A quality control method for intensity‐modulated radiation therapy planning based on generalized equivalent uniform dose

Abstract To ensure good quality intensity‐modulated radiation therapy (IMRT) planning, we proposed the use of a quality control method based on generalized equivalent uniform dose (gEUD) that predicts absorbed radiation doses in organs at risk (OAR). We conducted a retrospective analysis of patients who underwent IMRT for the treatment of cervical carcinoma, nasopharyngeal carcinoma (NPC), or non‐small cell lung cancer (NSCLC). IMRT plans were randomly divided into data acquisition and data verification groups. OAR in the data acquisition group for cervical carcinoma and NPC were further classified as sub‐organs at risk (sOAR). The normalized volume of sOAR and normalized gEUD (a = 1) were analyzed using multiple linear regression to establish a fitting formula. For NSCLC, the normalized intersection volume of the planning target volume (PTV) and lung, the maximum diameter of the PTV (left–right, anterior–posterior, and superior–inferior), and the normalized gEUD (a = 1) were analyzed using multiple linear regression to establish a fitting formula for the lung gEUD (a = 1). The r‐squared and P values indicated that the fitting formula was a good fit. In the data verification group, IMRT plans verified the accuracy of the fitting formula, and compared the gEUD (a = 1) for each OAR between the subjective method and the gEUD‐based method. In conclusion, the gEUD‐based method can be used effectively for quality control and can reduce the influence of subjective factors on IMRT planning optimization.

(RTOG) guidelines, or clinical knowledge and intuition. Indeed, a lack of effective means for quality control in radiotherapy planning means that the quality of the radiotherapy depends on the experience of the radiation oncology team or center. To address this issue, retrospective optimization analysis was performed for patients who underwent IMRT for the treatment of cervical carcinoma, nasopharyngeal carcinoma (NPC), or non-small cell lung cancer (NSCLC); the goal of this study was to propose the use of a quality control method based on generalized equivalent uniform dose (gEUD) that predicts absorbed radiation doses in organs at risk (OAR) before IMRT optimization. Several treatment planning systems have been developed that incorporate gEUD cost functions for IMRT optimization. Previous investigations have confirmed the effectiveness of gEUD cost functions for plan optimization. [6][7][8] For more complex plans, more iterations are required because many parameters need to be finely tuned for dose-volume (DV)-based objective functions.
gEUD was developed with fewer parameter settings to improve the quality of plans. 9 The phenomenological form of gEUD is as follows: where, m is the number of voxels in the anatomical structure of interest, d i is the dose in the ith voxel, and a is the tumor or normal tissue specific parameter. For a = ∞, gEUD is equal to the maximum dose; for a = À∞, gEUD is equal to the minimum dose; for a = 1, gEUD is equal to the arithmetic mean dose; and for a = 0, gEUD is equal to the geometric mean dose. Because the mean dose is a critical evaluation condition for OAR, gEUD (a = 1) was used in this study as a restrictive and evaluative condition for OAR to evaluate the quality of radiotherapy planning and reduce the influence of subjective factors on the quality of the radiotherapy plan.

| MATERIALS AND METHODS
Previous studies have shown a correlation between the radiation dose absorbed by the OAR and the spatial position of the target region. 10,11 In this study, the prescription dose of the target region was considered to be the dose of the intersection area of the OAR and target area. The OAR included the bladder, rectum, and femoral head in patients with cervical carcinoma; the inner ears, oral cavity, parotid gland, larynx, postcricoid region of the hypopharynx, and esophagus in patients with NPC; and the lung in patients with NSCLC.

2.A | Patient information
Patients with cervical cancer, NPC or NSCLC who underwent IMRT planning at our department were randomly selected and divided into data acquisition and data verification groups. The data acquisition group included 50, 65, and 50 patients who underwent IMRT for the treatment of cervical carcinoma, NPC, and NSCLC, respectively. The data verification group included 20 patients with each disease. For NSCLC, the prescription dose was selected in accordance with the regulations of the RTOG 0617. 17 The prescription dose for the PTV was 60.0-70.0 Gy, and the per fraction doses was 2.00 Gy.

2.B | Target delineation
To evaluate the dose distribution of the target, the following parameters were calculated for the PTV: minimal dose delivered to 98% of the target volume (D98%), maximum dose delivered to 2% of the target volume (D2%), conformation number (CN), and homogeneity index (HI) according to ICRU report 83. 18 The CN was defined using the following equation: 19 where CN is the conformation number, TV RI is the target volume receiving the reference isodose, TV is the target volume, and V RI is the volume of the reference isodose. The CN ranged from 0 to 1, where 1 was the ideal value. The HI was calculated using the follow- where D2% is the near-maximum dose, D98% is the near-minimum dose, and D50% is the dose received by half of the PTV. An HI of 0 indicated that the absorbed dose distribution was almost homogenous.

