Generalization of the variance-covariance method for microdosimetric measurements

The variance method of microdosimetric measurements and its extension, the variance-covariance method, permit the determination of an essential parameter of radiation quality, the dose mean event size,y _d. The methods have — among other advantages — the feature that they permit measurements for smaller simulated sites than the conventional single-event technique. It is, therefore, desirable to employ them also for the determination of further moments of the distribution ofy. The formulae for the first three moments are here derived both for the case of constant dose rate and of fluctuating dose rates. A second article will use the same mathematical approach to deduce formulae that remain valid even if there are slow changes of the ratio of dose rates in the two detectors for the variance-covariance method. A third article will explore — in terms of microdosimetric data — the applicability of the formulae.     

Microdosimetric measurements and the variance-covariance method

Summary Systematic and statistical uncertainties in the variance-covariance method have been investigated. Two spherical wall-less detectors have been used to determine the dose mean lineal energy (y _D) in a neutron beam of 5.7 MeV produced by a Van de Graaff accelerator. It is shown that certain systematic uncertainties influenced the meany _D of the two detectors much less thany _D from only one of them. A statistical uncertainty of 6% (95% confidence level) was achieved ify _D was calculated from 2000 measurements. In this particular experiment insufficient shieldings of the preamplifiers positioned in the beam turned out to limit the possibility to measure below 20 nm.     

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.     

Computation of microdosimetric distributions for small sites

Summary Object of this study is the computation of microdosimetric functions for sites which are too small to permit experimental determination of the distributions by Rossi-counters. The calculations are performed on simulated tracks generated by Monte-Carlo techniques.The first part of the article deals with the computational procedure. The second part presents numerical results for protons of energies 0.5, 5, 20 MeV and for site diameters of 5, 10, 100 nm.This investigation was supported by Public Service Research Grants No. CA 12536 and CA 15307 from the National Cancer Institute and by Research Contract 208-76-7 BIO D of Euratom     

FLUKA capabilities for microdosimetric analysis

Delta-ray transport is important in microdosimetric studies, and how Monte Carlo models handle delta electrons using condensed histories is important for accurate simulation. The purpose of this study was to determine how well FLUKA can simulate energy deposition spectra in a tissue-equivalent proportional counter (TEPC) and produce a reliable estimate of delta-ray events produced when a TEPC is exposed to high-energy heavy ions (HZE) like those in the galactic cosmic-ray (GCR) environment. A 1.27-cm spherical TEPC with a low-pressure gas simulating a 1-μm site, typical of the one flown on the ISS, was constructed in FLUKA, and its response was compared to experimental data for an (56)Fe-ion beam at 360 MeV/nucleon. Several narrow beams at different impact parameters were used to explain the response of the same detector exposed to a uniform field of radiation. Additionally, the effect that wall thickness had on the response of the TEPC and the range of delta rays in the tissue-equivalent (TE) wall material was investigated, and FLUKA produced the expected wall effect for primary particles passing outside the sensitive volume. A final comparison to experimental data was made for the simulated TEPCs exposed to various broad beams in the energy range of 200-1000 MeV/nucleon. FLUKA overestimated energy deposition in the gas volume in all cases. The FLUKA results differed from the experimental data by an average of 25.2% for y(F) and 12.4% for y(D). It is suggested that this difference can be reduced by adjusting the FLUKA default ionization potential and density correction factors. Accurate transport codes are desirable because of the high cost of beam time for experimental evaluation of energy deposition spectra produced by HZE ions and the flexibility that calculations offer in the TEPC engineering and design process.     

The variance-covariance method: Microdosimetry in time-varying low dose-rate radiation fields

Summary The variance-covariance method is employed at low doses and in radiation fields of low dose rates from an²⁴¹Am (4 nGy/s) and a⁹⁰Sr (300 nGy/s) source. The preliminary applications and results illustrate some of the potential of the method, and show that the dose average of lineal energy or energy imparted can be determined over a wide range of doses and dose rates. The dose averages obtained with the variance-covariance method in time-varying fields, for which the conventional variance method is not suitable, agree well with results obtained under the condition of constant dose rate. The results are compared to data obtained in terms of the conventional single-event measurements. The method has evident advantages, such as facility and speed of measurement.     

