlo simulations for incident 10 and 20 MeV electron beams. The least accurate result underestimated the dose by 5% at the depth of dose maximum and overestimated the width of the 10% isodose line by 8 mm. These early results indicate that the dimensionally-reduced evolution method merits further investigation.



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