A multifield computational model explains the underlying mechanisms of cortical malformations in the developing brain. Issue 1 (25th January 2021)

• Record Type: Journal Article
• Authors: Zarzor, M. S.; Kaessmair, S.; Steinmann, P.; Budday, S.
• Other Names: Kuhl D. guestEditor.; Meister A. guestEditor.; Ricoeur A. guestEditor.; Wünsch O. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 20:Issue 1(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-01-25
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.202000171
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: The convoluted macroscopic shape of the mammalian brain plays an important role for brain function. To date, the link between the cellular processes during brain development and normal or abnormal cortical folding remains insufficiently understood. In the early stages of development, progenitor cells divide symmetrically and asymmetrically in the inner layers of our brain. The newly generated neurons then migrate from the inner layers towards the outer surface to form the cortex. After about 20 weeks of gestation, the neuronal cells in the cortex start to interconnect, which causes a significant expansion of the outer brain layers. As this expansion is constrained by slower growing inner layers, compressive stresses emerge, which eventually induce mechanical instabilities and cortical folding. Disruption of cellular division, migration, or connectivity may lead to malformations of cortical development associated with neurological disorders like schizophrenia, autism, or epilepsy. Here we present a computational model describing cellular division and migration on the cellular scale, as well as growth and cortical folding on the tissue or organ scale, in a continuous way by a coupled finite growth and advection‐diffusion model. We introduce the cell density as independent field controlling the volumetric growth. This allow us to study the influence of the migration velocity, the cell diffusivity, the local stiffness, and the local connectivity of cells on the cortical folding process during normal and abnormal brain development numerically. We show how disrupted cell migration leads to a thickened cortex and the absence of normal folds in patients with the malformation lissencephaly. When calibrated using clinical data, the presented model can help to understand and diagnose neurological disorders arising from abnormal cellular development and cortical malformations.