Simulation of a convective flow forming a pattern of the human brain

Abstract

To explain consistently determining the global shape of the brain, the vortex model of the brain was proposed by Nakada. He explained that structural organization of the brain is guided by the self-organization pattern based on the principal rule of free thermal convection. In the present study, a computer simulation of a simple thermal-driven convective-diffusive flow was performed to clarify the fundamental relation between this type of the flow and formation of the brain shape. The incompressible Navier-Stokes equations containing the external force dependent on temperature, and an equation for temperature were solved with projection method. The multi-directional finite-difference method was employed to discretize the governing equations. Computational results were suitably visualized and found to be consistent with the arguments in the vortex theory that the thermal-driven convective-diffusive flow is an essential mechanism for determining the global shape of the human brain.