A Metric Fractionator for Estimation of Total Cell Number in Paraffin-Embedded Flat or Hollow Organs

The physical fractionator is a convenient and practical solution for estimation of total cell number in a regulatory toxicology setting because it is insensitive to shrinkage allowing for paraffin processing/embedding and does not require measurement of the reference or organ volume. The principle involves sampling a known fraction of an organ in one or more steps and counting the total number of cells present in the final sample, physical disector section pairs. The total cell number in the organ is estimated by multiplying the cell count in the final fraction by the inverse of the sampling fraction(s). The key feature of the design is that tissue shrinkage due to paraffin processing occurs before the organ is uniformly sampled. Another requirement is that thermal expansion or contraction is avoided during the preparation of disector sections from the individual embedded subsamples, which ensures that the disector sections represent a known constant fraction. This vertical physical fractionator with subsampling is a simple and fast estimator to obtain precise and robust estimates of total cell number in large flat or hollow organs that do not prolong routine necropsy procedures. It is compatible with paraffin processing, avoids exhaustive sectioning, and allows for the collection of routine histopathology sections.

Estimation of the number of alveolar capillaries by the Euler number (Euler-Poincaré characteristic)

The lung parenchyma provides a maximal surface area of blood-containing capillaries that are in close contact with a large surface area of the air-containing alveoli. Volume and surface area of capillaries are the classic stereological parameters to characterize the alveolar capillary network (ACN) and have provided essential structure-function information of the lung. When loss (rarefaction) or gain (angiogenesis) of capillaries occurs, these parameters may not be sufficient to provide mechanistic insight. Therefore, it would be desirable to estimate the number of capillaries, as it contains more distinct and mechanistically oriented information. Here, we present a new stereological method to estimate the number of capillary loops in the ACN. One advantage of this method is that it is independent of the shape, size, or distribution of the capillaries. We used consecutive, 1 μm-thick sections from epoxy resin-embedded material as a physical disector. The Euler-Poincaré characteristic of capillary networks can be estimated by counting the easily recognizable topological constellations of “islands,” “bridges,” and “holes.” The total number of capillary loops in the ACN can then be calculated from the Euler-Poincaré characteristic. With the use of the established estimator of alveolar number, it is possible to obtain the mean number of capillary loops per alveolus. In conclusion, estimation of alveolar capillaries by design-based stereology is an efficient and unbiased method to characterize the ACN and may be particularly useful for studies on emphysema, pulmonary hypertension, or lung development.

A design-based method for estimating glomerular number in the developing kidney

Low glomerular (nephron) endowment has been associated with an increased risk of cardiovascular and renal disease in adulthood. Nephron endowment in humans is determined by 36 wk of gestation, while in rats and mice nephrogenesis ends several days after birth. Specific genes and environmental perturbations have been shown to regulate nephron endowment. Until now, design-based method for estimating nephron number in developing kidneys was unavailable. This was due in part to the difficulty associated with unambiguously identifying developing glomeruli in histological sections. Here, we describe a method that uses lectin histochemistry to identify developing glomeruli and the physical disector/fractionator principle to provide unbiased estimates of total glomerular number ( Nglom). We have characterized Nglom throughout development in kidneys from 76 rats and model this development with a 5-parameter logistic equation to predict Nglom from embryonic day 17.25 to adulthood ( r2 = 0.98). This approach represents the first design-based method with which to estimate Nglom in the developing kidney.

ESTIMATING NUMBER DENSITY NV – A COMPARISON OF AN IMPROVED SALTYKOV ESTIMATOR AND THE DISECTOR METHOD

Two methods for the estimation of number per unit volume NV of spherical particles are discussed: the (physical) disector (Sterio, 1984) and Saltykov's estimator (Saltykov, 1950; Fullman, 1953). A modification of Saltykov's estimator is proposed which reduces the variance. Formulae for bias and variance are given for both disector and improved Saltykov estimator for the case of randomly positioned particles. They enable the comparison of the two estimators with respect to their precision in terms of mean squared error.

NEPHRON NUMBER IN THE OFFSPRING OF RATS FED A LOW PROTEIN DIET DURING PREGNANCY

In experimental studies it has been shown that intrauterine growth retardation and reduced kidney growth during development are associated with significant decreases in nephron endowment. However, the results of previous studies may be inaccurate as nephron counts were obtained using a maceration technique, which can lead to breakdown of glomeruli, and other potentially biased techniques. In the present study, the total number of glomeruli (and thereby nephrons) in the offspring of rats fed a low (9%) or normal (20%) protein diet during pregnancy were estimated using a physical disector/fractionator technique. The offspring of rats fed a low protein diet had a significantly lower birth weight than rats fed a normal protein diet, their kidneys were smaller and they contained 30% fewer nephrons (20,386 ± 4,818 in the low protein diet vs. 28,731 ± 3,290 in the control rats). Our results, obtained using an unbiased stereological technique confirm previous findings that administration of a low protein diet during pregnancy results in reduced nephron endowment in the offspring.