Investigation on the physical dose filtered by linear energy transfer for treatment plan evaluation in carbon ion therapy

Abstract

Background: Large tumor size has been reported as a predicting factor for inferior clinical outcome in carbon ion radiotherapy (CIRT). Besides the clinical factors accompanied with such tumors, larger tumors receive typically more low linear energy transfer (LET) contributions than small ones which may be the underlying physical cause. Although dose averaged LET is often used as a single parameter descriptor to quantify the beam quality, there is no evidence that this parameter is the optimal clinical predictor for the complex mixed radiation fields in CIRT.

Purpose: Purpose of this study was to investigate on a novel dosimetric quantity, namely high-LET-dose ( $D_{>L_{\mathrm{thr}}}$ , the physical dose filtered based on an LET threshold) as a single parameter estimator to differentiate between carbon ion treatment plans (cTP) with a small and large tumor volume.

Methods: Ten cTPs with a planning target volume, $\mathrm{PTV}\ge 500{\mathrm{cm}}^3$ (large) and nine with a $\mathrm{PTV}<500{\mathrm{cm}}^3$ (small) were selected for this study. To find a reasonable LET threshold ( $L_{\mathrm{thr}}$ ) that results in a significant difference in terms of $D_{>L_{\mathrm{thr}}}$ , the voxel based normalized high-LET-dose ( ${\hat{D}}_{>L_{\mathrm{thr}}}$ ) distribution in the clinical target volume (CTV) was studied on a subset (12 out of 19 cTPs) for 18 LET thresholds, using standard distribution descriptors (mean, variance and skewness). The classical dose volume histogram concept was used to evaluate the $D_{>L_{\mathrm{thr}}}$ and ${\hat{D}}_{>L_{\mathrm{thr}}}$ distributions within the target of all 19 cTPs at the before determined $L_{\mathrm{thr}}$ . Statistical significance of the difference between the two groups in terms of mean $D_{>L_{\mathrm{thr}}}$ and ${\hat{D}}_{>L_{\mathrm{thr}}}$ volume histogram parameters was evaluated by means of (two-sided) t-test or Mann-Whitney-U-test. In addition, the minimum target coverage at the above determined $L_{\mathrm{thr}}$ was compared and validated against three other thresholds to verify its potential in differentiation between small and large volume tumors.

Results: An $L_{\mathrm{thr}}$ of approximately $30\mathrm{keV}/\mu m$ was found to be a reasonable threshold to classify the two groups. At this threshold, the $D_{>L_{\mathrm{thr}}}$ and ${\hat{D}}_{>L_{\mathrm{thr}}}$ were significantly larger ( $p<0.05$ ) in small CTVs. For the small tumor group, the near-minimum and median $D_{>L_{\mathrm{thr}}}$ (and ${\hat{D}}_{>L_{\mathrm{thr}}}$ ) in the CTV were in average $9.3\pm 1.5\mathrm{Gy}$ (0.31 ± 0.08) and $13.6\pm 1.6\mathrm{Gy}$ (0.46 ± 0.06), respectively. For the large tumors, these parameters were $6.6\pm 0.2\mathrm{Gy}$ (0.20 ± 0.01) and $8.6\pm 0.4\mathrm{Gy}$ (0.28 ± 0.02). The difference between the two groups in terms of mean near-minimum and median $D_{>L_{\mathrm{thr}}}$ ( ${\hat{D}}_{>L_{\mathrm{thr}}}$ ) was 2.7 Gy (11%) and 5.0 Gy (18%), respectively.

Conclusions: The feasibility of high-LET-dose based evaluation was shown in this study where a lower $D_{>L_{\mathrm{thr}}}$ was found in cTPs with a large tumor size. Further investigation is needed to draw clinical conclusions. The proposed methodology in this work can be utilized for future high-LET-dose based studies.

Keywords: LET-based filtered dose; carbon ion radiotherapy; dirty dose; high-LET-dose; treatment plan evaluation.