Radiobiological analysis of cancerogenic risk values in radioepidemiological investigations

The aim of the present article consisted in critical analysis of the epidemiological approach to radiocancerogenic risk estimation in region of low level radiation (LLR). The estimation is making by means of mathematician models that ignore a principal difference in biological action of LLR and high level radiation (HLR). The main formal characteristic of LLR action is the presence of a plateau in beginning of a dose-effect curve of radiogenic risk. It may be argued by the following positions: repeating the plateau-phenomenon on various radiobiological effects, in different tests and bioobjects, first; a paradoxical trend of reciprocal ERR/Sv increasing regarding dose decreasing in region of plateau, second, and third, the increasing of the curvature in dose-effect curve beginning. The presence of a plateau is associated with the presence of a real radiogenic risk threshold. Besides, the analysis of processes influencing significantly the dynamics of initial radiation injury of biologically important macromolecules showed the preference in region of LLR those, decreasing/eliminating genome damages. There is follows from mentioned above a necessity to evaluate radiogenic risks in LLR region separately from HLR region.     

The influence of multiple types of occupational exposure to radon, gamma rays and long-lived radionuclides on mortality risk in the French "post-55" sub-cohort of uranium miners: 1956-1999

The adverse health effects of radon on uranium miners, especially on their lungs, are well documented, but few studies have considered the effects of other radiation exposures. This study examined the mortality risks associated with exposure to radon, external γ rays and long-lived radionuclides (LLR) in the French "post-55" sub-cohort, which includes uranium miners first employed between 1956 and 1990 for whom all three types of exposure were assessed individually. Exposure-risk relationships were estimated with linear excess relative risk models and a 5-year lag time. The post-55 sub-cohort includes 3377 miners, contributing 89,405 person-years, followed up through the end of 1999 with a mean follow-up of 26.5 years. Mean cumulative exposure was 17.8 WLM for radon, 54.7 mSv for γ rays, and 1,632 Bq.m(-3).h for LLR. Among the 611 deaths observed, 66 were due to lung cancer. Annual individual exposures were significantly correlated. Increased mortality was observed for lung cancer (SMR = 1.30; 95% CI: 1.01, 1.65) and for brain and central nervous system (CNS) cancer (SMR = 2.00; 95% CI: 1.09, 3.35). Cumulative exposure to radon, γ rays and LLR was associated only with a significant risk of lung cancer. These new results could suggest an association between lung cancer and exposure to γ rays and LLR. They must nonetheless be interpreted with caution because of the correlation between the types of exposure. The calculation of organ doses received by each of these exposures would reduce the collinearity.     

Molecular mechanisms of radiation carcinogenesis and the linear, non-threshold dose response model of radiation risk estimation

Recent research in molecular radiation carcinogenesis is reviewed with the specific aim of exploring the implications this research may have on the dose response relationship of radiation-induced cancer at low doses and low dose rates. It is concluded that the linear non-threshold dose response hypothesis may be used in radiation protection planning as a simple, convenient method to optimize procedures and regulations, but should not be mistaken as a stringent scientific conclusion directly derived from the present state of knowledge of the processes involved in radiation carcinogenesis.     

Dose-response and thresholds in mutagenicity studies: a statistical testing approach

The analysis of dose-response relationships is an important objective in toxicology, and one in which both modelling and testing approaches are used. One particular question is whether a threshold exists at low doses. The concept of a pragmatic threshold is used, i.e. low doses with biologically unimportant effects are assumed to be threshold doses. "Biologically unimportant" means, in statistical terms, a lower effect than the effect of the negative control, or at least a just-tolerable margin delta higher than the effect of the negative control. Therefore, threshold doses can be tested in terms of a one-sided hypothesis of equivalence. A new approach is proposed, assuming, at the least, that the low dose is a threshold dose, and the highest dose is superior to the negative control. By analogy to the k-fold rule commonly used in mutagenicity studies, tests on ratio-to-control are used. The a priori definition of the threshold margin is inherently needed. A further approach proposes the analysis of dose-response relationships by means of order-restricted inference (the so-called trend test). A modification of a multiple-contrast test is used, in which only those contrasts are included that are sensitive for no effects at low doses. A further modification treats the complicated, but real, problem of simultaneous existence of a threshold, a monotonic increase, and a downturn effect at high dose(s). A parametric procedure is considered, together with an extension for proportions. The important problem of a priori sample size definition is discussed. The approaches are demonstrated by means of examples based on real data.     

Fitting Regression Models to Ordinal Data

This paper deals with the analysis of ordinal data by means of a threshold model. Maximum likelihood estimation is discussed and two examples are used to illustrate the methods.     

