// MODEL NAME: MicroCircIllusoryCooperativity_1
// SHORT DESCRIPTION:
// 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.
import nsrunit; unit conversion on;
math MicroCircIllusoryCooperativity_1{
// DOMAINS
realDomain t sec; t.min = 0; t.max = 100; t.delta=0.1; // Time domain
realDomain x cm; x.min = 0; x.max = 0.1; x.ct = 81; // Spatial domain, along the capillary length
// //////////// Varying Adenosine Infusion Levels ////////////
// This domain essentially allows looping of model runs over differing inflowing
// adenosine levels. Within each run, the adenosine infusion concentration is
// fixed, but between runs, it is varied. It is important to make sure that your
// simulation time is sufficiently long for your slowest adjusting system response
// to reach steady state. This domain is set up as the log of the infusion concentration
// because we generally want equally spaced points in log space, since that is how
// we will plot it.
realDomain logCin dimensionless; logCin.min = -1; logCin.max = 1; logCin.ct = 20;
real Cin(logCin) uM; // Inflowing adenosine concentration
real Cp(t,x,logCin) mM; // Plasma adenosine concentration
real Cisf(t,x,logCin) mM; // ISF adenosine concentration
real F(t,logCin) ml/min/g; // Flow per gram tissue
real Fmin = 0.6 ml/min/g; // Minimum value for flow (baseline with no infused adenosine)
real Fmax = 5.5 ml/min/g; // Maximum value for flow (saturating value for high concentrations of infused adenosine)
real PSg(x) ml/min/g; // Endothelial cleft permeability-surface area product per gram tissue
real PSg_max = 1 ml/min/g; // Maximum capillary permeability. Approach to this value is exponental from 0.
real impermx = 0.02 cm; // The segment from x=0 to x=impermx is impermeable to adenosine (PS=0)
real PSg_relax = 0.01 cm; // Controls rate of exponential approach to PSg_max after impermeable region
real Vp =0.05 ml/g; // Volume of plasma in capillary per gram tissue
real Visf = 0.15 ml/g; // Volume of interstitial fluid per gram tissue
real L = x.max-x.min; // Length of capillary
real Dp = 8.45e-5 cm^2/s; // Diffusion coefficient for adenosine in plasma
real Disf = 8.45e-5 cm^2/s; // Diffusion coefficient for adenosine in ISF
real xRecept = 0.01 cm; // Receptor x location
real Rkm = .1 uM; // Receptor Km
real ReceptOcc(t,logCin) dimensionless;// Receptor fractional occupancy
// Lumped Consuming Process parameters
real G_Km = 1 uM; // Michaelis Menten consumption Km
real G_Vmax = 1 uM/min; // Michaelis Menten consumption Vmax
real C_atR(t,logCin) = Cisf(t,xRecept,logCin); // Concentration of adenosine at the receptor
ReceptOcc = C_atR/(Rkm+C_atR); // Michaelis-Menten type receptor binding
F = ReceptOcc*(Fmax-Fmin)+Fmin; // Flow depends linearly on receptor occupancy
PSg = if (x