Emerging Brain Morphologies from Axonal Elongation

Abstract

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.

Mechanism of Consistent Gyrus Formation: an Experimental and Computational Study

“…With this idea in mind, the past several years have witnessed computational modeling evolving into an influential technique for validating or verifying experimental results, supporting and augmenting analytical models31. For example, finite element (FE) analysis has offered noteworthy insights into the growth, instability, morphogenesis, and functions of the brain3233. Recent 2D and 3D FE models have been designed and implemented to elucidate the role of mechanical parameters during brain development2331.…”

Size and curvature regulate pattern selection in the mammalian brain

“…With 80 elements along the circumference, this is the finest discretization that still runs on a single laptop computer, and yet captures the folding pattern with five to 15 elements per wavelength. We assume elastic parameters of µ w = 3kPa and λ w = 33kPa, an elastic stiffness ratio of E g /E w = 3 and a growth ratio of G g /G w = 1/10 [29]. Figure 3 illustrates the emerging pattern formation of a growing shell on a spheroidal substrate for varying radius-tothickness ratios R/t at fixed semi-axes R x = R y = R and R z = 1.2R.…”

On the Variable Clinical Presentation of Molar-Incisor Hypomineralization

“…3) [Marieb and Hoehn, 2012]. This peculiar shape is the result of tangential expansion of the cortical layer relative to the sublayers that generates compressive stress, leading to the mechanical folding of the cortex, which is submersed in liquid which in turn provides external pressure [Richman et al, 1975;Toro and Burnod, 2005;Nie et al, 2010;Xu et al, 2010;Bayly et al, 2013Bayly et al, , 2014Budday et al, 2014;Ronan et al, 2014;Tallinen et al, 2014;Holland et al, 2015;Striedter et al, 2015]. Modeling brain convolution development by physical experiments and mathematical simulations [Tal- , 2016] has shown that the human brain is likely to have small interindividual variations in shape, tissue properties and growth rates, and the sensitivity of mechanical folding to such variations could explain the variability of gyrification patterns, although primary convolutions are consistently reproducible in their location and timing.…”