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It was shown in our previous works [2 6] that the problem of formation of optimal dose fields in remote and contact radiation therapy (RT) could be formalized and reduced to linear and nonlinear mathematical pro gramming problems. Synthesized methods for formation of optimal therapeutic dose fields suggested in this work combine the conventional approach to this problem with mathematical programming methods.The problem of formation of optimal dose fields in RT of malignant tumors was often solved using a trial and error method, also designated as the visual optimiza tion method (VOM). The VOM is interactive and itera tive. It does not provide an algorithm for selecting the irradiation parameters for each iteration. It should be noted that the requirements for the dose field depend on the patient's state, dose distribution in the target volume and adjacent normal tissues, and the therapeutic goal.The VOM is interactive because the changes in the irradiation parameters intended to improve the dose field characteristics are made by an operator (expert). Optimization of the dose field is performed in several steps (iterations).The VOM can be considered as an imitation of mathematical programming methods used for solution of conditional and unconditional extremal problems. These methods have been widely used in programming for the last 40 50 years. The VOM is implemented as follows. A medical physicist selects an initial irradiation plan and calculates the corresponding dose field. Then the irradia tion parameters are varied by a trial and error method to improve the dose field characteristics according to the requirements of the radiologist.The goal of this work was to describe a new approach to formation of effective therapeutic dose fields in RT of malignant tumors. It is shown that the VOM can be effec tively combined with mathematical programming meth ods. Synthesis of these methods makes it possible to improve the procedure for formation of effective thera peutic dose fields. In many cases, it is more effective to change the irradiation parameters manually than to mod ify the structure of the optimization problem.Determination of the optimal irradiation plan by mathematical programming methods can involve the fol lowing difficulties.1. The restrictions imposed by the radiologist on the dose field can prove incompatible. In this case, it is nec essary to find a compromise plan of irradiation by varying restrictions on the dose field at control points. The prob lem of restriction variation can be as hard to solve as the initial extremal problem. Its solution requires high skill and experience of the radiologist and medical physicist. 2. The system of restrictions on the dose field cannot take into account all parameters that can possibly affect the resulting dose filed distribution.3. The problem of determination of the optimal irra diation plan is multiextremal. Thus, solution of the prob lem can lead to determination of a local rather than the global extremum. To continue the search for the global extremum it is...

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