In the analytical model of brain development, specifically focusing on
cortical folding, the scenario of a growing cortex on an elastic subcortex is
considered. Here are the key aspects of this analytical model:
1. Model Description: The model involves interpreting the subcortex as an
infinite half-space and imposing a sinusoidal deflection on its upper boundary.
The deflection is considered as the sum of an elastic subcortical deflection
and subcortical growth, reflecting the dynamic nature of the tissue.
2. Deflection Analysis: The deflection of the growing cortex on the elastic
subcortex is analyzed using the Föppl–von Kármán theory and the classical
fourth-order plate equation. This analysis helps in understanding the
deformation behavior of the cortical tissue as it grows and interacts with the
underlying subcortical layer.
3. Parameter Variation: The model explores the effects of varying parameters
such as cortical thickness, stiffness ratios between the cortex and subcortex,
and growth rates. By systematically changing these parameters, researchers can
investigate how different mechanical properties influence the folding patterns
and surface morphologies of the brain.
4. Sensitivity Studies: Sensitivity studies are conducted to analyze how
changes in cortical thickness and stiffness ratios impact the wavelength of
folding patterns. These studies provide insights into the relationship between
mechanical properties and the resulting brain surface morphology.
5. Computational Validation: The analytical estimates derived
from this model are validated computationally using finite element analysis.
Computational modeling allows for a more detailed exploration of the complex
folding patterns and surface morphologies that arise from the interactions
between the growing cortex and elastic subcortex.
6.
Implications: By studying the growth of the cortex on the elastic
subcortex, researchers can gain a better understanding of the mechanical
mechanisms underlying cortical folding in the brain. This model helps in
predicting realistic surface morphologies and provides insights into the
development of complex brain structures.
In summary, the analytical model of a growing cortex on an elastic
subcortex provides a framework for investigating the mechanical interactions
that drive cortical folding during brain development. By combining analytical
and computational approaches, researchers can elucidate the role of growth,
stiffness, and other factors in shaping the intricate surface morphologies of
the mammalian brain.
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