Investigation of Target Minimum and Maximum Dosimetric Criteria for the Evaluation of Standardized Radiotherapy Plan —Target Minimum and Maximum Evaluation

Purpose: Standardization of tumor dosimetric coverage is essential for the evaluation of radiotherapy treatment plan quality. National clinical trials network RTOG protocols include tumor target dosimetric criteria that specify the prescription dose and minimum and maximum dose (D min and D max ) co-verages. This study investigated the impact of various minimum and maximum dose definitions using tumor control probability (TCP) models. Methods and Materials: Three disease sites (head and neck, lung, and prostate) were studied using target volume dosimetric criteria from the RTOG 0920, 1308, and 0938 protocols. Simulated target dose-volume histograms (DVHs) of D min and D max were modeled using the protocol specifications. Published TCP models for the three disease sites were applied to the DVH curves. The effects of various dose definitions on TCP were studied. Results: While the prescription dose coverage was maintained, a −3.7% TCP difference was observed for head and neck cancer when the target doses varied by 3.5% of the tumor volume from the point dose. For prostate and lung cancers, −3.3% and −2.2% TCP differences were observed, respectively. The TCPs for head and neck and prostate cancers were more negatively affected by deviations in the D min than the TCP for lung cancer. The lung TCP increased to a greater extent with a change in the D max compared with the head and neck and prostate TCPs. Conclusions: These results can be used to evaluate plan quality when the target dose only slightly deviates from the dosimetric criteria. When the overall target prescription dose coverage is maintained, the D max is recommended to be within 3% of the target volume: 98% (for head and neck and prostate) and 97% (for lung) of the target volume, satisfying the D min needed to maintain TCP variations at less than 2.1%. Using 0.03 cc instead of a point dose for D min and D max criteria minimally impacts TCPs.

of D min and D max were modeled using the protocol specifications. Published TCP models for the three disease sites were applied to the DVH curves. The effects of various dose definitions on TCP were studied. Results: While the prescription dose coverage was maintained, a −3.7% TCP difference was observed for head and neck cancer when the target doses varied by 3.5% of the tumor volume from the point dose. For prostate and lung cancers, −3.3% and −2.2% TCP differences were observed, respectively. The TCPs for head and neck and prostate cancers were more negatively affected by deviations in the D min than the TCP for lung cancer. The lung TCP increased to a greater extent with a change in the D max compared with the head and neck and prostate

Introduction
The imaging and radiation oncology core (IROC) provides radiation therapy (RT) quality assurance services within the national clinical trials network [ Developing dosimetry review criteria is an important part of trial design support. Adding the planning tumor volume (PTV) to the dosimetry review criteria is necessary to achieve the tumor control probability (TCP) of the protocol [5].
PTV dosimetry review usually includes checking the prescription dose coverage of the PTV, as well as the minimum absorbed dose (D min ) and the maximum absorbed dose (D max ) in the PTV [6]. According to the ICRU report [7], the D min might not be accurately determined since it is often located in a high-gradient region at the edge of the PTV, making it highly sensitive to the resolution of the calculation and the accuracy of either delineating the CTV or determining the PTV. Reporting of the D min was replaced by the more accurate near-minimum absorbed dose, which is the dose covering 98% of the PTV (D98%) [7]. Similarly, the dose covering 2% of the PTV (D2%) was recommended to be reported as the D max [7]. However, alternative specifications of D min and D max are being used in different clinical settings, for example, the dose covering 99% of the PTV (D99%) and the dose covering 1% of the PTV (D1%), respectively. In RTOG protocols [6], D min is usually reported as the dose covering the total PTV minus 0.03 cc (Dvol -0.03 cc), and D max is usually reported as the dose covering 0.03 cc of the PTV (D 0.03 cc).
The purpose of this study is to show the effects on TCP of different specifications of D min and D max of the target volume. The dosimetric criteria for three disease sites (head and neck, lung, and prostate) from the RTOG 0920, 1308, and 0938 protocols were adopted. We propose a simulated model for PTV dose-volume histograms (DVHs) of typical RT plans that incorporate the specified D min and D max values as variables. The DVHs were applied to the published TCP models to investigate the variations in TCP when the D min is between 0% and 3.5% of the PTV and when the D max is between 100% and 96.5% of the PTV.
The effects of PTV changes on lung cancer were also studied.

Target DVH Models
RTOG protocols are used to specify radiotherapy treatment plan quality criteria for clinical trials. Our study adopted the tumor target coverage criteria from the RTOG 0920 protocol for head and neck cancer, the RTOG 1308 protocol for non-small cell lung cancer (NSCLC), and the RTOG 0938 protocol for prostate cancer. The tumor volume dosimetry criteria for these three protocols are listed in Table 1, which include 1) the prescription dose coverage of D95%; 2) D max criteria that specify the maximum dose for the PTV; and 3) D min criteria that specify the minimum dose for the PTV. As the DVH represents the cumulative coverage of a distributed dose obtained in individual PTV voxels, when such a dose is simulated by a truncated, skewed, Gaussian distribution, the DVH curve can be simulated to satisfy all three dosimetry criteria. The truncated points at the left and right two tails represent the D min and D max that the tumor receives, respectively. Figure 1 plots the simulated DVHs for the three disease sites.
Variations in the nominal DVH can be reconstructed when the defined D min and D max values deviate from the point dose. Here, the D max deviation is defined  as η% of the PTV, and the D min deviation is defined as (100 − δ)% of the PTV. In this study, we investigated the variations in the D min and D max values up to 3.5% of the PTV, that is, η and δ variations from 0 to 3.5. The actual D min and D max values of the entire PTV were considered additional variables that were assumed to vary from 5 to 30 Gy from the defined D min and D max criteria.

