Growth in a Turing Model of Cortical Folding

Abstract

BIOMATH h t t p : / / w w w. b i o m a t h f o r u m . o r g / b i o m a t h / i n d e x . p h p / b i o m a t h /cortical folding may be more realistic than previous static domain models of cortical folding since it incorporates the growth that naturally occurs as the brain develops. By comparing patterns generated by our growing prolate spheroid Turing system with those generated by a static prolate spheroid Turing system, we show that the addition of growth causes a significant change in system behavior; the system produces transient patterns instead of converging to one final pattern. Our model illustrates the importance of including growth in a model of cortical folding and can be utilized to explain certain human diseases of cortical folding.

Generation of ECG signals from a reaction-diffusion model spatially discretized

“…The Barrio-Varea-Aragon-Maini (BVAM) model 25 is a generic reaction-diffusion system obtained by assuming mass conservation of two morphogens and by a Taylor expansion around an equilibrium point, retaining up to cubic non-linearities. This model has been used for describing a wide diversity of patterns present in biological or chemical systems 29,30 . The BVAM model exhibits extremely rich dynamics, ranging from Turing patterns, traveling waves, temporal oscillations and chaotic behavior 31 .…”