OPTIMAL RADIATION BEAM PROFILES CONSIDERING UNCERTAINTIES IN BEAM PATIENT ALIGNMENT

The often large uncertainties that exist in beam patient alignment dur ing radiation therapy may require modification of the incident beams t o ensure an optimal delivered dose distribution to the target volume. This problem becomes increasingly severe when the required dose distri bution of the incident beams becomes more heterogeneous. A simple anal ytical formula is derived for the case when the fraction number is hig h, and the desired relative dose variations are small. This formula ad justs the fluence distribution of the incident beam so that the result ant dose distribution will be as close as possible to the desired one considering the uncertainties in beam patient alignment. When sharp do se gradients are important, for instance at the border of the target v olume, the problem is much more difficult. It is shown here that, if t he tumor is surrounded by organs at risk, it is generally best to open up the field by about one standard deviation of the positional uncert ainty-that is sigma/2 on each side of the target volume. In principle it is simultaneously desirable to increase the prescribed dose by a fe w per cent compared to the case where the positional uncertainty is ne gligible, in order to compensate for the rounded shoulders of the deli vered dose distribution. When the tissues surrounding the tumor no lon ger are dose limiting even larger increases in field size may be advan tageous. For more critical clinical situations the positional uncertai nty may even limit the success of radiotherapy. In such cases one gene rally wants to create a steeper dose distribution than the underlying random Gaussian displacement process allows. The problem is then best handled by quantifying the treatment outcome under the influence of th e stochastic process of patient misalignment. Either the coincidence w ith the desired dose distribution, or the expectation value of the pro bability of achieving complication-free tumor control is maximized und er the influence of this stochastic process. It is shown that the most advantageous treatment is to apply beams that are either considerably widened or slightly widened and over flattened near the field edges f or small and large fraction numbers respectively.