Dose Optimization for Single-Channel Vaginal Cylinder High-Dose-Rate Brachytherapy: A Double Prescription Method for Patients With Endometrial Adenocarcinoma

Purpose This study aimed to explore the relationship between applicator surface dose and 5 mm-depth dose and to optimize both locations simultaneously for three most used cylinder sizes (2.5, 3.0, and 3.5 cm in diameter) in treating patients with endometrial adenocarcinoma. Materials and methods A total of 216 plans were created for each dose level and applicator size. For each dose level, four plans were created with single or double prescription doses. For plans with double prescription doses, the dose constraints were applied to all those points on the surface and 5 mm depth and optimize the two sites simultaneously. Results A dose table between surface and 5 mm depth and its fifth order polynomial mapping functions were established for each applicator size, so any prescribed dose at one site can find the prescription dose on the other site in optimization on both locations. For plans with a 5 mm-depth prescription, the maximum dose on the surface can be reduced from 145% to 133% if the surface prescription dose is also used; for plans with surface dose prescription, the minimum dose and mean dose can be improved by 2% if 5 mm-depth dose prescription is also used in optimization. Conclusion Dose table and their mapping functions between surface prescription dose and their corresponding 5 mm-depth doses were created. A new optimization method that uses two prescription doses on both surface and 5 mm-depth sites was proposed to reduce the hot dose on the surface and improve the cold dose at 5 mm depth.


Introduction
Endometrial cancer is the most common gynecological cancer among women in the United States. Surgery is the primary treatment for endometrial cancer. However, the most common local recurrence site has been in the upper vagina. Vaginal cylinder brachytherapy is as effective as pelvic radiation with lower toxicities at preventing vaginal recurrence for high-intermediate risk group of stage 1 endometrial carcinoma [1]. The American Brachytherapy Society (ABS) published detailed guidelines for endometrial high-dose-rate (HDR) brachytherapy, which include applicator selection, insertion techniques, target volume definition, dose fractionation, etc., and the vagina at risk needs proper coverage for 3-5 cm along the cylinder with the dose prescribed either at the applicator surface or at 5 mm depth from the surface [2]. Lots of research on HDR optimization has been published and a comprehensive review can be found in [3][4][5]. In this study, we compared the surface dose and 5 mm-depth dose and created a connection between these two sites. We analyzed the dose gradient of applicators with the three different sizes and proposed a new corresponding dose table between surface and 5 mm depth to make prescription doses on both sites possible in treatment planning. Based on the dose table, we also generated six mapping functions so any prescription dose at 5 mm depth can be found through the known prescription surface dose or from its mapping function. The same method can be applied to obtain the surface prescription dose through the known 5 mm-depth prescription dose. Later, we evaluated dose distribution at the surface and 5 mm depth from four different prescription methods.

Materials And Methods
The cylinder applicator we used has a single channel ( Figure 1). Before planning, three reference lines (left and right straight lines and one apex line) were created on the applicator surface and another three reference lines at 5 mm distance away from the surface. The source dwelling step size was always 5 mm. The dose points from these six lines can be used for dose constrains in volume optimization, which is VEGO TG-43 volume optimization in Varian's Eclipse Brachytherapy planning system (Palo Alto, CA: Varian Medical System, Inc.) ( Figure 1). We collected a total of nine dose levels for the three common cylinder sizes used in our department. For each prescription dose level, four plans were created for treatment planning.

