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A/B = outer/inner radius of cortex
gs, gc = growth rates of cortex, core
gt = sqrt(deformed/undeformed) cortex outer surface area
The authors of the paper write:
“The grooves in the convoluted brain are called sulci and the ridges between them are called gyri. The outer layer of the brain is composed of folded gray matter, called the cortex, which is made up of cell bodies and capillaries. The subcortex, or inner core, consists mostly of the white myelinated sheaths of neuronal axons. Human brain development involves a series of intricate and overlying processes, including neuronal precursor proliferation at the ventricular zone, neuroblast exodus from the ventricular zone, neuroblast migration, migration arrest, and neuronal organization. During the development, the cerebral cortex experiences a noticeable expansion in volume and surface area accompanied by tremendous tissue folding, which may be attributed to many possible factors, such as cranial constraint, differential growth on the cellular base, and axon maturation.
“Despite decades of endeavors, the fundamental mechanism and key regulators of this crucial process remain incompletely understood. Since cortical folding is a complicated phenomenon, computational modeling has begun to emerge as a powerful tool to validate or verify the results from experiments in addition to analytical models. For example, finite element (FE) analysis has offered valuable insight into the growth, morphology, and function of the brain. With FE models, it has been shown that a faster tangential cortical expansion leads to a shorter gyral wavelength, and that neither inner nor outer constraint (skull) is needed to produce folding. Recently more 2D and 3D brain models have been implemented to clarify the role of mechan- ics during the brain development, and their results show that morphological abnormalities related to the developing brain can be presented by the mechanical models.”
This and the next three slides are from:
Mir Jalil Razavi (1), Tuo Zhang (2,3), Tianming Liu (2) and Xianqiao Wang (1)
(1) Dept. of Chemistry, College of Engineering and the Center for Nanoscale Science and Engineering, University of Georgia, Athens, Georgia 30602, USA
(2) Cortical Architecture Imaging and Discovery Lab, Department of Computer Science and Bioimaging Research Center, University of Georgia, Athens, Athens, GA 30602, USA
(3) School of Automation and Brain Decoding Research Center, Northwestern Polytechnical University, Xi'an 710072, China
“Cortical folding pattern and its consistency induced by biological growth”, Scientific Reports, 09/2015, Vol. 5: 14477, September 2015, DOI: 10.1038/srep14477
ABSTRACT: Cortical folding, characterized by convex gyri and concave sulci, has an intrinsic relationship to the brain's functional organization. Understanding the mechanism of the brain's convoluted patterns can provide useful clues into normal and pathological brain function. In this paper, the cortical folding phenomenon is interpreted both analytically and computationally, and, in some cases, the findings are validated with experimental observations. The living human brain is modeled as a soft structure with a growing outer cortex and inner core to investigate its developmental mechanism. Analytical interpretations of differential growth of the brain model provide preliminary insight into critical growth ratios for instability and crease formation of the developing brain. Since the analytical approach cannot predict the evolution of cortical complex convolution after instability, non-linear finite element models are employed to study the crease formation and secondary morphological folds of the developing brain. Results demonstrate that the growth ratio of the cortex to core of the brain, the initial thickness, and material properties of both cortex and core have great impacts on the morphological patterns of the developing brain. Lastly, we discuss why cortical folding is highly correlated and consistent by presenting an intriguing gyri-sulci formation comparison.
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