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The purpose of this work was the development of a probabilistic planning method with biological cost functions that does not require the definition of margins. Geometrical uncertainties were integrated in tumor control probability (TCP) and normal tissue complication probability (NTCP) objective functions for inverse planning. For efficiency reasons random errors were included by blurring the dose distribution and systematic errors by shifting structures with respect to the dose. Treatment plans were made for 19 prostate patients following four inverse strategies: Conformal with homogeneous dose to the planning target volume (PTV), a simultaneous integrated boost using a second PTV, optimization using TCP and NTCP functions together with a PTV, and probabilistic TCP and NTCP optimization for the clinical target volume without PTV. The resulting plans were evaluated by independent Monte Carlo simulation of many possible treatment histories including geometrical uncertainties. The results showed that the probabilistic optimization technique reduced the rectal wall volume receiving high dose, while at the same time increasing the dose to the clinical target volume. Without sacrificing the expected local control rate, the expected rectum toxicity could be reduced by 50% relative to the boost technique. The improvement over the conformal technique was larger yet. The margin based biological technique led to toxicity in between the boost and probabilistic techniques, but its control rates were very variable and relatively low. During evaluations, the sensitivity of the local control probability to variations in biological parameters appeared similar for all four strategies. The sensitivity to variations of the geometrical error distributions was strongest for the probabilistic technique. It is concluded that probabilistic optimization based on tumor control probability and normal tissue complication probability is feasible. It results in robust prostate treatment plans with an improved balance between local control and rectum toxicity, compared to conventional techniques.

The minimum margins required to compensate for random geometric uncertainties in the delivery of radiotherapy treatment were determined for a spherical Clinical Target Volume, using an analytic model for the cumulative dose. Margins were calculated such that the minimum dose in the target would be no less than 95% of the prescribed dose for 90% of the patients. The dose distribution model incorporated two Gaussians, and could accurately represent realistic dose profiles for various target sizes in lung and water. It was found that variations in target size and tissue density lead to significant changes in the minimum margin required for random errors. The random error margin increased with tissue density, and decreased with target size. The required margins were similar for dose distributions of spherical and cylindrical symmetry. Significant dose outside the spherical high dose region, as could result from multiple incident beams, lead to an increased margin for the larger targets. We could confirm that the previously proposed margin of 0.7 times the standard deviation of the random errors is safe for standard deviations up to 5 mm, except for very small targets in dense material.

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