Allometric Analysis Detects Brain Size-Independent Effects of Sex and Sex Chromosome Complement on Human Cerebellar Organization

Abstract

The cerebellum is a large hindbrain structure that is increasingly recognized for its contribution to diverse domains of cognitive and affective processing in human health and disease. Although several of these domains are sex biased, our fundamental understanding of cerebellar sex differences-including their spatial distribution, potential biological determinants, and independence from brain volume variation-lags far behind that for the cerebrum. Here, we harness automated neuroimaging methods for cerebellar morphometrics in 417 individuals to (1) localize normative male-female differences in raw cerebellar volume, (2) compare these to sex chromosome effects estimated across five rare sex (X/Y) chromosome aneuploidy (SCA) syndromes, and (3) clarify brain size-independent effects of sex and SCA on cerebellar anatomy using a generalizable allometric approach that considers scaling relationships between regional cerebellar volume and brain volume in health. The integration of these approaches shows that (1) sex and SCA effects on raw cerebellar volume are large and distributed, but regionally heterogeneous, (2) human cerebellar volume scales with brain volume in a highly nonlinear and regionally heterogeneous fashion that departs from documented patterns of cerebellar scaling in phylogeny, and (3) cerebellar organization is modified in a brain size-independent manner by sex (relative expansion of total cerebellum, flocculus, and Crus II-lobule VIIIB volumes in males) and SCA (contraction of total cerebellar, lobule IV, and Crus I volumes with additional X- or Y-chromosomes; X-specific contraction of Crus II-lobule VIIIB). Our methods and results clarify the shifts in human cerebellar organization that accompany interwoven variations in sex, sex chromosome complement, and brain size.SIGNIFICANCE STATEMENT Cerebellar systems are implicated in diverse domains of sex-biased behavior and pathology, but we lack a basic understanding of how sex differences in the human cerebellum are distributed and determined. We leverage a rare neuroimaging dataset to deconvolve the interwoven effects of sex, sex chromosome complement, and brain size on human cerebellar organization. We reveal topographically variegated scaling relationships between regional cerebellar volume and brain size in humans, which (1) are distinct from those observed in phylogeny, (2) invalidate a traditional neuroimaging method for brain volume correction, and (3) allow more valid and accurate resolution of which cerebellar subcomponents are sensitive to sex and sex chromosome complement. These findings advance understanding of cerebellar organization in health and sex chromosome aneuploidy.

Keywords: cerebellum; development; genetics; neuroimaging.

Figure 1.

Cerebellar segmentation scheme. We used the recently developed the MAGeT Brain algorithm for multiatlas segmentation to profile cerebellar anatomy according to a nested scheme that fractionates total cerebellar volume into ever finer levels of spatial resolution spanning phylogenetic, lobar, and lobular divisions. These divisions are color coded on 3D surface renderings of the cerebellum shown from ventral (top row) and dorsal (bottom row) views, and these same color codes are used to distinguish cerebellar regions in Figures 3 and 4.

Figure 2.

Global and regional cerebellar volumes in each group (cm³) and tests for group differences. Mean (SEM) volumes are shown for all volumetric indices in each karyotype group within the core sample along with (1) results of an F test for the omnibus effect of karyotype group on each volume and (2) a heat map of −log10 p values for all unique pairwise t tests for karyotype group differences in each volume.

Figure 3.

Point–range plots detailing cerebellar volume variation across the seven groups in our core sample. Mean volumes (±95% confidence intervals) of all cerebellar volumes and aTBVs are shown in each karyotype group as effect size shifts relative to XY males as a common reference group. A–C, Effect sizes are plotted separately for phylogenetic (A), lobar (B), and lobular (C) divisions using color codes that are identical to those in Figure 1.

Figure 4.

Normative allometry of cerebellar volume across lobules. A, A point–range plot showing the estimated scaling coefficient (±95% confidence intervals) with aTBV for the TCbV, the three major phylogenetic subdivisions, and each cerebellar lobule. Color codes are identical to those in Figure 1. B, Cerebellar heat map with colors coding the allometric slope.

Figure 5.

Normative cerebellar scaling. Scatter plots of volumetric data and best-fit scaling models for selected cerebellar regions. Gray points indicate volumetric observations for females (circles) and males (triangles) in the allometric sample. Superimposed lines show the best fit log–log relationship between aTBVs and cerebellar volumes (±95% confidence intervals). Sexes are modeled separately in regions with statistically significant sex differences in scaling or offset (p < 0.05). The cerebellum as a whole scales hypoallometrically with aTBV, and shows an aTBV-independent volume increase in males vs females. Note the diversity of scaling models across different cerebellar subregions. These plots show the reference fit lines used for “allometrically corrected” reanalysis of cerebellar anatomy in SCA.

Figure 6.

Comparison of pairwise group differences in cerebellar volumes across methods for accounting for aTBV. Heat maps show p values for significant volume differences between karyotype groups for multiple measures of cerebellar volume. Each heat map refers to a different method of controlling for brain size effects. p values are shown on a −log10 scale, with more intense colors representing smaller p values. Gray cells denote pairwise contrasts that are not statistically significant (Bonferroni-corrected, p > 0.05). All significant contrasts involve volume reductions.