A quantitative assessment of the consequences of allowing dose heterogeneity in prostate radiation therapy planning

Abstract Target dose uniformity has been historically an aim of volumetric modulated arc therapy (VMAT) planning. However, for some sites, this may not be strictly necessary and removing this constraint could theoretically improve organ‐at‐risk (OAR) sparing and tumor control probability (TCP). This study systematically investigates the consequences of PTV dose uniformity that results from the application or removal of an upper dose constraint (UDC) in the inverse planning process for prostate VMAT treatments. OAR sparing, target coverage, hotspots, and plan complexity were compared between prostate VMAT plans with and without the PTV UDC optimized using the progressive resolution optimizer (PRO, Varian Medical Systems, Palo Alto, CA). Removing the PTV UDC, the median D1cc reached 144.6% for the CTV and the PTV, and an average increase of 3.2% TCP was demonstrated, while CTV and PTV coverage evaluated by D99% was decreased by less than 0.6% with statistical significance. Moreover, systematic improvement in the rectum dose volume histograms was shown (a 5–10% decrease in the volume receiving 50% to 75% prescribed dose), resulting in an average decrease of 1.3% (P < 0.01) in the rectum normal tissue complication probability. Additional consequences included potentially increased dose to the urethra as evaluated by PTV D0.035cc (median: 153.4%), delivering 283 extra monitor units (MUs), and slightly higher degrees of modulation. In general, the results were consistent when a different optimizer (Photon Optimizer, Varian Medical Systems) was used. In conclusion, removing the PTV UDC is acceptable for localized prostate cases given the systematic improvement of rectal dose and TCP. It can be particularly useful for cases that do not meet the rectum dose constraints with the PTV UDC on. This comes with the foreseeable consequences of increased dose heterogeneity in the PTV and an increase in MUs and plan complexity. It also has a higher requirement for reproducing the position and size of the target and OARs during treatment. Finally, with the PTV UDC completely removed, in some cases the maximum doses within the PTV did approach levels that may be of concern for urethral toxicity and therefore in clinical implementation it may still be necessary to include a PTV UDC, but one based on limiting toxicity rather than enforcing dose homogeneity.


| INTRODUCTION
The treatment planning goals of intensity modulated radiation therapy (IMRT) and volumetric modulated arc therapy (VMAT) are to give a specific and conformal dose to the prescribed target volume and limit the dose to the surrounding normal tissues and organs-atrisk (OARs) to acceptable levels. Besides, target dose uniformity has been a default objective during inverse planning for several reasons. Using a simple model of biological response, it can be shown that for a uniform distribution of clonogenic tumor cells, a uniform dose distribution is the optimal dose distribution for tumor control (assuming constant integral dose through the volume). 1 It could also be argued that there are pressures in terms of historical consistency and clinical experience to maintain dose uniformity. Before 2010, it was recommended by the International Commission on Radiation Units and Measurements (ICRU) in Reports 50 and 62 that dose heterogeneity within the planning target volume (PTV) should be within the range of −5% to +7% of the prescribed dose. 2,3 In the more recent ICRU report 83, this constraint is not mandatory if normal tissue sparing is a greater concern. 4 Clinical trial protocols for the treatment of prostate cancer commonly state maximum dose constraints for the PTV. A survey of recent clinical trial protocols for maximum dose constraints is shown in Table 1.
A recent letter from Craft et al. 5 to the International Journal of Radiation Biology Oncology Physics has drawn the strict enforcement of dose homogeneity into question. In principle, when a target volume dose distribution is nonuniform, the clonogenic cells with the highest probability for survival should be those in the subvolumes receiving the lowest doses, and therefore the low-dose tail of a heterogeneous distribution is more likely to dictate tumor control.
