Inclusion of geometric uncertainties in treatment plan evaluation

To correctly evaluate realistic treatment plans in terms of absorbed dose to the clinical target volume (CTV), equivalent uniform dose (EUD), and tumor control probability (TCP) in the presence of execution (random) and preparation (systematic) geometric errors.

The dose matrix is blurred with all execution errors to estimate the total dose distribution of all fractions. To include preparation errors, the CTV is randomly displaced (and optionally rotated) many times with respect to its planned position while computing the dose, EUD, and TCP for the CTV using the blurred dose matrix. Probability distributions of these parameters are computed by combining the results with the probability of each particular preparation error. We verified the method by comparing it with an analytic solution. Next, idealized and realistic prostate plans were tested with varying margins and varying execution and preparation error levels.

Probability levels for the minimum dose, computed with the new method, are within 1% of the analytic solution. The impact of rotations depends strongly on the CTV shape. A margin of 10 mm between the CTV and planning target volume is adequate for three-field prostate treatments given the accuracy level in our department; i.e., the TCP in a population of patients, TCP(pop), is reduced by less than 1% due to geometric errors. When reducing the margin to 6 mm, the dose must be increased from 80 to 87 Gy to maintain the same TCP(pop). Only in regions with a high-dose gradient does such a margin reduction lead to a decrease in normal tissue dose for the same TCP(pop). Based on a rough correspondence of 84% minimum dose with 98% EUD, a margin recipe was defined. To give 90% of patients at least 98% EUD, the planning target volume margin must be approximately 2.5 Sigma + 0.7 sigma - 3 mm, where Sigma and sigma are the combined standard deviations of the preparation and execution errors. This recipe corresponds accurately with 1% TCP(pop) loss for prostate plans with clinically reasonable values of Sigma and sigma.

The new method computes in a few minutes the influence of geometric errors on the statistics of target dose and TCP(pop) in clinical treatment plans. Too small margins lead to a significant loss of TCP(pop) that is difficult to compensate for by dose escalation.