Correctness of the microdosimetric approach in radiobiology

The application of Bernoulli model to describe the response of irradiated cell populations permits to formulate the task strictly in terms of the probability theory. The important results obtained are useful in analyzing more critically the applicability of the microdosimetric approach. The well known Kellerer-Rossi and Chadwick-Leenhouts theories were shown to have very serious contradictions in their basis.     

A variance-covariance model for analysis of pedigrees with inbreeding

A variance-covariance model is suggested for plotting the distribution of a quantitative trait analyzed in animal pedigrees resulting from crosses of outbred lines. The model takes inbreeding into account. A special parameter characterizing the degree of inbreeding has been introduced, which makes the model versatile. Pedigrees with the same structure that contain or not contain inbred individuals have been compared to analyze the effect of inbreeding on the parameters of the trait distribution, such as the mean genotypic value and variance of the trait.     

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.     

Determining the effective dimensionality of the genetic variance-covariance matrix

Determining the dimensionality of G provides an important perspective on the genetic basis of a multivariate suite of traits. Since the introduction of Fisher's geometric model, the number of genetically independent traits underlying a set of functionally related phenotypic traits has been recognized as an important factor influencing the response to selection. Here, we show how the effective dimensionality of G can be established, using a method for the determination of the dimensionality of the effect space from a multivariate general linear model introduced by Amemiya (1985). We compare this approach with two other available methods, factor-analytic modeling and bootstrapping, using a half-sib experiment that estimated G for eight cuticular hydrocarbons of Drosophila serrata. In our example, eight pheromone traits were shown to be adequately represented by only two underlying genetic dimensions by Amemiya's approach and factor-analytic modeling of the covariance structure at the sire level. In contrast, bootstrapping identified four dimensions with significant genetic variance. A simulation study indicated that while the performance of Amemiya's method was more sensitive to power constraints, it performed as well or better than factor-analytic modeling in correctly identifying the original genetic dimensions at moderate to high levels of heritability. The bootstrap approach consistently overestimated the number of dimensions in all cases and performed less well than Amemiya's method at subspace recovery.     

A variance-covariance model for analysis of hybrid pedigrees with inbreeding

A variance-covariance model is suggested for plotting the distribution of a quantitative trait analyzed in animal pedigrees resulting from crosses of outbred lines. The model takes inbreeding into account. A special parameter characterizing the degree of inbreeding has been introduced, which makes the model versatile. Pedigrees with the same structure that contain or not contain inbred individuals have been compared to analyze the effect of inbreeding on the parameters of the trait distribution, such as the genotypic mean and variance of the trait.     

Spectrophotometric method for high biomass concentration measurements

Continuous monitoring of concentration is important in the optimal control of bioreactors. Spectrophotometry provides a simple, accurate, and rapid way for measuring cell concentration of unicellular microorganisms, based on either Beer's law or calibration curves prepared using standard solutions. However, this method is limited to a low range of microbial concentrations, because Beer's law deviates significantly at high concentrations. In the present investigation, based on experimental work, a new technique is posed to monitor the concentration of microbial cells as high as 100 g DW/L. this is achieved by using a mixture of known concentration as reference, rather than the "ideal blank" with zero concentration of analyte. As a result, a new equation is developed that, although applied here only to microbial concentration, in principle can be used for monitoring the concentration of any optically sensitive material.     

A stereophotogrammetric method for measurements of ligament structure

A stereophotogrammetric method is presented to reconstruct the course of a curve in the three-dimensional space. This method is exclusively suitable as a non-destructive tool to determine the surface fiberstructure of ligaments, tendons and other organised collagenous structures. In addition, it is a convenient tool to measure the geometry of articular surfaces and other complicated surface shapes.     