This draws into question the reasons for limiting PTV dose on the high end. Certainly for target volumes containing relatively high quantities of nerves, blood vessels, or normal tissue stroma, restricting the maximum dose to the target volume is often necessary in order to control toxicity. 6 Otherwise, enforcing restrictions on the high end of PTV dose uniformity may not be warranted. Disease sites where ablative doses have been proven effective such as prostate, liver, or sarcoma, may achieve equal or better tumor control if dose is escalated to subvolumes of the PTV. 7 In radiation therapy modalities like brachytherapy, stereotactic body radiation therapy, and stereotactic radiosurgery, highly heterogeneous dose distributions are common within the target volume, which suggests that allowing heterogeneous dose distributions in an IMRT or VMAT context is not unreasonable. Craft et al. 5 suggested that allowing for greater dose heterogeneity while ensuring the minimum prescribed dose to the target volume would, in general, better spare critical structures around the target volume in IMRT or VMAT plans. From a physics perspective, a combination of beam penumbra and scatter results in nonsharp dose profiles, and extending the field edges beyond the PTV border is typically done to ensure adequate coverage at the PTV periphery; however, allowing higher and nonuniform doses within the PTV core could achieve adequate coverage by putting the steepest part of the dose profile at PTV border, leading to lower dose to the normal tissue. From an optimization perspective, removing the PTV upper dose limit removes a constraint on the optimization problem, increasing the viable solution space, potentially allowing for improvements in the overall goals of the plan. While Craft et al. 5 presented an example pancreatic cancer plan, to our knowledge, the effect of enforcing PTV dose uniformity on OAR sparing has not been thoroughly and quantitatively studied yet.
In this study, we looked specifically at the consequences of limiting the upper dose to the PTV for low-and intermediate-risk prostate cancer VMAT treatment plans. We investigated this site because (a) ablative doses are generally acceptable for prostate radiation therapy, [8][9][10][11][12] which suggests minimal risk of toxicity from overdosing the PTV exclusively (within reason), (b) it is a site suggested by Craft et al., 5 and (c) prostate treatments are extremely common and make up a major fraction of the clinical workload for many clinics. We was defined as the rectum with a 3 mm margin in all directions. The bladder was defined as inferiorly from its base and superiorly to the dome. No PRV margin was added to the bladder for the optimizations, as this is not common planning practice at our center. However, we did retrospectively consider dosimetric consequences to a bladder PRV defined as a uniform 3 mm expansion of the bladder.
The overlap regions of PTV and rectal PRV as well as PTV and bladder were all contoured.
All cases were replanned with two full arcs in the treatment planning system (Eclipse version 13.6, Varian Medical System, Palo Alto, CA) using the progressive resolution optimizer (PRO). AcurosXB with a dose grid resolution of 2 mm was used for dose calculation in this study. Dose to medium was scored. Table 2 lists the dose objectives for the target volumes and OARs. Minor violations (±2.5% prescribed dose) of the dose objectives were allowed.
The optimization objectives were defined during the inverse planning process and they were parameters in the cost function.
Optimization objectives were usually set to be tighter than the dose objectives especially for the structures that were harder to meet the dose objectives (example in Table 3 For every dataset, two VMAT plans were created: • a plan with the PTV upper dose constraint using progressive resolution optimizer (PRO: with UDC) and, • a plan without the PTV upper dose constraint using progressive resolution optimizer (PRO: without UDC).
To test the robustness of our results against the specific optimization algorithm, we repeated our methods and performed the same evaluations for plans with and without the PTV UDC optimized using a separate optimization algorithm, the photon optimizer (PO) in Eclipse (Eclipse version 13.6, Varian Medical System) for the 17 datasets. Removing a constraint in the optimization process has the potential to alter, on average, the complexity of the plans delivered by the linear accelerator. It is important to know if any improvements in OAR DVHs come with a consequence of an increased treatment plan complexity since more complex plans can be more difficult to deliver for the machine, take longer, or be more likely to fail patient-specific QA. To this end, we calculated a modulation complexity score.
The modulation complexity score (MCS) was originally defined by McNiven et al. 13 for evaluating IMRT plans. Later, Masi et al. 14 applied it with modification to VMAT plans based on control points of an arc and it was found that MCS was closely correlated with VMAT dosimetric accuracy, which made it to be a candidate for scoring plan complexity. consecutive control points and then summed over all CP in the arc 16,17 : where MU CPiþ1;i indicates the MU delivered between two successive control points. Plan modulation complexity score was performed by a MATLAB script (2016a, The MathWorks, Inc, Natick, Massachusetts, USA).
The MCS arc has a value ranging from 0 to 1. 13 When modulation increases, MCS arc decreases. MCS arc ¼ 1 indicates that the arc is delivered with a fixed rectangular aperture without the MLC leaves moving. MCSv is an average of MCS arc for the two arcs.