The Ambiguity of the Word "Complexity" a Proposal for Clarification

There are two different ways of defining complexity.1) Traditionally, the word "complexity" is considered synonymous to "organization". The transformation of species is an expression of victory against random indifferencism.2) The means of measuring complexity that was conceived by Kolmogorov has the advantage of having an external reference. Therefore, its logical reliability is considerable. But Kolmogorov's complexity will be at its best in cases of pure randomness.These mutually incompatible definitions explicitly demand a classification system.The first definition of complexity is contrary to the second one. This must be explained more precisely in order not to disturb the logic of Kolmogorov's conception and to enable to add to this conception, as closely as possible, along the logical rules derived from Gödel's incompleteness.The author proposes a beginning of complexity typology, founded on the necessity of laws that rule a random substract aiming at organization. The generality of laws to be selected will have a direct effect on the logical strength of the "biologists' definition" of complexity.Two fundamental laws are expressed, one derived from mathematics and the other from physics, two fields alien to biology. This fact improves the logical accordance to the argument.     

Bioelectrical parameters of the whole human body obtained through bioelectrical impedance analysis

Knowledge of electrical properties of body tissues across the frequency spectrum is useful for tissue characterization. The bioelectric impedance analysis method, operating from 1 to 250 kHz (multi-frequency), was used in 23 normal male human subjects between the ages of 21 and 52 years, for estimation of their bioelectrical parameters. Amplitude of the output current was set to 800 microA(RMS). The experimental data showed that bioelectric parameters were highly dependent on frequency and the presence of a threshold frequency around 4 kHz. In order to explain the unusual features observed in our experimental data, the human body was simulated through the Cole-Fricke-Cole model (RC circuit) and the Extended Cole-Fricke-Cole model (RLC circuit). The simulated data showed that the Extended Cole-Fricke-Cole model had a higher accuracy than the traditional Cole-Fricke-Cole model. These results suggest that the unusual features could be due to the possible existence of inductive effects in biological cells and body tissues and that the inductive parameter and the threshold frequency could be used for characterizing the healthy tissues as well as the traditional bioelectric parameters.     

Strategies for genetic mapping of categorical traits

The search for efficient and powerful statistical methods and optimal mapping strategies for categorical traits under various experimental designs continues to be one of the main tasks in genetic mapping studies. Methodologies for genetic mapping of categorical traits can generally be classified into two groups, linear and non-linear models. We develop a method based on a threshold model, termed mixture threshold model to handle ordinal (or binary) data from multiple families. Monte Carlo simulations are done to compare its statistical efficiencies and properties of the proposed non-linear model with a linear model for genetic mapping of categorical traits using multiple families. The mixture threshold model has notably higher statistical power than linear models. There may be an optimal sampling strategy (family size vs number of families) in which genetic mapping reaches its maximal power and minimal estimation errors. A single large-sibship family does not necessarily produce the maximal power for detection of quantitative trait loci (QTL) due to genetic sampling of QTL alleles. The QTL allelic model has a marked impact on efficiency of genetic mapping of categorical traits in terms of statistical power and QTL parameter estimation. Compared with a fixed number of QTL alleles (two or four), the model with an infinite number of QTL alleles and normally distributed allelic effects results in loss of statistical power. The results imply that inbred designs (e.g. F₂ or four-way crosses) with a few QTL alleles segregating or reducing number of QTL alleles (e.g. by selection) in outbred populations are desirable in genetic mapping of categorical traits using data from multiple families. This revised version was published online in July 2006 with corrections to the Cover Date.     

Intensity-time dependence dosing criterion in the EMF exposure guidelines in Russia

Major approaches of the Russian Federation in setting of exposure guidelines to electromagnetic fields (EMF) in occupational and public environments are discussed in this paper.

EMF exposure guidelines in Russia are based on the results of hygienic, clinical, physiological, epidemiological and experimental studies and are frequency-dependent. The concept of a threshold principle of occupational and environmental factors due to hazardous exposure effects has been used to set permissible exposure levels of different EMF frequency ranges. The data of experimental studies showed hazardous threshold levels of EMF effects. The main criteria of EMF hazardous exposure evaluated in the experimental study concerned both estimation of threshold levels of chronic (long-term) and acute exposure. Also, this paper contains some recent experimental study data on correlation of long-term radiofrequency and power-frequency EMF exposure effects with regard to time duration, the so-called time-dependence approach. It enables identification of the value of permissible EMF exposure levels depending on exposure duration. This approach is used in occupational exposure guideline setting and requires the introduction of “power exposition” (PE) and “maximal permissible level” (MPL). In general, EMF exposure guidelines are established with regard to possible duration of exposure per day.     

