A Monte Carlo code for the simulation of heavy-ion tracks in water

TILDA, a new Monte Carlo track structure code for ions in gaseous water that is valid for both high-LET (approximately 10(4) keV/microm) and low-LET ions, is presented. It is specially designed for a comparison of the patterns of energy deposited by a large range of ions. Low-LET ions are described in a perturbative frame, whereas heavy ions with a very high stopping power are treated using the Lindhard local density approximation and the Russek and Meli statistical method. Ionization cross sections singly differential with energy compare well with the experiment. As an illustration of the non-perturbative interaction of high-LET ions, a comparison between the ion tracks of light and heavy ions with the same specific energy is presented (1.4 MeV/nucleon helium and uranium ions). The mean energy for ejected electrons was found to be approximately four times larger for uranium than for helium, leading to a much larger track radius in the first case. For electrons, except for the excitation cross sections that are deduced from experimental fits, cross sections are derived analytically. For any orientation of the target molecule, the code calculates multiple differential cross sections as a function of the ejection and scattering angles and of the energy transfer. The corresponding singly differential and total ionization cross sections are in good agreement with experimental data. The angular distribution of secondary electrons is shown to depend strongly on the orientation of the water molecule.     

Development of modified microdosimetric kinetic model for relative biological effectiveness in proton therapy

To predict the biological effects of ionising radiation, the quantity of biological dose is introduced instead of the physical absorbed dose. In proton therapy, a constant relative biological effectiveness (RBE) of 1.1 is usually applied clinically as recommended by the International Commission of Radiation Units and Measurements. This study presents a new model, based on the modified microdosimetric kinetic model (MMKM), for calculating variable RBE values based on experimental data on the induction of DNA double-strand breaks (DSBs) within cells. The MMKM was proposed based on experimental data for the yield of DSBs in mammalian cells, which allows modification of the yield of primary lesions in the MKM. In this approach, a unique function named f(LET), which describes the relation between RBE and linear energy transfer (LET), was considered for charged particles. In the presented model (DMMKM), the MMKM approach was developed further by considering different f(LET)s for different relevant ions involved in energy deposition events in proton therapy. Although experimental data represent the dependence of the yield of primary lesions on the ion species, the DSB yield (assumed as the main primary lesion) is assumed independent of the ion species in the MMKM. In the DMMKM, by considering the yield of primary lesions as a function of the ion species, the α and β values are in better agreement with the experimental data as compared to those of the MKM and MMKM approaches. The biological dose in the DMMKM is predicted to be lower than that in the MMKM. Further, in the proposed model, the variation of the β parameter is higher than the constant value assumed in the MKM, at the distal end of the spread-out Bragg peak (SOBP). Moreover, the level of cell death estimated by the MMKM at the SOBP region is higher than that obtained based on the DMMKM. It is concluded that considering modified f(LET)s in the model developed here is more consistent with experimental results than when MMKM and MKM approaches are considered. The DMMKM examines the biological effects with full detail and will, therefore, be effective in improving proton therapy.

     

Mathematical simulation and analysis of cellular metabolism and regulation.

MOTIVATION: A better understanding of the biological phenomena observed in cells requires the creation and analysis of mathematical models of cellular metabolism and physiology. The formulation and study of such models must also be simplified as far as possible to cope with the increasing complexity demanded and exponential accumulation of the metabolic reconstructions computed from sequenced genomes. RESULTS: A mathematical simulation workbench, DBsolve, has been developed to simplify the derivation and analysis of mathematical models. It combines: (i) derivation of large-scale mathematical models from metabolic reconstructions and other data sources; (ii) solving and parameter continuation of non-linear algebraic equations (NAEs), including metabolic control analysis; (iii) solving the non-linear stiff systems of ordinary differential equations (ODEs); (iv) bifurcation analysis of ODEs; (v) parameter fitting to experimental data or functional criteria based on constrained optimization. The workbench has been successfully used for dynamic metabolic modeling of some typical biochemical networks (Dolgacheva et al., Biochemistry (Moscow), 6, 1063-1068, 1996; Goldstein and Goryanin, Mol. Biol. (Moscow), 30, 976-983, 1996), including microbial glycolytic pathways, signal transduction pathways and receptor-ligand interactions. AVAILABILITY: DBsolve 5. 00 is freely available from http://websites.ntl.com/ approximately igor.goryanin. CONTACT: gzz78923@ggr.co.uk     

Errors in differential infrared carbon dioxide analysis resulting from water vapor

Water vapor was added differentially to the gas streams entering the cells of three makes of differential infrared carbon dioxide analysers. Analyser deflections were compared with those expected from dilution of the carbon dioxide by the additional gas. Tests were made at 0, 365, and 730 cm³ m^–3 concentrations of carbon dioxide, and with the dewpoint in one cell of the analysers held constant at 15, 20, or 25°C. None of the analysers always responded in the ways predicted from dilution. The results showed that errors of a few cm³ m^–3 could occur in estimates of carbon dioxide differentials using the theoretical correction for dilution. Furthermore the amount of error varied with the carbon dioxide range, the difference in water content, and in some cases the dewpoint range.     

