Microdosimetry calculations in situ for clinically relevant photon sources and their correlation with the early DNA damage response

Abstract

Background: Radiobiological data suggests variations in relative biological effectiveness (RBE) between clinically used photon-based sources. A microdosimetric formalism using Monte Carlo (MC) methods can mechanistically describe the photon RBE. Experimentally derived RBE based on DNA double-strand breaks ( ${\mathrm{RBE}}_{\mathrm{DSB}}$ ) has been shown to scale with the microdosimetry quantity dose-mean lineal energy ( $y_D$ ).

Purpose: To calculate microdosimetric spectra for clinically relevant photon sources, spanning from soft x-rays produced by a 50 kVp x-ray source through various brachytherapy sources up to a 6 MV medical linac. Furthermore, we investigated the correlation between ${\mathrm{RBE}}_{\mathrm{DSB}}$ and $y_D$ of different photon sources.

Methods: Photon sources simulated include low-energy x-rays (50 kVp), orthovoltage x-rays (225 kVp), high-dose-rate brachytherapy sources (⁷⁵Se, ¹⁹²Ir and ⁶⁰Co), and a 6 MV medical linac. Secondary electron spectra at the cellular level were calculated for in vitro cell irradiation setups using Geant4 MC-based packages, RapidBrachyMCTPS and RapidExternalBeam. The obtained spectra were used in MicroDose, a microdosimetry simulation software, to obtain microdosimetric quantities, including single-event lineal energy ( $y$ ) and specific energy ( $z$ ) spectra, and dose-mean and frequency-mean quantities ( $y_F$ , $y_D$ , $z_F^s$ , $z_D^s$ ). Uniform spherical targets (1-14 $\mu m$ radius) and realistic HeLa and PC3 cell nucleus models were simulated using cell size data obtained from literature and nuclei size data from confocal microscopy imaging. Radiobiological experiments using $\gamma \text{H2AX}$ foci quantified DNA double-strand breaks for HeLa and PC3 cells after irradiations with 50 and 225 kVp, ¹⁹²Ir, and 6 MV linac, and ${\mathrm{RBE}}_{\mathrm{DSB}}$ was determined using 225 kVp as the reference.

Results: The calculated $y_D$ ( $y_F$ ) is within the 3.5-1.2 keV/ $\mu m$ range (1.8-0.2 keV/ $\mu m$ ) for 1 $\mu m$ simulated target size between the lowest energy 50 kVp x-ray source and the highest energy 6 MV linac source, respectively. For the HeLa and PC3 cell nuclei models based on microscopy data, $y_D$ ( $y_F$ ) spans from 1.6 to 0.6 keV/ $\mu m$ (0.7 to 0.2 keV/ $\mu m$ ). When compared between different target sizes, $y_D$ ( $y_F$ ) ranges from 3.5 to 1.0 (1.8-0.4) keV/ $\mu m$ between 1 and 10 $\mu m$ radius targets for the 50 kVp x-ray source. A smaller change is observed for 6 MV linac, ranging from 1.2 to 0.5 keV/ $\mu m$ and 0.23 to 0.22 keV/ $\mu m$ for $y_D$ and $y_F$ , respectively. For the simulated ⁷⁵Se source currently under investigation, the calculated $y_D$ values are 11%-24% higher relative to those of ¹⁹²Ir in the range of target sizes between 1 and 14 $\mu m$ in radius. ${\mathrm{RBE}}_{\mathrm{DSB}}$ for HeLa cells was 1.4 $\pm$ 0.7 for 50 kVp x-rays, 0.5 $\pm$ 0.2 for ¹⁹²Ir, and 0.7 $\pm$ 0.4 for 6 MV linac irradiations. For PC3 cells, ${\mathrm{RBE}}_{\mathrm{DSB}}$ was 1.3 $\pm$ 0.6, 0.8 $\pm$ 0.4 and 0.5 $\pm$ 0.3 for 50 kVp, ¹⁹²Ir and 6 MV linac, respectively. Measured ${\mathrm{RBE}}_{\mathrm{DSB}}$ values are consistent with $y_D$ ratios of the corresponding photon sources for HeLa and PC3 nucleus models.

