For almost a century radiation has been used to treat tumours. Over time the treatment has been performed with diverse types of radiation (treatment modalities) such as photons, electrons, protons, neutrons, and ions, with photons and electrons so far being the main clinical treatment modalities. The preparation for the treatment begins with the creation of a three-dimensional image of the tumour and surrounding healthy tissue, using techniques such as computed tomography or MRI.

The transport of the treatment radiation particles through the background is described by a system of coupled Boltzmann transport equations. A solution to this system is a vector of phase space number densities, that is, number of radiation particles per unit volume in phase space, i.e. position-direction-energy space. Even if the beam aimed at the tumour consists of only one particle type (for instance photons, as in X-ray), interactions between radiation particles and background will set in motion other types of particles. And so careful calculations always require consideration of several types of particles.

Interactions of radiation particles with each other are negligible in this context, so the relevant transport equations are linear. The high speed of the radiation particles implies that the relevant transport equations therefore contain no time derivatives. Information obtained through imaging, such as the locations of soft tissue, bone, or air gaps, yields coefficients in these equations.

Radiation therapy is fractionized, that is, delivered in multiple sessions. Furthermore, during a single session, several beam configurations may be used. A radiation therapy plan specifies beam positions, directions, energies, etc., as well as when and how long the specific beams are to be turned on. This can be viewed as specifying a sequence of inflow boundary value problems for a system of steady linear Boltzmann equations.

The full solutions to these boundary value problems are never considered in radiation therapy planning. Of greatest interest is the total dose, that is, the amount of energy per unit background mass deposited, during the entire course of the treatment, as a result of excitation and ionization events. In the language of kinetic theory dose is a macroscopic quantity depending on position. To emphasize this dependence, it is often called dose distribution. It is usually assumed that, for a given type of treatment, the effectiveness of a given treatment plan can be predicted from the dose distribution alone.

Most current treatment plans rely on calculation of the resulting dose distribution from a number of given treatment set-up parameters. One aim of the research is to solve the treatment plproblemanning problem by inverse methods (i.e. finding a set of treatment parameters that gives the desired result). It is, however, a difficult task to develop physical and mathematical models that will solve this problem without large approximations and within reasonable time.

##### Models and methods for light ion-beam transport

##### Biological models and optimization for IMRT planning

In order to further improve the quality of life for patients treated with this technique we will include biological parameters into the objective function that take into account the risk of different long-term complications in the patient (including both severe and minor ones). This involves providing statistically valid biological descriptions of dose absorption both in organs-at-risk and in normal tissues.

We will further also better utilise the capabilities of the IMRT technique by automatically and efficiently optimising the number of beams and their optimal directions for irradiation in 3D, including features such as smoother beam weights in order to avoid cold spots and lower beam-on time required for delivery. Taking into account the multi-objective property of the treatment planning problem, the final software will generate several solutions having similar properties regarding dose distribution in terms of physical and biological criteria; the planner then has the possibility to further analyse and adjust each of these in the search for an optimal one with respect to clinical experience.

At our disposal we will have the results of a current national study on tumour effect and side effects in 750 patients, including many treated with the IMRT technique.