Limitations of a convolution method for modeling geometric uncertainties in radiation therapy. II. The effect of a finite number of fractions.

Convolution methods can be used to model the effect of geometric uncertainties on the planned dose distribution in radiation therapy. This requires several assumptions, including that the patient is treated with an infinite number of fractions, each delivering an infinitesimally small dose. The error resulting from this assumption has not been thoroughly quantified. This is investigated by comparing dose distributions calculated using the Convolution method with the result of Stochastic simulations of the treatment. Additionally, the dose calculated using the conventional Static method, a Corrected Convolution method, and a Direct Simulation are compared to the Stochastic result. This analysis is performed for single beam, parallel opposed pair, and four-field box techniques in a cubic water phantom. Treatment plans for a simple and a complex idealized anatomy were similarly analyzed. The average maximum error using the Static method for a 30 fraction simulation for the three techniques in phantoms was 23%, 11% for Convolution, 10% for Corrected Convolution, and 10% for Direct Simulation. In the two anatomical examples, the mean error in tumor control probability for Static and Convolution methods was 7% and 2%, respectively, of the result with no uncertainty, and 35% and 9%, respectively, for normal tissue complication probabilities. Convolution provides superior estimates of the delivered dose when compared to the Static method. In the range of fractions used clinically, considerable dosimetric variations will exist solely because of the random nature of the geometric uncertainties. However, the effect of finite fractionation appears to have a greater impact on the dose distribution than plan evaluation parameters.