Transformation of a grid of quadrats to cope with perspective artifacts

The direct superimposition of a standard test grid of congruent quadrats onto an image bearing a population of particles exhibiting perspective artifacts, tends to increase the variance of the population size estimator, because the quadrat contents become unbalanced. If the quadrats are transformed according to the same projection mechanism affecting the particles, however, then the variance is restored into moderate values. Our purpose was to provide exact, easily programmable equations for the relevant transform

On the precisión of the nucleator

Abstract The nucleator is a design unbiased method of local stereology for estimating the volume of a bounded object. The only information required lies in the intersection of the object with an isotropic random ray emanating from a fixed point (called the pivotal point) associated with the object. For instance, the volume of a neuron can be estimated from a random ray emanating from its nucleolus. The nucleator is extensively used in biosciences because it is efficient and easy to apply. The estimator variance can be reduced by increasing the number of rays. In an earlier paper a systematic sampling design was proposed, and theoretical variance predictors were derived, for the corresponding volume estimator. Being the only variance predictors hitherto available for the nucleator, our basic goal was to check their statistical performance by means of Monte Carlo resampling on computer reconstructions of real objects. As a plus, the empirical distribution of the volume estimator revealed statistical properties of practical relevance

The invariator Design: An update

The invariator is a method to generate a test line within an isotropically oriented plane through a fixed point, in such a way that the test line is effectively motion invariant in three dimensional space. Generalizations exist for non Euclidean spaces. The invariator design is convenient to estimate surface area and volume simultaneously. In recent years a number of new results have appeared which call for an updated survey. We include two new estimators, namely the a posteriori weighting estimator for surface area and volume, and the peak-and-valley formula for surface area

On the precision of the isotropic Cavalieri design

ABSTRACT: The isotropic Cavalieri design is based on a isotropically oriented set of parallel systematic sections a constant distance apart. Its advantage over the ordinary Cavalieri design is twofold - first, besides volume it allows the unbiased estimation of surface area, and second, the error variance predictor for the volume estimator is much simpler, involving only the surface area of the object, and the distance between sections. In an earlier paper, the two hemispheres of a rat brain were arranged perpendicular to each other before sectioning, aiming at reducing the error variance with respect to other arrangements (such as the aligned one) by exploiting an intuitively plausible antithetic effect. Because the total surface area of the objects is unchanged under any arrangements, however, the error variance predictor for the volume estimator does not depend on object shape, which looks intriguing. Using reconstructions of the mentioned hemispheres, we dilucidate the aparent paradox by means of automatic Monte Carlo replications of the relevant volume estimates under the antithetic and the aligned arrangements.The authors acknowledge financial support from the Spanish project AYA2015-66357-R (MINECO/FEDER)

Stereology with cylinder probes

Intersection formulae of Croton type for general geometric probes are well known in integral geometry. For the special case of cylinders with non necessarily convex direktrix, however, no equivalent formula seems to exist in the literature. We derive such formula resorting to motion invariant probability elements associated with test systems, instead of using a traditional approach. Because cylinders are seldom used as probes in stereological practice, however, this note is mainly of a theoretical nature

New rotational integrals in space forms, with an application to surface area estimation

A surface area estimator for three-dimensional convex sets, based on the invariator principle of local stereology, has recently motivated its generalization by means of new rotational Crofton-type formulae using Morse theory. We follow a different route to obtain related formulae which are more manageable and valid for submanifolds in constant curvature spaces. As an application, we obtain a simplified version of the mentioned surface area estimator for non-convex sets of smooth boundary.Work was supported by the UJI project P11B2012-24 and the PROMETEOII/2014/062 project

Variance prediction for population size estimation

Design unbiased estimation of population size by stereological methods is an efficient alternative to automatic computer vision methods, which are generally biased. Moreover, stereological methods offer the possibility of predicting the error variance from a single sample. Here we explore the statistical performance of two alternative variance estimators on a dataset of 26 labelled crowd pictures. The empirical mean square errors of the variance predictors are compared by means of Monte Carlo resampling

