A model for predicting the dose to the parotid glands based on their relative overlapping with planning target volumes during helical radiotherapy

Abstract The sparing of the parotid glands in the treatment of head and neck cancers is of clinical relevance as high doses to the salivary glands may result in xerostomia. Xerostomia is a major cause of decreased quality of life for head and neck patients. This paper explores the relationship between the overlap of the target volumes and their expansions with the parotid glands for helical delivery plans and their ability to be spared. Various overlapping volumes were examined, and an overlap with a high statistical relevance was found. A model that predicts exceeding tolerance parotid mean dose based on its fractional overlapping volume with PTVs was developed. A fractional overlapping volume of 0.083 between the parotid gland and the high dose PTV plus 5 mm expansion – was determined to be the threshold value to predict parotid Dmean > 26 Gy for parotids that overlap with the high dose PTV plus 5 mm expansion. If the parotid gland only overlaps with the intermediate dose target (and/or low dose target) and the overlapping volume of the parotid gland and the intermediate dose target is less than 25%, the parotid mean dose is likely less than 26 Gy. If the parotid overlaps with the low dose target only then the mean dose to the parotid is likely to be less than 26 Gy. This finding will prove as a very useful guide for the physicians and planners involved in the planning process to know prior whether the parotid glands will be able to be spared with the current set of target volumes or if revisions are necessary. This work will serve as a helpful guide in the planning process of head and neck target cases.

mean dose based on its fractional overlapping volume with PTVs was developed. A fractional overlapping volume of 0.083 between the parotid gland and the high dose PTV plus 5 mm expansionwas determined to be the threshold value to predict parotid D mean > 26 Gy for parotids that overlap with the high dose PTV plus 5 mm expansion. If the parotid gland only overlaps with the intermediate dose target (and/or low dose target) and the overlapping volume of the parotid gland and the intermediate dose target is less than 25%, the parotid mean dose is likely less than 26 Gy. If the parotid overlaps with the low dose target only then the mean dose to the parotid is likely to be less than 26 Gy. This finding will prove as a very useful guide for the physicians and planners involved in the planning process to know prior whether the parotid glands will be able to be spared with the current set of target volumes or if revisions are necessary. This work will serve as a helpful guide in the planning process of head and neck target cases.  The focus of this study is to determine which parameter is capable of accurately predicting the mean dose of the parotid glands for plans developed using helical arc available on Accuray's Tomotherapy System (Accuray Inc, Sunnyvale, CA, USA). As discussed by Gensheimer, these findings will allow the clinical staff working on the case to determine if the target volumes require alteration to achieve dosimetric objectives before a considerable amount of time is spent planning the case only to discover that the desired sparing of the parotid glands is unachievable. This could avoid delaying the start date of the patient and utilize limited resources more efficiently.

2.A | Selection criteria
The following criteria were applied for inclusion of head and neck patients in this study: intact bilateral parotid glands and 2-4 simultaneously treated targets with prescriptions ranging from 54 Gy to 70 Gy. The dose schemes and the primary disease sites for the patients in this study are characterized in Table 1 and Table 2. Both parotid glands were contoured with the inclusion of deep and superficial lobes of the glands. The range of the parotid gland volumes was from 11.35 cc to 55.18 cc, and the mean parotid gland volume was 29.90 cc. Efforts were made to spare the parotid glands while ensuring that the target(s) coverage was not significantly compromised. The criterion used for determining if the target had acceptable coverage was 90% coverage of the target by the prescription dose and that the compromised target coverage was not overlapping with the GTV. Plans with unacceptable PTV coverage (V100% < 90% for PTV with the highest dose level) were excluded from the analysis. After applying all the inclusion criteria, 37 clinical plans were included in this study. Treatment planning was performed using Tomotherapy software version 5.1 utilizing the 2.5 cm field size (fixed jaws), 0.215 couch pitch, 3.5 modulation factor and fine dose resolution settings (256 9 256 9 #slices).

