Concepts of microdosimetry

This is the last part of an investigation of microdosimetric concepts relevant to numerical calculations. A formula is derived which permits the computation of the dose average lineal energy, yC, or the corresponding average of the specific energy without the need to determine the probability distributions, f(y) or f1(z). A detailed treatment is given for two cases of practical importance. The first case corresponds to spherical sites with diameters of the order of 1 mum and to neutrons up to 15 MeV. The second case corresponds to microscopic sites which are small enough that the change of the stopping power of charged particles traversing the site can be neglected.     

On the microdosimetric definition of quality factors

A formulation of the concept of quality factor based on the microdosimetric quantity lineal energy, y, is described. Toward this end, functions--denoted Specific Quality Functions (SQF)--are defined such that (a) they can be determined directly from observation and (b) a number of them can be used toward setting, by consensus, the values of a microdosimetrically-based quality factor. The determination of SQFs is exemplified by correlating data on the yields of dicentric aberrations in human lymphocytes with measured and calculated microdosimetric distributions. The implications of this approach to problems of radiation protection are discussed.     

Radiation quality of tritium beta-rays: microdosimetric distributions for nanometer-size targets in a medium containing tritiated water

To elucidate the characteristics of the action of tritium beta-rays, the following parameters are derived: electron slowing down spectra of primary electrons (beta-rays) and delta-rays in a medium containing tritiated water; and frequency distributions for the microdosimetric quantity j (number of effective primary events per track per target), fj, for nanometer-size targets exposed to tritiated water. Features of the radiation quality of tritium beta-rays are discussed by comparing the present results with those for 60Co gamma-rays and 7 MeV electrons. It is concluded that, although tritium beta-rays, 60Co gamma-rays, and 7 MeV electrons are classified as the same low l.e.t. radiation, the radiation quality of tritium beta-rays is considerably different from those of 60Co gamma-rays and 7 MeV electrons, and has specific features such as a high average l.e.t., a small total electron fluence per unit absorbed dose, and a different microdosimetric distribution, fj, for nanometer-size targets.     

Radiobiological effectiveness (RBE) of megavoltage X-ray and electron beams in radiotherapy

Recent experiments indicate that significant differences exist in the microdosimetric properties (i.e., lineal energy distributions) of megavoltage X-ray and electron beams used in radiation therapy. In particular, dose averaged values of lineal energy for 18 MeV electrons are 10-30% lower than for 10 MeV bremsstrahlung X rays, which in turn are 30-60% lower than for 250 kVp X rays. Differences of this magnitude may manifest themselves in observable radiobiological effectiveness (RBE) differences between these radiations. Cell survival data have been obtained for line DLD-1 human tumor cells on all three of the above radiation sources. Results clearly demonstrate an RBE difference between orthovoltage and megavoltage radiation (P = 0.001). A small difference is also measured in RBE between megavoltage photons and megavoltage electrons, but the difference is not statistically significant (P = 0.25). All biological, dosimetric, and microdosimetric data were obtained under nearly identical geometric conditions. These data raise interesting questions vis à vis the applicability of microdosimetric theories in the interpretation of biological effects.     

Concepts of microdosimetry

This is the first part of an investigation of microdosimetric concepts relevant to numerical calculations. The definitions of the microdosimetric quantities are reviewed and formalized, and some additional conventions are adopted. The common interpretation of the quantities in terms of energy imparted to spherical sites is contrasted with their interpretation as the result of a diffusing process applied to the initial spatial pattern of energy transfers in the irradiated medium.     

Monte Carlo investigation of electron specific energy distribution in a single cell model

Radiation and Environmental Biophysics - Knowledge of microdosimetric quantities of certain radionuclides is important in radio immune cancer therapies. Specific energy distribution of...     