Quantifying the relative importance of experimental data points in parameter estimation

Background

Ordinary differential equations (ODEs) are often used to understand biological processes. Since ODE-based models usually contain many unknown parameters, parameter estimation is an important step toward deeper understanding of the process. Parameter estimation is often formulated as a least squares optimization problem, where all experimental data points are considered as equally important. However, this equal-weight formulation ignores the possibility of existence of relative importance among different data points, and may lead to misleading parameter estimation results. Therefore, we propose to introduce weights to account for the relative importance of different data points when formulating the least squares optimization problem. Each weight is defined by the uncertainty of one data point given the other data points. If one data point can be accurately inferred given the other data, the uncertainty of this data point is low and the importance of this data point is low. Whereas, if inferring one data point from the other data is almost impossible, it contains a huge uncertainty and carries more information for estimating parameters.

Results

G1/S transition model with 6 parameters and 12 parameters, and MAPK module with 14 parameters were used to test the weighted formulation. In each case, evenly spaced experimental data points were used. Weights calculated in these models showed similar patterns: high weights for data points in dynamic regions and low weights for data points in flat regions. We developed a sampling algorithm to evaluate the weighted formulation, and demonstrated that the weighted formulation reduced the redundancy in the data. For G1/S transition model with 12 parameters, we examined unevenly spaced experimental data points, strategically sampled to have more measurement points where the weights were relatively high, and fewer measurement points where the weights were relatively low. This analysis showed that the proposed weights can be used for designing measurement time points.

Conclusions

Giving a different weight to each data point according to its relative importance compared to other data points is an effective method for improving robustness of parameter estimation by reducing the redundancy in the experimental data.

     

Visualizing "greengold" clusters in the STEM.

"Greengold" is a large metallic cluster thought to contain 75 gold atoms in a compact 1.4-nm-diameter core surrounded by an organic shell. Scanning transmission electron microscope imaging shows uniform mass and size distributions with an apparent mass of 24 kDa, unaffected by radiation damage. The signal-to-noise ratio is adequate for visualization at low dose and in the presence of a relatively thick biological matrix. Under some conditions these clusters have a slight tendency to form linear chains and 2-D hexagonal arrays with a spacing of 2.6 nm. The parameters presented permit estimation of the feasibility of proposed labeling experiments.     

Dynamics of Cellular Responses to Radiation

Understanding the consequences of exposure to low dose ionizing radiation is an important public health concern. While the risk of low dose radiation has been estimated by extrapolation from data at higher doses according to the linear non-threshold model, it has become clear that cellular responses can be very different at low compared to high radiation doses. Important phenomena in this respect include radioadaptive responses as well as low-dose hyper-radiosensitivity (HRS) and increased radioresistance (IRR). With radioadaptive responses, low dose exposure can protect against subsequent challenges, and two mechanisms have been suggested: an intracellular mechanism, inducing cellular changes as a result of the priming radiation, and induction of a protected state by inter-cellular communication. We use mathematical models to examine the effect of these mechanisms on cellular responses to low dose radiation. We find that the intracellular mechanism can account for the occurrence of radioadaptive responses. Interestingly, the same mechanism can also explain the existence of the HRS and IRR phenomena, and successfully describe experimentally observed dose-response relationships for a variety of cell types. This indicates that different, seemingly unrelated, low dose phenomena might be connected and driven by common core processes. With respect to the inter-cellular communication mechanism, we find that it can also account for the occurrence of radioadaptive responses, indicating redundancy in this respect. The model, however, also suggests that the communication mechanism can be vital for the long term survival of cell populations that are continuously exposed to relatively low levels of radiation, which cannot be achieved with the intracellular mechanism in our model. Experimental tests to address our model predictions are proposed.     

Estimation of protein secondary structure and error analysis from circular dichroism spectra

