Tessellation analysis of glomerular spatial arrangement in mice with heritable renal hypoplasia

Abstract

Renal hypoplasia results from an insufficient kidney volume caused, in part, by a deficient number of glomeruli. The purpose of this study was to apply tessellation analysis to determine whether glomerular point patterns differed between adult normal (WT) and mutant (Br) mice with heritable renal hypoplasia and to delineate a spatial distribution accounting for the observed patterns. Kidneys from adult WT and Br mice were collected, processed with routine light histology and representative transverse sections were photographed. Cortical area and perimeter were calculated from traced tissue contours and glomeruli were identified and digitized. Voronoi tessellations were constructed and average parameters for Voronoi polygon number, area, perimeter and edge counts as well as spatial metrics comprising nearest neighbor and centroidal distances were calculated and compared. Point distributions were simulated by randomizing glomerular coordinates from each section and plotting the new points utilizing uniform random, Gaussian random, or isotropic functions. Average nearest neighbor distances were generated for each specimen and ranked with respect to corresponding values generated from 1,000 iterations for each simulated set. Results showed that WT and Br were significantly different for each parameter suggesting that WT kidneys possessed more glomeruli, but these were less clustered compared to Br. Simulations suggested that WT and Br demonstrated similar, but not identical, underlying glomerular spatial distributions. Defective gene expression in Br is important for determining glomerular number and the defective pattern likely results from a heterochronic disturbance consisting of a truncated growth trajectory during embryonic kidney development.

Figure 1

Comparison of average body weight, total kidney weight, percent kidney wet weight to body weight ratio, and percent kidney wet weight to body weight ratio between WT and Br mice.

Figure 2

Representative cross-sections of WT (A) and Br (B) kidneys with digitized glomeruli (inset) and corresponding tessellations (C,D). Bar = 5.0 mm.

Figure 3

Average Voronoi polygon edge count, area, perimeter and centroidal distance for WT and Br triplicates showing no significant differences between values indicating a high degree of repeatability for the digitization process.

Figure 4

Voronoi tessellations for 1000 points based on a uniform random (A), Gaussian random (B) or isotropic (C) function.

Figure 5

Representative transverse sections from individual WT (A, B) or Br (C, D) specimens used in this study. Bar = 5.0 mm

Figure 6

Representative WT section showing the actual distribution of glomeruli (A) and simulated patterns using the same number of digitized points based on a uniform random (B), Gaussian random (C), or isotropic (D) function.