Proportional counter dosimetry and microdosimetry for radiotherapy with multiple pion beams

At the Swiss Institute for Nuclear Research (SIN) cancer patients are irradiated with negatively charged pi mesons using a 60-beam medical pion generator, the Piotron. A low-pressure tissue-equivalent proportional counter was used to measure absorbed dose and microdosimetric spectra. A method was developed to allow discrimination of events from different beam components, i.e., beam contamination (electrons and muons), pions in flight, and stopping pions. Measurements were performed along the axis and at lateral distances off one of these identical pion beams. The marked changes of total microdosimetric spectra with depth in phantom detected in earlier measurements are mainly due to large variations in the dose contributions of the beam components and much less to changes in the shapes of the individual microdosimetric spectra. The single beam measurements were used to calculate three-dimensional distributions of absorbed dose and of dose mean lineal energy, yD, for dynamic patient irradiations. Within the whole target volume yD remains nearly constant when irradiated with all 60 beams, whereas considerable changes were found for irradiations with 31 beams coming from a semicircle. Both size and shape of target volumes influence yD, the maximum values ranging from 30 to 45 keV/micron.     

On the distribution of plant abundance data

Plant abundance data are often analysed using standard statistical procedures without considering their distributional features and the underlying ecological processes. However, plant abundance data, e.g. when measured in biodiversity monitoring programs, are often sampled using a hierarchical sampling procedure, and since plant abundance data in a hierarchical sampling procedure are typically both zero-inflated and over-dispersed, the use of a standard statistical procedure is sub-optimal and not the best possible practice in the modelling of plant abundance data. Two distributions (the zero-inflated generalised binomial distribution and the zero-inflated bounded beta distribution) are suggested as possible distributions for analysing either discrete, continuous, or ordinal hierarchically sampled plant cover data.     

New Ranked Set Sampling for One‐Parameter Family of Distributions

Bhoj (1997c) proposed a new ranked set sampling (NRSS) procedure for a specific two‐parameter family of distributions when the sample size is even. This NRSS procedure can be applied to one‐parameter family of distributions when the sample size is even. However, this procedure cannot be used if the sample size is odd. Therefore, in this paper, we propose a modified version of the NRSS procedure which can be used for one‐parameter distributions when the sample size is odd. Simple estimator for the parameter based on proposed NRSS is derived. The relative precisions of this estimator are higher than those of other estimators which are based on other ranked set sampling procedures and the best linear unbiased estimator using all order statistics.     

Cell to Cell Variability of Radiation-Induced Foci: Relation between Observed Damage and Energy Deposition

Most studies that aim to understand the interactions between different types of photon radiation and cellular DNA assume homogeneous cell irradiation, with all cells receiving the same amount of energy. The level of DNA damage is therefore generally determined by averaging it over the entire population of exposed cells. However, evaluating the molecular consequences of a stochastic phenomenon such as energy deposition of ionizing radiation by measuring only an average effect may not be sufficient for understanding some aspects of the cellular response to this radiation. The variance among the cells associated with this average effect may also be important for the behaviour of irradiated tissue. In this study, we accurately estimated the distribution of the number of radiation-induced γH2AX foci (RIF) per cell nucleus in a large population of endothelial cells exposed to 3 macroscopic doses of gamma rays from ⁶⁰Co. The number of RIF varied significantly and reproducibly from cell to cell, with its relative standard deviation ranging from 36% to 18% depending on the macroscopic dose delivered. Interestingly, this relative cell-to-cell variability increased as the dose decreased, contrary to the mean RIF count per cell. This result shows that the dose effect, in terms of the number of DNA lesions indicated by RIF is not as simple as a purely proportional relation in which relative SD is constant with dose. To analyse the origins of this observed variability, we calculated the spread of the specific energy distribution for the different target volumes and subvolumes in which RIF can be generated. Variances, standard deviations and relative standard deviations all changed similarly from dose to dose for biological and calculated microdosimetric values. This similarity is an important argument that supports the hypothesis of the conservation of the association between the number of RIF per nucleus and the specific energy per DNA molecule. This comparison allowed us to calculate a volume of 1.6 μm³ for which the spread of the specific energy distribution could explain the entire variability of RIF counts per cell in an exposed cell population. The definition of this volume may allow to use a microdosimetric quantity to predict heterogeneity in DNA damage. Moreover, this value is consistent with the order of magnitude of the volume occupied by the hydrated sugar-phosphate backbone of the DNA molecule, which is the part of the DNA molecule responsible for strand breaks.     

