# A modified homogeneity index for multi- target radiotherapy plans by subtracting high-dose subvolumes

## TL;DR

This paper introduces a modified homogeneity index for multi-target radiotherapy plans that better aligns with clinical practice by adjusting how target volumes are calculated.

## Contribution

A novel homogeneity index calculation method is proposed by subtracting high-dose subvolumes from low-dose ones in multi-target radiotherapy.

## Key findings

- VPTVpro values were significantly smaller than original VPTVori for breast cancer and NPC target volumes.
- HIpro values were significantly lower than original HIori values for the same target volumes.
- Clinical experts agreed that the modified HI better reflects their practice for evaluating multi-target plans.

## Abstract

Considering the limitations of current homogeneity index (HI) in multi-target plans, we have redefined the volume (V)PTV in the formula for calculating the HI value of target volumes. This redefinition could provide a reference for clinical applications.

Since the three widely used HI formulas may not fully capture dose homogeneity in multi-target treatment plans, we have redefined the VPTV in the calculation formulas, which may allow for a better assessment of HI for the multi-target radiotherapy plans. Fifteen clinically treated breast cancer (BC) with conserving surgery patients and fifteen nasopharyngeal carcinoma (NPC) patients were chosen. We calculated the VPTV with the name of VPTVpro and the HIpro1, HIpro2, HIpro3. A paired, two-tailed non-parametric Wilcoxon signed-rank test was utilized to compare VPTVori and VPTVpro, HIori1 and HIpro1, HIori2 and HIpro2, HIori3 and HIpro3. The correlations between HIori1 and HIpro1, HIori2 and HIpro2, HIori3 and HIpro3 were also analyzed. We conducted a questionnaire survey among a panel of six senior radiation oncologists and physicists to validate the clinical applicability of this study.

For Planning Target Volume (PTV) of BC and PTV1 of NPC, the VPTVpro were significantly smaller than the VPTVori and HIpro were significantly lower than HIori. The correlation coefficient values of HIori1-HIpro1, HIori2-HIpro2, and HIori3-HIpro3 showed variations, though all demonstrated positive correlations with statistically significant p-values <0.01. The results for these two target volumes revealed a consistent pattern: the HIori1-HIpro1 pair exhibited the highest correlation coefficient values, while HIori2-HIpro2 consistently showed the lowest values. Meanwhile, clinical validation by the expert panel found that the VPTVpro and HIpro in this study do not affect clinical plan selection. All experts agreed that, compared to VPTVori and HIori, VPTVpro and HIpro better align with their clinical practice for evaluating multi-target radiotherapy plans.

The VPTVpro calculation subtracts the overlapping high-dose target volume from the low-dose target volume. This adjustment is intended to enable a more accurate assessment of dose HI specifically within the low-dose target. Additionally, the VPTVpro is also applicable for HI calculation in single-target volume. We suggest using the VPTVpro to calculate the HI of the target for multi-target plans such as BC with conserving surgery and NPC. Meanwhile, we recommend employing formula 1 for the calculation of HI among the three formulas.