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# MicroCircIllusoryCooperativity_1

A spatially distributed blood tissue exchange model which incorporates the regulation of coronary blood flow by adenosine acting through adenosine A2A receptors on the surface of vascular smooth muscle cells. This simplified version of the model lumps all interstitial adenosine consuming/transporting processes into a single process with Michaelis Menten kinetics.

Model number: 0375

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## Description


This is a spatially distributed blood tissue exchange model which incorporates
the regulation of coronary blood flow by adenosine acting through adenosine A2A
receptors on the surface of vascular smooth muscle cells. This simplified version
of the model lumps all interstitial adenosine consuming/transporting processes
into a single process with Michaelis Menten kinetics. This was done to reduce the
number of parameters when exploring the basic mechanisms underlying illusory
cooperativity.



## Equations

$\frac{\partial C_{p}(x,t)}{\partial t} = -\frac{F(t)\cdot L}{V_{p}}\frac{\partial C_{p}(x,t)}{\partial x}+D\frac{\partial^{2}C_{p}(x,t)}{\partial x^{2}}-\frac{PS_{g}(x)}{V_{p}}(C_{p}(x,t)-C_{isf}(x,t))$
$PS_{g}(x)= \left\{0 \text{ if } x
$\frac{\partial C_{isf}(x,t)}{\partial t} = D_{isf}\frac{\partial^{2}C_{isf}(x,t)}{\partial x^{2}}-\frac{PS_{g}(x)}{V_{isf}}(C_{isf}(x,t)-C_{p}(x,t)) -\frac{G_{Vmax}C_{isf}(x,t)}{G_{Km}+C_{isf}(x,t)}$
$\Theta(t)=\frac{C_{isf}(x_{recept},t)}{R_{Km}+C_{isf}(x_{recept},t)}$
$F(t)=F_{min}+\Theta(t)\cdot(F_{max}-F_{min})$

The equations for this model may also be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.

## Related Models

MicroCircIllusoryCooperativity_2

## Key Terms

illusory, cooperativity, adenosine, receptor, transport, PDE

## Model History

Get Model history in CVS.