Abstract The goal of radiotherapy is to destroy a tumour in the patient's body by means of radiation. At the same time, healthy tissue is to be damaged as little as possible. In mathematical terms this means: in certain parts of the body minimal doses - necessary to destroy the cancerous tissue - must be achieved; in other parts maximum doses should not be exceeded to preserve organs like liver, spinal cord, etc. If we minimize the total time of irradiation, taking into account these constraints, we find an optimal solution to the treatment problem. The dose depends on a number of parameters. By fixing some of them and determining the remaining ones so as to satisfy constraints given in advance, a model for radiation-treatment planning is obtained. It is discretized and so reduced to a practical form. The result of this discretization process is a mixed-integer problem or a problem with a nonlinear constraint. The implementation of the model as optimizing system for radiation-treatment planning is described. An example demonstrates the application of the system to a kidney tumour.
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