Emerging Brain Morphologies from Axonal Elongation

Understanding the characteristic morphology of our brain remains a challenging, yet important task in human evolution, developmental biology, and neurosciences. Mathematical modeling shapes our understanding of cortical folding and provides functional relations between cortical wavelength, thickness, and stiffness. Yet, current mathematical models are phenomenologically isotropic and typically predict non-physiological, periodic folding patterns. Here we establish a mechanistic model for cortical folding, in which macroscopic changes in white matter volume are a natural consequence of microscopic axonal growth. To calibrate our model, we consult axon elongation experiments in chick sensory neurons. We demonstrate that a single parameter, the axonal growth rate, explains a wide variety of in vitro conditions including immediate axonal thinning and gradual thickness restoration. We embed our axonal growth model into a continuum model for brain development using axonal orientation distributions motivated by diffusion spectrum imaging. Our simulations suggest that white matter anisotropy-as an emergent property from directional axonal growth-intrinsically induces symmetry breaking, and predicts more physiological, less regular morphologies with regionally varying gyral wavelengths and sulcal depths. Mechanistic modeling of brain development could establish valuable relationships between brain connectivity, brain anatomy, and brain function.