Using two dimensional sectional distributions to infer three dimensional volumetric distributions - Validation using tomography

The critical process parameter for mineral separation is the degree of mineral liberation achieved by comminution. The degree of liberation provides an upper limit of efficiency for any physical separation process. The standard approach to measuring mineral liberation uses mineralogical analysis based two-dimensional sections of particles which may be acquired using a scanning electron microscope and back-scatter electron analysis or from an analysis of an image acquired using an optical microscope. Over the last 100 years, mathematical techniques have been developed to use this two dimensional information to infer three-dimensional information about the particles. For mineral processing, a particle that contains more than one mineral (a composite particle) may appear to be liberated (contain only one mineral) when analysed using only its revealed particle section. The mathematical techniques used to interpret three-dimensional information belong, to a branch of mathematics called stereology. However methods to obtain the full mineral liberation distribution of particles from particle sections are relatively new. To verify these adjustment methods, we require an experimental method which can accurately measure both sectional and three dimensional properties. Micro Cone Beam Tomography provides such a method for suitable particles and hence, provides a way to validate methods used to convert two-dimensional measurements to three dimensional estimates. For this study ore particles from a well-characterised sample were subjected to conventional mineralogical analysis (using particle sections) to estimate three-dimensional properties of the particles. A subset of these particles was analysed using a micro-cone beam tomograph. This paper presents a comparison of the three-dimensional properties predicted from measured two-dimensional sections with the measured three-dimensional properties.

How many glomerular profiles must be measured to obtain reliable estimates of mean glomerular areas in human renal biopsies?

The objective of this study was to investigate the number of glomerular profiles that are required for accurate estimates of mean profile area in a renal biopsy series. Slides from 384 renal biopsies from one center were reviewed. They contained a median of seven glomerular profiles or of four profiles without sclerosis. Profile areas were measured using stereologic point counting. The true individual mean for each biopsy was calculated and the true population mean for groups of biopsies derived. Individual and population random sample means then were calculated from a random sampling of profiles in each biopsy and were compared with true means for the same biopsies. The effect on the true population means of the entire group of biopsies was also assessed, as the minimum number of glomerular profiles that were required for inclusion was changed. In a single biopsy, random sampling of >= 10 profiles without exclusions and of eight profiles or more without sclerosis reliably estimated the true mean areas. In a group of 30 biopsies, random sampling of five or more glomeruli per biopsy reliably estimated the true population mean. In the aggregate series, inclusion of all 384 biopsies produced the most robust true population mean; the reliability of the estimates decreased as the numbers of eligible biopsies diminished with increasing requisite minimum numbers of profiles per biopsy. We conclude that, while >= 10 profiles might be needed for reliable area estimates in a single biopsy, far fewer profiles per biopsy can suffice when groups of biopsies are studied. In analyses of groups of biopsies, all available biopsies should be used without consideration of the number of glomerular profiles in each. Stipulation of a specific minimum number of glomeruli in each biopsy for inclusion reduces the power of analyses because fewer biopsies are available for evaluation.

Hypertension, glomerular number, and birth weight in African Americans and white subjects in the southeastern United States

Low nephron number has been related to low birth weight and hypertension. In the southeastern United States, the estimated prevalence of chronic kidney disease due to hypertension is five times greater for African Americans than white subjects. This study investigates the relationships between total glomerular number (N-glom), blood pressure, and birth weight in southeastern African Americans and white subjects. Stereological estimates of N-glom were obtained using the physical disector/fractionator technique on autopsy kidneys from 62 African American and 60 white subjects 30-65 years of age. By medical history and recorded blood pressures, 41 African Americans, and 24 white subjects were identified as hypertensive and 21 African Americans and 36 white subjects as normotensive. Mean arterial blood pressure ( MAP) was obtained on 81 and birth weights on 63 subjects. For African Americans, relationships between MAP, N-glom, and birth weight were not significant. For white subjects, they were as follows: MAP and N-glom ( r = -0.4551, P = 0.0047); Nglom and birth weight ( r = 0.5730, P = 0.0022); MAP and birth weight ( r = -0.4228, P = 0.0377). For African Americans, average N-glom of 961 840 +/- 292 750 for normotensive and 867 358 +/- 341 958 for hypertensive patients were not significantly different ( P = 0.285). For white subjects, average N-glom of 923 377 +/- 256 391 for normotensive and 754 319 +/- 329 506 for hypertensive patients were significantly different ( P = 0.03). The data indicate that low nephron number and possibly low birth weight may play a role in the development of hypertension in white subjects but not African Americans.

Analysis of population dispersion in histological sections

Stereology and other image analysis methods have enabled rapid and objective quantitative measurements to be made on histological sections. These mesurements may include total volumes, surfaces, lengths and numbers of cells and blood vessels or pathological lesions. Histological features, however, may not be randomly distributed across a section but exhibit 'dispersion', a departure from randomness either towards regularity or aggregation. Information of population dispersion may be valuable not only in understanding the two-or three-dimensional structure but also in elucidating the pathogenesis of lesions in pathological conditions. This article reviews some of the statistical methods available for studying dispersion. These range from simple tests of whether the distribution of a histological faeture departs significantly from random to more complex methods which can detect the intensity of aggregation and the sizes, distribution and spacing of the clusters.