Plans with and without the PTV upper dose constraint optimized using PRO were compared in terms of CTV and PTV coverage by D99%, CTV and PTV hotspots by D1cc, tumor control probability, homogeneity index (HI), which was defined as HI ¼ ðD2% À D98%Þ=D50%, 4 the total number of monitor units (MUs), treatment time, plan modulation complexity scores, and dosimetric parameters for OARs as well as a rectal normal tissue complication probability. Statistical analysis was performed in MATLAB using two-tail paired Student's t-tests and a script was used to control the false discovery rate because of multiple testing by the Benjamini-Yekutieli method. 15 P ≤ 5% is considered statistically significant. Figure 1 is the CTV and PTV DVHs for plans with and without the PTV upper dose constraint (UDC) optimized using the PRO for the 17 datasets. Without the PTV UDC, the maximum dose of the CTV and PTV reached 135% to 180% of the prescribed dose, and nearly 50% to 75% of the PTV received a dose in excess of 105% of the prescribed dose.

| RESULTS
First, we wanted to quantitate the consequences to the dose distribution within the target volume when the PTV UDC was removed.
It is important to keep in mind that each plan was normalized such that 100% of the prescribed dose was delivered to 95% of the PTV [as can be seen from Fig. 1(b)]. Still, it was important to examine the consistency of the plans with respect to minimal coverage, which was quantified as the dose to 99% of the volume, D99%. Figure 1    V60Gy, V65Gy, V70Gy, and V75Gy (in cc), we found there were moderate to strong correlations between them (r = 0.7 between ΔV50Gy and the rectum volume with P < 0.01; r = 0.8 between ΔV60Gy and the rectum volume with P < 0.01; r = 0.8 between ΔV65Gy and the rectum volume with P < 0.01; r = 0.8 between ΔV70Gy and the rectum volume with P < 0.01; r = 0.5 between ΔV75Gy and the rectum volume with P = 0.05). This indicates that a greater improvement of the dosimetric parameters in absolute volume (V60Gy, V65Gy, V70Gy, and V75Gy) would be expected for a patient who has a larger rectum volume.
In order to quantitate the impact of the upper dose constraint on rectal dose distributions, a common metric is needed. We chose to translate the rectal DVHs into a normal tissue complication probability (NTCP) as a metric representative of a clinical end point using Lyman's model. [19][20][21]  Comparable or greater levels of dose heterogeneity are typically seen in prostate brachytherapy. 22,23 Overall, the results are consistent between optimization algorithms.
The improvements in the rectum DVHs and dosimetric parameters without the PTV UDC (Fig. 4)   Importantly, there were six cases whose dosimetric objectives (i.e., one or more of V50Gy, V60Gy, V65Gy, V70Gy, and V75Gy) were not met for the plan with the PTV UDC applied, largely because of the overlap in volume between the PTV and rectal PRV.
Without the PTV UDC applied, the optimizer was able to meet the specified constraints with one exception (dataset 2 resulted in V75Gy being reduced from 16.3% to 15.7% in attempting to meet a 15% volume objective when the PTV UDC was removed). These cases are datasets 1-6 in Table 4 and Fig. 3, and are depicted with dashed gray curves in Figs. 4 and 5.
In Fig. 4 For bladder, there was a very small variation when the PTV UDC was removed (Fig. 5). In general, for bladder, the optimization objectives were met even with the PTV UDC present. If the constraints were met, contributions to the cost function for the bladder in principle would equal zero and would not change when the PTV UDC was removed. Therefore, the optimization process tended to concentrate on improving the constraints yet to be met. The low to moderate dose volumes within the bladder DVH tended to increase slightly since they too were unconstrained. The number of volume elements receiving high dose remained the same or decreased slightly to maintain consistence with the planning constraints.
Improvements to the planned bladder DVH were modest, but this is also an organ that can move and change volume, and as such there is a question as the robustness of these results on delivery.
We retrospectively created a bladder PRV (bladder + 3 mm) and assessed the dose to this structure. The dosimetric parameters for the bladder PRV structure were well within the dose objectives for bladder (V65Gy < 50%, V70Gy < 35%, V75Gy < 25%, V80Gy < 15%) in all 17 plans without PTV UDC. This suggests that minor changes in bladder position are unlikely to push the planning metrics beyond their constraints.