FIGURE 1: Single applicator and three surface reference lines (color: tomato) and three 5 mm-depth reference lines (color: cyan)
If the primary prescription dose is at 5 mm depth, the dose constrains in the first plan "P1_5mm" are applied only to 5 mm depth. In the second plan "P2_5mm&Sur," the dose constraints are applied to dose points at 5 mm depth and on the surface simultaneously, and 5 mm-depth dose points are assigned to a higher priority (>100) and the surface dose points are assigned to a lower priority (<80). The dose constraints are similar to those in the external beam optimization; the doses of 98% target volume (dose points) are between ±50 cGy of the prescription doses. Dose constraints to the organs-at-risk (OAR), like rectum, bladder, small bowel, etc., were not considered as routine clinical practice in vaginal cylinder planning.
If the primary prescription dose is on the surface, the dose constraints in the third plan "P3_Sur" are applied only on the surface point doses. In the fourth plan "P4_Sur&5mm," the dose constraints are applied to dose points on the surface and 5 mm depth simultaneously, and the surface dose points are assigned to a higher priority (>100) and the 5 mm-depth points are assigned to a lower priority (<80).
Although P2_5mm&Sur and P4_Sur&5mm use the double prescription doses in the same plan, they use different priority strategies. In P2_5mm&Sur, the prescription dose at 5 mm depth is the primary and the dose points at this site are assigned a higher priority; in the P4_Sur&5mm plan, the above primary and priority are reversed. Even in the same higher or lower priority group, the priorities of the three lines are different due to the anisotropic effect of the source and cylinder construction. The apex line is usually assigned to a higher priority compared to the two straight lines and its priority is usually 10 ~ 50 higher ( Figure 1).
In all the optimization, the "smooth" parameter is assigned to the highest value, which is 300 to smooth out the dwelling time at each dwelling position to reduce the hot spot. The doses from both sites were normalized to their prescription dose respectively even in plans P1_5mm and P3_Sur which do not have the secondary prescription dose for easy comparison.

Results
A total of 216 plans were created (9 dose levels x 4 plans/level x 3 Cylinder size x 2 patients/size) and half of them were analyzed and compared in dosimetric parameters. A table between surface dose and 5 mm-depth dose for prescription was generated after dose distribution analysis from these examples ( Table 1). For each cylinder size, the first column shows the dose at 5 mm depth and the second column is the corresponding dose on the cylinder surface.

mm depth for three cylinder applicator sizes
The coefficients of three fifth order polynomial functions (y = a * x 5 + b * x 4 + c * x 3 + d * x 2 + e * x + f) for mapping 5 mm-depth dose to surface dose were obtained and another three functions for mapping in the reverse direction were listed in Table 2. The columns from two to four are the coefficients of the polynomial functions which are mapping any dose from 5 mm depth dose to the surface dose used for the dual prescriptions. The columns from five to seven are the opposite.      We also compared the maximum dose (DMax), minimum dose (DMin), and mean dose (DMean) of the 108 plans among the four prescription approaches ( Table 3).  The standard deviations (σ) were also calculated to show their variations. The maximum, minimum, and mean doses of surface are the maximum, minimum, and mean doses of all surface points from the left, right lines, and apex curves. The maximum, minimum, and mean doses of 5 mm-depth are the same.

