Beyond volume: Unraveling the genetics of human brain geometry

Brain geometry affects brain function. A quantitative encoding of form is provided by the Laplace-Beltrami operator's spectrum of eigenvalues (LBS). We examined LBS genetics of 22 subcortical brain structures and cerebellum in 19,862 healthy White-British UK Biobank participants by multivariate genome-wide association study on the first 49 eigenvalues each. Controlling for surface and volume, we identified 80 unique variants influencing the shapes of one or several structures, with the highest yield (37 variants) for brain stem. The previously known influence of several of these loci on basic morphology, such as volume, is thus shown to also influence complex shape. Known associations of observed loci with blood pressure, neurodegeneration, alcohol consumption, and mental disorders hint at preclinical stages of these conditions potentially mediating the genetic effect on brain morphology. Significant correlations between LBS of several brain structures and the polygenic risks of hypertension, ischemic stroke, and schizophrenia evince brain shapes as early biomarkers.