Validating a computational framework for ionic electrodiffusion with cortical spreading depression as a case study

Cortical spreading depression (CSD) is a wave of pronounced depolarization of brain tissue accompanied by substantial shifts in ionic concentrations and cellular swelling. Here, we validate a computational framework for modelling electrical potentials, ionic movement, and cellular swelling in brain tissue during CSD. We consider different model variations representing wild type or knock-out/knock-down mice and systematically compare the numerical results with reports from a selection of experimental studies. We find that the data for several CSD hallmarks obtained computationally, including wave propagation speed, direct current shift duration, peak in extracellular K + concentration as well as a pronounced shrinkage of extracellular space, are well in line with what has previously been observed experimentally. Further, we assess how key model parameters including cellular diffusivity, structural ratios, membrane water and/or K + permeabilities affect the set of CSD characteristics.

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TWO-DIMENSIONAL VISUALIZATION OF THE PROPAGATION SPEED OF CORTICAL SPREADING DEPRESSION IN RAT CORTEX

Journal of Innovative Optical Health Sciences ◽

10.1142/s1793545810000873 ◽

2010 ◽

Vol 03 (01) ◽

pp. 75-80

Author(s):

TINGTING XU ◽

PENGCHENG LI ◽

SHANGBIN CHEN ◽

WEIHUA LUO

Keyword(s):

Cortical Spreading Depression ◽

Spreading Depression ◽

Time Lag ◽

Polar Angle ◽

Propagation Speed ◽

Least Square ◽

Data Matrix ◽

Radial Coordinate ◽

Two Dimensional ◽

Polar Coordinate

Cortical spreading depression (CSD), which is a significant pathological phenomenon that correlates with migraines and cerebral ischemia, has been characterized by a wave of depolarization among neuronal cells and propagates across the cortex at a rate of 2–5 mm/min. Although the propagation pattern of CSD was well-investigated using high-resolution optical imaging technique, the variation of propagation speed of CSD across different regions of cortex was not well-concerned, partially because of the lack of ideal approach to visualize two-dimensional distribution of propagation speed of CSD over the whole imaged cortex. Here, we have presented a method to compute automatically the propagation speed of CSD throughout every spots in the imaged cortex. In this method, temporal clustering analysis (TCA) and least square estimation (LSE) were first used to detect origin site where CSD was induced. Taking the origin site of CSD as the origin of coordinates, the data matrix of each image was transformed into the corresponding points based on the polar-coordinate representation. Then, two fixed-distance regions of interest (ROIs) are sliding along with the radial coordinate at each polar angle within the image for calculating the time lag with correlating algorithm. Finally, we could draw a two-dimensional image, in which the value of each pixel represented the velocity of CSD when it spread through the corresponding area of the imaged cortex. The results demonstrated that the method can reveal the heterogeneity of propagation speed of CSD in the imaged cortex with high fidelity and intuition.

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