Analytical Model: Growing Cortex on elastic subcortex

Dr. Rishabh Pathak

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.

 

Having a strong interest in research, I began my work as a physiotherapist and went on to earn a master's degree in the field, specializing in neurology. I also finished a few post-graduation diplomas in between and with persistence. Research has always been a passion of mine, both for the advancement of my career and my personal life. A major factor in reaching my goals is education. Although my first bachelor's thesis was in the innovation area, I had been exposed to research work even in my informal school days. I always like working on creative initiatives and taking an interest in other people's experiences. The saying, "Healthy criticism is a way to learn more and more about your flaws to make them rectified," is true, in my opinion. In this way, we may hone our abilities and create a growth-oriented vision for both our personal and professional career pathways. I am thus constantly willing to learn and advance in my work. Additionally, I think that "it is in our hands to terminate our lives with a brand-new ending if we are unable to originate our lives with a brand-new start."

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