Conclusions: Microdosimetric spectra strongly depend on the simulated energy of photon sources and target size, with $y_D$ and $z_D^s$ decreasing by a factor of $\approx$ 2-3 between diagnostic 50 kVp and 6 MV therapeutic x-rays for target sizes from 1-14 $\mu m$ in radius. The early damage ${\mathrm{RBE}}_{\mathrm{DSB}}$ indicates this stochastic change in energy density between various photon sources as the yields of $\gamma \text{H2AX}$ foci per nucleus scale with $y_D$ of the source.

Keywords: double‐strand breaks; microdosimetry; multiscale dosimetry; relative biological effectiveness.

FIGURE 1

Experimental setups for in vitro cell irradiations: (a) 50 kVp low‐energy X‐rays setup, (b) ¹⁹²Ir irradiation setup with the afterloader, (c) linac setup for 6 MV irradiations.

FIGURE 2

Top panels: Photon energy spectra for external beam sources used for cell irradiations (a) and for brachytherapy sources (b). Bottom panels: secondary electron energy spectrum scored in the cell volume for the same sources (c and d).

FIGURE 3

Dose‐mean lineal energy for ⁶⁰Co reported in the literature, measured experimentally and calculated by Monte Carlo as a function of mean chord length. Simulated fixed‐size cell models correspond to eight chord lengths from 1.33 to 18.67 $\mu \mathrm{m}$ (blue squares).

FIGURE 4

Dose‐weighted lineal energy distributions $yd(y)$ shown in each panel for a different radiation quality: (a) 50 kVp, (b) 225 kVp, (c) ⁷⁵Se, (d)¹⁹²Ir, (e) ⁶⁰Co, (f) 6 MV linac. Distributions in each panel correspond to different simulated target sizes ‐ 1, 5, 10 $\mu \mathrm{m}$ fixed radius, and HeLa (black line) and PC3 (green line) cell and nuclei models.

FIGURE 5

Dose‐weighted specific energy distributions $z_{s}d(z_s)$ shown in each panel for a different radiation quality: (a) 50 kVp, (b) 225 kVp, C) ⁷⁵Se, (d)¹⁹²Ir, (e) ⁶⁰Co, (f) 6 MV linac. Distributions in each panel correspond to different simulated target sizes ‐ 1, 5, 10 $\mu \mathrm{m}$ fixed radius and HeLa (black line) and PC3 (green line) cell and nuclei models.

FIGURE 6

Dose‐mean lineal energy ${\mathrm{y}}_{\mathrm{D}}$ for all simulated photon sources as a function of the mean chord length for fixed‐radius nuclei. The lines present fit the corresponding data points. The uncertainties shown are statistical only.

FIGURE 7

$\gamma \text{H2AX}$ foci and DAPI stained nuclei induced by 50 kVp x‐ray source (left) and 6 MV irradiations (right) in HeLa cells. Each row corresponds to a different delivered dose of 0 (control), 1, and 2 Gy. DAPI, 4',6‐diamidino‐2‐phenylindole.

FIGURE 8

$\gamma \text{H2AX}$ foci and DAPI stained nuclei induced by 50 kVp x‐ray source (left) and 6 MV irradiations (right) in PC3 cells. Each row corresponds to a different delivered dose of 0 (control), 1, and 2 Gy. DAPI, 4',6‐diamidino‐2‐phenylindole.

FIGURE 9

Number of $\gamma \text{H2AX}$ foci per nucleus for diagnostic x‐rays (a) and therapeutic external beam (b) 30 min after irradiation as a function of the administered dose. The data from this study for PC3 and HeLa cells are compared to the literature., , , The error bars are the weighted errors of three independent replicas; in each replica, average and standard deviation are calculated for more than 50 cells nuclei.

FIGURE 10

${\mathrm{RBE}}_{\mathrm{DSB}}$ at 1 Gy irradiation dose for the 50 kVp x‐ray source (a), ¹⁹²Ir (b), and 6 MV linac (C) for HeLa and PC3 cells after background subtraction. The reference radiation is 225 kVp x‐rays. The solid black line represents the ratio of ${\mathrm{y}}_{\mathrm{D}}$ for the cell models with each irradiation source, and the dashed blue line shows the ratio for the 1 $\mu \mathrm{m}$ target size. The error bars for the ratios are propagated from the 1 Gy number of foci for three independent replicas after background subtraction.