TCP Models for the Three RTOG Protocols
To examine the effects of changes in the PTV DVH coverage, we employed published TCP models. RTOG 0920 is a phase III study of postoperative RT for locally advanced resected head and neck cancers, with a prescription dose of 60 Gy and D min and D max values of 70 Gy and 56 Gy, respectively. Okunieff et al. [8] published a TCP model with local control 50% dose (D 50 ) and 50 γ as the change in TCP when a 1% change in dose around D 50 occurs: The parameters for this model were obtained from a study by Martel et al. in 1999 [10] on local progression-free survival at 30 months, where D 50 and 50 γ were 84.5 Gy and 1.5, respectively (Table 1). To further study the volume effects on TCP, the Fenwick [11] and Martel models were used in a side-by-side comparison using 200-, 400-, and 600-cc tumor volumes having similar DVH curves: where D 50 = 84.6 Gy, m = 0.329, c = 9.58, V is the volume in cc, and φ is a Gaussian integral.
RTOG 0938 is a randomized phase II trial of hypofractionated radiotherapy for favorable-risk prostate cancer. In one of the two treatment legs, the prescription dose for PTV was 51.6 Gy in 4.3 Gy fractions; the D max (no more than 0.03 cc of the PTV as defined by the RTOG protocol) should not exceed 55.21 Gy, and the D min (no more than 0.03 cc of the PTV as defined by the RTOG proto-col) should not drop below 49.05 Gy ( Table 1). The same TCP formula, as shown in Equation (1), was used, with parameters from a study by Levegrun et al. [11] ( Table 1).
The differential DVH where a dose and corresponding volume fraction of the PTV was derived for a given DVH curve from the DVH model described above.
The values were utilized in the corresponding disease site TCP models to obtain the volumetric average TCP for a given DVH curve. For each disease site, the TCP was first calculated with the modeled nominal DVHs. The impact of the D min and D max variations was assessed using the calculated TCPs from the different DVHs.

Results
Using a truncated, skewed, Gaussian distribution, the nominal DVHs that satisfy all three RTOG protocols can be simulated to satisfy the specified PTV volume show the variations in TCP for head and neck cancer and prostate cancer caused by deviations in the D min and D max from the RTOG 0920 and 0938 protocols using the TCP models described by Okunieff et al. [9] and Levegrun et al. [11], respectively. The head and neck TCP was found to vary from −3.7% to 0.4% with the D min and D max deviations from the nominal TCP of 86.5% using the RTOG 0920 criteria. The prostate TCP was found to vary from the nominal TCP of 94.2%, and a large variation of −3.3% occurred when the D min deviated from the criteria. Figure 2( ., 200 cc), the nominal TCP is larger (54.0%) at the same prescription dose but is reduced to 35.7% and 23.1% at larger volumes of 400 cc and 600 cc, respectively. The variations in TCP due to the D max definition of η = 3.5% were 2.4%, 2.8%, and 2.8%, but was less than -0.3% from the D min defined as (100 − δ)% of the volume. The TCP variations with η or δ equaling 1%, 2%, or 3% in these models at the three disease sites are listed in Table 2. The TCP values for head and neck cancer and prostate cancer, but not lung cancer, are negatively affected by deviations in D min . The lung TCP value increased to a greater extent when the D max value varied Figure 2. Two-dimensional plots of TCP variations from head and neck, prostate, and lung models due to variations from the defined D min /D max values of (100 − δ)% and η% of the PTV.

Discussion
The TCP calculations performed in this study were all based on the simulated target DVHs that assume that the dose distribution in the target is a skewed

Conclusions
Our study investigated the effects on TCP by deviations in the D min and D max values up to 3.5% of the tumor volume for head and neck, lung, and prostate cancer patients, using published TCP models and parameters. The results of this study can be used for plan quality evaluations when the D min and D max values slightly deviate from the point dose. When the overall target prescription dose coverage is maintained, it is recommended that the D max be within 3% of the PTV: 98% (for head and neck and prostate) and 97% (for lung) of the target volume, satisfying the D min to maintain TCP variations at less than 2.1%. Using 0.03 cc instead of the point dose for D min and D max values at all three disease sites minimally impacts TCPs. One drawback of this study is that the conclusion is made solely based on simulations. There is no consensus on TCP models; therefore, two models were selected to compare the results. In the future, more clinical data from the above-mentioned clinical trials will be available with patient outcome. Tumor control probability should be evaluated with real patient dose distributions to make the conclusions from this research more acceptable to clinical practices.