In the analytical model of brain
development, the scenario of a growing cortex on a growing subcortex is
considered. Here are the key aspects of this analytical model:
1. Model Description: The model involves representing the cortex as a
morphogenetically growing outer layer and the subcortex as a strain-driven
growing inner core. This dual-layered approach captures the dynamic nature of
both layers as they interact and influence the folding patterns of the brain.
2. Mechanical Interactions: The model accounts for the
mechanical interactions between the growing cortex and subcortex, considering
how their respective growth rates and properties influence the deformation and
folding of the brain tissue. This approach integrates both axonal tension-driven
and differential growth-driven hypotheses of cortical folding.
3. Continuum Theory of Finite Growth: The model is based on the continuum
theory of finite growth, which describes the growth and deformation of
biological tissues over time. By incorporating growth mechanisms into the
model, researchers can simulate the evolving morphology of the brain surface
during development.
4. Parameter Exploration: The model explores the effects of varying parameters
such as cortical thickness, stiffness ratios, and growth rates between the
cortex and subcortex. By systematically varying these parameters, researchers
can analyze how different growth dynamics impact the folding patterns and
surface morphologies of the brain.
5. Analytical Estimates: The model provides analytical estimates for critical
parameters such as the critical time, pressure, and wavelength at the onset of
folding. These estimates offer insights into the conditions under which
cortical folding initiates and how the growth dynamics of the cortex and
subcortex contribute to this process.
6. Integration with Cellular Mechanisms: The model aims to connect the
macroscopic mechanical behavior of the cortex-subcortex system with underlying
cellular mechanisms such as axon elongation. By bridging the gap between
macroscopic and microscopic scales, researchers can better understand the
biological processes driving cortical folding.
In summary, the analytical model of a
growing cortex on a growing subcortex offers a comprehensive framework for
studying the mechanical and morphological aspects of brain development. By
incorporating growth dynamics and mechanical interactions into the model,
researchers can simulate the complex folding patterns observed in the
developing brain and gain insights into the underlying mechanisms shaping brain
morphology.
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