Neuro-evolutionary evidence for a universal fractal primate brain shape

Yujiang Wang; Karoline Leiberg; Nathan Kindred; Christopher R Madan; Colline Poirier; Christopher I Petkov; Peter Neal Taylor; Bruno Mota

doi:10.7554/eLife.92080.4

The cerebral cortex displays a bewildering diversity of shapes and sizes across and within species. Despite this diversity, we present a universal multi-scale description of primate cortices. We show that all cortical shapes can be described as a set of nested folds of different sizes. As neighbouring folds are gradually merged, the cortices of 11 primate species follow a common scale-free morphometric trajectory, that also overlaps with over 70 other mammalian species. Our results indicate that all cerebral cortices are approximations of the same archetypal fractal shape with a fractal dimension of d f = 2.5. Importantly, this new understanding enables a more precise quantification of brain morphology as a function of scale. To demonstrate the importance of this new understanding, we show a scale-dependent effect of ageing on brain morphology. We observe a more than fourfold increase in effect size (from two standard deviations to eight standard deviations) at a spatial scale of approximately 2 mm compared to standard morphological analyses. Our new understanding may, therefore, generate superior biomarkers for a range of conditions in the future. Many of the brain’s essential functions – from decision-making to movement – take place in its outer layer known as the cerebral cortex. The shape of the cerebral cortex varies significantly between species. For instance, in humans, it is folded in to grooves and ridges, whereas in other animals, including mice, it is completely smooth. The structure of the cortex can also differ within a species, and be altered by aging and certain diseases. This vast variation can make it difficult it to characterize and compare the structure of the cortex between different species, ages and diseases. To address this, Wang et al. developed a new mathematical model for describing the shape of the cortex. The model uses a method known as coarse graining to erase, or ‘melt away’, any cortical folds or structures smaller than a given threshold size. As this threshold increases, the cortex becomes progressively smoother. The relationship between surface areas and threshold sizes indicates the fractal dimension – that is, how fragmented the cortex is across different scales. Wang et al. applied their model to the brain scans of eleven primates, including humans, and found the fractal dimension of the cortex was almost exactly 2.5 for all eleven species . This suggests that the cortices of the different primates follow a single fractal shape, which means the folds of each cortex have a similar branching pattern. Although there were distinctions between the species, they were mainly due to the different ranges of fold sizes in each cortex. The model revealed that the broader the range of fold sizes, the more folded the brain – but the fractal pattern remains the same. The brain melting method created by Wang et al. provides a new way to characterise cortical shape. Besides revealing a hitherto hidden regularity of nature, they hope that in the future their new method will be useful in assessing brain changes during human development and ageing, and in diseases like Alzheimer’s and epilepsy.

Neuro-evolutionary evidence for a universal fractal primate brain shape

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