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PubMed1989

Clustered distribution and variability in kinetics of transient K channels in molluscan neuron cell bodies.

The spatial distribution of transient K current, IA, was studied using a combination of patch-clamp and whole-cell voltage-clamp techniques. The average IA current density in somatic patches is 0.64 times the current density in the entire axotomized cell body, a finding which suggests that the axon hillock or initial segment of the axon has a higher concentration of IA channels than much of soma. The highest density of active channels during the peak IA is 1/micron2 at a membrane voltage of -20 mV. There is no evidence for a gradient in the distribution of IA channels in the cell body, but the channels are not evenly distributed. The variability in the number of channels per patch for multiple patches on the same neuron is much higher than expected for a random distribution. Statistical analysis of the data yields a coefficient of dispersion of 8.1, a value indicating a high degree of clustering. The utility of this statistic for evaluating channel distributions is discussed. Several lines of evidence suggest that the upper limit for the area of IA channel clusters is approximately 250 micron2. Single-channel currents attributed to IA were recorded in the cell-attached configuration. The voltage dependence of channel opening and inactivation are the same as measured in whole-cell voltage-clamp experiments. The single-channel conductance is about 9 pS in normal saline. Patches 9-30 micron2 in areas that contain IA channels are often devoid of other K channel types, suggesting that IA channels can occur in isochannel clusters. IA inactivation follows an exponential time course in all of the neurons examined, but the time constant of inactivation ranges from 25 to 560 msec in different cells. The voltage dependence of activation and inactivation and the reversal potential of the current are approximately the same in all cells. When multiple patches on the same neuron are studied, it is found that IA inactivates exponentially with approximately the same time constant in each patch, regardless of patch area. The data suggest that each neuron expresses predominantly, and perhaps exclusively, a single type of IA channel with distinct kinetic properties. The wide range of IA inactivation time constants observed in different cell suggests that a large number of channel types are available for expression. Possible mechanisms for generating diversity in channel types are discussed.

Animals↗
PubMed2002

Estimation in medical imaging without a gold standard.

RATIONALE AND OBJECTIVES: In medical imaging, physicians often estimate a parameter of interest (eg, cardiac ejection fraction) for a patient to assist in establishing a diagnosis. Many different estimation methods may exist, but rarely can one be considered a gold standard. Therefore, evaluation and comparison of different estimation methods are difficult. The purpose of this study was to examine a method of evaluating different estimation methods without use of a gold standard. MATERIALS AND METHODS: This method is equivalent to fitting regression lines without the x axis. To use this method, multiple estimates of the clinical parameter of interest for each patient of a given population were needed. The authors assumed the statistical distribution for the true values of the clinical parameter of interest was a member of a given family of parameterized distributions. Furthermore, they assumed a statistical model relating the clinical parameter to the estimates of its value. Using these assumptions and observed data, they estimated the model parameters and the parameters characterizing the distribution of the clinical parameter. RESULTS: The authors applied the method to simulated cardiac ejection fraction data with varying numbers of patients, numbers of modalities, and levels of noise. They also tested the method on both linear and nonlinear models and characterized the performance of this method compared to that of conventional regression analysis by using x-axis information. Results indicate that the method follows trends similar to that of conventional regression analysis as patients and noise vary, although conventional regression analysis outperforms the method presented because it uses the gold standard which the authors assume is unavailable. CONCLUSION: The method accurately estimates model parameters. These estimates can be used to rank the systems for a given estimation task.

Diagnostic Imaging↗
PubMed2000

Estimating age-related trends in cross-sectional studies using S-distributions.

