Sensitivity analysis of tolerance limits for dose escalation

The potential tradeoff between small relaxations in a dose volume limit and large increases in minimum tumor dose is unavailable in current planning programs. This study shows how the sensitivities to individual limits can be discovered using an optimization program based on combinatorial mathematics. Treatment for a prostate tumor was planned from a set of 36 beams with intensities chosen using a previously described integer program. Tumor dose was maximized for a range of rectal dose volume limits. Changing the volume of rectum that must meet a threshold level of dose produced a more severe effect than changing the threshold dose level for any given volume to protect. A 5% reduction, from 80% to 75%, in the rectal volume that must receive a dose <75 Gy allowed the minimum tumor dose to rise from 76 Gy to 89 Gy, a 17% gain. Making the dose threshold higher or lower than 75 Gy produced only gradual changes in the tumor dose. The sensitive limits were discovered from a three dimensional plot of dose and volume bounds against tumor dose. A large gain in tumor dose can be obtained by changing some limits a small amount. Those limits that affect tumor dose by the greatest amount should be identified, and tolerance studies designed to reduce their uncertainties. By understanding the tradeoffs between tighter limits and lower doses, physicians and patients can choose constraints that best the serve the needs of improving tumor control at an acceptable level of risk