Efficient and Unbiased Estimation of Population Size

Population sizing from still aerial pictures is of wide applicability in ecological and social sciences. The problem is long standing because current automatic detection and counting algorithms are known to fail in most cases, and exhaustive manual counting is tedious, slow, difficult to verify and unfeasible for large populations. An alternative is to multiply population density with some reference area but, unfortunately, sampling details, handling of edge effects, etc., are seldom described. For the first time we address the problem using principles of geometric sampling. These principles are old and solid, but largely unknown outside the areas of three dimensional microscopy and stereology. Here we adapt them to estimate the size of any population of individuals lying on an essentially planar area, e.g. people, animals, trees on a savanna, etc. The proposed design is unbiased irrespective of population size, pattern, perspective artifacts, etc. The implementation is very simple—it is based on the random superimposition of coarse quadrat grids. Also, an objective error assessment is often lacking. For the latter purpose the quadrat counts are often assumed to be independent. We demonstrate that this approach can perform very poorly, and we propose (and check via Monte Carlo resampling) a new theoretical error prediction formula. As far as efficiency, counting about 50 (100) individuals in 20 quadrats, can yield relative standard errors of about 8% (5%) in typical cases. This fact effectively breaks the barrier hitherto imposed by the current lack of automatic face detection algorithms, because semiautomatic sampling and manual counting becomes an attractive option

Ultrastructural changes in chemically induced preneoplastic focal lesions in the rat liver: a stereological study

Ultrastructural changes were investigated and quantified, using a stereological approach, in early gamma-glutamyl transpeptidase (GGT)-positive focal lesions, induced in the rat liver by treatment with a single initiating dose of diethylnitrosamine (DENA) followed by promotion with phenobarbitone (PB) for 30 weeks. Within the extra-hepato cyte environment of focal tissue, the mean volume occupied by Ito cells was markedly decreased, whilst that occupied by endothelial and Kupffer cells was increased, when compared to uninvolved tissue from the same rat livers. The bile canalicull were dilated, but nosignificant differences in the mean volume occupkd by the sinusoidal and Disse spaces were noted. In focal hepatocytes there was a striking overproduction of lipid droplets and proliferation of smooth endoplasmic reticulum (sER). Whorls of concentrically arranged, parallel ER membranes were found only in the hepatocytes of preneoplastic foci, in association with the proliferated sER, and never in the surrounding, uninvolved tissue. The Increase In mean volume of the sER, lipid droplet and cytoplasmic matrix compartments, together with the appearance of whorls, were the major contributing factors to the marked hypertrophy seen in focal hepatocytes. The mean volume of the rough endoplasmic reticulum, mitochondrial, lysosomal, peroxisomal and nuclear compartments per hepatocyte also Increased, but contributed to a lesser extent to the cellular hypertrophy. It is speculated that whorls may be structural adaptations, resulting from a possible alteration in the normalfeedback control of cholesterol synthesis, for the production of sterols and the biogenesis of sER in eosinophilic-type focal cells. The significance of changes observed in focal tissue, and the high biological variation noted between foci, is discussed in relation to the hepatocarcinogenic proces

Carboxymethylchitosan/poly (amidoamine) dendrimer nanoparticles in central nervous systems-regenerative medicine: effects on neuron/glial cell viability and internalization efficiency

The applicability of CMCht/PAMAM dendrimer nanoparticles for CNS applications was investigated. AFM and TEM observations revealed that the nanoparticles possessed a nanosphere- like shape with a size from 22.0 to 30.7 nm. The nanoparticles could be bound to fluorescent-probe FITC for tracing purposes. Post-natal hippocampal neurons and cortical glial cells were both able to internalize the FITC-labeled CMCht/PAMAM dendrimer nanoparticles with high efficiency. The percentage of positive cells internalizing the nanoparticles varied, reaching a peak after 48 h of incubation. Further experiments for periods up to 7 d revealed that the periodical addition of FITC-labelled CMCht/ PAMAM dendrimer nanoparticles was needed to maintain the overall percentage of cells internalizing them. Finally, it was also observed that cell viability was not significantly affected by the incubation of dendrimer nanoparticles.Financial support from the Portuguese Foundation for Science and Technology through funds from POCTI and/or FEDER programs (Funding to ICVS, 3B's Research Group, post-doctoral and pre-doctoral fellowships to A.J. Salgado and J.M. Oliveira - SFRH/BPD/17595/2004; SFRH/BD/21786/2005) is gratefully acknowledged. This work was also carried out under the scope of the European NoE EXPERTISSUES (NMP3-CT-2004-500283) and HIPPOCRATES STREP (NMP3-CT-2003-505758) projects