Growth trends in children are often based on cross-sectional studies, in which a sample of the population is investigated at one given point in time. Estimating age-related percentiles in such studies involves fitting data distributions, each of which is specific for one age group, and a subsequent smoothing of the percentile curves. The first requirement for this process is the selection of a distributional form that is expected to be consistent with the observed data. If a goodness-of-fit test reveals significant discrepancies between the data and the best-fitting member of this distributional form, an alternative distribution must be found. In practice, there is seldom an objective argument for selecting any particular distribution. Also, different distributions can yield very similar fits, so that any selection is somewhat arbitrary. Finally, the shapes of the observed distributions may change throughout the age range so drastically that no single traditional distribution can fit them all in a satisfactory manner. To overcome these difficulties in population studies, non-parametric smoothing techniques and normalizing transformations have been used to derive percentile curves. In this paper we present an alternative strategy in the form of a flexible parametric family of statistical distributions: the S-distribution. We suggest a method that guides the search for well-fitting S-distributions for groups of observed distributions. The method is first tested with simulated data sets and subsequently applied to actual weight distributions of girls of different ages. As far as the results can be tested, they are consistent with observations and with results from other methods.

Adolescent↗
PubMed1999

Molecular evolution and phylogeny of the Drosophila saltans species group inferred from the Xdh gene.

The Drosophila saltans group of the subgenus Sophophora consists of five species subgroups whose phylogenetic relationships are poorly known. We have analyzed 2085 coding nucleotides from the xanthine dehydrogenase (Xdh) gene in six species, at least one from each subgroup. We follow a model-based maximum likelihood framework. We first model the substitution process using a tree topology that is approximately accurate. Then we evaluate several candidate tree topologies using a working model of nucleotide substitution. We found that a minimally realistic description of the substitution process along the Xdh region should allow two transition and four transversion rate parameters and different fixed rates for codon positions, which are distributed statistically according to different gamma distributions. The phylogeny obtained using this description differs in significant respects from a phylogeny based on anatomical criteria. We have also analyzed data from five additional (three nuclear and two mitochondrial) gene regions. In our analysis, these relatively short DNA sequences, either separately or jointly, fail to discriminate statistically among alternative phylogenies. When the data for these five gene regions are combined with the Xdh sequences, the strong phylogenetic signal emerging from Xdh becomes somewhat diluted rather than reinforced. The phylogeny of the species and biogeographical considerations suggest that the D. saltans group originated in the tropics of the New World, similarly as the closely related D. willistoni group.

Alcohol Dehydrogenase↗
PubMed1998

[Interpopulation diversity of the gene pool: beta distribution of Wright's F(ST) statistics].

The distribution of FST(i) estimates were studied in representative samples of ith genes for the gene pools of the major human populations, including the populations of Europe, Asia, Africa, Australia, America, North-eastern Eurasia, and five subregions of the latter. An average of 80 FST(i) estimates were analyzed for each sample of marker genes with a level of polymorphism (q) from 0.05 to 0.95. For each gene pool, the empirical distributions of FST(i) estimates were approximated by the main types of theoretical distributions--the normal, chi 2, Weibull, gamma, and beta distributions. In all gene pools, only beta distributions were good approximations of the empirical FST(i) distributions. The parameters of the beta distributions are reported in this study. It was demonstrated that the characteristics of beta distributions for all major gene pools studied could be interpolated to the smaller constituent gene pools. since the use of the traditional parametric tests starts from an assumption of normal distribution, they are inapplicable to analysis of FST statistics. Therefore, the obtained parameters of beta distributions should be used. These parameters allow the confidence intervals of the average FST values to be determined and permit correct comparison between the characteristics of both individual genes and gene pools to be performed.

Africa↗
PubMed2001

Spontaneous chiral separation in noncovalent molecular clusters.

A new method is introduced to determine the extent to which spontaneous chiral separation occurs in small noncovalently bound clusters. Soft-sampling electrospray ionization was used to transfer noncovalent complexes from solution to the gas phase. Mixing D and L enantiomers with one of the pair isotopically labeled reveals the effect of chirality on cluster stability. The observed cluster distribution is compared to the predicted statistical distribution to determine any preference for homo- or heterochirality. Arginine, for example, forms a stable trimer with no preference for the chirality of the individual amino acids. Serine, however, forms a protonated octamer with a pronounced preference for homochirality. The implications of these results for the structures of the complexes are discussed along with the broader implications for the origins of homochirality in living systems (homochirogenesis).

Journal Article↗
PubMed2006

Intraclass correlation coefficients and bootstrap methods of hierarchical binary outcomes.

