A Spectrum of Cortical Surface Complexity in Autism, Dyslexia, and Controls As Measured by Spherical Harmonics

Background:  In many aspects of cortical development, autism and dyslexia occupy opposing extremes of a neuroanatomical distribution. Autism exhibits increased density of neocortical minicolumns, increased gyrification, decreased gyral window size, reduced corpus callosal volume, and enhanced radiate white matter volume; dyslexia, in contrast, exhibits increased minicolumnar density, reduced gyrification, greater gyral window size, and increased corpus callosal volume. Both conditions are typified by neurogenic anomalies and heterogeneous ectopic clusters, pinpointing early cortical development in their respective etiologies. While gyral complexity has previously been estimated using various gyrification indices, Spherical Harmonics (SH) offers the researcher a greater precision in recapitulating the shape of a 3-D form such as the brain, lending itself well to the study of gyral complexity in autism and dyslexia.

Objectives:   Based upon previous evidence, we have utilized SH, a set of basic functions defined on the unit sphere, to measure cerebral surface complexity in autistics, dyslexics, and controls to determine overall levels of complexity and divergence between groups.

Methods:  Raw data for our measurements of overall surface complexity utilizing spherical harmonics comprised T1-weighted MRI of the brains of 8 individuals, 1 of them female, with autism (8 y–38 y of age, mean 24 y); 13 dyslexic men (18.5 y–40.5 y of age, mean 30 y); and 431 controls, 224 female, comprising our normative data (4.7 y–22.3 y of age, mean 12 y). Triangular mesh representations of the cerebral cortical surface in scanner-based, RAS coordinate system were mapped to the unit sphere using an attraction-repulsion algorithm. Mesh topology was preserved, so that the transformed meshes triangulated the sphere. This mapping defined three scalar functions on the sphere: R(θ, φ), A(θ, φ), and S(θ, φ), each of which was represented as an SH series. Truncating the series at a particular maximum degree L_max provides an approximation to the cortical surface that incorporates greater detail as L_max is increased. We computed a shape index, s, for each surface by summing the truncation error as L_maxranged from 1 to 80, inclusive. Measurements for cellular analysis of individual gyri were taken from our previous postmortem studies.

Results:  As predicted by our theoretical model, the shape index varied significantly by diagnostic category. Autism exhibited a greater level of surface complexity, dyslexia presented within the lower ranges of our three groups, while controls occupied the median ranges.

Conclusions: When utilizing SH to measure overall surface complexity of the brain, autism and dyslexia display two extremes of a single distribution, while controls occupy an intermediate range between the two. Autism and dyslexia occupy similar diametric positions when measuring other aspects of corticalization. Together, this evidence supports our theory of a cerebral spectrum, one in which autism and dyslexia illustrate its two phenotypic extremes.