Nanodosimetric quantities and RBE of a clinically relevant carbon-ion beam

Purpose: Although carbon-ion therapy is becoming increasingly attractive to the treatment of tumors, details about the ionization pattern formed by therapeutic carbon-ion beam in tissue have not been fully investigated. In this work, systematic calculations for the nanodosimetric quantities and relative biological effectiveness (RBE) of a clinically relevant carbon-ion beam were studied for the first time.

Methods: The method combining both track structure and condensed history Monte Carlo (MC) simulations was adopted to calculate the nanodosimetric quantities. Fragments and energy spectra at different positions of the radiation field of a clinically relevant carbon-ion pencil beam were generated by means of MC simulations in water. Nanodosimetric quantities such as mean ionization cluster size ( $M_1$ ), the first moment of conditional cluster size ( $M_1^{C_2}$ ), cumulative probability ( $F_2$ ), and conditional cumulative probability ( $F_3^{C_2}$ ) at these positions were then acquired based on the spectra and the pre-calculated nanodosimetric database created by track structure MC simulations. What's more, a novel approach to calculate RBE based on the said nanodosimetric quantities was introduced. The RBE calculations were then conducted for the carbon-ion beam at different water-equivalent depths.

Results: Lateral distributions at various water-equivalent depths of both the nanodosimetric quantities and RBE values were obtained. The values of $M_1$ , $M_1^{C_2}$ , $F_2$ , and $F_3^{C_2}$ were 1.49, 2.67, 0.30, and 0.38 at the plateau at the beam central axis and maximized at 2.79, 5.69, 0.47, and 0.68 at the depths around the Bragg peak, respectively. At a given depth, $M_1$ and $F_2$ decreased laterally with increasing the distance to the beam central axis while $M_1^{C_2}$ and $F_3^{C_2}$ remained nearly unchanged at first and then decreased except for $M_1^{C_2}$ at the rising edge of the Bragg peak. The calculated RBE values were 1.07 at the plateau and 3.13 around the Bragg peak. Good agreement between the calculated RBE values and experimental data was obtained.

Conclusions: Different nanodosimetric quantities feature the track structure of therapeutic carbon-ion beam in different manners. Detailed ionization patterns generated by carbon-ion beam could be characterized by nanodosimetric quantities. Moreover the combined method adopted in this work to calculate nanodosimetric quantities is not only valid but also convenient. Nanodosimetric quantities are significantly helpful for the RBE calculations in carbon-ion therapy.