2.D | Limiting requirements for OAR
For cervical carcinoma, the bladder and rectum were restricted to V45 ≤ 50%, V50 ≤ 50% for individual patients, and V50 of the femoral head ≤5%, thus controlling the volume of "hot spots". 14  For NSCLC, the V20 and V5 of the lung were kept below 30% and 65%, respectively. The mean dose was no more than 20 Gy. 23 A window width of 1300-1700 HU and window level of À600 to À800 HU is recommended when the lung is being delineate, and the CT scan slice thickness is recommended to be 2.5 mm.
2.E | IMRT plan design for the data acquisition The intersection areas of ring1~ringn and OAR (ring1~ring-n∩OAR) were considered to be independent sub-organs at risk (sOAR); gEUD (a = 1) for sOAR was regarded as the optimization restrictive condition to make constant adjustments for values and weight. The dose of the intersection area of OAR and the target area was recognized as the prescription dose, and the dose of the target area was guaranteed to keep the absorbed dose of each OAR as low as possible so that the requirements of the evaluation were met. When numerous sOAR were present, sOAR weight parameters were adjusted to smaller values (with respect to the target region). Figure 1 illustrates the intersection area of ring1 $ ringn and the right parotid gland in a patient with NPC (case 39).
Given the distinctiveness of the lung's position for NSCLC treatment, this study did not divide the OAR into sOAR in patients with NSCLC. During optimization, the values and weights of V5 and V20 were adjusted repeatedly. Under the precondition of meeting the target area's evaluation conditions, V5, V20, and the mean dose to the lung were minimized as much as possible.

2.F | Fitting formula
The following methods were used for cervical carcinoma and NPC in the data acquisition group. Using SPSS 13 software, the Spearman rank correlation test was used to analyze the correlation between volume of sOAR and gEUD (a = 1) of each OAR, and a multiple linear regression analysis was used to fit the experimental data for the normalized volume of sOAR (V ring1 $ ringn∩OAR /V OAR ) and normalized F I G . 1. The red shadow indicates PCTV2, the purple line indicates the right parotid gland, the yellow line indicates the intersection of ring1 and the right parotid gland (the nearest ring area to the right parotid gland), the green line indicates the intersection of ring4 and the right parotid gland (the middle of ring area to the right parotid gland), and the blue line indicates the intersection of ring7 and the right parotid gland (the farthest ring area to the right parotid gland). There are eight rings in total.
gEUD (gEUD/D prescription , a = 1, for cervical carcinoma, D prescription is the prescription dose of PTV; for NPC, D prescription is the prescription dose of PCTV2) of each OAR. The following formula was obtained: where Y is the normalized gEUD (gEUD/D prescription ) of OAR when where Y is the normalized gEUD (gEUD/D prescription , a = 1) of the lung, V 0 is the normalized intersection volume of the PTV and lung

2.G | IMRT Plan design for the data verification group
Optimization was carried out on 20 patients with each disease using two methods: a subjective method (Method 1) and a gEUD-based optimization method (Method 2). In Method 1, conventional, experience-based limits (optimization goals referenced from populationbased data, RTOG guidelines, or clinical knowledge and intuition) were used for the investigated OAR. Method 2 was used to gEUD (a = 1) as the optimization parameter for each OAR, the planner had to repeatedly adjust the optimized parameters of the OARs and target area (gEUD for each OAR was calculated using Formula 1 or 2 just as the reference optimization parameter). The dose of the target area and OARs were guaranteed to satisfy the requirements of the evaluation in Method 1 and Method 2. Using SPSS 13 software, statistical differences were determined using a two-sided paired t-test.
Differences with a p value of <0.05 were considered significant.

| RESULTS
The volume of the sOAR had a significant correlation with gEUD  For the data verification group, gEUD plan1 was calculated using Method 1, gEUD plan2 was calculated using Method 2, and gEUD pred was calculated using Formula 1 or 2. Using  Table 4.

CONF LICTS OF INTEREST
The authors declare no conflict of interest.
T A B L E 4 Conformation number (CN) and homogeneity index (HI) of nasopharyngeal carcinoma in the data acquisition group for each PTV.