A new homogeneity index definition for evaluation of radiotherapy plans

Abstract Purpose The goal of this study was to define a new homogeneity index (HI) to evaluate dose homogeneity within a target volume. Materials and Methods The new HI is based on the area under an ideal dose‐volume histogram curve (IA), the area under the achieved dose‐volume histogram curve (AA), and the overlapping area between the IA and AA (OA). It is defined as the ratio of the square of OA to the product of the IA and AA. To evaluate the performance of the new HI, 88 cases were selected and two plans were designed for each case. The homogeneity of the two plans was first evaluated by three physicists, with their judgments forming the evaluation standard and then evaluated by the new HI and other HIs of D max/Dp, D 5/D 95, (D 2 − D 98)/Dp, (D 2 − D 98)/D 50 and S‐index. An evaluation was determined to be accurate if its result was agreed upon by physicists. The percentage accuracy of evaluation was calculated as the ratio of the number of accurate evaluations to the total number of evaluations. Pearson's chi‐square test was performed for statistical analysis. Results The percentage accuracies of the new HI, D max/D p, D 5/D 95, (D 2 − D 98)/Dp, (D 2 − D 98)/D 50, and S‐index were 98.51%, 88.80%, 94.78%, 94.78%, 96.27%, and 97.01%, respectively. The newly defined HI had the highest accuracy of all the HIs, with the difference being statistically significant (P < 0.05). Conclusions The newly defined HI was shown to be effective in the evaluation of dose homogeneity, and we recommended it for evaluating the homogeneity of radiotherapy plans.

future technology and treatment protocols. In turn, this can help us to find the means by which treatment plans can be improved in future.
Several HIs have been reported in the literature, [9][10][11][12][13] including D max /D p , D 5 /D 95 , (D 2 − D 98 )/D p , (D 2 − D 98 )/D 50 , and S-index. The conventional HI of D max /D p is defined as the ratio of the maximum dose (D max ) in the target volume to the prescribed dose (D p ), with a value closer to one indicating better homogeneity. 9 The D max value is sensitive to calculation parameters, such as grid size and grid placement, so the D max /D p index may not be reliable. The HI of D 5 /D 95 , choosing the minimum dose in a target volume rather than a dose point, is described as the ratio of the minimum dose in 5% of the target volume (D 5 ) to the minimum dose in 95% of the target volume (D 95 ). 10 Another HI is calculated as (D 2 − D 98 )/D p , 11 where D 2 and D 98 are the minimum dose covering 2% and 98% of the target volume respectively, although report 83 of the ICRU suggests (D 2 − D 98 )/D 50 instead, 12

2.A | Definition of the new HI
The ideal DVH for a target volume would be a step function, with 100% of the target receiving exactly the prescribed dose. However, the A-DVH deviates from this step function. The new HI can be defined as: where IA is the area under the I-DVH curve, AA is the area under the A-DVH curve, and OA is the overlapping area between IA and AA. The relationship between IA, AA, and OA is shown in Fig. 1 where V is the target volume. Formula (2) depends on the prescribed doses and the volumes of the targets, and does not depend on the other variables of the radiotherapy plan. If a plan has only one steep dose gradient, formula (2) for the I-DVH is simplified into a unit step function, and the I-DVH of PTV 1 is shown in Fig. 2. If a plan has two steep dose gradients and two target volumes, the I-DVH of PTV 1 is simplified into a second-order step function. The I-DVH of PTV 1 and PTV 2 are shown in Fig. 3.

2.D | Statistical analysis
To determine whether there is a significant difference among the         Table 3.

| DISCUSSION
In this study, we defined a new HI and evaluated it alongside previ-  evaluation, but it cannot give a specific quantitative evaluation.
Despite the benefits described above, the new HI also has limitation, and its evaluation sensitivity is not as high as the S-index. This may affect the percentage accuracy of the evaluation. If two achieved DVHs are a little different, the quantitative evaluations achieved using the new HI could be the same. Therefore, further work to improve the sensitivity of the evaluation is necessary.

| CONCLUSIONS
In the present study, a new HI definition is given, one which evalu-

CONFLI CT OF INTEREST
None.