Recent studies have shown that changing the fractionation scheme to deliver higher doses per fraction can potentially increase bladder toxicity. 24 Because removing the PTV UDC systematically increases the mean and maximum PTV dose, there may be concerns about increasing bladder toxicity even in light of modest improvements to the bladder DVH, although we would expect a number of factors to play a mitigating role. First, the existing hypofractionated studies deliver a relatively uniform dose to the whole PTV, presumably including any regions of overlap with the bladder. In our study, we limited the dose to the bladder and PTV overlap region to be less than 102% of the prescription (78 Gy in 39 fractions). It seems reasonable to expect any toxicity to correlate more strongly with planned dose to the overlap volume than with the PTV as a whole, when these values are different. Second, movement of portions of the bladder into the directly irradiated volume on delivery seems a reasonable factor for contributing to the reported increases in toxicity, but because removal of the PTV UDC tends not to increase dose on the PTV periphery, this factor would be mitigated. Third, removal of the PTV UCD may allow more flexibility to introduce and achieve tighter bladder dose constraints if those were to become a higher priority during the optimization process.
When the PTV UDC was removed, dose heterogeneity within the PTV was naturally expected to increase. In this study, we wanted to quantitate how much of an increase was reasonable to expect when the optimization algorithm was unrestricted on the high end and whether that increase pushed outside the realm of clinical experience across modalities. As shown in Fig. 3, HI increased 6.3 times on average, but always remained below a value of 0.6. The median D1cc of the CTV and PTV reached 144.6% using PRO (Fig. 2). Although these are certainly dramatic increases, they are not outside the realm of clinical experience. In prostate low-dose rate brachytherapy, it is common for portions of the CTV to receive in excess of 200% of the prescribed dose. There are of course dose rate effects to consider, which may mitigate a direct comparison, but even if the HI results scaled up by a factor of 2 (i.e., D1cc values in the order of 200% of the prescribed dose) to obtain "brachytherapy equivalent" doses, the HI would still be less than that typically seen in brachytherapy prostate cancer treatments.
Removing the UDC increases the planned dose to regions of the PTV. With increased PTV dose comes a responsibility for increased vigilance in terms of setup and monitoring of patient position, as geographic miss-type errors could potentially have more extreme consequences. It is important to note that the high doses we report with the PTV UDC removed are to small subvolumes of the PTV and the hotspots (D1cc) are in fact confined within the CTV (i.e., back from the outer periphery of the PTV). Because these subvolumes are relatively displaced from the bladder and rectum, the probability of a shifted bladder or rectum being exposed to these higher doses is relatively low. That said, the increased PTV dose may necessitate, for example, daily cone-beam CT imaging which would include PTV alignment as well as assessments of the OAR positions and thresholds for treat/no treat decisions as a part of the setup protocol. This technique may be particularly well suited to hypo-fractionated treatments where more detailed monitoring is already in place.
It is also important that the UDC remains in place for the overlap region of the PTV and bladder as well as the overlap region of PTV and rectal PRV, and that the location of the hotspots relative to the OARs be scrutinized, as these will further help to reduce any differences between the planned and delivered dose distributions.
There is a statistically significant decrease in D1cc for the overlap region of the PTV and the rectal PRV (Fig. 2). The rectal PRV is a 3-mm expansion from the rectum to account for the uncertainty in rectal position, relative to the target volume. Visual inspection of the spatial dose distribution in the plans with and without the PTV UDC shows that the overlap region is fully covered by 70 Gy isodose line and without the PTV UDC applied, the 70 Gy isodose does not "penetrate" as far into the rectal volume, which is why this manifests as a decrease in the rectal volume receiving 70 Gy. As a consequence, the rectum, which is perhaps the OAR of greatest concern for toxicities induced by prostate cancer radiation therapy, was not likely to receive a higher dose by removing the PTV UDC if an upper optimization objective was set for this overlap region.
As can be seen in Fig. 2 as well as Fig. 1, there is a case that has the most extreme gain in CTV and PTV D1cc (176.0%). This is from the patient who had the smallest overlap between the PTV and the rectal PRV. As a consequence, this case had the most freedom to escalate dose in the PTV (recall the PTV and rectal PRV overlap was still subject to an upper dose constraint), while working to meet the PRV objectives. Thus, for cases like this, removing the PTV UDC has the potential risk of giving the CTV and PTV a high dose that may not be acceptable.
