The optimization of treatment plans

In optimizing fixed field treatment planning it is desired to minimize the badness of the treatment. In the assessment of a plan the badness can be expressed in terms of variables such as tumour dose, integral dose, dose gradient across the tumour, physical complexity of treating, etc. Each variable can have constraints imposed upon it, for example, minimum acceptable tumour dose, but these variables are dependent on a more basic set which includes number of fields, field positions, wedge angles and field weights, each having its own inherent constraints defined by available facilities. Further, the dependent variables, tumour dose etc., are heterodimensional and the assessment cannot be carried out by combining them directly. It is necessary to replace each dependent variable by a score function which relates the magnitude of a deviation from the ideal value to the importance of this deviation. The analogy between the optimizing process and curve fitting by least squares suggests that the individual scores should be added to evaluate badness. The score functions are, in fact, measures of the deviations. Deviations correspond to residuals which are squared and added to assess the goodness of fit of a curve, though in general the score functions in treatment planning will not be squares of the deviations. The two problems to be solved before optimized treatment planning is a practical reality are: (a) the organization of the search for the optimum; and (b) the definition of score functions to recognize it. In the next section score functions are considered while the problem of searching is examined later in the paper