Analysis of different evaluation indexes for prostate stereotactic body radiation therapy plans: conformity index, homogeneity index and gradient index

This study analyzed different definitions of the conformity index (CI), homogeneity index (HI), and gradient index (GI) used in evaluation of prostate cancer stereotactic body radiation therapy.

of interest, can be obtained. [6][7][8][9] However, the main disadvantage of DVH is that the dose distribution is reduced to a one-dimensional histogram, while losing the spatial details of dose distribution. Currently, effective tools, including conformity indexes (CI), homogeneity indexes (HI), and gradient indexes (GI), have been proposed as a simple way to quantitatively evaluate the dose distribution, which represents the conformance between the prescribed dose area and planned TV, the degree of uniformity inside the target, and the dose fall-off outside the target. [10][11][12] The concept of a CI was first proposed by the Radiation Therapy Oncology Group (RTOG) in 1993, and described in Report 62 of the International Commission on Radiation Units and Measurements. 13,14 It is suggested to play a significant role in the assessment of plan quality with the growth of conformal radiotherapy. 15 According to the RTOG Report 63, the CI was defined as the ratio of the reference isodose volume (V RI ) to the TV, while the major drawback is not to take into account the shape of the target and reference isodose, as well as the degree of spatial intersection of the two volumes. 13,16,17 For another criteria by Saint-Anne, Lariboisiere, and Tenon (SALT) for CI, the global quality of treatment planning is quantified by the standard deviation based on the differential DVHs calculated for each vascular lesion, and the geometric CI, which is another quantitative method for the prescription isodose based on coverage of the lesion, is proposed. [18][19][20][21] Lomax and Scheib considered the TV covered by the prescribed dose and the volume of the adjacent normal tissue, and proposed two different CIs according the SALT group. 22 However, there is a problem, in that the real significance of CI = 1 might be different from the ideal distribution, as the reference isodose can be totally included in the target, but the TV might not be covered by the prescribed dose. 10 To compensate for the effect of the target and healthy volume, Van't Riet et al.
proposed the conformity number (CN),which consists of two parts: the first part represents the quality of target coverage, and the second part represents the normal tissues volume sparing. 23 Baltas et al. used the CN with brachytherapy by applying the supplementary parameter, the critical organs. 24 Wu et al. studied the effect of target shape complexity and size on the CI, and introduced a different conformity parameter -conformity distance index -which measures the average distance of prescription isodose and TV. 25 Park et al. also presented a new CI based on the distance between the surfaces of the TV and reference dose volume, which not only evaluates the shape prescription isodose, but also the target coverage. 26 The HI is used to evaluate the homogeneity of dose distribution in planning TV (PTV). 13,27,28 The conventional HI is mainly defined as the ratio of the maximum dose (D max ) to minimum dose (D min ) or prescription dose (D p ) in PTV, from which CI equals 1 indicates the ideal homogeneity. 10,17 To avoid the effect of grid size on the point dose, such as D max and D min , D 5% (the dose covers 5% of the PTV) was suggested to alternate D max , and the D 95% (the dose covers 95% of the PTV) to replace D min . [29][30][31] Another most commonly used formula is the HI = (D 2% -D98 % ) / D p , in which D 2% and D 98% were applied to represent the D max and D min , respectively, because it is more sensitive to the point dose-related parameters, such as the grid size and grid placement. 32 The lower value of HI indicates a more homogenous dose distribution within the PTV. Meanwhile, Yoon et al. developed a new HI based on statistical analysis of the DVH, which was defined as the standard deviation of the differential DVH curve of PTV. 33 Another objective tool for evaluation of radiotherapy plans is the GI, which describes the dose fall-off steepness outside the TV. A commonly used definition of GI is the ratio of the volume of 50% prescribed dose to that of the prescribed dose. 34,35 The GI is used to evaluate the dose fall-off outside the target, and shows the optimal dose distribution outside the target. The lower GI value means a steeper gradient of dose distribution outside the target, as well as better normal tissue sparing. 35 Ohtakara et al. modified the GI by multiplying the ratio of the volume of prescription dose by the TV, mainly taking into account the degree of dose conformity. 36

Patient selection
A total of 10 patients with low-risk prostate cancer staged T1-T2a treated with CK SBRT were randomly selected. Computed tomography (CT) simulation was carried out using a Brilliance TM Big Bore 16slice CT scanner (Philips, Amsterdam, the Netherlands) with 1.5-mm slice thickness in the head-first supine position with a full bladder and empty rectum. The clinical TV and critical organ structures were outlined by an oncologist and radiologist based on the fusion of the CT and magnetic resonance images on MultiPlan system (version 4.02; Accuray Inc.). PTV was delineated by expanding from the clinical TV with a 5-mm isotropic margin, except 3-mm posteriorly according to the literature. 38 Organs at risk, including the bladder, rectum, small bowel, penile bulb, femoral heads, and urethra, were also contoured.