Dosimetric uncertainties impact on cell survival curve with low energy proton

There is an increasing number of radiobiological experiments being conducted with low energy protons (less than 5 MeV) for radiobiological studies due to availability of sub-millimetre focused beam. However, low energy proton has broad microdosimetric spectra which can introduce dosimetric uncertainty. In this work, we quantify the impact of this dosimetric uncertainties on the cell survival curve and how it affects the estimation of the alpha and beta parameters in the LQ formalism. Monte Carlo simulation is used to generate the microdosimetric spectra in a micrometer-sized water sphere under proton irradiation. This is modelled using radiobiological experiment set-up at the Centre of Ion Beam Application (CIBA) in National University of Singapore. Our results show that the microdosimetric spectra can introduce both systematic and random shifts in dose and cell survival; this effect is most pronounced with low energy protons. The alpha and beta uncertainties can be up to 10% and above 30%, respectively for low energy protons passing through thin cell target (about 10 microns). These uncertainties are non-negligible and show that care must be taken in using the cell survival curve and its derived parameters for radiobiological models.     

Microdosimetric measurements in the secondary radiation field produced in 12C-therapy irradiations

The ambient dose equivalent from the secondary radiation produced during irradiation of a cylindrical water phantom with 200 MeV/u ¹²C-ions was investigated at the biophysics cave at GSI Helmholtzzentrum für Schwerionenforschung in Darmstadt, Germany. Pencil-like ion beams were delivered by the heavy-ion synchrotron SIS18 using the slow extraction mode. Since the secondary radiation field outside the phantom is complex in its particle composition and particle energy distribution, microdosimetric methods developed for the dosimetry of the cosmic radiation field at flight altitudes, which is similar in terms of complexity, were applied. Lineal energy distributions and the ambient dose equivalent were measured with a tissue-equivalent proportional counter at different particle emission angles. An additional veto counter allowed the identification of the different contributions of charged and neutral particles. A significant increase in the mean quality factor was observed at large emission angles which could be attributed to the decreasing contributions of charged particles compared to the (relative) contributions from neutrons.     

The statistical analysis of the differential blood count

The differential blood count obtained by unbiased sampling mathematically follows a multinomial distribution. The variation between individuals can be formalized by a mixing distribution of the parameters of the multinomial distribution. By DIRICHLET-distributions used as mixing distributions the main phenomena of the observed data can be described, and they are useful in estimating and testing treatment effects. If the correlation between the different types of leucocytes is taken into account in an appropriate manner, univariate test procedures can be applied also.     

The microdosimetry of the (10)B reaction in boron neutron capture therapy: a new generalized theory

The microdosimetry of (10)B thermal neutron capture reactions should be considered as an essential step to be followed before studying the radiobiological aspects of boron neutron capture therapy. The boron dose itself is insufficient as the only quantity used to describe the biological effectiveness of the (10)B reaction for two important reasons: the specific microdistribution that the (10)B carrier compound exhibits at the cellular level and the primarily stochastic nature of the energy deposition process, which influences the biological response to the particulate radiation. In this work, these two aspects are analyzed in detail and an innovative rigorous analytical framework is developed in the microdosimetry domain. This formalism provides the necessary microdosimetric tools for more precisely describing the (10)B dose distribution deposited in sensitive microscopic structures and offers improved approaches for analyzing the biological dose--effect relationship of (10)B reactions.     