Discussion
The ABS recommends reporting doses at both the vaginal surface and at 5 mm vaginal mucosal depth. Also, the ABS recommends placing optimization points both at the apex and along the curved portion of the cylinder dome in addition to the lateral vaginal mucosa as shown in this dosimetry study. Our study offered a method to transfer from prescribing to 5 mm to prescribing to surface while still having the same 5 mm depth dose and a more uniform surface dose. Although some "rules of thumb" of doses between cylinder surface and 5 mm depth exist in the HDR brachytherapy community, they are not accurate enough for prescription. Our study showed the relationship between surface dose and 5 mm dose is nonlinear and that is the reason we chose the fifth order polynomial functions for mapping ( Figure 2).  [6]. Patients with VBT arm experienced better social functioning, less bowel toxicity, and better quality of life.
Vaginal dryness, shortening, or pain was not significantly different between the two treatment arms. In VBT arm, G3-G4 late vaginal toxicities were in less than 2% which consisted of slight atrophy, bleeding, and stenosis, VBT is very well tolerated even using different hypo-fractionated dose schedules.
Previous research almost covered every aspect from applicator size, tip space, dwelling step size, dose calculation models, optimization methods, etc., and their effects on dose distribution [6][7][8][9][10][11][12]. For example, Li et al. compared the three dose models: an isotropic and anisotropic dose calculation based on TG-43 formalism and the benchmark calculation using Monte-Carlo calculated dosimetry data [7]. Kim et al. studied the effect of the apex optimization line and found the use of this line is important, which can improve the cold dose at 5 mm depth, especially for their new vaginal cylinders which have thicker tops [8].
Optimization methods, classified as forward and inverse optimization, were also studied to compare the dose distribution, target coverage, and OAR sparing [9]. Li et al. studied the effects of the prescription depth, cylinder size, treatment length, tip space, and curved end on dose distribution and found the surface prescription has a more uniform dose at all depths in the target volume than 5 mm-depth prescription which creates large dose variations (50% ~ 70%) at the surface [10].
In our study, we proposed a new method: prescription doses to both sites. So optimizer can optimize dose distribution on surface and 5 mm depth simultaneously. The benefits are obvious: the doses in the whole treatment volume are more uniform. Figure 4 shows the point dose sorted from the highest to lowest on the lines, the hot dose points are usually located in the apex lines. If we compared the four plans, the surface doses are much more uniform in P3_Sur and P4_Sur&5mm than in P1_5mm and P2_5mm&Sur. This conclusion is similar to one of the conclusions described in [9]. Our work further provides a solution on how to change the prescription at 5 mm depth to prescription on the surface. For those physicians who usually prescribe dose to 5 mm depth, the prescription dose table and the mapping functions can provide specific prescription doses on the surface, which greatly reduce the hot spots from 30~40% higher to around 15% higher ( Table 1).
If we compare P2_5mm&Sur and P4_Sur&5mm, the two plans optimize dose points on both sites simultaneously but with different optimization priorities, the D Max on the surface can be reduced from 33% higher to 15% higher while the other parameters are almost the same. In P2_5mm&Sur, the 5 mm-depth dose prescription is primary and surface prescription is secondary in optimization; in P4_Sur&5mm, the surface prescription is primary and the 5 mm-depth prescription is secondary. The secondary site can be used for dose comparison and reference. We normalized all point doses to their respective prescription dose to compare the dose uniformity even in P1_5mm and P3_Sur. This is different from the normalization method in Li et al.'s study in which a mean dose was used [8]. So the low doses at 5 mm depth in the plan P3_Sur and P4_Sur&5mm were not really cold dose.
Among the four plans, P4_Sur&5mm has the highest quality and P3_Sur the second, P2_5mm&Sur the third and P1_5mm is the least if we use dose uniformity to evaluate these four plans (Figure 4). If higher dose is needed in the vaginal cuff (apex area), then the sequence will be reversed.
In this study dose constraints to the regional OAR were not included in the optimization, as performed in routine clinical practice for vaginal cylinder applicator. This is because of the relatively lower energy of iridium-192 compared to the external beam, and the dose to the surrounding organs decreases very quickly from 5 mm prescription dose lines. So, we focus on the dosimetry and corresponding prescription doses between applicator surface and 5 mm depth. Due to specific features of fifth order polynomial function, our mapping functions are only for interpolation, not for extrapolation in the prescription dose range list in Table 1.

Conclusions
A dose table for each applicator size from 2.5 cm to 3.5 cm was presented to illustrate the relationship between dose on the applicator surface and dose at 5 mm depth, which can be used to prescribe dose on one site or both sites. The mapping functions make it more flexible not only for the nine dose levels, basically any dose from one site to its interpolated corresponding dose on the other site. The double-dose prescription approaches (P2_5mm&Sur and P4_Sur&5mm) in our study are better than the traditional single-site prescription methods (P1_5mm and P3_Sur), making it possible to lower the hot dose on the surface and improve the cold dose at 5 mm depth, which improves the mean dose in general.

Additional Information Disclosures
Human subjects: All authors have confirmed that this study did not involve human participants or tissue. Animal subjects: All authors have confirmed that this study did not involve animal subjects or tissue.

Conflicts of interest:
In compliance with the ICMJE uniform disclosure form, all authors declare the following: Payment/services info: All authors have declared that no financial support was received from any organization for the submitted work. Financial relationships: All authors have declared that they have no financial relationships at present or within the previous three years with any organizations that might have an interest in the submitted work. Other relationships: All authors have declared that there are no other relationships or activities that could appear to have influenced the submitted work.