Cell Survival Computation via the Generalized Stochastic Microdosimetric Model (GSM2); Part II: Numerical Results

In the present paper we numerically investigate, using Monte Carlo simulation, the theoretical results predicted by the Generalized Stochastic Microdosimetric Model (GSM2), as shown in the published companion paper. Taking advantage of the particle irradiation data ensemble (PIDE) dataset, we calculated GSM2 biological parameters of human salivary gland (HSG) and V79 cell lines. Further, exploiting the TOPAS-microdosimetric extension, we simulated the microdosimetric spectra of different radiation fields of therapeutic interest generated by four different ions (protons, helium-4, carbon-12 and oxygen-16) each at three different residual ranges. We investigated the properties of the initial damage distributions as well as the cell survival curve predicted by GSM2, focusing especially on the non-Poissonian effects naturally included in the model. GSM2 successfully computed cell survival curves, accurately describing experimental behavior even under challenging LET and dose conditions.

Microdosimetric analysis of the radiation quality of two different proton beams in the distal edge of the depth-dose profile

Proton-therapy exploits the advantageous depth-dose profile of protons to induce the highest damage to tumoral cells in the last millimetres of their range in sharp Bragg Peak. To cover the whole tumoral volume, beams of different energies are combined to create the Spread Out Bragg Peak (SOBP). In passive modulated beams, the energy spread is created with modulators in which the highest energy beam is degraded through different thicknesses of calibrated plastic materials. The highest energy is chosen depending on the deepest point that needs to be treated. This study aims to investigate differences in the radiation quality in the distal edge of SOBP beams with different initial energy and modulation techniques based on microdosimetric measurements with mini Tissue-Equivalent Proportional Counters. The beams investigated are the 62 MeV proton SOBP of the clinical facility of CATANA and the 148 MeV proton SOBP of the research beam line of the proton-therapy centre of Trento.

Microdosimetry of a 62-MeV clinical proton beam with five detectors

In proton therapy, most treatment planning systems (TPS) use a fixed relative biological effectiveness (RBE) of 1.1 all along the depth-dose profile. Innovative TPS are now investigated considering the variability of RBE with radiation quality. New TPS need an experimental verification in the quality assurance (QA) routine in clinics, but RBE data are usually obtained with radiobiological measurements that are time consuming and not suitable for daily QA. Microdosimetry is a useful tool based on physical measurements which can monitor the radiation quality. Several microdosimeters are available in different research institutions, which could potentially be used for the QA in TPS. In this study, the response functions of five detectors in the same 62-MeV proton Spread Out Bragg Peak is compared in terms of spectral distributions and their average values and microdosimetric RBE. Their different response function has been commented and must be considered in the clinical practice.

Generalized stochastic microdosimetric model: The main formulation

The present work introduces a rigorous stochastic model, called the generalized stochastic microdosimetric model (GSM^{2}), to describe biological damage induced by ionizing radiation. Starting from the microdosimetric spectra of energy deposition in tissue, we derive a master equation describing the time evolution of the probability density function of lethal and potentially lethal DNA damage induced by a given radiation to a cell nucleus. The resulting probability distribution is not required to satisfy any a priori conditions. After the initial assumption of instantaneous irradiation, we generalized the master equation to consider damage induced by a continuous dose delivery. In addition, spatial features and damage movement inside the nucleus have been taken into account. In doing so, we provide a general mathematical setting to fully describe the spatiotemporal damage formation and evolution in a cell nucleus. Finally, we provide numerical solutions of the master equation exploiting Monte Carlo simulations to validate the accuracy of GSM^{2}. Development of GSM^{2} can lead to improved modeling of radiation damage to both tumor and normal tissues, and thereby impact treatment regimens for better tumor control and reduced normal tissue toxicities.

Microdosimetric measurements as a tool to assess potential in-field and out-of-field toxicity regions in proton therapy

Relative biological effectiveness (RBE) variations are thought to be one of the primary causes of unexpected normal-tissue toxicities during tumor treatments with charged particles. Unlike carbon therapy, where treatment planning is optimized on the basis of the RBE-weighted dose, a constant RBE value of 1.1 is currently used in proton therapy. Assuming a uniform value can lead to under- or over-dosage, not just to the tumor but also to surrounding normal tissue. RBE changes have been linked with dose/fraction, the biological endpoint and beam properties. Understanding radiation quality and the associated RBE can improve the prediction of normal-tissue toxicities. In this study, we exploited microdosimetry for characterizing radiation quality in proton therapy in-field, and off-beam at 20 (beam edge), 50 (close out-of-field) and 100 (far out-of-field) mm from the beam center. We measured the lineal energy y spectra in a water phantom irradiated with 152 MeV protons, from which beam quality as well as the physical dose could be obtained. Taking advantage of the linear quadratic model and a modified version of the microdosimetric kinetic model, the microdosimetric data were combined with radiobiological parameters (α and β) of human salivary gland tumor cells for assessing cell survival RBE and RBE-weighted dose. The results indicate that if a dose of 60 Gy is delivered to the peak, the beam edge receives up to 6 Gy while the close and far out-of-field regions receive doses on the order of 10^-3 Gy and 10^-4 Gy, respectively. The RBE estimate in-beam shows large variations, ranging from 1.0 ± 0.2 at the entrance channel to 2.51 ± 0.15 at the tail. The beam edge follows a similar trend but the RBE calculated at the Bragg peak depth is 2.27 ± 0.17, i.e. twice the RBE in-beam (1.05 ± 0.15). Out-of-field, the estimated RBE is always significantly higher than 1.1 and increases with increasing lateral distance, reaching the overall highest value of 3.4 ± 0.3 at a depth of 206 mm and a lateral distance of 10 mm. The combination of RBE and dose into the biological dose points to the beam edge and the end-of-range in-beam as the areas with the highest risk of potential toxicities.