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PubMed2005

Assessment of drug permeability distributions in two different model skins.

Past in vitro studies with human skin have indicated that drug permeability coefficient (Kp) distributions do not always follow a Gaussian-normal pattern. This has major statistical implications, exemplified by the fact that use of t-tests to evaluate significance is limited to normally distributed populations. Percutaneous absorption research often involves using animal or synthetic skins to simulate less readily available human skin. However, negligible work has been performed on assessing the permeability variabilities of these model membranes. This paper aims to fill this gap. To this end, four studies were undertaken representing two different drugs (caffeine and testosterone) with each drug penetrating through two different model skins (silicone membrane and pig skin). It was determined that in the silicone membrane studies, both compounds' Kp distributions could be fitted to a normal pattern. In contrast, in the pig skin studies, there were notable differences between each drug. While the testosterone Kp values could be fitted to a normal distribution, this was not possible with the caffeine Kp data, which could be fitted to a log-normal distribution. There is some evidence from the literature as well as physicochemical considerations that these outcomes may reflect general trends that are dependent upon both membrane and penetrant properties.

Animals↗
PubMed1996

Interindividual variations in susceptibility and sensitivity: linking risk assessment and risk management.

In the past few years, our knowledge of mammalian genomes has increased enormously. Our understanding of the molecular basis of the normal cellular processes of DNA replication and repair and cell cycle control, together with how their fidelity malfunctions as part of tumor development, has increased in parallel. This has led to a clearer appreciation that there are subpopulations that have been generically described as being genetically or otherwise susceptible to the induction of cancer or birth defects. The term susceptibility is a default option, since there clearly will be a very broad range of sensitivities among the so-called susceptible populations, dependent upon the specific underlying mechanism. This could lead to the conduct of risk assessments for each specific situation, involving both genotypes of individuals and agents of concern. This would ideally take into account the effects on response of various modifying factors, genetic and other. One advantage to be gained from this approach is the ability to determine if a particular susceptibility places subpopulations at extreme risk as compared to the overall normal distribution of risk in the population, or whether such a susceptible population presents a slight extension of the upper bound of the risk distribution or lies within the normal distribution. In addition, the specific mechanism of the susceptibility as related to exposure scenarios and the magnitude and demographics of the susceptible populations need to be taken into account. Thus, the management of risk has to be linked to the specific risk assessment. For many of the so-called susceptible populations an uncertainty factor of less than 10, even including 1, would be predicted to bring the risk within the normal distribution. It is hoped that as more mechanistic information on susceptibility becomes available and a specific risk can be defined, the practice of risk management will be considerably improved.

Animals↗
PubMed2005

Fine structure of distributions and central limit theorem in diffusive billiards.

We investigate deterministic diffusion in periodic billiard models, in terms of the convergence of rescaled distributions to the limiting normal distribution required by the central limit theorem; this is stronger than the usual requirement that the mean-square displacement grow asymptotically linearly in time. The main model studied is a chaotic Lorentz gas where the central limit theorem has been rigorously proved. We study one-dimensional position and displacement densities describing the time evolution of statistical ensembles in a channel geometry, using a more refined method than histograms. We find a pronounced oscillatory fine structure, and show that this has its origin in the geometry of the billiard domain. This fine structure prevents the rescaled densities from converging pointwise to Gaussian densities; however, demodulating them by the fine structure gives new densities which seem to converge uniformly. We give an analytical estimate of the rate of convergence of the original distributions to the limiting normal distribution, based on the analysis of the fine structure, which agrees well with simulation results. We show that using a Maxwellian (Gaussian) distribution of velocities in place of unit speed velocities does not affect the growth of the mean-square displacement, but changes the limiting shape of the distributions to a non-Gaussian one. Using the same methods, we give numerical evidence that a nonchaotic polygonal channel model also obeys the central limit theorem, but with a slower convergence rate.

Journal Article↗
PubMed2005

Mast cell distribution in normal adult skin.

AIMS: To investigate mast cell distribution in normal adult skin to provide a reference range for comparison with mastocytosis. METHODS: Mast cells (MCs) were counted in uninvolved skin adjacent to basal cell carcinomas and other dermatological disorders in adults. RESULTS: There was an uneven distribution of MCs in different body sites using the anti-tryptase monoclonal antibody technique. Numbers of MCs on the trunk, upper arm, and upper leg were similar, but were significantly different from those found on the lower leg and forearm. Two distinct groups were formed--proximal and distal. There were 77.0 MCs/mm2 at proximal body sites and 108.2 MCs/mm2 at distal sites. Adjusted for the adjacent diagnosis and age, this difference was consistent. The numbers of MCs in uninvolved skin adjacent to basal cell carcinomas and other dermatological disorders were not different from those in the control group. Differences in the numbers of MCs between the distal and the proximal body sites must be considered when MCs are counted for a reliable diagnosis of mastocytosis. A pilot study in patients with mastocytosis underlined the variation in the numbers of MCs in mastocytosis and normal skin, but showed a considerable overlap. The observed numbers of MCs in adults cannot be extrapolated to children. CONCLUSIONS: MC numbers varied significantly between proximal and distal body sites and these differences must be considered when MCs are counted for a reliable diagnosis of mastocytosis. There was a considerable overlap between the numbers of MCs in mastocytosis and normal skin.

