Early Path Dominance as a Principle for Neurodevelopment*

To understand how the neural networks of brains acquire their topological structures upon development, we perform a computational study of human diffusion MRI across adults (UK Biobank, N =19,380, adolescents (Adolescent Brain Cognitive Development Study, N =15,593) and neonates (Developing Human Connectome Project, N =758), as well as mouse viral tracing (Allen Institute). We perform targeted attack, a systematic unlinking of the network, to analyze its effects on global communication across the network through its giant cluster.  We find that brain networks differ from scale-free and small-world structures. Time-reversing the attack computation suggests a mechanism for how brains develop, the validity for which we establish experimentally for targeted attack on increasing white matter tract lengths and densities shown to be invariant to aging and disease.  We derive an analytical equation using percolation theory for the fraction of brain regions in the giant cluster as a function of connectivity. 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 that tracts that appear earliest in neurodevelopment are those that become the longest and densest.