The dose-volume response of tumours and normal tissues is discussed in terms of 'parallelity' and 'seriality'. The volume dependence of the radiation response of a tumour depends primarily on the eradication of all its clonogenic cells and the tumour has a parallel organization. The response of heterogeneous tumours is examined, and it is shown that a small resistant clonogen population may cause a low dose-response gradient, gamma. Injury to normal tissue is a much more complex and gradual process. It depends on earlier effects induced long before depletion of stem cells or differentiated cells that in addition may have a complex structural and functional organization. The volume dependence of the dose-response relation of normal tissues is therefore described here by a new parameter, the 'relative seriality', s, of the infrastructure of the organ. The model is compared with clinical and experimental data on normal tissue response, and shows good agreement both with regard to the shape of dose-response relation and the volume dependence of the isoeffect dose. For example, the spinal cord has a high and the lung a low 'relative seriality', which is reasonable with regard to the organization of these tissues. The response of tumours and normal tissues to non-uniform dose delivery is quantified for fractionated therapy using the linear quadratic cell survival parameters alpha and beta. The steepness, gamma, and the 50% response dose, D50, of the dose-response relationship are derived both for a constant dose per fraction and a constant number of dose fractions.

New radiobiological models are used to describe tumour and normal tissue reactions and to account for their dependence on the irradiated volume and inhomogeneities of the delivered dose distribution and cell sensitivity. The probability of accomplishing complication-free tumour control is maximized by an iterative algorithm. The algorithm is demonstrated by applying it to a one-dimensional (1D) tumour model but also to a more clinically relevant 2D case. The new algorithm is n-dimensional so it could simultaneously optimize the dose delivery in a 3D volume and in principle also select the ideal beam orientations, beam modalities (photons, electrons, neutrons, etc) and optimal spectral distributions of the corresponding modalities. To make calculation time reasonable, 2D-3D problems are most practical, and suitable beam orientations are preselected by the choice of irradiation kernel. The energy deposition kernel should therefore be selected in order to avoid irradiation through organs at risk. Clinically established dose response parameters for the tissues of interest are used to make the optimization as relevant as possible to the clinical problems at hand. The algorithm can be used even with a poorly selected kernel because it will always, as far as possible, avoid irradiating organs at risk. The generated dose distribution will be optimal with respect to the spatial distribution and assumed radiobiological properties of the tumour and normal tissues at risk for the kernel chosen. More specifically the probability of achieving tumour control without fatal complications in normal tissues is maximized. In the clinical examples a reduced tumour dose is seen at the border to sensitive organs at risk, but instead an increased dose just inside the tumour border is generated. The increased tumour dose has the effect that the dose fall-off is as steep as possible at the border to organs at risk.

All current optimization techniques in radiation therapy benefit from the use of strongly non-uniform radiation beams. The most flexible way of generating these fields under real time control is by elementary beam scanning and/or dynamic multileaf collimation. In this work general analytical expressions are derived for the required motion of the collimator leaves to achieve a desired energy fluence distribution or collimator opening density in the patient in the shortest possible time. By simplification of the general expressions the equations of motion have been derived for both the shrinking field and the curtain shutter techniques with the associated approximations clearly quantified. The mechanical limitations on leaf motion, caused by the finite velocity and acceleration, are taken into account. It is shown that almost any desired energy fluence distribution can be created even when the limitations on velocity and acceleration are considered. The basic rule with the curtain shutter technique is that when the energy fluence gradient along the direction of motion of the leaves is positive, the leading leaf should move at maximum speed and the lagging leaf should modulate the field. In regions where the gradient is negative the lagging leaf should instead move at full speed and the leading leaf should modulate the field. The overall treatment time is then proportional to the total increment in energy fluence or opening density between consecutive minima and maxima. For energy fluence profiles with numerous high peaks the treatment time may therefore increase considerably over that for conventional uniform dose delivery. However, in general the treatment time is prolonged by a factor of about two compared to a traditional uniform treatment. Obviously the method developed here for multileaf collimators is also suitable for simple block collimators since it can be used to deliver arbitrary regular or irregular 'dynamic wedge' profiles along the direction of motion of the collimator blocks.

Traditionally, the shaping of non-uniform dose distributions has been performed by using wedges or compensating filters. The advent of high resolution multileaf collimators may largely eliminate the need for material attenuators for modification of the beam. This is achieved by a new technique for the shaping of arbitrary dose distributions by dynamic motion of the collimator leaves. By employing narrow elementary slit beams that correspond to the smallest possible opening of the multileaf collimator, the optimal density of such slit beams, i.e. opening density, can be determined automatically using a newly developed inversion algorithm. The present method has two major advantages (1) internal structures in the field can be created, controlled solely by steering the collimator leaves, (2) the opening density determined by the algorithm never gives rise to underdosage: this is important from a radiobiological point of view.