A phenomenological relative biological effectiveness approach for proton therapy based on an improved description of the mixed radiation field.

Proton therapy treatment planning systems (TPSs) are based on the assumption of a constant relative biological effectiveness (RBE) of 1.1 without taking into account the found in vitro experimental variations of the RBE as a function of tissue type, linear energy transfer (LET) and dose. The phenomenological RBE models available in literature are based on the dose-averaged LET (LET D ) as an indicator of the physical properties of the proton radiation field. The LET D values are typically calculated taking into account primary and secondary protons, neglecting the biological effect of heavier secondaries. In this work, we have introduced a phenomenological RBE approach which considers the biological effect of primary protons, and of secondary protons, deuterons, tritons (Z = 1) and He fragments (3He and 4He, Z = 2). The calculation framework, coupled with a Monte Carlo (MC) code, has been successfully benchmarked against clonogenic in vitro data measured in this work for two cell lines and then applied to determine biological quantities for spread-out Bragg peaks and a prostate and a head case. The introduced RBE formalism, which depends on the mixed radiation field, the dose and the ratio of the linear-quadratic model parameters for the reference radiation [Formula: see text], predicts, when integrated in an MC code, higher RBE values in comparison to LET D -based parameterizations. This effect is particular enhanced in the entrance channel of the proton field and for low [Formula: see text] tissues. For the prostate and the head case, we found higher RBE-weighted dose values up to about 5% in the entrance channel when including or neglecting the Z = 2 secondaries in the RBE calculation. TPSs able to proper account for the mixed radiation field in proton therapy are thus recommended for an accurate determination of the RBE in the whole treatment field.

Biologically optimized helium ion plans: calculation approach and its in vitro validation.

Treatment planning studies on the biological effect of raster-scanned helium ion beams should be performed, together with their experimental verification, before their clinical application at the Heidelberg Ion Beam Therapy Center (HIT). For this purpose, we introduce a novel calculation approach based on integrating data-driven biological models in our Monte Carlo treatment planning (MCTP) tool. Dealing with a mixed radiation field, the biological effect of the primary (4)He ion beams, of the secondary (3)He and (4)He (Z = 2) fragments and of the produced protons, deuterons and tritons (Z = 1) has to be taken into account. A spread-out Bragg peak (SOBP) in water, representative of a clinically-relevant scenario, has been biologically optimized with the MCTP and then delivered at HIT. Predictions of cell survival and RBE for a tumor cell line, characterized by [Formula: see text] Gy, have been successfully compared against measured clonogenic survival data. The mean absolute survival variation ([Formula: see text]) between model predictions and experimental data was 5.3% ± 0.9%. A sensitivity study, i.e. quantifying the variation of the estimations for the studied plan as a function of the applied phenomenological modelling approach, has been performed. The feasibility of a simpler biological modelling based on dose-averaged LET (linear energy transfer) has been tested. Moreover, comparisons with biophysical models such as the local effect model (LEM) and the repair-misrepair-fixation (RMF) model were performed. [Formula: see text] values for the LEM and the RMF model were, respectively, 4.5% ± 0.8% and 5.8% ± 1.1%. The satisfactorily agreement found in this work for the studied SOBP, representative of clinically-relevant scenario, suggests that the introduced approach could be applied for an accurate estimation of the biological effect for helium ion radiotherapy.

Noise evaluation of Compton camera imaging for proton therapy.

Compton Cameras emerged as an alternative for real-time dose monitoring techniques for Particle Therapy (PT), based on the detection of prompt-gammas. As a consequence of the Compton scattering process, the gamma origin point can be restricted onto the surface of a cone (Compton cone). Through image reconstruction techniques, the distribution of the gamma emitters can be estimated, using cone-surfaces backprojections of the Compton cones through the image space, along with more sophisticated statistical methods to improve the image quality. To calculate the Compton cone required for image reconstruction, either two interactions, the last being photoelectric absorption, or three scatter interactions are needed. Because of the high energy of the photons in PT the first option might not be adequate, as the photon is not absorbed in general. However, the second option is less efficient. That is the reason to resort to spectral reconstructions, where the incoming γ energy is considered as a variable in the reconstruction inverse problem. Jointly with prompt gamma, secondary neutrons and scattered photons, not strongly correlated with the dose map, can also reach the imaging detector and produce false events. These events deteriorate the image quality. Also, high intensity beams can produce particle accumulation in the camera, which lead to an increase of random coincidences, meaning events which gather measurements from different incoming particles. The noise scenario is expected to be different if double or triple events are used, and consequently, the reconstructed images can be affected differently by spurious data. The aim of the present work is to study the effect of false events in the reconstructed image, evaluating their impact in the determination of the beam particle ranges. A simulation study that includes misidentified events (neutrons and random coincidences) in the final image of a Compton Telescope for PT monitoring is presented. The complete chain of detection, from the beam particle entering a phantom to the event classification, is simulated using FLUKA. The range determination is later estimated from the reconstructed image obtained from a two and three-event algorithm based on Maximum Likelihood Expectation Maximization. The neutron background and random coincidences due to a therapeutic-like time structure are analyzed for mono-energetic proton beams. The time structure of the beam is included in the simulations, which will affect the rate of particles entering the detector.

Distributions of secondary particles in proton and carbon-ion therapy: a comparison between GATE/Geant4 and FLUKA Monte Carlo codes.

