Calculation of complication probability factors for non-uniform normal tissue irradiation: the effective volume method

An estimation of normal tissue complication probability factors is important, particularly for evaluating 3-dimensional treatment plans. A method has been developed to calculate complication probability factors for non-uniformly irradiated normal organs using dose volume histograms and complication probabilities for uniform partial organ irradiation. In the effective volume method each volume element of the histogram is considered independently and subject to a power law dose volume relationship. Thus, a non-uniform dose volume histogram is reduced to a uniform one with an effective volume, and a dose equal to the maximum dose to the organ. The complication probability is then obtained from known complication probabilities for uniform partial organ irradiation. The effective volume histogram transformation method is shown to obey various boundary conditions, and is illustrated by comparing probability calculations for alternative 3-dimensional treatment plans for the pelvis. In addition, the limitations of this histogram reduction method are discussed and compared to other calculational techniques. The use of probability factor calculations in treatment plan evaluation, and their role in numerical scoring is explored.