A new approach for simulating inhomogeneous chemical kinetics.

In this paper, inhomogeneous chemical kinetics are simulated by describing the concentrations of interacting chemical species by a linear expansion of basis functions in such a manner that the coupled reaction and diffusion processes are propagated through time efficiently by tailor-made numerical methods. The approach is illustrated through modelling [Formula: see text]- and [Formula: see text]-radiolysis in thin layers of water and at their solid interfaces from the start of the chemical phase until equilibrium was established. The method's efficiency is such that hundreds of such systems can be modelled in a few hours using a single core of a typical laptop, allowing the investigation of the effects of the underlying parameter space. Illustrative calculations showing the effects of changing dose-rate and water-layer thickness are presented. Other simulations are presented which show the approach's capability to solve problems with spherical symmetry (an approximation to an isolated radiolytic spur), where the hollowing out of an initial Gaussian distribution is observed, in line with previous calculations. These illustrative simulations show the generality and the computational efficiency of this approach to solving reaction-diffusion problems. Furthermore, these example simulations illustrate the method's suitability for simulating solid-fluid interfaces, which have received a lot of experimental attention in contrast to the lack of computational studies.

On the Equivalence of the Biological Effect Induced by Irradiation of Clusters of Heavy Atom Nanoparticles and Homogeneous Heavy Atom-Water Mixtures.

A multiscale local effect model (LEM)-based framework was implemented to study the cell damage caused by the irradiation of clusters of gold nanoparticles (GNPs) under clinically relevant conditions. The results were compared with those obtained by a homogeneous mixture of water and gold (MixNP) irradiated under similar conditions. To that end, Monte Carlo simulations were performed for the irradiation of GNP clusters of different sizes and MixNPs with a 6 MV Linac spectrum to calculate the dose enhancement factor in water. The capabilities of our framework for the prediction of cell damage trends are examined and discussed. We found that the difference of the main parameter driving the cell damage between a cluster of GNPs and the MixNP was less than 1.6% for all cluster sizes. Our results demonstrate for the first time a simple route to intuit the radiobiological effects of clusters of nanoparticles through the consideration of an equivalent homogenous gold/water mixture. Furthermore, the negligible difference on cell damage between a cluster of GNPs and MixNP simplifies the modelling for the complex geometries of nanoparticle aggregations and saves computational resources.

Oxygen diffusion in ellipsoidal tumour spheroids.

Oxygen plays a central role in cellular metabolism, in both healthy and tumour tissue. The presence and concentration of molecular oxygen in tumours has a substantial effect on both radiotherapy response and tumour evolution, and as a result the oxygen micro-environment is an area of intense research interest. Multi-cellular tumour spheroids closely mimic real avascular tumours, and in particular they exhibit physiologically relevant heterogeneous oxygen distribution. This property has made them a vital part of in vitro experimentation. For ideal spheroids, their heterogeneous oxygen distributions can be predicted from theory, allowing determination of cellular oxygen consumption rate (OCR) and anoxic extent. However, experimental tumour spheroids often depart markedly from perfect sphericity. There has been little consideration of this reality. To date, the question of how far an ellipsoid can diverge from perfect sphericity before spherical assumptions break down remains unanswered. In this work, we derive equations governing oxygen distribution (and, more generally, nutrient and drug distribution) in both prolate and oblate tumour ellipsoids, and quantify the theoretical limits of the assumption that the spheroid is a perfect sphere. Results of this analysis yield new methods for quantifying OCR in ellipsoidal spheroids, and how this can be applied to markedly increase experimental throughput and quality.

Variations in the Processing of DNA Double-Strand Breaks Along 60-MeV Therapeutic Proton Beams.