Treatment planning
The SBRT plans of prostate cancer were generated in the CK  The HI was used to evaluate the degree of the uniformity of dose distribution inside the TV. In the present study, five definitions were selected to calculate the HI in the SBRT plans, as shown in Table 2. The ideal values of the first four formulas are equal to 1, which shows that each voxel of TV receives the same dose. 33 The last formula for HI proposed by Myonggeun et al. is called the S-index, which is defined as the standard deviation of the differential DVH. The idea value of S-index is 0, and a lower value that shows better uniformity.

Objective tools of evaluation
The conventional GI is defined as follows: where V x% represent the volume irradiated by x% of the prescribed dose. The value of GI is positive, and a lower value mean steeper dose fall-off outside the target and better sparing of normal tissue. 34,35

Formula Ideal value
Knoos et al. 17  Another method to describe the degree of dose fall-off is to apply the effective radius of the volume covered by specific isodose lines. The GI can be defined as follows: where the R x%iso is the effective radius of the volume covered by x% isodose. The lower value of ∆R iso indicates the steeper dose fall-off. 37 To takes into account the TV coverage, a modified GI (mGI) was proposed, which is defined as formula (12):

Statistical analysis
All indexes were calculated based on DVH. IBM SPSS version 20 (IBM Corporation, Armonk, NY, USA) was used for the statistical analysis, and a paired t-test was carried out. We not only compared the difference of different formulas in the same type of index in the same system, but also analyzed the difference between different systems.

RESULTS
In the present study, the analysis of different formulas for one index was carried out in different SBRT plans for prostate cancer. The SBRT plans were generated on the CK and EDGE system, and meet the criteria of the RTOG-0938 and previous study.

Conformity index
A transverse view of dose distribution and DVH of PTV is shown in in Figure 1. As can be seen in Figure 1, the prescription isodose line of EDGE is closer to the surface of the TV than that of CK. This shown better dose conformity of the EDGE system. The data of CI with different definitions are shown in Figure 3a-d, respectively. For the CK plans of prostate cancer, it showed that the CI 2 , CI 3 , and CI 4 values (calculated by equation [2], [3], and [4]) were <1, except the CI 1 calculated by equation (1) (Fig. 3a), whereas all CI values were all <1 in EDGE plans. The CI 4 values (Fig. 3d) were lower compared with other CIs for CK and EDGE SBRT plans.
The average values of CIs are listed in Table 3. As shown in Figure 2 and Table 3, the values of CI 4 were lower than CI 2 and CI 3 for both CK and EDGE plans. Meanwhile, the results of CI 1 , CI 2 , and CI 4 showed that the EDGE plans had better conformity for the prescribed dose area and TV.

Homogeneity index
The results of different types of HI are shown in Figure 4a- (7) and (8) (Fig. 4). HI closer to 1 showed better homogeneity for the former. For the latter definition, GI closer to 0 is considered more homogeneous. For the HI 1 and HI 2 , the HI 2 values were lower than HI 1 both in CK and EDGE plans, as well as for HI 3 and HI 4 , as shown in Table 3. The HI 5 calculated by equation (9), which was based on the differential DVH, had the larger value (>2; Fig. 4e) compared with others. According Figure 4 and Table 3, the results of HI 1 to HI 5 all showed that the CK plans had lower values, which showed better uniformity of dose distribution inside PTV compared with that of EDGE plans, which is consistent with Figure 2. As shown in Table 3, there is no significant difference only for HI 2 and HI 4 .

