Theoretical considerations in the optimisation of dose distribution in radiation therapy

The development of an optimum radiation treatment regimen requires manipulation of many variables of which one of the most important is the actual spatial distribution of the radiation dose. A mathematical formula has been developed which permits a rational approach to the problem of choosing an optimal dose distribution. Initially, the tumour is described by a cell density function which measures the expected concentration of cells at any point in the tumour bearing volume. The formalism then generates the appropriate cell density function which would be expected to apply after any particular treatment.From this information, the probability of cure of the tumour and the probability of recurrence in any region can be calculated. It is suggested that a dose distribution which produces a uniform recurrence probability throughout the original tumour volume will frequently be most advantageous. The proper dose distributions to achieve this result have been derived for several sample tumours under the simplifying assumptions that the population is homogeneous and that multi-target type kill statistics apply. The influence of tumour geometry and of basic restrictions in the treatment plan such as a requirement to use parallel opposed field upon this optimal dose distribution is described.