PURPOSE: To investigate the variations in induction and repair of DNA damage along the proton path, after a previous report on the increasing biological effectiveness along clinically modulated 60-MeV proton beams. METHODS AND MATERIALS: Human skin fibroblast (AG01522) cells were irradiated along a monoenergetic and a modulated spread-out Bragg peak (SOBP) proton beam used for treating ocular melanoma at the Douglas Cyclotron, Clatterbridge Centre for Oncology, Wirral, Liverpool, United Kingdom. The DNA damage response was studied using the 53BP1 foci formation assay. The linear energy transfer (LET) dependence was studied by irradiating the cells at depths corresponding to entrance, proximal, middle, and distal positions of SOBP and the entrance and peak position for the pristine beam. RESULTS: A significant amount of persistent foci was observed at the distal end of the SOBP, suggesting complex residual DNA double-strand break damage induction corresponding to the highest LET values achievable by modulated proton beams. Unlike the directly irradiated, medium-sharing bystander cells did not show any significant increase in residual foci. CONCLUSIONS: The DNA damage response along the proton beam path was similar to the response of X rays, confirming the low-LET quality of the proton exposure. However, at the distal end of SOBP our data indicate an increased complexity of DNA lesions and slower repair kinetics. A lack of significant induction of 53BP1 foci in the bystander cells suggests a minor role of cell signaling for DNA damage under these conditions.

Relative biological effectiveness variation along monoenergetic and modulated Bragg peaks of a 62-MeV therapeutic proton beam: a preclinical assessment.

PURPOSE: The biological optimization of proton therapy can be achieved only through a detailed evaluation of relative biological effectiveness (RBE) variations along the full range of the Bragg curve. The clinically used RBE value of 1.1 represents a broad average, which disregards the steep rise of linear energy transfer (LET) at the distal end of the spread-out Bragg peak (SOBP). With particular attention to the key endpoint of cell survival, our work presents a comparative investigation of cell killing RBE variations along monoenergetic (pristine) and modulated (SOBP) beams using human normal and radioresistant cells with the aim to investigate the RBE dependence on LET and intrinsic radiosensitvity. METHODS AND MATERIALS: Human fibroblasts (AG01522) and glioma (U87) cells were irradiated at 6 depth positions along pristine and modulated 62-MeV proton beams at the INFN-LNS (Catania, Italy). Cell killing RBE variations were measured using standard clonogenic assays and were further validated using Monte Carlo simulations and the local effect model (LEM). RESULTS: We observed significant cell killing RBE variations along the proton beam path, particularly in the distal region showing strong dose dependence. Experimental RBE values were in excellent agreement with the LEM predicted values, indicating dose-averaged LET as a suitable predictor of proton biological effectiveness. Data were also used to validate a parameterized RBE model. CONCLUSIONS: The predicted biological dose delivered to a tumor region, based on the variable RBE inferred from the data, varies significantly with respect to the clinically used constant RBE of 1.1. The significant RBE increase at the distal end suggests also a potential to enhance optimization of treatment modalities such as LET painting of hypoxic tumors. The study highlights the limitation of adoption of a constant RBE for proton therapy and suggests approaches for fast implementation of RBE models in treatment planning.

A new mechanism for hydroxyl radical production in irradiated nanoparticle solutions.

The absolute yield of hydroxyl radicals per unit of deposited X-ray energy is determined for the first time for irradiated aqueous solutions containing metal nanoparticles based on a "reference" protocol. Measurements are made as a function of dose rate and nanoparticle concentration. Possible mechanisms for hydroxyl radical production are considered in turn: energy deposition in the nanoparticles followed by its transport into the surrounding environment is unable to account for observed yield whereas energy deposition in the water followed by a catalytic-like reaction at the water-nanoparticle interface can account for the total yield and its dependence on dose rate and nanoparticle concentration. This finding is important because current models used to account for nanoparticle enhancement to radiobiological damage only consider the primary interaction with the nanoparticle, not with the surrounding media. Nothing about the new mechanism appears to be specific to gold, the main requirements being the formation of a structured water layer in the vicinity of the nanoparticle possibly through the interaction of its charge and the water dipoles. The massive hydroxyl radical production is relevant to a number of application fields, particularly nanomedicine since the hydroxyl radical is responsible for the majority of radiation-induced DNA damage.