International Journal of Radiation Oncology*Biology*Physics
Physics contributionsThe probability of correct target dosage: dose-population histograms for deriving treatment margins in radiotherapy
Introduction
Knowledge of geometrical uncertainties in radiotherapy is steadily increasing. Numerous publications (of which only a few recent ones are referenced as example) have presented data on the accuracy of target volume delineation 1, 2, 3, organ motion 4, 5, and setup accuracy 6, 7, 8. In principle, the full characterization of all geometrical uncertainties should lead to objective choices for treatment margins (9). However, no unambiguous guidelines have been presented thus far for this purpose, indicating that the statistical methods required to choose treatment margins are still unclear. Many studies and reports describing margin choice do not fully address the difference between (treatment) variations (often called random or day-to-day variations) and (treatment) variations 10, 11. The latter errors are often called systematic, because they are systematic for a single radiotherapy course of a single patient, but they are stochastic over a group of patients. In those studies that do separate these two types of variations, the authors are unsure how to combine them (12). The most advanced approaches that have been presented to date concern Monte Carlo-like simulations based on real patient data to determine the impact of geometrical variations on the dose delivery 13, 14. These studies are highly specific to a certain technique and their results are sometimes difficult to extrapolate to other situations. Another numerical approach is to use coverage probabilities to derive margins 15, 16.
In this paper, we will use the terms clinical target volume (CTV) and planning target volume (PTV) as defined by the ICRU (17). The definition of CTV is: “The CTV is a tissue volume that contains a gross tumor volume (GTV) which is the gross palpable or visible/demonstrable extent and location of the malignant growth, and/or subclinical microscopic malignant disease, which has to be eliminated. This volume has to be treated adequately in order to reach the aim of therapy: cure or palliation.” The definition of PTV is: “The PTV is a geometrical concept, and it is defined to select appropriate beam sizes and beam arrangements, taking into consideration the net effect of all the possible geometrical variations and inaccuracies in order to ensure that the prescribed dose is actually absorbed in the CTV.”
The aim of this study is to provide an analytical description of the influence of geometrical deviations occurring during both the preparation and execution stage of treatment on the dose delivered to the CTV. Next, this model will be used to derive the margin that is required between the CTV and the PTV. The computations will be based on the probability distribution of the dose delivered to the CTV. Solutions will be given for a simplified situation. Finally, we will discuss the validity of the current PTV definition and propose some refinements.
Section snippets
Theory
In this study, the impact of geometric deviations will be quantified in terms of the dose delivered to the CTV. The method is based on the probability distribution of geometrical deviations. First, the cumulative dose distribution (including geometric deviations) is computed. Next, the probability that the CTV actually receives a given dose is computed. The derivations in this paper are classical in the sense that no biological response parameters are used but that the effects are solely
Dose-population histograms
Table 1 lists some recent data on the accuracy of prostate irradiation from studies performed by our group. We will use these data to derive more or less realistic minimum dose-population histograms for various margins and an ideal homogeneous dose distribution. However, one should consider that these computations exclude rotations and shape variations (thereby underestimating some of the error sources) and assume perfect conformity of the dose distribution (thereby overestimating the impact of
Discussion
In our analysis we have derived margins based on the of correct target dosage. In our opinion, the definition of PTV should therefore be modified and be: “The PTV is a geometrical concept, and it is defined to select appropriate beam sizes and beam arrangements, taking into consideration the net effect of all the possible geometrical variations and inaccuracies in that the prescribed dose is actually absorbed in the CTV
Conclusion
Probability histograms of the cumulative dose in a population of patients (dose-population histograms) are a simple and effective means for describing the effect of a specific choice of a margin on the population of patients and allow the design of simple margin recipes. The impact of treatment preparation (systematic) errors is much larger than the impact of treatment execution (random) variations. Large treatment execution (random) variations lead to a moderate underdosage for a large number
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