21 April 2016 Computational model of cerebral blood flow redistribution during cortical spreading depression
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In recent decades modelling studies on cortical spreading depression (CSD) and migraine waves successfully contributed to formation of modern view on these fundamental phenomena of brain physiology. However, due to the extreme complexity of object under study (brain cortex) and the diversity of involved physiological pathways, the development of new mathematical models of CSD is still a very relevant and challenging research problem.

In our study we follow the functional modelling approach aimed to map the action of known physiological pathways to the specific nonlinear mechanisms that govern formation and evolution of CSD wave patterns. Specifically, we address the role of cerebral blood flow (CBF) redistribution that is caused by excessive neuronal activity by means of neurovascular coupling and mediates a spatial pattern of oxygen and glucose delivery. This in turn changes the local metabolic status of neural tissue. To build the model we simplify the web of known cell-to-cell interactions within a neurovascular unit by selecting the most relevant ones, such as local neuron-induced elevation of extracellular potassium concentration and biphasic response of arteriole radius. We propose the lumped description of distance-dependent hemodynamic coupling that fits the most recent experimental findings.
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Andrey Yu. Verisokin, Andrey Yu. Verisokin, Darya V. Verveyko, Darya V. Verveyko, Dmitry E. Postnov, Dmitry E. Postnov, "Computational model of cerebral blood flow redistribution during cortical spreading depression", Proc. SPIE 9917, Saratov Fall Meeting 2015: Third International Symposium on Optics and Biophotonics and Seventh Finnish-Russian Photonics and Laser Symposium (PALS), 99171Z (21 April 2016); doi: 10.1117/12.2229572; https://doi.org/10.1117/12.2229572

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