Technical and dosimetric implications of respiratory induced density variations in a heterogeneous lung phantom

Heterogeneous density calculations were performed using the Quasar Phantom in a static configuration. A single anterior field (3.0 × 3.0 cm²) was aligned perpendicular to the phantom and prescribed with fixed monitor units of 500 MU for photon energy of 6 MV flattening filter free as shown in Fig. 2a. Dose distributions along the beam central axis, as function of depth, were then calculated using AAA and AXB algorithms with 0.2 cm³ grid size. As illustrated in Fig. 2b, points of interest were selected along the central axis where P1 is located 3 cm anterior to the target, P2 at the target isocenter, P3 is 3 cm posterior to the target center, and P4 beyond the lung cavity located 2 cm below P3. To mimic density variation effects caused by tumor movement, the CT values of the target structure were systematically overridden from − 200 to + 200 in increments of 25 HU. Due to the density variation of the target structure, a relationship between the dose errors was represented as percentage dose change relative to nominal HU value of the target for each point of interest.

4DCT image sets were acquired using a GE Lightspeed Pro 16 slice scanner (General Electric, Milwaukee, WI), with a slice width setting of 1.25 mm. Respiratory cycle information was subsequently recorded using a Real-time Position Management (RPM) system (Varian, Palo Alto, CA). In general, the external movement of the phantom was synchronized to the internal movement of the target via an illuminated infrared signal reflected from a marker block and directed to a CCD camera. The recorded respiratory waveform was then referenced in the binning process to coordinated projected image sets, with respect to their appropriate anatomical locations, over the course of one respiratory period. Reconstructed images and respiratory data were then transferred to Advantage 4D workstation (General Electric, Milwaukee, WI). These images were sorted and binned with respect to couch position and corresponding respiratory phase at ten uniformly spaced intervals within the respiratory cycle, with CT_0% indicating the max-inhalation phase and CT_50% the max exhalation phase. From these bins, AIP and MIP image sets were automatically generated by selecting the average and the maximum pixel densities across all respiratory phases of the 4DCT dataset, respectively. A subsequent helical image was also taken immediately after the 4DCT acquisitions and was designated as the corresponding free-breathing (FB) scan. This procedure was repeated for target amplitudes ranging from ±0.5 to ±1.5 cm at ±0.5 cm increments, for which the processed images were imported into Eclipse (version 13.6) treatment planning system (TPS). Furthermore, an additional FB scan was taken with the no phantom motion and planned accordingly for verification of image registration and dose calibration process.

In order to infer the motion information using Eclipse, manual contouring of individual GTVs was performed on individual CT image sets within multiple respiratory phases (CT_0% - CT_90%). To avoid any interplanner differences, all contours were segmented by one individual using the same lung window setting in all image sets. The internal target volume (ITV) structure was then generated using Boolean “OR” operation to union all 10 GTV phased structures from individual CT image sets corresponding to set motion amplitude. In accordance with RTOG 0915 protocol, the planned treatment volume (PTV) was then created by expanding a uniformly isotropic 0.5 cm margin from the ITV [9]. All ITV and PTV structures were initially created in the FB image set and subsequently copied to the AIP, MIP and PWD datasets.

It is noted in a similar study, the Mid-Ventilation (CT_50%) image set was included for comparative analysis [25]. With the exception of target location, the target density associated with CT_50% is very similar to that represented by the FB image set. Therefore, since the central focus of this current study is to evaluate the extreme density variations between datasets, examination of CT_50% was not taken into consideration in order to circumvent redundancy.

In addition to the FB, AIP and MIP CT datasets, we created a hybrid phase weighted density (PWD) structure for comparison. In principle, the changing density of the target region over time can be generalized by the following relation:where 흆_GTV is the target density, and 흆_lung represents the density of the lung. It follows that a solution for the density for a PWD structure (흆_PWD) yields the following expressionwhere t is the occupational time of the GTV at one location, and T is the period of the respiratory cycle. In practice, the duration of t occurs at discrete increments of 1/10th of the respiratory period in association with the phase binning process. Thus, as illustrated in Fig. 3, the final t value reflects how many times the GTV has overlapped with itself during the period of oscillation, giving rise to higher density within a particular sub-region.

Discrete sub-regions within the ITV were created by the addition and/or subtraction of the 10 individually defined GTV phase binned structures, using Boolean operations within the TPS. CT values for each sub-region were then overridden and weighted accordingly to the mean GTV (− 50 HU) and lung (− 625 HU) density value as defined by the FB image set.

