Gamma Dose Distribution Evaluation Tool

Quantitative comparisons of dose distributions are an integral component of a medical physicist’s responsibility of assuring high quality radiation therapy dose delivery. While overlays and other displays of multiple dose distributions are useful for such evaluations, quantitative evaluations require a mathematical comparison. The dose-difference is the most straightforward method for comparing two dose distributions, but it can show large differences in steep dose gradient regions, even for relatively small misalignments. A tool, termed ,was developed to take both dose and spatial difference into account. It does this automatically, evaluating distributions for dose difference and spatial discrepancies in regions of shallow and steep dose gradients, respectively. The tool has been used extensively in commercial dose measurement and evaluation software. This chapter describes the tool, some alternative techniques, and limitations of the tool. 1. Dose Distribution Evaluations Dosimeters provide critically important information about the characteristics of dose distributions. They allow us to directly measure a physical phenomenon that is capable of irradiation tumors such that they are sterilized while nearby normal organs retain their function. The dose accuracy required is typically assumed to be within a few percent in order to provide the potential benefit. This is quite challenging to achieve in a complex structure such as the human body, so radiation therapy relies on sophisticated computer dose calculations to predict the dose inside the patient and allow the treatment planner to visualize the impact of selecting different beam orientations, energies, and intensities. Computer-optimized dose distributions are also used, and these have very complex dose deliveries and consequently dose distribution characteristics, such as steep conformal dose gradients that wrap around the tumors and normal organs. The complexity of the dose delivery and the resulting distributions, and the tight requirement for accuracy, result in the need for direct measurement-based verification of the calculated dose distributions. This has led to the main purpose of this conference; the 3-dimensional measurement of dose distributions. However, having a 3-dimensional calculation and measurements are only part of the dose distribution quality assurance (QA) process. The dose distributions need to be compared to one another using methods that are quantitative, efficient, and that take maximum advantage of the limited capability for visualizing the dose distributions, which are 3-dimensional scalar fields. The first group to publish on applying quantitative tools for dose distribution comparisons was the group of Van Dyk et al. 1 They showed that dose comparisons should consider the local dose gradient when determining the best way to compare doses. The most straightforward way to compare two dose distributions is to take the numerical difference. Presumably, if you want to know by how much the two dose distributions disagree, the difference makes it clear. However, there are practical limitations IC3DDose: The 6th International Conference on 3D Radiation Dosimetry IOP Publishing Journal of Physics: Conference Series 250 (2010) 012071 doi:10.1088/1742-6596/250/1/012071 c © 2010 IOP Publishing Ltd 1 to this method. First, the dose distributions may not be precisely aligned. If one of them is measured, there is a spatial tolerance on the ability to position the detector, align the phantom to the linear accelerator, and to conduct the readout process (e.g. optical densitometry). If there is a spatial error in the measurement, the dose distribution differences that lie within steep dose gradients will be artificially enhanced by the spatial offset of the two distributions. While a spatial offset leads to sometimes large dose differences in steep dose gradient regions, one can ask the question; why are these differences not relevant to the patient’s treatment? They existed when a physicist made the dose distribution measurements, so why not consider them when evaluating the dose distribution quality? This is a valid argument, and the answer has to do with the purpose of the measurement. For most cases, the purpose of the measurement is to validate the output of the treatment planning system, or to validate the system-wide process of calculation, data transfer, and dose delivery. A reflection of the impact of measurement-induced errors is typically not desired by the person conducting or evaluating the QA results. Therefore, one of the desired features of dose distribution comparisons is to be somewhat immune to experimental error. Van Dyk et al 1 published on the importance of applying a particular dose distribution comparison test based on the local dose gradient. In regions of shallow dose gradient, the dose difference provided the physicist with a quantitative and straightforward method for comparing two dose distributions. However, in steep dose gradient regions, the dose difference was sensitive to the small spatial offsets commonly encountered in experiments, so even if the dose distributions agreed exactly, the dose differences were very large when even a small spatial error was encountered. As an example, IMRT dose distributions often dose gradients of close to 3% mm -1 . Even a small position shift of one dose distribution relative to the other will cause large dose differences. In this example, a 1 mm shift will cause a 3% dose difference. Selecting a 3% dose difference criterion when comparing the two dose distributions will lead to false positive detections of regions where the calculation appears to fail to accurately model the dose distribution. Van Dyk 1 developed the concept of distance to agreement (DTA), which Harms et al 2 applied in a software tool to compare two-dimensional dose distributions. The DTA is typically computed by measuring the closest distance between one dose distribution to where the second distribution has the same dose level. This is equivalent to determining the closest approach to a point in one distribution of the isodose line that in the other distribution that has the same dose as the point. The DTA is a non-local function, meaning that when it is evaluated at a point, the other distribution is queried at a distance. The DTA function also does not commute. While the dose difference merely changes sign when the two dose distributions are swapped, the DTA is not the same value of the roles of the two distributions are swapped. Therefore it is useful to label the two distributions as the reference and evaluated distributions. The reference distribution is the one whereby the DTA is computed point by point, while the evaluated distribution is the one queried for the closest approach of the specific isodose. One of the nice features of the dose difference distribution is its relatively straightforward interpretation. Most physicists can glance at a dose difference distribution and see and interpret the data. Because of the impact of steep dose gradients, the dose differences may not be clinically relevant, but the meaning behind the numbers is clear. While the dose difference is overly sensitive in steep dose gradient regions, the DTA is overly sensitive in shallow dose gradient regions. As an example, if the reference dose point has dose D, lying in a shallow dose gradient region, and the evaluated dose at that point is D+D, the distance in the evaluated distribution from the reference point that has the same dose D may be very far away. The DTA will therefore be very large, even if D is small and has no clinical consequence. Because of the large values in shallow dose gradient regions, regions that typically dominate IMRT dose distributions, the DTA distribution is difficult, if not impossible to interpret by eye. In steep dose gradient regions, the DTA can be interpreted as the distance between the two dose distributions. This interpretation is based on the assumption that the distance is caused primarily by a spatial offset between the two distributions. For distributions that differ by such an offset, the DTA distribution provides an effective and accurate measurement of the offset. However, as described IC3DDose: The 6th International Conference on 3D Radiation Dosimetry IOP Publishing Journal of Physics: Conference Series 250 (2010) 012071 doi:10.1088/1742-6596/250/1/012071