A Cerebral Spectrum From Autism to Dyslexia: Determining Cortical Surface Complexity Utilizing Spherical Harmonics

Background: Autism and dyslexia occupy extremes of a neuroanatomical distribution. While autism exhibits characteristics indicative of increased neocortical progenitor proliferation, including increased density of minicolumns, increased gyrification, decrease in gyral window size, reduced corpus callosal volume, and enhanced radiate white matter volume, dyslexia presents with the opposite phenotype, including reduced minicolumnar density and gyral complexity, greater gyral window size, and increased corpus callosal volume.

Objectives: Based upon this evidence, we have utilized spherical harmonics (SH), a set of complex functions defined on the unit sphere, in order to measure cortical surface complexity in autism and dyslexia so that we may further explore this spectrum distribution.

Methods:

Raw data comprised T1-weighted MRI of the brains of 13 individuals with autism (aged 8 y–38 y, mean 22.5 y), 16 with dyslexia (aged 18 y–40 y, mean 28.2 y), and 31 neurotypical comparison participants within the same age range. All participants were male. 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 SH 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_max ranged from 1 to 65, inclusive.

Results: As predicted by our theoretical model, the shape index varied significantly by diagnostic category. Autism exhibited a greater level of surface complexity, mean s = 279 (95 % confidence interval [255, 305]), dyslexia presented within the lower ranges of our three groups, mean s = 99.5 (95 % confidence interval [91.8, 108]), while controls occupied the median ranges, mean s = 181 (95 % confidence interval [171, 192]).

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.