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A Mathematical Model of Cerebral Cortical Folding Development

A. Kilinc[1]
[1]Florida State University, USA
Published in 2019
  • The setup of the problem: To develop a mathematical model of cerebral cortical folding development, half-hemisphere geometry is used and the outer layer (gray matter) is allowed to move inward under the effect of both physical and biochemical factors. The model is time-dependent, nonlinear, 2D and 3D, therefore more biologically relevant than the previous models of cerebral cortical folding.
  • Use of COMSOL Multiphysics® simulation software: Structural Mechanics and Nonlinear Structural Materials modules.
  • Use of Application Builder: Some variables (the radius of the brain, elasticity of the matter comprising the layers, Young's Modulus, Poisson Ratio, etc.) are all significant variables and put on the Application Builder.
  • Obtained results: Cortical folding patterns were obtained in 2D for two cases: The outer layer assumed to exist, and both inner and outer layers assumed to exist. The patterns formed in both cases are quite close to the real patters of brain foldings.
  • Expected results: Via carrying the model to 3D, and using different linear growth mechanisms (linear and exponential growth) I expect to build a more biologically relevant model by mid-August. The comparison of the key results (total change in the length of gray matter, how deep the foldings are) with those of previous models done in 2D will be completed by then.
  • Conclusions or broad implications: To date, there have been three leading biological hypotheses that explain the development of cortical folding. Two of them are biomechanical and one is biochemical. Many mathematical models of cortical folding have been proposed based on these biological hypotheses. However, all of these models demonstrate some inconsistencies in finding the major mechanism for cortical folding.

    My model utilizes three leading hypotheses, and is non-linear, time-dependent, and includes volumetric growth, which makes it more biologically relevant. It is a unique model in the sense utilizing all three leading hypotheses for cortical folding. To date, brain folding models are all based on either one or two of these hypotheses.

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