For this retrospective study, a total of 15 lung cancer patients who underwent IMRT between September 2018 and December 2018 were selected. All patients were enrolled in an institutional review board-approved retrospective data collection protocol, and completed lung radiotherapy treatment.
Patients were acquired 4DCT using a Big Bore CT simulator (Brilliance, Philips Healthcare, Cleveland, OH, USA) with a real‑time position management system (RPM, Varian Medical Systems, Palo Alto, CA, USA). The gross tumor volume (GTV) was contoured on average-weighted CT images. The GTV to CTV margin for inclusion of microscopic extension of the tumor was 2 mm. To simplify our analysis, only tumors in one side of lungs were selected. In addition, all OARs, such as lungs and spinal cord were contoured on average-weighted CT images. The average-weighted CT images were used for plan optimization and dose calculation.
Beam-specific PTV concept
To generate the BSPTV for photon radiotherapy, we expanded the CTV perpendicularly to each incident beam direction using the 2D version of van Herk’s margin concept. We chose not to add margins in the CTV in the incident beam direction, because the percentage depth dose reduction in the incident beam direction was very small. We obtained the final BSPTV by merging each beam expansions. Fig. 1 shows the simulation of target coverage differences between the target moving parallel to beam direction and perpendicular to beam direction. Fig. 2 shows the geometric differences between the original PTV and the BSPTV for the same CTV in the axial slice.
The setup inter-fractional uncertainties considered in this study were defined in the patient’s left-right, anterior-posterior and superior-inferior directions, and were assumed to be normally distributed with no correlations between them. The projection of the 3D Gaussian distribution, in beam direction, into a 2D Gaussian distribution was defined using the van Herk’s margin concept [4, 9, 11].
Variables Σ, σ, and σp are two-dimensional column vectors for the directions perpendicular to the incident beam angle, thereby representing the systematic uncertainties, random uncertainties and the beam penumbra, defined as the distance between the 20% and 80% isodose levels, respectively. In this study, the beam penumbras (σp) was 3.2 mm in water. The coefficients α and β, which depend on the intended probability of target dose coverage, were calculated by solving the closed-formed dose population histogram, following the integral formula in appendix 2 of a previous study . Our method to calculate the 2D margin from the direction perpendicular to each beam was implemented as a standalone MATLAB (MathWorks, Natick, MA, USA) program. To ensure that 90% of the patients received at least 95% of the prescribed dose across the whole of the target, in our programmed 2D margin script, the corresponding coefficients were α = 2.15 and β = 1.64. In addition, we set the systematic uncertainties to Σ = 2 mm, and random uncertainties to σ=2mm according to the previous study and our clinical results [4, 12], the Margin (M) » 4.4 mm. The automatic generated 2D margins of each beam were imported into Eclipse TPS (Varian Medical Systems, Palo Alto, CA, USA) and merged as the BSPTV for subsequent optimization.
The general PTV was margined by the 3D van Herk’s margin concept, with the same systematic and random uncertainties as the BSPTV as follows: the systematic uncertainties Σ = 2 mm, random uncertainties σ = 2 mm, α = 2.5, β = 1.64, amd M » 5 mm.
A digital water phantom simulation was used to evaluate the conformity of the dose distribution to the OAR sparing of these two margin concepts. The influence of the number of beams to the volume of the BSPTV was also evaluated using this digital water phantom.
In this simulation model, the water phantom was 40´40´40 cm3 with a spherical CTV of 4 cm diameter in the center, which roughly corresponded to the average CTV sizes of our patient data. The dose grid resolution for the dose calculation was 2.5 mm. Two types of 50Gy/25F treatment plans were designed for both general PTV and BSPTV, and the generated dose distributions were such that 98% of the PTV received 100% of the prescribed dose. The general PTV margin (M » 5 mm) was applied around the GTV for the plans with general PTV as the target volume. The BSPTV margin (M » 4.4 mm, in 0°, 30°, 60° and 90° directions) was applied around the GTV for plans with the BSPTV as a target volume. The first type involved two clinical IMRT plans using 4 coplanar beams with 0°, 30°, 60° and 90° directions with the general PTV and BSPTV as the target volume, respectively. The plan conformity index (CI, CI = 100% ´ [TVPI]2/[PI100 ´ TV]) was optimized to keep the CI in both general PTV and BSPTV plans above 80%. TV represented the target volume, TVPI represented the volume of the target covered by the prescribed isodose, and PI100 represented the volume receiving 100% of the prescribed isodose. The conformity was better as the index approached 100%. The second type involved hypothetical plans with an ideal dose distribution (such as a VMAT plan with a spherically symmetric dose that falls off in all directions), resulting in a CI above 90%.