HU voxel values for each PTV structure were extracted using an in-house program written in Matlab (MATLAB, The MathWorks Inc., Natick, MA, 2017). For FB, AIP and MIP data set, original DICOM CT images and RT structures were directly imported into Matlab software. Based on the corresponding contoured structure set, a binary mask was created to segment out the region of interest (ROI) for HU data export. The output of all HU values inside the ROI for each image set were then analyzed as a histogram format ranging from CT numbers − 850 to 50 HU with bin size of 20. Plotting and statistical analysis was performed using Origin (version 6.0) software. Using the HU density extraction method, Fig. 4 shows the histogram representations for the (a) cedar insert, (b) polystyrene target, and (c) PTV structure.

Individual treatment plans were created from FB, AIP, MIP and PWD datasets in Eclipse. Irradiation of the target structure was planned for a photon 6 MV flattening filter free beam using simple Anterior-Posterior (AP) and Posterior-Anterior field configurations. The MLC was fitted to the shape of the PTV and collimator jaws were set to the recommended position determined by the TPS, with width spacing no less than 3.5 cm as dictated by RTOG protocol [9]. Dose calculations for each plan were executed using AAA and AXB algorithms at a predetermined value of 500 MU per field for 0.2 cm grid size. The initial parameters for segmented ITV and PTV structures for each range of motion are summarized in Table 1.

Phantom set up was done using the same simulation positions for dose delivery by means of a TrueBeam STx. The dose from the treatment planning system was verified using an identical cedar insert phantom (Modus, Model No. 500–3332) specifically designed to house a PTW 0.125 cc ion chamber (Fig. 1c). Gafchromic EBT3 film (International Specialty Products, Wayne, NJ, Lot #: 03311401) was used for both film calibration and phantom measurements. The film was positioned inside the cedar insert, central to the target location and marked at the time of irradiation. Each phantom irradiation measurement was repeated 3 times for which subsequent measurements were taken to reference machine output and scaled to film response. The film was then stored in a dry, dark environment for 24 h and later scanned using Epson Perfection V700 flatbed scanner (Epson America, Inc. Long Beach, Ca) with 48 bit color and 150 dpi resolution. RIT113 (Radiological Imaging Technology, Inc., Colorado Springs, CO) version 5.1 software was used to analyze the film using the red channel. A dose calibration curve for the red channel was generated by irradiating individual films for known doses from 0 to 10 Gy.

Due to phantom motion, the center of film does not remain in the center of dose distribution over the time of delivery. Hence, dose generated from a static CT by the TPS cannot be directly compared to the dose measured on moving film (consult Ref [26] for an excellent review of the dose smearing effect and compensation). Film motion was accounted for by convolving the TPS dose using a custom script written in MATLAB developed by Wiant et al. [26]. Convolved dose plane distributions were then imported into RIT113 software for gamma analysis. As formulated by Low, the standard criterion for “measured” versus “calculated” dose was evaluated for a particular dose threshold within an acceptance radius (i.e. 3%, 3 mm) [28].

The results of our phantom calculations in a static configuration are shown in Fig. 5a, b. For a single AP field as shown in Fig. 2a, the percent depth dose (PDD) profiles for AAA and AXB are plotted in Fig. 5a. When compared to calculations with no heterogeneity, both the AAA and AXB profiles are virtually identical as indicated by the dashed line. The algorithms reveal a subtle distinction between lung versus tumor media, which is unnoticeable when heterogeneity is turned off. Interestingly, the first time these curves intersect after the build-up region, is near isocenter of the target. This is where the target density is roughly equivalent to that of water.

Figure 5b shows the trend in dose errors at particular points of interest in reference to Fig. 2b. For each point, the percentage dose error is defined relative to the nominal CT value of the GTV structure, which was overridden spanning from − 200 to 200 HU. For the fixed point located just above the target (P1), both AAA and AXB traces are flat lined and unaffected by the downstream change of target density. At isocenter (P2), the negative slope associated with AXB calculation indicates the relative increase in target density, or photon attenuation. This attenuation is compensated for by the decrease of photon fluence. On the other hand, the slightly positive slope associated with the AAA algorithm indicates an opposing effect caused by secondary electron transport. As interpreted in a related study by Liu, the density variation of the target when using AAA makes a larger impact on electron fluence over photon attenuation, where electron fluence becomes the dominating factor for compensation [29]. For points beyond the target structure, both algorithms show a similar attenuation response to the target density variation within the lung (P3), and beyond (P4) where electron equilibrium is re-established.

