Abstract
Our brain is our most precious yet most mysterious organ. It consists of nearly 100 billion neurons, of which typically has 10,000 connections that extend up to a meter. As such, it is an intricate web that enable us to experience the world. In addition to neurons, the brain consists of about the same number of glial cells, around 700 kilometers of blood vessels, the extracellular matrix, and is surrounded by clear water-like cerebrospinal fluid, which together all work to maintain the delicate neurons' environment in a healthy state. At the whole-organ level, this is already incredibly complex, yet this is only part of the story; at any given time, various processes are happening in the brain, such as the electrical impulses between neurons and the complex chemical signaling that helps to maintain homeostasis. Due to the innate micro-scale complexity of the brain, a natural approach, in attempting to understand the brain's physiology and function, is offered by homogenized, continuum-based modeling; here, the focus is on modeling the large-scale behavior arising from the aggregate of small-scale contributions.
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Mardal, KA., Rognes, M.E., Thompson, T.B., Valnes, L.M. (2022). Introduction. In: Mathematical Modeling of the Human Brain. Simula SpringerBriefs on Computing, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-030-95136-8_1
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DOI: https://doi.org/10.1007/978-3-030-95136-8_1
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