The interpolated doses based on the coarser grid points generally predicted lower doses than those predicted based on finer grid points in high-dose gradient regions of the generally prescribed isodose level (e.g., 60 to 90%) [1, 11]. In addition, the beam penumbra region shows a steeper dose fall-off due to lateral electron disequilibrium, when the small fields are irradiated . Because underdosage around the PTV periphery becomes severe since the effect of electron disequilibrium is critical when using small fields, the dose error in the dose distribution predicted using a coarser grid would be increased at high-dose gradients. We were able to observe the largest dose increase for the PTV and OARs in the plan for S
Niemierko and Goitein evaluated the accuracy of interpolated doses by using linear interpolation according to the grid size and a Fermi function presenting a one-dimensional high-gradient dose profile for beam penumbra . They also described how large grid sizes showed interpolated doses that were lower than the reference doses around the general prescribed isodose level. A lower isodose level should be selected to deliver a higher dose than the prescribed value to meet the PTV dose and coverage . We were able to compare the prescribed isodose level according to the PTV size in a planning system. Selecting a lower prescribed isodose level owing to the lower dose estimated by using large grid sizes required a larger number of MUs. Unintended overdose might be delivered to the patients. This phenomenon was also explored by Dempsey et al. by showing lower PTV coverage for large grid sizes . The discrete beam arrangement based on the angular increment showed a jagged isodose distribution, which is not expected in actual continuous beam delivery. Dose undulation becomes severe as the interval between beam axes increases with large angular increment . As the irradiated field size is decreased for smaller PTVs, the probability that a small critical organ is located outside of the fields would also increase. The larger angular increment effect on structure doses was shown in the plan for S
2 in our study.
Because the discretized dose calculation based on the dose mesh determined by the grid size and its errors are inevitable in a treatment planning system, evaluation of dose distributions with the predicted dose differences according to the variable plan parameters is useful for guiding appropriate plan parameters to achieve a balance between accuracy and efficiency. The possible dose variation due to the angular increment should be considered for OARs in serial tissue such as the spinal cord to avoid unnecessary complications, as the spinal cord showed the largest dose difference under the large angular increment. Sometimes, the spinal cord dose could be insignificant, but even in those cases, it would be necessary to get more accurate dose information for future use such as for the case of either retreatment or treatment of adjacent regions. As one of the alternative methods for efficient dose computation in a planning system, we can consider applying the small angular increment for critical organs and a relatively large angular increment for normal tissues.
We found that a plan parameter set consisting of a 3-mm grid size and a 4° angular increment is suitable for the phantom study and a 3-mm grid size and a 6° angular increment is suitable for patient cases. A phantom study systemically evaluating the range of probable dose differences under the angular increment effect showed that a dose difference of 3% can occur even for spinal cords at the same distance. We were able to observe that one of the hypothetical spinal cords in the intermediate and distant groups showed a dose difference from the reference value of higher than 3%. This could suggest that the dose difference on a small critical organ that is distant from the isocenter can be higher than the acceptable dose error owing to the slight difference in angular position although the dose distributions were created for patients with structures of similar size and anatomical geometry. The 3-mm grid size and 4° angular increment would be more appropriate for DCAT plans for lung SBRT.
To judge whether a 3-mm grid size and 10° angular increment are applicable only to patients with proximal spinal cords, we evaluated dose distributions in three more patient cases with PTVs of different sizes and proximal spinal cords. All evaluated PTV and OARs doses also showed dose differences of less than 1%. We might consider a 3-mm grid size and a 10° angular increment for patients with all small OARs, such as the spinal cord and esophagus, placed within a 6-cm distance from the isocenter. However, it might be difficult to satisfy the dose constraint of spinal cord in lung SBRT, as the spinal cord gets closer to the isocenter. Dose evaluation of small OAR becomes more critical even though the dose difference by the variable plan parameters is insignificant. If we use the plan parameter set of 3-mm grid size and 10° angular increment in dose calculation for patients with a proximal small OAR in serial tissue type, maximum dose of the OAR should be evaluated.
The use of a larger grid size and angular increment led to a reduction in computation time. Although the dose calculation is required for complex tissue composition in patient studies, the time reduction ratio achieved by applying variable plan parameter sets was similar in the phantom and patient studies. When the large grid size is used in the dose calculation, it was possible to reduce the calculation time by approximately at a rate inverse square of the grid sizes. We were also able to speed up the dose calculation by a factor of the inverse ratio of the number of beams for the larger grid size to the number of beams for the reference case, for a particular angular increment. The appropriate plan parameter set can be efficiently determined based on the correlation of the dose calculation accuracy and the time consumption.
Both DCAT and VMAT calculate and deliver optimal planned doses during gantry rotation based on the discrete beam configuration and dynamic MLC apertures at each angular increment. While DCAT delivers conformal doses using a relatively small number of MUs, a constant dose rate, and MLC apertures corresponding to the projection of the PTV at each angular increment , VMAT provided a high dose gradient using intensity modulation through a number of deliverable MLC segments converted from non-uniform fluence optimized to satisfy the dose–volume constraints of primary structures in inverse planning [12, 24, 25]. Under the case where various dynamic components, such as gantry rotation speed, dose rate, and MLC leaf moving speed, are synchronized, VMAT achieves conformal dose distributions. However, VMAT can have more uncertainty when using an intensity modulation technique, particularly for targets involved in significant respiratory motion, owing to the systematic interplay effect between the target motion and the beam aperture motion, as demonstrated by Berbeco et al. . Such uncertainty is expected to be even larger under hypo-fractionation treatment, which is typical in SBRT. In the current health care system, the higher cost of VMAT compared to DCAT is of concern for both billing and human resource utilization. Thus, DCAT is the first choice in our clinic, and VMAT is used only in situations in which it is very difficult to obtain an acceptable dose distribution with DCAT. Examples of such situations include cases where multiple targets are close together, or when critical organs are located extremely close to the target.
In general, it is not easy to predict dose errors for OARs in advance with variable angular increments [8, 27]. The systematic evaluation of the dosimetric effect of plan parameters on normal structures in different positions would provide a reference to estimate the approximate error range in DCAT plans. The analysis of dose variation as a function of plan parameters enabled us to determine an optimal set of plan parameters to achieve a balance between accuracy and efficiency in the planning process. Under the conditions considered in this study, a 3-mm grid size and a 4° angular increment are suggested as an optimal set of planning parameters for routine clinical practice with acceptable time efficiency and without a significant compromise in dose accuracy in DCAT.