Adolescent↗
PubMed1981

Examination of a lognormal distribution equation for describing distributions of diameters of bovine adipocytes.

Samples of subcutaneous, intermuscular and mesenteric adipose tissues from beef steers were fixed with osmium tetroxide, and freed adipocytes were counted with an automatic particle counter to determine whether a lognormal distribution function would describe adipocyte size distributions more accurately than a normal distribution function. Modes and medians of size distributions generally were larger than means for adipocyte size distributions modeled with a lognormal distribution function. Normalized third and fourth moments of predicted lognormal distributions often were close to 0 and 3, respectively, which are expected values for a normally distributed population. Considerable variation was observed in the skewness of adipocyte size distributions. Both normal and lognormal models for adipocyte size distribution yielded similar means. The lognormal model yielded a greater standard deviation than the normal model for adipocyte size distributions. Smaller chi-square values were found for size distributions modeled with a lognormal than with a normal distribution function. Results suggest that a lognormal distribution function more accurately models the size distributions of bovine adipocytes.

Adipose Tissue↗
PubMed2000

Induced sputum cellularity. Reference values and distribution in normal volunteers.

Sputum induction has recently been proposed as the only direct noninvasive method for measuring airway inflammatory indices. The reference values and the distribution of cells in induced sputum in a control population have not yet been well defined. We therefore evaluated data from a large number of healthy volunteers. One hundred fourteen healthy, nonatopic, nonsmoking volunteers without airway hyperreactivity were enrolled (age: 38 +/- 13 yr [mean +/- SD]; FEV(1): 105 +/- 10% predicted; provocative dose of methacholine inducing a 20% decrease FEV(1) > 3,200 microgram). Ninety-six subjects (84%) produced adequate analysis samples. The subjects had a normal age distribution. Their induced sputum was rich in macrophages (69.2 +/- 13%) and neutrophils (27.3 +/- 13%), and poor in eosinophils (0.6 +/- 0.8%), lymphocytes (1.0 +/- 1.2%), and epithelial cells (1.5 +/- 1.8%). Only macrophages and neutrophils showed a normal distribution; total and differential counts of other cells did not. We propose that these data be used in comparison of the induced sputum cells of normal subjects and those of patients with airway inflammation.

Adult↗
PubMed1996

Sonographic appearance and distribution of normal cervical lymph nodes in a Chinese population.

In 100 normal subjects who had a sonographic examination of the neck, 1211 lymph nodes were detected. In all the subjects, at least five lymph nodes were seen. The distribution, number, echogenicity, shape, presence or absence of echogenic hilus, and the sharpness of nodal borders of normal cervical lymph nodes were determined. The usefulness of these sonographic features in understanding the normal distribution and characteristics of the nodes in the Chinese population is discussed. The relationship between the shape and size of lymph node also was assessed.

Adolescent↗
PubMed2001

The size distribution of human hematogenous metastases.

The development of primary cancers and their subsequent metastases occur through a complex sequence of discrete steps. A hypothesis is proposed here whereby the time available for the growth of metastases is normally distributed, presumably as a consequence of the summation of multiple independently distributed time intervals from each of the steps and of the Central Limit Theorem. For exponentially growing metastases, the corresponding size distribution would be lognormal; Gompertzian growth would imply a modified (Gompertz-normal) distribution, where larger metastases would occur less frequently as a consequence of a decreased growth rate. These two size distributions were evaluated against 18 human autopsy cases where precise size measurements had been collected from over 3900 macroscopic hematogenous organ metastases. The lognormal distribution provided an approximate agreement. Its main deficiency was a tendency to over-represent metastases greater than 10 mm diameter. The Gompertz-normal distribution provided more stringent agreement, correcting for this over-representation. These observations supported the hypothesis of normally distributed growth times, and qualified the utility of the lognormal and Gompertz-normal distributions for the size distribution of metastases.

Autopsy↗
PubMed1978

The correlation between relatives with assortative mating.

