a reaction-diffusion model of human brain development人类大脑的反应扩散模型的发展.pdfVIP

A Reaction-Diffusion Model of Human Brain Development ` 1,2 2 Julien Lefevre *, Jean-Franc¸ois Mangin ´ 1 LSIS, UMR CNRS 6168, Universite Aix-Marseille II, Marseille, France, 2 LNAO, Neurospin, I2BM, CEA Saclay, Gif-sur-Yvette, France Abstract Cortical folding exhibits both reproducibility and variability in the geometry and topology of its patterns. These two properties are obviously the result of the brain development that goes through local cellular and molecular interactions which have important consequences on the global shape of the cortex. Hypotheses to explain the convoluted aspect of the brain are still intensively debated and do not focus necessarily on the variability of folds. Here we propose a phenomenological model based on reaction-diffusion mechanisms involving Turing morphogens that are responsible for the differential growth of two types of areas, sulci (bottom of folds) and gyri (top of folds). We use a finite element approach of our model that is able to compute the evolution of morphogens on any kind of surface and to deform it through an iterative process. Our model mimics the progressive folding of the cortical surface along foetal development. Moreover it reveals patterns of reproducibility when we look at several realizations of the model from a noisy initial condition. However this reproducibility must be tempered by the fact that a same fold engendered by the model can have different topological properties, in one or several parts. These two results on the reproducibility and variability of the model echo the sulcal roots theory that postulates the existence of anatomical entities around which the folding organizes itself. These sulcal roots would correspond to ini