The wide range of density variations for each PTV structure is illustrated in Fig. 6. As shown from left to right, each column represents an additional 1 cm increase in target movement. Each row displays voxel count versus CT number as defined by the AIP, FB, MIP and PWD data sets. Due to the 5 mm isotropic margin expansion from the ITV, the PTV will include a significant portion of low density media concentrated at approximately − 625 HU. In general, as the range of target movement increases, the GTV peak (center around − 50 HU) will essentially become absorbed into the lower density media. This effect is most pronounced for FB data sets, where the average CT number decreases from − 479 to − 569 HU, versus AIP − 473 to − 524 HU, and PWD − 472 to − 507. For MIP data sets, the average CT number remains fairly consistent ranging from − 352 to − 370 HU. Thus, in our most extreme case scenario, the difference between low density FB and high density MIP data sets is greater than 200 HU. The PTV average CT values extracted from each dataset are listed in Table 2.

Results for mean PTV HU values and dosimetric differences between AXB versus AAA are listed in Table 2. In this analysis we considered the dosimetric parameters (D_max, D_2%,, D_mean, D_95%, D_98%) as evaluated from dose volume histograms (DVH). When compared with AXB, AAA will consistently overestimate the dose to the treatment volume. This is indicated by a negative sign for a predominant portion of the analysis with exceptions occurring at D_mean (D_50%) –the approximate location of where the two curves may intersect. In general, the near maximum dose (D_2%) discrepancies are marginal (< 2.2%), with a greater variability occurring within the near minimum (D_98%) dose regime (< 7.0%). Considering that the size of the PTV structure increases as range of motion increases (see Table 1), the resulting widening of collimator jaws will yield a slight increase in dose at target isocenter. This can be depicted by the standard deviation. Thus, even for extended range of target motion, the dose discrepancies between the two algorithms near target isocenter are still small, with the greatest differences observed for MIP (2.1 ± 0.1%), followed by PWD (1.9 ± 0.6%), AIP (1.3 ± 0.1%), and least with FB (0.9 ± 0.4%).

A direct comparison of AAA versus AXB calculated planner dose distributions are illustrated in Fig. 7. Plans generated using the AIP, FB, MIP and PWD image sets for all ranges of motion are benchmarked with respect to AXB-based computations. Using nominal gamma criteria of 3%, 3 mm, all plans are virtually identical with pass rates of 100%. However, when switching to a most stringent criteria of 1%, 0 mm, the gamma index is anywhere from 73.2–54.0%. This predominantly high region of failure is occurring on the left side of the dose distribution in each case, and is caused by a relatively larger cedar gap in the phantom geometry (see Fig. 2b). Hence, in the lower density region the AAA calculation is overestimating the dose to the target, while the AXB algorithm compensates for photon attenuation of the target itself. Likewise, the greater overall discrepancies are generally occurring with the higher density MIP datasets.

All plans were measured using an identical lung insert phantom modified for PTW 0.125 cc ion chamber and were determined to be within < 2% agreement with the treatment planning system. However, these measurements yield only one data point at isocenter. Therefore, gafchromic film analysis was used for complete distribution comparisons for which the verification of the image registration and dose calibration process is shown in Fig. 8. Each static measurement was repeated three times in conjunction with our motion runs, for which the film was analyzed for the same plans calculated for AAA and AXB. These results demonstrate the accuracy and reproducibility for the systematic method of measurement used in this study when no motion was employed. Furthermore, they tend to rule out the inherent uncertainty that may be associated with the differences between both algorithms in question, and suggest the subsequent discrepancies have to do with the density distributions that are represented by the CT datasets once the phantom was sent into motion.

Table 3 summarizes the film results for target motion amplitudes up to ±1.5 cm. Under conventional tolerances (gamma 3%, 3 mm), AIP and FB image sets generated plans with pass rates greater than 98% for both AAA and AXB based computations. When switching to SBRT tolerances (3%, 1 mm), MIP and PWD based AAA computations generally fell below 85% pass rates, and gradually degraded as range of motion increased. However, AXB pass rates for all image sets showed a substantial improvement in delivery accuracy when compared to AAA. Interestingly, the pass rates for the higher density MIP image set yielded comparable results (> 85%) to those of AIP and FB when calculated for AXB algorithm. Although PWD dataset did not perform well for large ranges of motion when evaluated with AAA, PWD demonstrated a slightly better conformance over AIP and FB when using Acuros XB.

A comparison of the dose profiles for 3 cm of motion are shown in Fig. 9a–h. As seen in the left column, the TPS calculated dose for AAA is consistently overestimated with respect to that being measured, and more prominent with respect to MIP and PWD based computations. On the other hand, in the right column the AXB profiles show better conformance with TPS calculated versus measured dose, which give rise to higher pass rates.