Measuring the intrarenal distribution of glomerular volumes from histological sections

Abstract

Glomerular volume is an important metric reflecting glomerular filtration surface area within the kidney. Glomerular hypertrophy, or increased glomerular volume, may be an important marker for renal stress. Current stereological techniques report the average glomerular volume (AVglom) within the kidney. These techniques cannot assess the spatial or regional heterogeneity common in developing renal pathology. Here, we report a novel "unfolding" technique to measure the actual distribution of individual glomerular volumes in a kidney from the two-dimensional glomerulus profiles observed by optical microscopy. The unfolding technique was first developed and tested for accuracy with simulations and then applied to measure the number of glomeruli (Nglom), AVglom, and intrarenal distribution of individual glomerular volume (IVglom) in the oligosyndactyl (Os/(+)) mouse model compared with wild-type (WT) controls. The Os/(+) mice had fewer and larger glomeruli than WT mice: Nglom was 12,126 ± 1,658 (glomeruli/kidney) in the WT mice and 5,516 ± 899 in the Os/(+) mice; AVglom was 2.01 ± 0.28 × 10(-4) mm(3) for the WT mice and 3.47 ± 0.35 × 10(-4) mm(3) for the Os/(+) mice. Comparing the glomerular volume distributions in Os/(+) and WT kidneys, we observed that the Os/(+) distribution peaked at a higher value of IVglom than the WT distribution peak, and glomeruli with a radius greater than 55 μm were more prevalent in the Os/(+) mice (3.4 ± 1.6% of total glomeruli vs. 0.6 ± 1.2% in WT). Finally, the largest profiles were more commonly found in the juxtamedullary region. Unfolding is a novel stereological technique that provides a new quantitative view of glomerular volume distribution in the individual kidney.

Keywords: chronic kidney disease; glomerular hypertrophy; glomerular volume distribution; kidney stereology; nephron number; unfolding algorithm.

Fig. 1.

A: a sphere with radius R cut by sampling planes at a random height (h) will produce a distribution of profiles, each with radius r. B: distribution of profile radii expected from randomly slicing a sphere of r = 39 μm. Since the measured data are a collection of profiles cut from spheres of different sizes, we developed an unfolding algorithm to estimate the original distribution of spheres from the collection of observed profiles. C: the unfolding procedure is based on the principal that the largest profiles are sections cut from the center of the largest population of spheres. Beginning with the largest size class, we calculated the number of spheres (bottom right) of that radius that produce the observed number of large profiles. Next, we subtracted all of the profiles that would arise from those spheres from the histogram (shown in gray; bottom left). This process was repeated until all of the observed profiles were accounted for. AU, arbitrary units.

Fig. 2.

An unfolding algorithm was developed to calculate the true radii of glomeruli from measured profiles. Here, the algorithm was validated using simulated data based on normally distributed spheres (left) or bimodally distributed spheres (right). We calculated the correlation coefficient between the known simulated particle radii and the calculated particle radii; the algorithm was accurate even with a broad distribution of particle radii (inset).

Fig. 3.

Left: sample microscopy image after smoothing, showing full resolution detail in the inserts; scale bars are 1 mm (white) and 0.2 mm (black). Right: masks showing the segmented medulla, cortex, and glomeruli.

Fig. 4.

Unfolding of measured glomerular profiles for wild-type (left) and Os/⁺ mice (right). Dashed line indicates original distribution of the measured profile radii. Small profiles were observed less frequently than expected based on the profiles.

Fig. 5.

Comparison of the volume distributions of glomeruli in wild-type (WT; n = 5) and Os/⁺ mice (n = 4). Error bars indicate intermouse standard deviation. *Significant (P < 0.05) differences between WT and Os/⁺ mice.

Fig. 6.

A: overview of spatial distribution of glomeruli in representative wild-type (WT) and Os/⁺ mice mapped by glomerulus area. Color indicates the area of each measured glomerular profile. Larger glomeruli and increased frequency of glomeruli near large vessels were observed in the Os/⁺ mice. On average, larger glomerular profiles were found closer to the center of the kidney section. B: average shortest distance to the edge of the coronal sections for all profiles compared with the largest 10% of profiles in WT (n = 3) and Os/⁺ mice (n = 3). *Statistically significant differences (P < 0.05, t-test).