2.B | Parotid dose vs. overlap with combined PTVs and expansions
The mean parotid dose was first analyzed against the relative overlapping volume with the combined PTV (union of PTVs for all dose levels) and its expansions. The following three parameters were computed: fractional overlap of the parotid glands with the combined targets (OLV CT ), fractional overlap of the parotid glands with the 0.5 cm isotropic expansion of combined PTV (OLV CT05 ), and fractional overlap of the parotid glands with the 1 cm isotropic expansion of the combined PTV (OLV CT10 ). Throughout this article, the term "fractional overlap" is defined as the ratio of the overlapping volume between the parotid and the target contour to the volume of the parotid contour. Univariate analysis was done using linear regression between parotid D mean and each of the three overlapping parameters. Multivariate analysis was done using a linear regression model with all three overlapping parameters, followed by a stepwise model selection to determine the T A B L E 1 Disease sites.

Primary site Number of cases per site
Base of tongue 9 Floor of mouth 2  Linear regression was done to examine the correlation between parotid mean dose and either OLV HD , or OLV HD05 . ROC analysis was then performed to compare these two parameters as parotid dose predictors and identify optimal thresholds. ROC curves were then generated against OLV HD and OLV HD05 . The areas under the ROC curves were compared to select the best predictor. After selecting the best predictor, an optimal point on the ROC curve was identified to establish a threshold value.
The statistical analysis in this study was performed using R   for OLV HD05 , both with associated P-values < 0.01. OLV HD05 seems to be better correlated with parotid mean dose.
ROC analysis was performed for OLV HD and OLV HD05 . The corresponding ROC curves are shown in Fig. 6. The AUCs are found to be 0.8625 and 0.9188, respectively. Again, OLV HD05 seems to be the better predictor. OLV HD05 also has a higher AUC than OLV CT , and therefore was determined to be the best parotid D mean predictor. The optimal point with best overall sensitivity and specificity was identified with a threshold value of 0.0829, a sensitivity of 0.81, and a specificity of 0.90. This demonstrates that an OLV HD05 of greater than 0.0829 (or 8.29%) is a reasonable threshold for predicting a mean parotid D mean greater than 26 Gy.

| DISCUSSION
It is interesting to observe that when analyzing combined targets and their expansions, the overlap with PTVs only is the better fit compared to overlapping with PTV expansions. This differs from the findings of Gensheimer et al. 6 However, it is plausible, considering This model intentionally does not differentiate between the contralateral and ipsilateral parotids as the model is purely based on overlap volume. It is reasonable to assume that the ipsilateral parotid will tend to share more of an overlap with the target especially the high dose target which in turn will yield an unfavorable mean dose prediction with this model.  Fig. 3 (method 1) are based on the full data set, while the ROC curves in overlap with the high dose target, method 2 essentially yields a perfect prediction (100% sensitivity and specificity). When there is overlap, method 2 yields a slightly higher AUC compared to method 1.
Therefore, the overall performance of method 2 is better than method 1.
Future work includes collecting more data to strengthen the presented model, and applying similar analysis to other normal tissues, such as the duodenum in pancreatic cases. Additionally, this analysis can be used for treatment modality comparison, such as Tomotherapy vs. VMAT which is now widely used for the conformal treatment of complicated tumors.

| CONCLUSION
We analyzed the relation between parotid mean dose and the overlapping volume between parotid and various PTVs and their expansions, and found out that: 1. When the parotid is overlapping with the low dose target only (with overlapping volumes all less than 16% in our data set), the parotid mean dose is likely under 26 Gy.
F I G . 6. ROC analysis of OLVHD, OLVHD05 as predictors for parotid D mean > 26 Gy.

2.
When the parotid is overlapping with the intermediate dose target only, but the overlapping volume is less than 25%, the parotid mean dose is likely less than 26 Gy.

3.
When the parotid is overlapping with the high dose PTV plus 5 mm expansion, then an overlapping volume of 8.3% could be used as a threshold to predict parotid D mean > 26 Gy.

CONF LICT OF I NTEREST
The authors of this manuscript bear no conflicts of interest.