The equilibrium correlation between various close relatives is calculated for phenotypic assortative mating for a character determined by additive loci without dominance and an uncorrelated environment. It is supposed that the phenotypes of spouses have a bivariate normal distribution and environment and heredity are normally distributed. Heredity is Gaussian if either there are many alleles with approximately normally distributed effects at each of an arbitrary number of loci or the trait is controlled by many loci, each of which makes only a small contribution. It is also assumed that the regression of the phenotype or genotype of an individual on the phenotype or genotype of any one of his relatives is linear. The results show that with the above assumptions Fisher's formulae for the correlation between relatives hold with no restrictions on the linkage map.

Female↗
PubMed1982

A multi-stage Gaussian transformation algorithm for clinical laboratory data.

We have developed a multi-stage computer algorithm to transform non-normally distributed data to a normal distribution. This transformation is of value for calculation of laboratory reference intervals and for normalization of clinical laboratory variates before applying statistical procedures in which underlying data normality is assumed. The algorithm is able to normalize most laboratory data distributions with either negative or positive coefficients of skewness or kurtosis. Stepwise, a logarithmic transform removes asymmetry (skewness), then a Z-score transform and power function transform remove residual peakedness or flatness (kurtosis). Powerful statistical tests of data normality in the procedure help the user evaluate both the necessity for and the success of the data transformation. Erroneous assessments of data normality caused by rounded laboratory test values have been minimized by introducing computer-generated random noise into the data values. Reference interval endpoints that were estimated parametrically (mean +/- 2 SD) by using successfully transformed data were found to have a smaller root-mean-squared error than those estimated by the non-parametric percentile technique.

Adult↗
PubMed1986

Distributional expectations and the induction of category structure.

Previous research on how categories are learned from observation of exemplars has largely ignored the possible role of prior expectations concerning how exemplars will be distributed. The experiments reported here explored this issue by presenting subjects with category-learning tasks in which the distributions of exemplars defining the categories were varied. In Experiments 1 and 2 the distributional form of a category was found to affect speed of learning. Learning was faster when a category's distribution was normal than when it was multimodal. Also, subjects in the early stages of learning a multimodal category responded as if it were unimodal. These results suggested that subjects enter category-learning tasks with expectations of unimodal, possibly normal, distributions of exemplars. Experiments 3 and 4 attempted to manipulate subjects' prior expectations by varying the distribution of exemplars in the first of two consecutive category-learning tasks. Learning a multimodal category was influenced by the shape of a previously learned distribution and was facilitated when the earlier distribution was either multimodal or skewed, rather than normal. These results are interpreted as support for a dual-process model of category learning that incorporates the effects of prior expectations concerning exemplar distributions.

Adolescent↗
PubMed1994

Computing the central location of immunofluorescence distributions: logarithmic data transformations are not always appropriate.

The idea of the "average" intensity of immunofluorescence data is often poorly defined, with such terms as average, mean, and peak used interchangeably. In addition, the common use of logarithmic amplifiers with immunofluorescence data further complicates the problem. Log amplifiers permit the display of a wider range of fluorescence intensities. At the same time, they effect a log transformation of the data. This transformation decreases the variance resulting in narrower fluorescence distributions, which are assumed to approximate normal distributions. When the log transform is used, the distribution mean is the geometric mean of the untransformed data, which is computed simply as the mean of the channel values. This mean value serves as a simple indicator of the population center. Despite the prevalence of log transformations in flow cytometry, this transformation may not yield normally distributed immunofluorescence data, whereas the square root or other fractional power transformations can yield normal distributions.

Flow Cytometry↗
PubMed1976

Differential transglutaminase distribution in normal rat liver and rat hepatoma.

Distribution of transglutaminase activity was determined in normal rat liver, a 3'-methyl-4-dimethylaminoazobenzene-induced primary hepatoma, and the Novikoff hepatoma. Over 90% of the total enzyme activity was found in the 105,000 X g supernatant of normal liver, whereas only 30% was found in this fraction of the hepatomas, the remainder being found in the particulate fraction. The is distribution pattern did not correlate with protein distribution nor did it change during cellular proliferation, since regenerating liver and embryonic tissue had the same pattern as normal liver. Cell protein was a suitable acceptor substrate for the enzyme. Kinetic analyses showed that liver and hepatoma enzymes had a similar Km and Vmax for putrescine incorporation into cell protein. Hepatoma particulate enzyme was more stable than either liver or hepatoma supernatant enzyme. The enzyme may also act as the acceptor molecule.

Animals↗
PubMed2001

Modeling the effects of inhomogeneous dose distributions in normal tissues.

Conformal radiation therapy frequently produces inhomogeneous dose distributions in normal tissues near the target. Most mathematical models of normal tissue complication probabilities (NTCP) are based on uniform whole or partial organ irradiation, and the model parameters are chosen to obtain agreement with clinical outcomes in these simple situations. Frequently used NTCP models and methods for including inhomogeneous dose distributions in model calculations are outlined in this report. It has been found that the model adopted may qualitatively affect prediction of complications. Limitations placed on current models by the scarcity of reliable complications data and other approaches to using the calculated dose distribution to predict NTCP are discussed.

