Linear Energy Transfer and Relative Biological Effectiveness Investigation of Various Structures for a Cohort of Proton Patients With Brain Tumors

Abstract

Purpose: The current knowledge on biological effects associated with proton therapy is limited. Therefore, we investigated the distributions of dose, dose-averaged linear energy transfer (LET_d), and the product between dose and LET_d (DLET_d) for a patient cohort treated with proton therapy. Different treatment planning system features and visualization tools were explored.

Methods and materials: For a cohort of 24 patients with brain tumors, the LET_d, DLET_d, and dose was calculated for a fixed relative biological effectiveness value and 2 variable models: plan-based and phenomenological. Dose threshold levels of 0, 5, and 20 Gy were imposed for LET_d visualization. The relationship between physical dose and LET_d and the frequency of LET_d hotspots were investigated.

Results: The phenomenological relative biological effectiveness model presented consistently higher dose values. For lower dose thresholds, the LET_d distribution was steered toward higher values related to low treatment doses. Differences up to 26.0% were found according to the threshold. Maximum LET_d values were identified in the brain, periventricular space, and ventricles. An inverse relationship between LET_d and dose was observed. Frequency information to the domain of dose and LET_d allowed for the identification of clusters, which steer the mean LET_d values, and the identification of higher, but sparse, LET_d values.

Conclusions: Identifying, quantifying, and recording LET distributions in a standardized fashion is necessary, because concern exists over a link between toxicity and LET hotspots. Visualizing DLET_d or dose × LET_d during treatment planning could allow for clinicians to make informed decisions.

Figure 1

Relative biological effectiveness (RBE) dose distributions for a selection of organs at risk, calculated using the constant clinical factor of 1.1 (red), McNamara's model (green; α/β of 2 Gy), and Unkelbach's model (blue). Both histograms and bars present the frequency distribution (differential dose and number of voxels per unit of RBE dose). The boxplots show the interquartile range, median, and outliers.

Figure 2

Dose-averaged linear energy transfer (LET_d) distributions for a selection of organs at risk, calculated using dose thresholds of 0 Gy (red), 5 Gy (blue), and 20 Gy (green). Both histograms and bars present the frequency distribution, or the number of voxels per unit of LET_d value. The boxplots show the interquartile range, median, and outliers according to the individual distribution.

Figure 3

Product between dose and dose-averaged linear energy transfer (DLET_d) distributions for a selection of organs at risk, calculated using 0 Gy (red), 5 Gy (blue), and 20 Gy (green) relative biological effectiveness dose threshold. Both histograms and bars present the frequency distribution, or the number of voxels per unit of DLET_d value. The boxplots show the interquartile range, median, and outliers according to the individual distribution.

Figure 4

(A) Example patient with planning dose, dose-averaged linear energy transfer (LET_d), and product between dose and dose-averaged linear energy transfer (DLET_d) distributions with the optic chiasm contoured in yellow. (B) Distribution of dose and LET_d values for the chiasm (orange) and pituitary (blue) for all patients (N = 24) in the study. (C, D) Relationship between mean values of dose, LET_d, and DLET_d (for dose threshold of 20 Gy) for the chiasm and pituitary gland. Dose, LET_d, and DLET_d are represented by the blue, red, and green axes, respectively.

Figure 5

Dose and dose-averaged linear energy transfer (LET_d) histograms of a selection of investigated structures for a single patient. Dose and LET_d values are represented on the x- and y-axes, respectively, for each subplot. Next to each structure name, the percentage of voxels >0 is indicated, as used for the graph. The color bar on the right indicates the frequency in the same scale for all plots.

Figure 6

(A) Clinical target volume (CTV; gray color map) and periventricular space (PVS; multiple colors) dose-averaged linear energy transfer (LET_d) distribution spatial representation. (B) Dose–LET_d histograms of the PVS for different patients. Dose and LET_d values are represented on the x- and y-axes, respectively, for each subplot. The color bar on the right indicates the frequency in the same scale for all plots.