The estimation of protein secondary structure from circular dichroism spectra is described by a multivariate linear model with noise (Gauss-Markoff model). With this formalism the adequacy of the linear model is investigated, paying special attention to the estimation of the error in the secondary structure estimates. It is shown that the linear model is only adequate for the alpha-helix class. Since the failure of the linear model is most likely due to nonlinear effects, a locally linearized model is introduced. This model is combined with the selection of the estimate whose fractions of secondary structure summate to approximately one. Comparing the estimation from the CD spectra with the X-ray data (by using the data set of W.C. Johnson Jr., 1988, Annu. Rev. Biophys. Chem. 17, 145-166) the root mean square residuals are 0.09 (alpha-helix), 0.12 (anti-parallel beta-sheet), 0.08 (parallel beta-sheet), 0.07 (beta-turn), and 0.09 (other). These residuals are somewhat larger than the errors estimated from the locally linearized model. In addition to alpha-helix, in this model the beta-turn and "other" class are estimated adequately. But the estimation of the antiparallel and parallel beta-sheet class remains unsatisfactory. We compared the linear model and the locally linearized model with two other methods (S. W. Provencher and J. Gl?ckner, 1981, Biochemistry 20, 1085-1094; P. Manavalan and W. C. Johnson Jr., 1988, Anal. Biochem. 167, 76-85). The locally linearized model and the Provencher and Gl?ckner method provided the smallest residuals. However, an advantage of the locally linearized model is the estimation of the error in the secondary structure estimates.     

What can epidemiology tell us about risks at low doses?

Puskin, J. S. What Can Epidemiology Tell Us about Risks at Low Doses? Radiat. Res. 169, 122-124 (2008). Limitations on statistical power preclude direct detection and quantification of radiogenic cancer risks at very low (environmental) levels of low-LET radiation through epidemiological studies. Given this limitation and our incomplete understanding of cellular processes leading to radiation carcinogenesis, an "effective threshold" in the dose range of interest for radiation protection cannot yet be ruled out. Ongoing epidemiological studies of chronically exposed individuals receiving very low daily doses of radiation can be used, however, together with radiobiological data, to critically test whether such a threshold is plausible.     

Adapting-bump model for eccentric cells of Limulus

Light-evoked intracellular voltage noise records have been obtained from Limulus eccentric cells, from threshold light intensity to an intensity .10(5) times threshold. These data are analyzed in terms of a simple "adapting-bump" noise model. It is shown how the model yields a data reduction procedure that slightly generalizes the familiar use of Campbell's theorem for Poisson shot noise: the correlative effect of adaptation amends Campbell's theorem by a single multiplicative factor, which may be estimated directly from the power spectrum of the noise data. The model also permits direct estimation of the bump shape from the power spectrum. The bump shape estimated from noise at dim light is in excellent agreement with the average shape of bumps observed directly in the dark. The data yield a bump rate that is linear with light up through about 50 times threshold intensity but that falls short of linearity by a factor of 35 at the brightest light. The bump height decreases as the -0.4 power of light intensity across the entire range. Bump duration decreases by a factor of 2 across the entire range, and the adaptation correlation factor descends from unity to about one-third. The modest change of the adaptation correlation shows that naive application of Campbell's theorem to such data is adequate for rough estimation of the model's physiological parameters. This simple accounting for all the data gives support to the adapting-bump model.     

An Extended Threshold Model for Analyzing Ordered Categorical Data

This paper presents an extended threshold model for analyzing ordered categorical data. The model admits interactions between the position of the thresholds and the levels of the effective factors. These interactions are described according to the approach of Milliken and Graybill (1970). Especially important for practical application is the special assumption that there is a linear relation between interactions and thresholds, and that the slopes of the concerning regression lines may be different for samples. This means that the latent variables are distributed according to the same type of distributions, but may have different expectations and variances. Underlying this submodel, the estimation of parameters and the testing of hypotheses according to the maximum likelihood method is described. The procedure is illustrated by a numerical example, and an outline is given about a cluster analysis using model parameters.     

Comparison among three approaches for evaluation of sexual precocity in Nellore cattle

Restricted breeding seasons used in beef cattle produce censored data for reproduction traits measured in regard to these seasons. To analyze these data, adequate methods must be used. The objective of this paper was to compare three approaches aiming to evaluate sexual precocity in Nellore cattle. The final data set contained 6699 records of age at first conception (AFC14) (in days) and of heifer pregnancy (HP14) (binary) obtained from females exposed to the bulls for the first time at about 14 months of age. Records of females that did not calve in the following year after being exposed to a sire were considered censored (77.5% of total). The models used to obtain genetic parameters and expected progeny differences (EPDs) were a Weibull mixed and a censored linear model for AFC14 and threshold model for HP14. The mean heritabilities obtained were 0.76 and 0.44, respectively, for survival and censored linear models (for AFC14), and 0.58 for HP14. Ranking and Pearson correlations varied (in absolute values) from 0.54 to 0.99 (considering different percentages of sires selected), indicating moderate changes in the classification. Considering survival analysis as the best selection criterion (that would result in the best response to selection), it was observed that selection for HP14 would lead to a more significant decrease in selection response if compared with selection for AFC14 analysed by censored linear model, from which results were very similar to the survival analysis.