Dose-Response Relationship, Radiation↗
PubMed2002

Estimation of an errors-in-variables regression model when the variances of the measurement errors vary between the observations.

It is common in the analysis of aggregate data in epidemiology that the variances of the aggregate observations are available. The analysis of such data leads to a measurement error situation, where the known variances of the measurement errors vary between the observations. Assuming multivariate normal distribution for the 'true' observations and normal distributions for the measurement errors, we derive a simple EM algorithm for obtaining maximum likelihood estimates of the parameters of the multivariate normal distributions. The results also facilitate the estimation of regression parameters between the variables as well as the 'true' values of the observations. The approach is applied to re-estimate recent results of the WHO MONICA Project on cardiovascular disease and its risk factors, where the original estimation of the regression coefficients did not adjust for the regression attenuation caused by the measurement errors.

Algorithms↗
PubMedDate not supplied

Dystrophin and dystrophin-related protein (utrophin) distribution in normal and dystrophin-deficient skeletal muscles.

The respective localizations of dystrophin and dystrophin-related protein (DRP or utrophin) along the sarcolemmal membrane and at the neuromuscular junctions (NMJs) in normal and dystrophin-deficient skeletal muscles, were determined using confocal laser microscopy. The analysis was prompted by the recent availability of a new anti-utrophin mAb [Bewick et al. NeuroReport 1992; 3:857-860] and different mAbs that react with dystrphin or both dystrophin and utrophin. In dystrophin-deficient muscles, utrophin was expressed and detectable over large subcellular areas normally occupied by dystrophin along the sarcolemmal membranes and at the NMJs. Utrophin was expressed in a non-uniform, discontinuous way on the sarcolemmal membrane in dystrophin-deficient skeletal muscles, similar to dystrophin in normal muscle fibres. The respective distributions of both related muscle proteins and their positions relative to the alpha-bungarotoxin acetylcholine (ACh) receptor marker were determined. Double-staining experiments and superimposition of the confocal images showed that utrophin was more closely associated with ACh receptors than dystrophin at the NMJs in normal muscles. Utrophin distribution consequently differed from that of dystrophin.

Adolescent↗
PubMed1995

Quantitative analysis of senile plaques in Alzheimer disease: observation of log-normal size distribution and molecular epidemiology of differences associated with apolipoprotein E genotype and trisomy 21 (Down syndrome).

The discovery that the epsilon 4 allele of the apolipoprotein E (apoE) gene is a putative risk factor for Alzheimer disease (AD) in the general population has highlighted the role of genetic influences in this extremely common and disabling illness. It has long been recognized that another genetic abnormality, trisomy 21 (Down syndrome), is associated with early and severe development of AD neuropathological lesions. It remains a challenge, however, to understand how these facts relate to the pathological changes in the brains of AD patients. We used computerized image analysis to examine the size distribution of one of the characteristic neuropathological lesions in AD, deposits of A beta peptide in senile plaques (SPs). Surprisingly, we find that a log-normal distribution fits the SP size distribution quite well, motivating a porous model of SP morphogenesis. We then analyzed SP size distribution curves in genotypically defined subgroups of AD patients. The data demonstrate that both apoE epsilon 4/AD and trisomy 21/AD lead to increased amyloid deposition, but by apparently different mechanisms. The size distribution curve is shifted toward larger plaques in trisomy 21/AD, probably reflecting increased A beta production. In apoE epsilon 4/AD, the size distribution is unchanged but the number of SP is increased compared to apoE epsilon 3, suggesting increased probability of SP initiation. These results demonstrate that subgroups of AD patients defined on the basis of molecular characteristics have quantitatively different neuropathological phenotypes.

Aged↗
PubMed1987

Glandular elements around the intrahepatic bile ducts in man; their morphology and distribution in normal livers.

The morphology and distribution of the glandular elements around the intrahepatic bile ducts, hitherto poorly described, were examined in autopsied human livers with the aid of postmortem cholangiographs. The glands could be divided into intramural and extramural. The former were small in number, scattered within the bile duct walls, and were simple tubular mucous glands. The latter were more abundant, located in the periductal connective tissue, and were branched tubuloalveolar seromucous glands. Serial section observations revealed that neither gland communicated with the hepatic parenchyma, and the extramural glands drained into the large bile duct lumina via the conduits. The mucous cells of both glands contained neutral, carboxylated and sulfated glycoproteins. The extramural glands were distributed from the hepatic to the segment ducts in almost all livers, and were also discerned around the area ducts in two-fifths of the livers. The glands seemed to decrease in number as the bile ducts became more branched.

Aged↗