Dose-rate dependent stochastic effects in radiation cell-survival models

Summary When cells are subjected to ionizing radiation the specific energy rate (microscopic analog of dose-rate) varies from cell to cell. Within one cell, this rate fluctuates during the course of time; a crossing of a sensitive cellular site by a high energy charged particle produces many ionizations almost simultaneously, but during the interval between events no ionizations occur. In any cell-survival model one can incorporate the effect of such fluctuations without changing the basic biological assumptions. Using stochastic differential equations and Monte Carlo methods to take into account stochastic effects we calculated the dose-survival relationships in a number of current cell survival models. Some of the models assume quadratic misrepair; others assume saturable repair enzyme systems. It was found that a significant effect of random fluctuations is to decrease the theoretically predicted amount of dose-rate sparing. In the limit of low dose-rates neglecting the stochastic nature of specific energy rates often leads to qualitatively misleading results by overestimating the surviving fraction drastically. In the opposite limit of acute irradiation, analyzing the fluctuations in rates merely amounts to analyzing fluctuations in total specific energyvia the usual microdosimetric specific energy distribution function, and neglecting fluctuations usually underestimates the surviving fraction. The Monte Carlo methods interpolate systematically between the low dose-rate and high dose-rate limits. As in other approaches, the slope of the survival curve at low dose-rates is virtually independent of dose and equals the initial slope of the survival curve for acute radiation.     

The Structure of Ellipsoidal Distributions I. Canonical Analysis

This study is concerned with the structure of variables having ellipsoidal distributions. In Part I it is shown that many normal-theory results in canonical analysis are exact for all ellipsoidal distributions under a specified model for sampling. In Part II similar conclusions are drawn regarding the use of principal components. These findings suggest using normal-theory procedures in canonical and principal components analyses as approximate large-sample procedures for distributions attracted to ellipsoidal stable laws.     

Multiple modes in a coral species abundance distribution

Species abundance distributions are an important measure of biodiversity and community structure. These distributions are affected by sampling, and alternative species-abundance models often make similar predictions for small sample sizes. Very large samples reveal the relative abundances of rare species, and thus provide information about species relative abundances that small samples cannot. Here, we present the species-abundance distribution for a sample of > 40,000 coral colonies at a single site, exceeding existing samples of coral local assemblages by over an order of magnitude. This abundance distribution is multimodal when examined on a logarithmic scale. Four different model selection procedures all indicate that the underlying community abundance distribution has at least three modes. We show that the multiple modes are not caused by mixtures of species with different habitat preferences. However, spatial aggregation partially explains our results. We inspect published work on species abundance distributions, and suggest that multimodality may be a common feature of large samples.     

Characterisation of grids of point detectors in maximum skin dose measurement in fluoroscopically-guided interventional procedures

PurposePoint detectors are frequently used to measure patient's maximum skin dose (MSD) in fluoroscopically-guided interventional procedures (IP). However, their performance and ability to detect the actual MSD are rarely evaluated. The present study investigates the sampling uncertainty associated with the use of grids of point detectors to measure MSD in IP.MethodChemoembolisation of the liver (CE), percutaneous coronary intervention (PCI) and neuroembolisation (NE) procedures were studied. Spatial dose distributions were measured with XR-RV3 Gafchromic^® films for 176 procedures. These distributions were used to simulate measurements performed using grids of detectors such as thermoluminescence detectors, with detector spacing from 1.4 up to 10 cm.ResultsThe sampling uncertainty was the highest in PCI and NE procedures. With 40 detectors covering the film area (36 cm × 44 cm), the maximum dose would be on average 86% and 63% of the MSD measured with Gafchromic^® films in CE and PCI procedures, respectively. In NE procedures, with 27 detectors covering the film area (14 cm × 35 cm), the maximum dose measured would be on average 82% of the MSD obtained with the Gafchromic^® films.ConclusionThermoluminescence detectors show good energy and dose response in clinical beam qualities. However the poor spatial resolution of such point-like dosimeters may far outweigh their good dosimetric properties. The uncertainty from the sampling procedure should be estimated when point detectors are used in IP because it may lead to strong underestimation of the MSD.     

Microdosimetry of diagnostic X rays: applications of the variance-covariance method.

Microdosimetric measurements in beams of diagnostic X rays (between 30 and 125 kV) have been performed. In these pulsed radiation fields, microdosimetric measurements are possible only by application of the variance-covariance technique. The dose mean lineal energy, yD, is determined for various simulated diameters, at different depths in the absorber, and at different points within the pulse intervals. From the measured temporal dependences one can also obtain values of yD for different X-ray pulse generators. The results demonstrate the potential of the variance-covariance method for a diversity of microdosimetric measurements in radiation protection and in the quality control of radiation beams.