Gradient index
The result of the GI values calculated by equations (1) (Table 3). As shown in Table 3, the GI 2 values F I G U R E 2 The integral and differential dose-volume histogram of planning target volume.  Table 2) were lower than GI 1 and GI 3 both in the CK and EDGE plans. In addition, there was likely to be steeper dose fall-off for EDGE plans according the results of GI 2 and GI 3 , except GI 1 . There was no significant difference for GI values between the CK and EDGE plans, except GI 3

DISCUSSION
The present study compared different evaluation indexes, including the CI, HI, and gradient GI in SBRT plans. The main function of CI is to  (Table 1). Meanwhile, CI 4 showed the lowest value among all CI. For HI calculated by equations (5)-(9), respectively (Table 2), the results showed that HI 1 , HI 2 , and HI 5 were all >1, whereas both HI 3 and HI 4 were <1, as detailed in Table 3.
As for GI, GI 2 values were lower than GI 1 and GI 3 both in the CK and EDGE plans. According the CI and HI (as shown in Fig. 4 and Table 3), it was shown that EDGE plans were more conformable, whereas CK plans showed better uniformity of dose distribution inside the target.
The CI has been proposed based on the relationship between the TV and V RI . [13][14][15][16] According to the RTOG guideline, CI RTOG equal to 1 corresponds to the ideal conformity. If CI RTOG is <1, the TV is not totally irradiated, whereas CI RTOG >1 shows that the irradiated volume is larger than the TV and includes normal tissue, as shown in was not strict in the optimization process. Meanwhile, some studies pointed out that D max or D min might be just one voxel, and were very sensitive to the parameters of dose calculation, such as the grid size and grid placement. [30][31][32] As shown in Figure 4a and b, and Table 3, HI 2 values were lower than HI 1 both in the CK and EDGE plans. As expressed in equations (7) and (8), the D 2 (D 5 ) and D 98 (D 95 ) were applied to replace the maximum and minimum to overcome the effect of grid size and grid placement. The present results showed that HI 3 and HI 4 had lower values. When using HI 4 to assess the uniformity of PTV for CK and EDGE plans, there were significant statistical differences. The S-index was based on the differential DVHs, which can consider the dose of each voxel. However, it is easy for the S-index to neglect the effect of hot or cold points. 27,33 As our studies showed, the results of HIs all indicated that CK plans provided more uniformity of dose distribution inside PTV compared with EDGE plans.
The dose GI provides a method to evaluate the degree of dose falloff steepness outside PTV. [34][35][36][37] In the present study, conventional GI (GI 1 ), difference of effective radius (∆R iso ,GI 2 ), and modified GI (GI 3 ) were compared. GI 1 and GI 2 (∆R iso ) were all based on the volume of 50% and 100% prescribed dose, whereas GI 2 tended to directly reflect the absolute distance between 50% and 100% prescribed dose. However, the drawback of this index is that the shape of the isodose volume is not considered. When using GI 1 and GI 2 to evaluate the dose falloff for CK and EDGE plans, GI 1 had lower values in CK plans, whereas GI 2 had lower values in EDGE plans, mainly due to the shape of the isodose volume. According the Figure 1, the shape of 50% isodose line was more irregular in EDGE plans than CK plans. According the equation (3) of mGI, the PTV was applied to substitute the denominator of GI 1 to evaluate the dose gradient based on the TV. At the same time, mGI was also interpreted as: mGI = GI × VRI / TV = GI × CI 1 , mainly taking into account the degree of conformity. [35][36][37] The results of mGI (GI 3 ) in Table 3 showed that the EDGE plans had lower values, as well as the GI 2 , with statistical significance (P = 0.011).
CI, HI, and GI as an effective tool can facilitate the work of evaluating the treatment planning to quantify the conformity, uniformity of dose distribution, and dose gradient. There are several limitations to these three types index. The information of target location and shape are not considered in the equation of CI. There is also a lack of information about the possible relationship between these parameters and clinical data. Hence, the development of these parameters should be correlated with the local control and complications in the future research, in which better conformity, homogeneity, and steeper dose fall-off are associated with a better clinical outcome.
The present study were carried out to analyze the different definitions of CI, HI, and dose GIs to quality the dose distribution in SBRT plans. For the conformity index, the CN (CI 4 ) proposed by Van't Riet et al. could be more effective than others when considering the TV, prescription dose volume, and irradiated TV. For the HI, the HI 3 , HI 4 , and S-index could also be recommended to quality the dose fall-off than HI 1 and HI 2 , which mainly reduce the effect of grid size on point dose.
As for dose gradient, the ∆R iso and mGI show slight superiority compared with GI 1 , according to the present study.