6 March 2009 Computation and visualization of spreading depression based on reaction-diffusion equation with recovery
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Abstract
Spreading depression (SD) shows as propagating suppression of electrical activity, which relates with migraine and focal cerebral ischaemia. The putative mechanism of SD is the reaction-diffusion hypothesis involving potassium ions. In part inspired by optical imaging of two SD waves collision, we aimed to show the merged and large wavefront but not annihilation during collision by experimental and computational study. This paper modified Reggia et al established bistable equation with recovery to compute and visualize SD. Firstly, the media tissue of SD was assumed as one-dimensional continuum. The Crank-Nicholson method was used to solve the modified equations with recovery term. Then, the computation results were extended to two-dimensional space by symmetry. One individual SD was visualized as a concentric wave initiating from the stimulation point. The mergence but not annihilation of two colliding waves of SD was demonstrated. In addition, the dynamics of SD depending on the parameters was studied and presented. The results allied SD with the emerging concepts of volume transmission. This work not only supplied a paradigm to compute and visualize SD but also became a tool to explore the mechanisms of SD.
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Hongxia Ding, Shangbin Chen, Shuai Zeng, Shaoqun Zeng, Qian Liu, Qingming Luo, "Computation and visualization of spreading depression based on reaction-diffusion equation with recovery", Proc. SPIE 7280, Seventh International Conference on Photonics and Imaging in Biology and Medicine, 72801F (6 March 2009); doi: 10.1117/12.823357; https://doi.org/10.1117/12.823357
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