Intraclass correlation coefficients are designed to assess consistency or conformity between two or more quantitative measurements. When multistage cluster sampling is implemented, no methods are readily available to estimate intraclass correlations of binomial-distributed outcomes within a cluster. Because statistical distribution of the intraclass correlation coefficients could be complicated or unspecified, we propose using a bootstrap method to estimate the standard error and confidence interval within the framework of a multilevel generalized linear model. We compared the results derived from a parametric bootstrap method with those from a non-parametric bootstrap method and found that the non-parametric method is more robust. For non-parametric bootstrap sampling, we showed that the effectiveness of sampling on the highest level is greater than that on lower levels; to illustrate the effectiveness, we analyse survey data in China and do simulation studies.

Biometry↗
PubMed2006

Fast method for computing pore size distributions of model materials.

Recently developed atomistic models of highly disordered nanoporous materials offer hope for a much more realistic description of the pore morphology and topology in such materials; however, a factor limiting their application has been the computationally intensive characterization of the models, particularly determination of the pore size distribution. We report a new technique for fast computation of pore size distributions of model materials from knowledge of the molecular coordinates. The pore size distribution (PSD) is defined as the statistical distribution of the radius of the largest sphere that can be fitted inside a pore at a given point. Using constrained nonlinear optimization, we calculate the maximum radii of test particles at random points inside the pore cavity. The final pore size distribution is then obtained by sampling the test particle radii using Monte Carlo integration. The computation time depends on factors such as the number of atoms, the sampling resolution, and the desired accuracy. However, even for large systems, PSDs with very high accuracy (>99.9%) are obtained in less than 24 h on a 3 GHz Pentium IV processor. The technique is validated by applying it to model structures, whose pore size distributions are already known. We then apply this method to investigate the pore structures of several mesoporous silica models such as SBA-15 and mesostructured cellular foams.

Journal Article↗
PubMed2003

Bilateral symmetry analysis of breast MRI.

Mammographic interpretation often uses symmetry between left and right breasts to indicate the site of potential tumour masses. This approach has not been applied to breast images obtained from MRI. We present an automatic technique for breast symmetry detection based on feature extraction techniques which does not require any efforts to co-register breast MRI data. The approach applies computer-vision techniques to detect natural biological symmetries in breast MR scans based on three objective measures of similarity: multiresolution non-orthogonal wavelet representation, three-dimensional intensity distributions and co-occurrence matrices. Statistical distributions that are invariant to feature localization are computed for each of the extracted image features. These distributions are later compared against each other to account for perceptual similarity. Studies based on 51 normal MRI scans of randomly selected patients showed that the sensitivity of symmetry detection rate approached 94%. The symmetry analysis procedure presented in this paper can be applied as an aid in detecting breast tissue changes arising from disease.

Breast↗
PubMed1998

Comparative study of different weighting methods in non-linear regression analysis: implications in the parametrization of carebastine after intravenous administration in healthy volunteers.

The influence of different weighting methods in non-linear regression analysis was evaluated in the pharmacokinetics of carebastine after a single intravenous dose of 10 mg in 8 healthy volunteers. Plasma concentrations were measured by HPLC using an on-line solid-phase extraction method and automated injection. The analytical method was fully validated and the function of the analytical error subsequently determined. The parametric approach was performed using different weighting methods, including the homoscedastic method (W = 1) and heteroscedastic methods using weights of 1/C, 1/C2, and the inverse of the concentration variance calculated through the analytical error function (1/V), and the results were statistically evaluated according to the normal distribution. Statistically significant differences were observed in the representative parameters of the disposition kinetics of carebastine. The use of a multiple comparison test for statistical analysis of all differences among group means indicated that differences were generated between the homoscedastic method (W = 1) and the heteroscedastic methods (1/C, 1/C2, and 1/V). The results obtained in the present study confirmed the utility of the analytical error function as a weighting method in non-linear regression analysis and reinforced the importance of the correct choice of weights to avoid the estimation of imprecise or erroneous pharmacokinetic parameters.

Adult↗
PubMed2000

Shear stress distribution in the trabeculae of human vertebral bone.

