Abstract
The cortical thickness is a characteristic biomarker for a wide variety of neurological disorders. While the structural organization of the cerebral cortex is tightly regulated and evolutionarily preserved, its thickness varies widely between 1.5 and 4.5 mm across the healthy adult human brain. It remains unclear whether these thickness variations are a cause or consequence of cortical development. Recent studies suggest that cortical thickness variations are primarily a result of genetic effects. Previous studies showed that a simple homogeneous bilayered system with a growing layer on an elastic substrate undergoes a unique symmetry breaking into a spatially heterogeneous system with discrete gyri and sulci. Here, we expand on that work to explore the evolution of cortical thickness variations over time to support our finding that cortical pattern formation and thickness variations can be explained – at least in part – by the physical forces that emerge during cortical folding. Strikingly, as growth progresses, the developing gyri universally thicken and the sulci thin, even in the complete absence of regional information. Using magnetic resonance images, we demonstrate that these naturally emerging thickness variations agree with the cortical folding pattern in n = 9 healthy adult human brains, in n = 564 healthy human brains ages 7–64, and in n = 73 infant brains scanned at birth, and at ages one and two. Additionally, we show that cortical organoids develop similar patterns throughout their growth. Our results suggest that genetic, geometric, and physical events during brain development are closely interrelated. Understanding regional and temporal variations in cortical thickness can provide insight into the evolution and causative factors of neurological disorders, inform the diagnosis of neurological conditions, and assess the efficacy of treatment options.
Highlights
We know that measurements of the cortical thickness play an important role in normal development and can serve as biomarkers in a wide variety of neurodegenerative and psychiatric disorders: Alterations in cortical thickness are common in normal aging, and closely associated with Alzheimer’s disease, dementia, Huntington’s disease, amyotropic lateral sclerosis, and schizophrenia
The theory postulates that k is related to the cortical tension [10], a physics-based metric that changes with alterations in cerebrospinal fluid pressure [9] and white matter stiffness [45]
Cortical thickness variations across the human brain play a critical role during neurodevelopment and are characteristic biomarkers for a wide variety of neurological disorders
Summary
2.1 Analytical modelTo analytically study thickness variations upon folding, we consider the idealized model problem of a bilayered system at the onset of folding [37] using the method described in [21]. We decompose the deformation gradient, the spatial gradient of the nonlinear deformation map, F = F e · F g, into an elastic contribution F e and a growth contribution F g [39] We model both layer and substrate as incompressible neo-Hookean materials with a Cauchy stress σ = μ (F e)t · F e − p I, where μ is the shear modulus, I is the second order unit tensor, and p is the Langrange multiplier that enforces incompressibility. To compute the critical growth factor θcrit at which the folding instability occurs, we use a variational method that probes the stability of the homogeneous layer by studying emerging folding modes with the lowest elastic energy [40]. The layer covers the domain (Y, X) ∈ [0, 1] × R and the substrate the domain (Y, X) ∈
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