Comparison of microdosimetric simulations using PENELOPE and PITS for a 25 keV electron microbeam in water

The calculations presented compared the performances of two Monte Carlo codes used for the estimation of microdosimetric quantities: Positive Ion Track Structure code (PITS) and a main user code based on the PENetration and Energy Loss of Positrons and Electrons code (PENELOPE-2000). Event-by-event track structure codes like PITS are believed to be superior for microdosimetric applications, and they are written for this purpose. PITS tracks electrons in water down to 10 eV. PENELOPE is one of the few general-purpose codes that can simulate random electron-photon showers in any material for energies from 100 eV to 1 GeV. The model used in the comparison is a water cylinder with an internal scoring geometry made of spheres 1 microm in diameter where the scoring quantities are calculated. The source is a 25 keV electron pencil beam impinging normally on the sphere surface. This work shows only the lineal energy y and spectra graphical presentation as a function of y since for microdosimetry and biology applications, and for discussion of radiation quality in general, these results are more appropriate. The computed PENELOPE results are in agreement with those obtained with the PITS code and published previously in this journal. This paper demonstrates PENELOPE's usefulness at low energies and for small geometries. What is still needed are experimental results to confirm these analyses.     

A microdosimetric analysis of the interactions of mono-energetic neutrons with human tissue

Nuclear reactions induced during high-energy radiotherapy produce secondary neutrons that, due to their carcinogenic potential, constitute an important risk for the development of iatrogenic cancer. Experimental and epidemiological findings indicate a marked energy dependence of neutron relative biological effectiveness (RBE) for carcinogenesis, but little is reported on its physical basis. While the exact mechanism of radiation carcinogenesis is yet to be fully elucidated, numerical microdosimetry can be used to predict the biological consequences of a given irradiation based on its microscopic pattern of energy depositions. Building on recent studies, this work investigated the physics underlying neutron RBE by using the microdosimetric quantity dose-mean lineal energy $\left({\bar{y}}_D\right)$ as a proxy. A simulation pipeline was constructed to explicitly calculate the ${\bar{y}}_D$ of radiation fields that consisted of (i) the open source Monte Carlo toolkit Geant4, (ii) its radiobiological extension Geant4-DNA, and (iii) a weighted track-sampling algorithm. This approach was used to study mono-energetic neutrons with initial kinetic energies between 1 eV and 10 MeV at multiple depths in a tissue-equivalent phantom. Spherical sampling volumes with diameters between 2 nm and 1 $\mathrm{\mu }$m were considered. To obtain a measure of RBE, the neutron ${\bar{y}}_D$ values were divided by those of 250 keV X-rays that were calculated in the same way. Qualitative agreement was found with published radiation protection factors and simulation data, allowing for the dependencies of neutron RBE on depth and energy to be discussed in the context of the neutron interaction cross sections and secondary particle distributions in human tissue.     

Mathematical simulation of forced expiration

Flow limitation during forced expiration is simulated by a mathematical model. This model draws on the pressure-area law obtained in the accompanying paper, and the methods of analysis for one-dimensional flow in collapsible tubes developed by Shapiro (Trans. ASME J. Biomech. Eng. 99: 126-147, 1977). These methods represent an improvement over previous models in that 1) the effects of changing lung volume and of parenchymal-bronchial interdependence are simulated; 2) a more realistic representation of collapsed airways is employed; 3) a solution is obtained mouthward of the flow-limiting site by allowing for a smooth transition from sub- to supercritical flow speeds, then matching mouth pressure by imposing an elastic jump (an abrupt transition from super- to subcritical flow speeds) at the appropriate location; and 4) the effects of levels of effort (or vacuum pressure) in excess of those required to produce incipient flow limitation are examined, including the effects of potential physiological limitation.     

Mathematical simulation of gliding contusions

A gliding contusion in the acute phase is characterized by a streaklike hemorrhage of venous origin situated subcortically in a paramedial convolution. In later stages perivascular necrosis may develop. This type of injury is caused by head angular acceleration and is often seen in traffic casualties when the head has hit the steering wheel, the dashboard or the windshield.

The deformation of the brain matter close to the superior sagittal sinus has been simulated by means of a mathematical viscoelastic model in order to clarify the genesis of the gliding contusions. The blood vessels in the brain matter will be strained as a consequence of the brain deformation which results from head angular acceleration. The highest values of the strain occur subcortically where the blood vessels are injured first. The tolerance levels for gliding contusions have been determined. The calculations which were based on experiments regarding the dynamic properties of the superior cerebral veins and on two alternative injury criteria proposed, indicate that a gliding contusion is not likely to arise if the maximal angular acceleration does not exceed 4500 rad/sec² or the change in angular velocity does not exceed 70 rad/sec.     

Mathematical modeling and simulation of seated stability

Various methods have been used to quantify the kinematic variability or stability of the human spine. However, each of these methods evaluates dynamic behavior within the stable region of state space. In contrast, our goal was to determine the extent of the stable region. A 2D mathematical model was developed for a human sitting on an unstable seat apparatus (i.e., the “wobble chair”). Forward dynamic simulations were used to compute trajectories based on the initial state. From these trajectories, a scalar field of trajectory divergence was calculated, specifically a finite time Lyapunov exponent (FTLE) field. Theoretically, ridges of local maxima within this field are expected to partition the state space into regions of qualitatively different behavior. We found that ridges formed at the boundary between regions of stability and failure (i.e., falling). The location of the basin of stability found using the FTLE field matched well with the basin of stability determined by an alternative method. In addition, an equilibrium manifold was found, which describes a set of equilibrium configurations that act as a low dimensional attractor in the controlled system. These simulations are a first step in developing a method to locate state space boundaries for torso stability. Identifying these boundaries may provide a framework for assessing factors that contribute to health risks associated with spinal injury and poor balance recovery (e.g., age, fatigue, load/weight, and distribution). Furthermore, an approach is presented that can be adapted to find state space boundaries in other biomechanical applications.