Another potential consequence of increased dose to the PTV is increasing dose to the urethra. Because the urethra is not clearly visible in a CT scan, contouring and assigning constraints for the urethra during planning are not feasible using conventional approaches.
A rough calculation can compare the urethral biological effective dose (BED) in EBRT to the dose in 125 I implant low-dose rate prostate brachytherapy according to Stock et al. 25 For EBRT, For 125 I implant brachytherapy, The urethra toxicity rate is higher in brachytherapy than in EBRT. 27 So when the optimization process is completely unconstrained on the upper end of the PTV (i.e., no PTV UDC), the maximum PTV doses have the potential to encroach on established urethral toxicity thresholds. Therefore, rather than completely eliminating the PTV UDC, users may wish instead to apply a PTV UDC based on urethral toxicity (e.g., PTV UDC in the range of 120-150% of prescription), which would still be expected to result in a moderate improvement for rectal dose while constraining the hotspots within the PTV to acceptable levels.
While CTV and PTV coverage was degraded slightly after the removal of the PTV UDC because of the normalization mode we used (100% of the prescribed dose to 95% of the PTV), it was still clinically acceptable (Fig. 1). Moreover, there was a 3.2% increase in TCP ( As another consequence, the total number of MUs increased with statistical significance when the PTV UDC was removed as shown in Fig. 3. Interestingly, the calculated time needed for delivering the two kinds of plans did not change. In general, the dose rate increased to compensate for the increase in MUs. As shown in Table 5, the plan modulation complexity score decreased slightly after removing the PTV UDC, meaning an increase in plan complexity. Although this change was statistically significant, we would not expect the increased plan complexity to result in an increase in dosimetric errors between the delivered dose and the treatment planning system calculated dose for patient-specific QA. 13,14 Plans optimized using the PO algorithm showed an even smaller decrease in plan complexity. This is probably due to the internal differences between the two optimizers. For PRO, every structure is represented by its own point cloud and dose is calculated for every dose point of each structure with a different resolution, while PO uses a consistent structure model where each structure location, DVH calculation and dose sampling are defined spatially by using one single matrix over the image. 31,32 In general the PO algorithm resulted in more complex plans to begin with but less complexity change. Overall, it seems that the specific optimization algorithm had little effect on the results.

| CONCLUSION
In this study, we made quantitative comparisons between prostate VMAT plans with and without the PTV UDC optimized using two separate optimization algorithms, PRO and PO. With the PTV UDC removed, an average increase of 3.2% (P < 0.01) in tumor control probability was shown as a result of increased equivalent uniform dose. Removing the PTV UDC also systematically lowered the dose to the rectum as indicated by the general DVH differences and improvements in specific DVH points of interest (average improvement for V50Gy, V60Gy, V65Gy, V70Gy, and V75Gy was 9.1%, 4.0%, 2.4%, 1.4%, and 0.6%, respectively, P < 0.01). This led to an average decrease of 1.3% (P < 0.01) in the rectal normal tissue complication probability. There was no risk of overdosing the rectum. In fact, D1cc for the overlap region of the PTV and rectal PRV was systematically lower without the PTV UDC (note that an upper dose constraint was still applied to the overlap volume of the PTV and rectal PRV when it was removed for the PTV). On the other hand, these benefits came with costs. D99% for CTV and PTV was reduced, albeit by less than 0.6% (P = 0.01 and 0.02, respectively). We observed a | 589 apply a PTV UDC, but one based on urethral toxicity limited rather than enforced dose homogeneity (e.g., a PTV UDC in the range of 120-150% of the prescription dose), which would still increase the freedom in the optimization process. The results were generally consistent between the two optimizers. Therefore, based on the evidence in this work, we conclude that removing the PTV UDC or basing it on urethral toxicity rather than enforcing dose heterogeneity offers moderate, but significant, planning advantages and it could be particularly useful for patients who are not meeting the rectum dose objectives with the PTV UDC applied.

ACKNOWLEDGMENT
The authors thank Dosimetrist Kim Campbell for her guidance on planning process and plan checking.

CONF LICT OF I NTEREST
The authors declare that they have no conflict of interest.