Abstract
The aim of radiotherapy is to destroy a malignant tumour. In accomplishing this goal one has to spare the healthy tissue and organs as much as possible since otherwise they could perish. Thus, the total irradiation time should be short.
These considerations lead to a mathematical model in which constraints reflect the restrictions on the dosage — lower bounds in the tumour and upper bounds in the healthy tissue. The time of irradiation becomes the objective function of the optimization problem. By fixing some of the possible parameters of the treatment one gets a model in which the velocity of the source of radiation can be determined. This solution is approximated, solving a linear and quadratic or parametric programming problem. The model is implemented as a programming system for radiation-treatment planning. An example is given showing its application to a kidney tumour.
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Ebert, U. (1977). Planning of Radiation Treatment. In: Micchelli, C.A., Rivlin, T.J. (eds) Optimal Estimation in Approximation Theory. The IBM Research Symposia Series. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-2388-4_11
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DOI: https://doi.org/10.1007/978-1-4684-2388-4_11
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