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bioRxiv · 10.1101/2022.07.14.500044

Percolation Theory Identifies Critical Constraints on White Matter Tract Development

Razban, R. M.·Dill, K. A.·Mujica-Parodi, L. R.
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Abstract

We perform targeted attack, a systematic computational unlinking of the network, to analyze its effects on global communication across the network through its giant cluster. Across diffusion magnetic resonance images from individuals in the UK Biobank, Adolescent Brain Cognitive Development Study and Developing Human Connectome Project, we find that targeted attack procedures on increasing white matter tract lengths and densities are remarkably invariant to aging and disease. Time-reversing the attack computation suggests a mechanism for how brains develop, for which we derive an analytical equation using percolation theory. Based on a close match between theory and experiment, our results demonstrate that tracts are limited to emanate from regions already in the giant cluster and tracts that appear earliest in neurodevelopment are those that become the longest and densest. SignificanceAs brains develop through neural growth and specialization, what mechanism ensures that new neurons are integrated into a fully connected brain, avoiding "bridges to nowhere"? Here, we study brain structure development from the perspective of percolation, a global measure of communication. Analyzing over 35,000 diffusion MRI scans on human individuals, from newborns to adults, we identify the following rules of brain neurogenesis through percolation theory: earlier tracts become longer and denser while maintaining a giant cluster. This signature, invariant to age or mental health, suggests a fundamental condition for the brain to function as an emergent whole.

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Razban, R. M., Dill, K. A., Mujica-Parodi, L. R.. 2022-07-16. Percolation Theory Identifies Critical Constraints on White Matter Tract Development. https://doi.org/10.1101/2022.07.14.500044

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