Fifteen lung cancer patients treated with IMRT between September 2018 and December 2018 were selected for this retrospective study. All patients in this study were enrolled in an institutional review board-approved retrospective data collection protocol. Each patient had completed lung radiotherapy treatment.
Patients were acquired 4DCT using a Big Bore CT simulator (Brilliance, Philips Healthcare, Cleveland, OH) with the real‑time position management system (RMP, Varian Medical Systems, Palo Alto, CA, USA). The gross tumor volume (GTV) was contoured on the average-weighted CT images. The GTV to clinical target volume (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. And all organs at risk (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 beam-specific PTV (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 margin the CTV in the incident beam direction, since the percentage depth dose reduction in the incident beam direction is very small. We obtained the final BSPTV by merging each beam expansions together. Fig. 1 shows the dose deviation in simulation that we ignored the longitudinal (parallel to beam direction) margins and retained the transverse (perpendicular to beam direction) margins. Fig. 2 shows the geometric differences between the original PTV and the BSPTV for the same CTV in the axial slice.
The inter-fractional uncertainties considered in this study are defined in the patient’s left-right, anterior-posterior and superior-inferior directions, and are assumed to be normally distributed with no correlations between them. The collapse of the 3D Gaussian distribution, in beam direction, into a 2D Gaussian distribution has been defined with the van Herk’s margin concept .
Variables Σ, σ and σp are two-dimensional column vectors for the directions perpendicular to the incident beam angle, representing the systematic uncertainties, random uncertainties and the beam penumbra, defined as the distance between the 20% and 80% isodose levels, respectively. The beam penumbras (σp) was 3.2 mm in water in this study. The coefficients α and β which depend on the intended probability of target dose coverage are calculated by solving the closed-formed dose population histogram, following the integral formula in appendix 2 of the previous research . Our method to calculate the 2D margin from the direction perpendicular to each beam is implemented as a standalone MATLAB (MathWorks, Natick, MA) program. In our programmed 2D margin script, to ensure that 90% of the patients receive at least 95% of the prescribed dose across the whole of the target, the corresponding coefficients are α = 2.15 and β = 1.64. And we set the systematic uncertainties Σ = 2 mm, random uncertainties σ=2mm according to the previous research and our clinical results [4, 11], the Margin (M) » 4.4 mm. The automatic generated 2D margins of each beam were imported into Eclipse TPS (Varian Medical Systems) and merged as the BSPTV for subsequent optimization. The conventional PTV is margined by the 3D van Herk’s margin concept, with the same systematic and random uncertainties as the BSPTV, the systematic uncertainties Σ = 2 mm, random uncertainties σ = 2 mm, α = 2.5 and β = 1.64, the M » 5 mm.
A digital water phantom simulation is 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 is also examined using this digital water phantom.
In this simulation model, the tumor consisted of a spherical CTV of 4 cm diameter, which corresponds roughly to the average CTV sizes with our patient data. 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 conventional PTV margin (M » 5 mm) was applied around the GTV for the plans with conventional PTV as target volume. The BSPTV margin (M » 4.4 mm, in 0°, 30°, 60° and 90° in directions) was applied around the GTV for the plans with BSPTV as target volume. First type was two clinical IMRT plans using 4 coplanar beams with 0°, 30°, 60° and 90° with the conventional PTV and BSPTV as the target volume, respectively. The plan conformity index (CI, CI = 100% ´ [TVPI]2/[PI100 ´ TV]) were optimized to keep the CI in both general PTV and BSPTV plans above 80%. TV is the target volume, TVPI is the volume of the target covered by the prescribed isodose, and PI100 is the volume receiving 100% of the prescribed isodose; conformity is better as the index approaches 100%. Second type was hypothetical plans with an ideal dose distribution (such as a VMAT plan with spherically symmetric dose that falls off in all directions), resulting in CI above 90%.
Three plans were created to evaluate the influence of the number of beams to the volume of the BSPTV. The three plans were generated with three, five, and seven coplanar beams with equal angle intervals. The volume difference between the conventional PTV and BSPTV of the same spherical CTV of each plans were calculated.
CTV projection area analysis
We analyzed the mathematical relationship between the margin volume and the projection area of the target. The calculation and analysis details are showed 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°. Since the BSPTV of a beam is a 2D margin of CTV in the beam direction, the projection area of CTV in the beam direction is an index to evaluate the volume of 2D expansion of the CTV. The projection area of 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 beam angle. As an example, Fig. 3(a) shows one patient’s CTV projection area 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 dose were calculated with 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 the 2D margins of each beam could be the maximum. We also set most beams incident in the AP directions, to avoid the beam penetrating both lungs. Second, we margined the conventional PTV and BSPTV as the description in Beam-specific PTV concept Section for comparison. We designed 2 plan optimization strategies to compare the dose distribution differences between the conventional PTV and BSPTV. The optimization objective for all plans was to achieve 100% of the prescribed dose to the target volume first and then to minimize the dose to OARs. We first optimized all patients’ plans on the target volume of the conventional PTV. Then we kept all optimization objective parameters unchanged; copied a new plan and only changed the target volume to BSPTV, then re-optimize this BSPTV plan. After both plan optimizations 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, the plans with CI below 80% were re-optimized until above 80%.
To quantify the differences between the conventional 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%, conformity index (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 closer to 0% . V5, V20 and mean doses to both lungs were compared. For the spinal cord, the D1% was compared. In order to evaluation the adjacent normal tissue of CTV, a 2 cm ring of CTV was margined as CTV margin. The Ring PTV or Ring BSPTV was created by CTV margin subtract the conventional PTV or BSPTV. The volume and mean doses of Ring PTV and Ring BSPTV were compared.
Interfractional uncertainties occur between treatment fractions, such as set-up uncertainties and anatomical variations over the course of radiation therapy. In this study, we evaluated the set-up uncertainties using the uncertainty dose evaluation of Eclipse treatment planning system (Varian Medical Systems, Palo Alto, CA), assuming the inter-fractional setup uncertainties of ± 5 mm in AP, LR and SI directions, total 6 scenarios. Since the van Herk margin recipe is designed for 90% of coverage of the patients with a minimal dose of 95% to 100% of the target volume. The ratio of scenarios satisfied the clinical specification that the 100% of CTV being above the 95% prescription dose was evaluated.
SPSS 24.0 software (IBM, Armonk, NY) was used for statistical analyses of all dosimetric metrices. We conducted a paired, two-tailed Wilcoxon signed-rank test to compare the dose distributions between the conventional PTV and BSPTV plans. P values of less than 0.05 were considered statistically significant.