The statistical distribution of von Mises stress in the trabeculae of human vertebral cancellous bone was estimated using large-scale finite element models. The goal was to test the hypothesis that average trabecular von Mises stress is correlated to the maximum trabecular level von Mises stress. The hypothesis was proposed to explain the close experimental correlation between apparent strength and stiffness of human cancellous bone tissue. A three-parameter Weibull function described the probability distribution of the estimated von Mises stress (r2>0.99 for each of 23 cases). The mean von Mises stress was linearly related to the standard deviation (r2=0.63) supporting the hypothesis that average and maximum magnitude stress would be correlated. The coefficient of variation (COV) of the von Mises stress was nonlinearly related to apparent compressive strength, apparent stiffness, and bone volume fraction (adjusted r2=0.66, 0.56, 0.54, respectively) by a saturating exponential function [COV = A + B exp(-x/C)]. The COV of the stress was higher for low volume fraction tissue (<0.12) consistent with the weakness of low volume fraction tissue and suggesting that stress variation is better controlled in higher volume fraction tissue. We propose that the average stress and standard deviation of the stress are both controlled by bone remodeling in response to applied loading.

Adult↗
PubMed2001

Bayesian analysis of systems with random chemical composition: renormalization-group approach to Dirichlet distributions and the statistical theory of dilution.

We investigate the statistical properties of systems with random chemical composition and try to obtain a theoretical derivation of the self-similar Dirichlet distribution, which is used empirically in molecular biology, environmental chemistry, and geochemistry. We consider a system made up of many chemical species and assume that the statistical distribution of the abundance of each chemical species in the system is the result of a succession of a variable number of random dilution events, which can be described by using the renormalization-group theory. A Bayesian approach is used for evaluating the probability density of the chemical composition of the system in terms of the probability densities of the abundances of the different chemical species. We show that for large cascades of dilution events, the probability density of the composition vector of the system is given by a self-similar probability density of the Dirichlet type. We also give an alternative formal derivation for the Dirichlet law based on the maximum entropy approach, by assuming that the average values of the chemical potentials of different species, expressed in terms of molar fractions, are constant. Although the maximum entropy approach leads formally to the Dirichlet distribution, it does not clarify the physical origin of the Dirichlet statistics and has serious limitations. The random theory of dilution provides a physical picture for the emergence of Dirichlet statistics and makes it possible to investigate its validity range. We discuss the implications of our theory in molecular biology, geochemistry, and environmental science.

Algorithms↗
PubMed1984

The significance of morphometric procedures in the investigation of age changes in cytoarchitectonic structures of human brain.

The investigations were performed on NISSL-stained cytoarchitectonic images of totally 78 human brains (aged between 18 and 111 years) in the frontal area 11 (inside sulcus olfactorius) with 60 samples and in the visual cortex (area 17) with 45 samples. The morphometric measurements were taken by using a semiautomatic equipment. The largest projection areas of neurons were digitized over a drawing mirror. The arrangement of fields made it possible to get values for the total cortex and its layering. During the calculation the age-dependent embedding shrinkage was paid attention to. Therefore, the values concern the fresh tissue. The neuronal and glial densities, the neuronal sizes and size-distributions were calculated by using stereological and statistical principles. The results outline the following points: A basic description of the cytoarchitectonics is given in their qualitative and quantitative aspects. The individual variation shows high differences, which however, are in accordance with a normal statistical distribution. In area 11 we could find a significant difference of neuronal densities between males and females. The cell-sizes and the aging behavior are not different. In area 17 the amount of female brains was too small for statistics. The aging of both areas showed that the densities of neurons and glial cells do not decrease. A small increase may be possible. The neuronal sizes of area 11 are constant up to 60 years, then a distinct decrease can be observed. During aging the size decrease of neurons is very small in area 17. The layer III usually shows a distinct decrease of neuronal size during aging while layer V has a nearly constant size. The results were discussed and compared with other publications. The differences between our results and earlier publications seem to be mainly due to methodical problems. The older papers do and could probably not observe the stereological procedures of measuring and the age differences of the embedding procedures. The main result is that every gray structure of the brain has its own history.

Adolescent↗