Implementação da rotina de unfolding para determinação de distribuição de tamanho de grãos esféricos via distribuição de interceptos lineares e de área de seção

Na unfolding method of linear intercept distributions and secction área distribution was implemented for structures with spherical grains. Although the unfolding routine depends on the grain shape, structures with spheroidal grains can also be treated by this routine. Grains of non-spheroidal shape can be treated only as approximation. A software was developed with two parts. The first part calculates the probability matrix. The second part uses this matrix and minimizes the chi-square. The results are presented with any number of size classes as required. The probability matrix was determined by means of the linear intercept and section area distributions created by computer simulation. Using curve fittings the probability matrix for spheres of any sizes could be determined. Two kinds of tests were carried out to prove the efficiency of the Technique. The theoretical tests represent ideal cases. The software was able to exactly find the proposed grain size distribution. In the second test, a structure was simulated in computer and images of its slices were used to produce the corresponding linear intercept the section area distributions. These distributions were then unfolded. This test simulates better reality. The results show deviations from the real size distribution. This deviations are caused by statistic fluctuation. The unfolding of the linear intercept distribution works perfectly, but the unfolding of section area distribution does not work due to a failure in the chi-square minimization. The minimization method uses a matrix inversion routine. The matrix generated by this procedure cannot be inverted. Other minimization method must be used

Análise gráfica de estruturas porosas sobre a ótica da estereologia

In this work we developed a computer simulation program for physics porous structures based on programming language C + + using a Geforce 9600 GT with the PhysX chip, originally developed for video games. With this tool, the ability of physical interaction between simulated objects is enlarged, allowing to simulate a porous structure, for example, reservoir rocks and structures with high density. The initial procedure for developing the simulation is the construction of porous cubic structure consisting of spheres with a single size and with varying sizes. In addition, structures can also be simulated with various volume fractions. The results presented are divided into two parts: first, the ball shall be deemed as solid grains, ie the matrix phase represents the porosity, the second, the spheres are considered as pores. In this case the matrix phase represents the solid phase. The simulations in both cases are the same, but the simulated structures are intrinsically different. To validate the results presented by the program, simulations were performed by varying the amount of grain, the grain size distribution and void fraction in the structure. All results showed statistically reliable and consistent with those presented in the literature. The mean values and distributions of stereological parameters measured, such as intercept linear section of perimeter area, sectional area and mean free path are in agreement with the results obtained in the literature for the structures simulated. The results may help the understanding of real structures.

Simulação computacional de medidas estereológicas em estruturas de metal duro (WC-Co)

This work focuses on the creation and applications of a dynamic simulation software in order to study the hard metal structure (WC-Co). The technological ground used to increase the GPU hardware capacity was Geforce 9600 GT along with the PhysX chip created to make games more realistic. The software simulates the three-dimensional carbide structure to the shape of a cubic box where tungsten carbide (WC) are modeled as triangular prisms and truncated triangular prisms. The program was proven effective regarding checking testes, ranging from calculations of parameter measures such as the capacity to increase the number of particles simulated dynamically. It was possible to make an investigation of both the mean parameters and distributions stereological parameters used to characterize the carbide structure through cutting plans. Grounded on the cutting plans concerning the analyzed structures, we have investigated the linear intercepts, the intercepts to the area, and the perimeter section of the intercepted grains as well as the binder phase to the structure by calculating the mean value and distribution of the free path. As literature shows almost consensually that the distribution of the linear intercepts is lognormal, this suggests that the grain distribution is also lognormal. Thus, a routine was developed regarding the program which made possible a more detailed research on this issue. We have observed that it is possible, under certain values for the parameters which define the shape and size of the Prismatic grain to find out the distribution to the linear intercepts that approach the lognormal shape. Regarding a number of developed simulations, we have observed that the distribution curves of the linear and area intercepts as well as the perimeter section are consistent with studies on static computer simulation to these parameters.

Maternal glucose intolerance reduces offspring nephron endowment and increases glomerular volume in adult offspring

Background: Animal studies report a nephron deficit in offspring exposed to maternal diabetes, yet are limited to models of severe hyperglycaemia which do not reflect the typical clinical condition and which are associated with foetal growth restriction that may confound nephron endowment. We aimed to assess renal morphology and function in offspring of leptin receptor deficient mice (Leprdb/+) and hypothesized that exposure to impaired maternal glucose tolerance (IGT) would be detrimental to the developing kidney.

Methods: Nephron endowment was assessed in offspring of C57BKS/J Leprdb/+ and +/+ mice at embryonic day (E)18 and postnatal day (PN)21 using design-based stereology. Transcutaneous measurement of renal function and total glomerular volume were assessed in 6-month-old offspring. Only +/+ offspring of Leprdb/+ dams were analysed.

Results: Compared with +/+ dams, Leprdb/+ dams had a 20% and 35% decrease in glucose tolerance prior to pregnancy and at E17.5 respectively. Offspring of IGT Leprdb/+ dams had approximately 15% fewer nephrons at E18.5 and PN21 than offspring of +/+ dams. There was no difference in offspring bodyweight. Despite normal renal function, total glomerular volume was 13% greater in 6-month-old offspring of IGT Leprdb/+ dams than in +/+ offspring.

Conclusions: IGT throughout gestation resulted in a nephron deficit that was established early in renal development. Maternal IGT was associated with glomerular hypertrophy in adult offspring, likely a compensatory response to maintain normal renal function. Given the increasing prevalence of IGT, monitoring glucose from early in gestation may be important to prevent altered kidney morphology.