Diagram of the model.

<p>Neurons (mustard) consist of various sodium and potassium channels as well as the Na⁺ = K⁺–ATPase. Dendrites additionally consist of NMDA channels. Glia (teal) are incorporated as potassium buffers. Blood vessels (pink) bring in oxygen to supply the Na⁺/K⁺–ATPase. The cellular-level model is taken into the continuum limit (upper right) to yield a model with 5 compartments: neural cell bodies, neural dendrites, glial, vascular, and extracellular space.</p

“Typical” vascular coupling.

<p>Time courses at a fixed position, 780 µm downstream of the original stimulus. Simulations performed using vessel of Farr and David <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0070469#pone.0070469-Farr1" target="_blank">[36]</a>. After a short dilation period, the vessels constrict significantly to about 40% of their rest radii, before recovering.</p

Relationship between vascular caliber and [K⁺]_<i>e</i>.

<p>Effective vascular radius <i>r</i> as a function of ECS potassium concentration [K⁺]_<i>e</i>.</p

Fixed vascular caliber.

<p>Time courses at a fixed position, 780 µm downstream of the original stimulus. These simulations show the effects of oxygen consumption on CSD for a range of the oxygen coupling parameters, γ. Increasing γ prolongs the duration and magnifies the amplitude of the CSD because it implies that the pump consumes more of the available oxygen, thereby resulting in larger oxygen depletions.</p

Speed of CSD for different vascular responses.

<p>Increasing the constriction parameter <i>a</i> makes the vessel less sensitive to potassium, weakening the resulting constriction. The speed decreases as <i>a</i> increases from 30 mM up to 80 mM, but increasing the amount of dilation by increasing <i>b</i> seems to have a greater effect.</p

CSD in absence of oxygen consumption.

<p>Shown are the time-courses of the propagating waves of ECS potassium concentration, free buffer capacity, membrane potential, and Na⁺/K⁺–ATPase pump rate at positions 120 microns apart for simulations performed in the absence of oxygen consumption by the Na⁺/K⁺– ATPase. The Na⁺/K⁺–ATPase operates at rates determined solely by [K⁺]_<i>e</i> and [Na⁺]_<i>i</i>.</p

Duration of CSD for different vascular responses.

<p>Shown are CSD durations plotted against percent dilation <i>b</i> (the maximum vasodilation), constriction parameter <i>a</i> (this parameter from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0070469#pone.0070469.e064" target="_blank">Eq. (10)</a> has the units of mM and is the width of a Gaussian curve that controls how fast <i>r</i> drops as [K⁺] increases), and oxygen coupling constant γ. Duration is defined by the length of time that potassium concentration is elevated to a level greater than 6 mM. Increasing <i>a</i>, (shown from 30–80 mM) decreases the amount of constriction, resulting in quicker recovery from CSD. Likewise, increasing <i>b</i>, which increases the maximum dilation of the vessels, also reduces the duration of CSD.</p

Oxygen availability affects the Na⁺/K⁺–ATPase.

<p>Shown is the relationship between tissue oxygen concentration and the oxygen-dependent portion of the pump rate (Eq (7)). Since some ATP is generated even in the absence of oxygen, the pump rate does not completely go to zero as the oxygen concentration approaches zero. The steady state oxygen concentration is 0.2 mM.</p