Monte Carlo simulations play a crucial role for in-vivo treatment monitoring based on PET and prompt gamma imaging in proton and carbon-ion therapies. The accuracy of the nuclear fragmentation models implemented in these codes might affect the quality of the treatment verification. In this paper, we investigate the nuclear models implemented in GATE/Geant4 and FLUKA by comparing the angular and energy distributions of secondary particles exiting a homogeneous target of PMMA. Comparison results were restricted to fragmentation of (16)O and (12)C. Despite the very simple target and set-up, substantial discrepancies were observed between the two codes. For instance, the number of high energy (>1 MeV) prompt gammas exiting the target was about twice as large with GATE/Geant4 than with FLUKA both for proton and carbon ion beams. Such differences were not observed for the predicted annihilation photon production yields, for which ratios of 1.09 and 1.20 were obtained between GATE and FLUKA for the proton beam and the carbon ion beam, respectively. For neutrons and protons, discrepancies from 14% (exiting protons-carbon ion beam) to 57% (exiting neutrons-proton beam) have been identified in production yields as well as in the energy spectra for neutrons.

Radiation transport calculations and simulations.

This article is an introduction to the Monte Carlo method as used in particle transport. After a description at an elementary level of the mathematical basis of the method, the Boltzmann equation and its physical meaning are presented, followed by Monte Carlo integration and random sampling, and by a general description of the main aspects and components of a typical Monte Carlo particle transport code. In particular, the most common biasing techniques are described, as well as the concepts of estimator and detector. After a discussion of the different types of errors, the issue of quality assurance is briefly considered.

Human exposure to space radiation: role of primary and secondary particles.

Human exposure to space radiation implies two kinds of risk, both stochastic and deterministic. Shielding optimisation therefore represents a crucial goal for long-term missions, especially in deep space. In this context, the use of radiation transport codes coupled with anthropomorphic phantoms allows to simulate typical radiation exposures for astronauts behind different shielding, and to calculate doses to different organs. In this work, the FLUKA Monte Carlo code and two phantoms, a mathematical model and a voxel model, were used, taking the Galactic Cosmic Rays (GCR) spectra from the model of Badhwar and O'Neill. The time integral spectral proton fluence of the August 1972 Solar Particle Event (SPE) was represented by an exponential function. For each aluminium shield thickness, besides total doses the contributions from primary and secondary particles for different organs and tissues were calculated separately. More specifically, organ-averaged absorbed doses, dose equivalents and a form of 'biological dose', defined on the basis of initial (clustered) DNA damage, were calculated. As expected, the SPE doses dramatically decreased with increasing shielding, and doses in internal organs were lower than in skin. The contribution of secondary particles to SPE doses was almost negligible; however it is of note that, at high shielding (10 g cm(-2)), most of the secondaries are neutrons. GCR organ doses remained roughly constant with increasing Al shielding. In contrast to SPE results, for the case of cosmic rays, secondary particles accounted for a significant fraction of the total dose.

The FLUKA code: new developments and application to 1 GeV/n iron beams.

The modeling of ion transport and interactions in matter is a subject of growing interest, driven by the continuous increase of possible application fields. These include hadron therapy, dosimetry, and space missions, but there are also several issues involving fundamental research, accelerator physics, and cosmic ray physics, where a reliable description of heavy ion induced cascades is important. In the present work, the capabilities of the FLUKA code for ion beams will be briefly recalled and some recent developments presented. Applications of the code to the simulation of therapeutic carbon, nitrogen and oxygen ion beams, and of iron beams, which are of direct interest for space mission related experiments, will be also presented together with interesting consideration relative to the evaluation of dosimetric quantities. Both applications involve ion beams in the AGeV range.

The FLUKA code for space applications: recent developments.

The FLUKA Monte Carlo transport code is widely used for fundamental research, radioprotection and dosimetry, hybrid nuclear energy system and cosmic ray calculations. The validity of its physical models has been benchmarked against a variety of experimental data over a wide range of energies, ranging from accelerator data to cosmic ray showers in the earth atmosphere. The code is presently undergoing several developments in order to better fit the needs of space applications. The generation of particle spectra according to up-to-date cosmic ray data as well as the effect of the solar and geomagnetic modulation have been implemented and already successfully applied to a variety of problems. The implementation of suitable models for heavy ion nuclear interactions has reached an operational stage. At medium/high energy FLUKA is using the DPMJET model. The major task of incorporating heavy ion interactions from a few GeV/n down to the threshold for inelastic collisions is also progressing and promising results have been obtained using a modified version of the RQMD-2.4 code. This interim solution is now fully operational, while waiting for the development of new models based on the FLUKA hadron-nucleus interaction code, a newly developed QMD code, and the implementation of the Boltzmann master equation theory for low energy ion interactions.

Nuclear reactions in Monte Carlo codes.

The physics foundations of hadronic interactions as implemented in most Monte Carlo codes are presented together with a few practical examples. The description of the relevant physics is presented schematically split into the major steps in order to stress the different approaches required for the full understanding of nuclear reactions at intermediate and high energies. Due to the complexity of the problem, only a few semi-qualitative arguments are developed in this paper. The description will be necessarily schematic and somewhat incomplete, but hopefully it will be useful for a first introduction into this topic. Examples are shown mostly for the high energy regime, where all mechanisms mentioned in the paper are at work and to which perhaps most of the readers are less accustomed. Examples for lower energies can be found in the references.

The FLUKA radiation transport code and its use for space problems.

FLUKA is a multiparticle transport code capable of handling hadronic and electromagnetic showers up to very high energies (100 TeV), widely used for radioprotection and detector simulation studies. The physical models embedded into FLUKA are briefly described and their capabilities demonstrated against available experimental data. The complete modelling of cosmic ray showers in the earth atmosphere with FLUKA is also described, and its relevance for benchmarking the code for space-like environments discussed. Finally, the ongoing developments of the physical models of the code are presented and discussed.