Rapid divergence of genetic variance-covariance matrix within a natural population

The matrix of genetic variances and covariances (G matrix) represents the genetic architecture of multiple traits sharing developmental and genetic processes and is central for predicting phenotypic evolution. These predictions require that the G matrix be stable. Yet the timescale and conditions promoting G matrix stability in natural populations remain unclear. We studied stability of the G matrix in a 20-year evolution field experiment, where a population of the cosmopolitan parthenogenetic soil nematode Acrobeloides nanus was subjected to drift and divergent selection (benign and stress environments). Selection regime did not influence the level of absolute genetic constraints: under both regimes, two genetic dimensions for three life-history traits were identified. A substantial response to selection in principal components structure and in general matrix pattern was indicated by three statistical methods. G structure was also influenced by drift, with higher divergence under benign conditions. These results show that the G matrix might evolve rapidly in natural populations. The observed high dynamics of G structure probably represents the general feature of asexual species and limits the predictive power of G in phenotypic evolution 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.     

Orientation of the genetic variance-covariance matrix and the fitness surface for multiple male sexually selected traits

Stabilizing selection has been predicted to change genetic variances and covariances so that the orientation of the genetic variance-covariance matrix (G) becomes aligned with the orientation of the fitness surface, but it is less clear how directional selection may change G. Here we develop statistical approaches to the comparison of G with vectors of linear and nonlinear selection. We apply these approaches to a set of male sexually selected cuticular hydrocarbons (CHCs) of Drosophila serrata. Even though male CHCs displayed substantial additive genetic variance, more than 99% of the genetic variance was orientated 74.9 degrees away from the vector of linear sexual selection, suggesting that open-ended female preferences may greatly reduce genetic variation in male display traits. Although the orientation of G and the fitness surface were found to differ significantly, the similarity present in eigenstructure was a consequence of traits under weak linear selection and strong nonlinear (convex) selection. Associating the eigenstructure of G with vectors of linear and nonlinear selection may provide a way of determining what long-term changes in G may be generated by the processes of natural and sexual selection.     

A microdosimetric understanding of low-dose radiation effects

This paper presents a microdosimetric approach to the problem of radiation response by which effects produced at low doses and dose rates can be understood as the consequences of radiation absorption events in the nucleus of a single relevant cell and in its DNA. Radiation absorption at the cellular level, i.e. in the cell nucleus as a whole, is believed to act through radicals. This kind of action is called 'non-specific' and leads to the definition of an 'elemental dose' and the 'integral response probability' of a cell population. Radiation absorption at the molecular level, i.e. in sensitive parts of the DNA, is thought to act through double-strand breaks. This kind of action is called 'specific' and leads to a 'relative local efficiency'. In general, both mechanisms occur for all types of radiation; however, it is the dose contribution of both specific and non-specific effects that determines the radiation quality of a given radiation. The implications of this approach for the specification of low-dose and low dose-rate regions are discussed.     

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.

     

Epistasis and the temporal change in the additive variance-covariance matrix induced by drift

The effect of population bottlenecks on the components of the genetic covariance generated by two neutral independent epistatic loci has been studied theoretically (additive, covA; dominance, covD; additive-by-additive, covAA; additive-by-dominance, covAD; and dominance-by-dominance, covDD). The additive-by-additive model and a more general model covering all possible types of marginal gene action at the single-locus level (additive/dominance epistatic model) were considered. The covariance components in an infinitely large panmictic population (ancestral components) were compared with their expected values at equilibrium over replicates randomly derived from the base population, after t consecutive bottlenecks of equal size N (derived components). Formulae were obtained in terms of the allele frequencies and effects at each locus, the corresponding epistatic effects and the inbreeding coefficient Ft. These expressions show that the contribution of nonadditive loci to the derived additive covariance (covAt) does not linearly decrease with inbreeding, as in the pure additive case, and may initially increase or even change sign in specific situations. Numerical examples were also analyzed, restricted for simplicity to the case of all covariance components being positive. For additive-by-additive epistasis, the condition covAt > covA only holds for high frequencies of the allele decreasing the metric traits at each locus (negative allele) if epistasis is weak, or for intermediate allele frequencies if it is strong. For the additive/dominance epistatic model, however, covAt > covA applies for low frequencies of the negative alleles at one or both loci and mild epistasis, but this result can be progressively extended to intermediate frequencies as epistasis becomes stronger. Without epistasis the same qualitative results were found, indicating that marginal dominance induced by epistasis can be considered as the primary cause of an increase of the additive covariance after bottlenecks. For all models, the magnitude of the ratio covAt/covA was inversely related to N and t.