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### Abstract

When exposed to ionising radiation, living tissue can potentially suffer somatic and genetic damage - effects depending mainly on the radiation dose or energy absorbed, the type of radiation, and the type and mass of cells affected. It is well known that large doses of radiation lead to high damage of the cell nucleus and additional cell structures, which results in harmful somatic effects, and even rapid death of the individual exposed, while at low doses, cancer is by far the most important possible consequence. Understanding the mechanisms by which low doses of radiation cause cell damage is thus of great significance, not only from this viewpoint but also from that of practical medical physics applications such as radiotherapy treatment planning. Ionising radiation, such as electrons and positrons, begins to cause damage to the genome of a living cell by direct ionisation of atoms, thus depositing energy in the DNA double helix itself. The energy threshold for inducing strand-breaks by electrons, however, is around 7 eV, well below the energy levels required for direct ionization. The low-energy electrons that are set in motion around the tracks of energetic charged particles, for example, are responsible for a multitude of low-energy events (energy transfer of the order of 10 eV), which play a significant role in inducing molecular damage. Assessing the spatial configuration of energy transfer events and the deposited energy spectra, in regions of cellular and sub-cellular dimensions, can be aimed at via the application of appropriate Monte Carlo simulation tools. Such calculations depend primarily on an accurate knowledge of the production and subsequent slowing down of secondary electrons that form the basic structure of the charged particle track. In the above context, an important requirement is the provision of detailed quantitative information concerning the interaction cross sections of electrons over an energy range extending down to low energies, i.e. including the sub-excitation domain. In addition, developing fast particle-transport simulation algorithms to cover the entire slowing down process efficiently is a key aspect. Thus, the present doctoral research has, as global goal, the development and validation of new Monte Carlo calculational tools for electron and positron transport in biological materials, both at high and low energies. More specifically, it aims at providing (i) a comprehensive and accurate set of appropriate cross section data, and (ii) a fast and reliable algorithm for the simulation of charged particle transport. Thus, the first part of the thesis concerns the assessment, further development and validation of standard theoretical models for generating electron and positron cross sections to cover the main interactions of these particles with matter, in particular with the basic atomic components of biomaterials (water, bio-polymers, etc.). This has been done for bremsstrahlung, and both elastic and inelastic scattering, considering a wide range of atomic numbers and high up to thermal incident particle energies. In particular, the excitation cross sections for medium and low energies (down to 1 eV) have been derived by using a new formalism based on many-body field theory. The accuracy of the presently obtained data sets are assessed against other theoretical models, as also a large experimental database for each type of interaction, so that both a comprehensive coverage and adequate accuracies have been ensured for the cross section data sets generated. In the second part of the thesis, an extension of the Monte Carlo code system PENELOPE is first undertaken such that use can be made of elastic scattering differential cross sections which have been made available in numerical form. Thereby, new computational routines (incorporated into the new code PENELAST) prepare the cross sections, needed for a given energy and scattering angle, by applying a fast and accurate sampling technique to a provided data set. The present development will allow various electron and positron cross section data libraries, appropriately formatted, to be used with PENELOPE for benchmarking purposes. The development of a high calculation-speed (Class I) Monte Carlo tool for charged particle transport in biological materials has then been addressed. Thereby, a numerical algorithm for calculating the multiple-scattering angular distributions of high energy electrons and positrons is developed, based on the multiple-scattering theory of Lewis which accounts for energy losses within the continuous slowing down approximation. Partial-wave elastic scattering differential cross sections made available in numerical form, as indicated above, are used for the calculations, the inelastic scattering differential cross sections being obtained from the Sternheimer-Liljequist generalized oscillator strength model implemented in PENELOPE. The new code LEWIS has been used to calculate multiple-scattering angular distributions for given path lengths and can be readily adopted for Class I Monte Carlo simulations. The simultaneous generation of a large number of Legendre expansion coefficients is rendered possible, both rapidly and accurately. Results from LEWIS have been found to be in satisfactory agreement, both with detailed simulations carried out using PENELAST and with various sets of experimental data for high to medium energy electrons. In brief, the present research represents a significant improvement in the quality of Monte Carlo modelling of charged particle slowing down processes, thus contributing to understanding the. role of low-energy secondary electrons in radiation protection studies. It will also allow the further development of a complete Class I Monte Carlo code, which can then be reliably used in practical applications such as radiation treatment planning.