Three plans were generated to evaluate the influence of the number of beams to the volume of the BSPTV. The three plans were generated using three, five, or seven coplanar beams with equal angle intervals. Subsequently, the volume difference between the general PTV and BSPTV of the same spherical CTV of each plan was calculated.
CTV projection area analysis
In this study, the mathematical relationship between the margin volume and the projection area of the target was analyzed. The calculation and analysis details are shown in Appendix 1. Based on a patient’s CT data set, we calculated the CTV projection area in a beam direction from 0° to 359°. Because the BSPTV of a beam is a 2D margin of the CTV in the beam direction, the projection area of the CTV in the beam direction is an index that can be used to evaluate the volume of 2D expansion of the CTV. The projection area of the CTV was calculated for a full circle of beam angles (0-359) at increments of 1 to yield a patient-specific CTV projection area curve as a function of the beam angle. For example, Fig. 3(a) shows the CTV projection area of one patient with respect to the beam angle.
IMRT plans were optimized by the Eclipse v13.6 treatment planning system (Varian Medical System, Palo Alto, CA, USA) and simulated with 6 MV Xray of Trilogy linac (Varian Medical System, Palo Alto, CA, USA). The plan final dose was calculated using the Acuros algorithm and prescribed to 60 Gy in 30 fractions. First, we selected 4 to 5 beam angles according to the CTV projection area curve to make sure that the projection area on the YOZ plane had higher values than other beam angles. To avoid the beam penetrating both lungs, most beams incidents were set in the AP directions. Second, the general PTV and BSPTV margins were generated as the description in Beam-specific PTV concept section. Next, two plan optimization strategies were designed to compare the dose distribution differences between the general PTV and BSPTV. The optimization objective for all plans was to first achieve 100% of the prescribed dose to the target volume, then to minimize the dose to OARs. We first optimized all patients’ plans on the target volume of the general PTV. Then, all optimization objective parameters were kept unchanged, a new plan was created, and only the target volume was changed to BSPTV and this BSPTV plan was re-optimized. After the optimization of both plans was completed, all plans were normalized to facilitate dose comparisons. The normalization point was the target D98% of 60 Gy, where Dx% was defined as the lowest dose covering x% of the volume. To exclude the influence of the conformity of the dose distribution to the plan evaluation, plans with a CI below 80% were re-optimized until the CI was above 80%.
To quantify the differences between the general PTV and BSPTV plans, dose-volume histograms were used to assess the dose coverage and conformity of targets and the protection of OARs. The target evaluation parameters were D98% (target coverage), D2%, CI, and homogeneity index (HI) . The HI, defined as 100% × (D2% − D98%)/D50%, was used to evaluate dose homogeneity within each target volume. Plans that are more homogenous, have HI values that are closer to 0% . V5, V20, and mean doses to both lungs were compared. For the spinal cord, the D1% was compared. To evaluation the adjacent normal tissue of CTV, a 2-cm ring of the CTV was margined as the CTV margin. The Ring PTV or Ring BSPTV were created by the CTV margin with the general PTV or BSPTV being subtract. The volume and mean doses of Ring PTV and Ring BSPTV were compared.
Over the course of radiation therapy, interfractional uncertainties occur between treatment fractions, such as set-up uncertainties and anatomical variations. In this study, we evaluated the set-up uncertainties using the uncertainty dose evaluation of Eclipse treatment planning system, assuming inter-fractional setup uncertainties of ± 5 mm in AP, LR and SI directions, total 6 scenarios. The van Herk margin recipe was designed for 90% of coverage of the patients with a minimal dose of 95% to 100% of the target volume, therefore, the ratio of scenarios that satisfied the clinical specification that the 100% of CTV above the 95% prescription dose was evaluated.
SPSS 24.0 software (IBM, Armonk, NY, USA) was used for statistical analyses of all dosimetric metrics. We conducted a paired, two-tailed Wilcoxon signed-rank test to compare the dose distributions between general PTV and BSPTV plans. P < 0.05 was considered statistically significant.