Four region, distributed model for the O2-CO2 transport, exchange and metabolism.

Description

  A detailed nonlinear four-region (red blood cell, plasma, interstitial fluid, and 
  parenchymal cell) axially distributed convection-diffusion-permeation-reaction-binding 
  computational model is developed to study the simultaneous transport and exchange of 
  oxygen (O2) and carbon dioxide (CO2) in the blood-tissue exchange system of an organ. 
  Since the pH variation in blood and tissue influences the transport and exchange of O2 
  and CO2 (Bohr and Haldane effects), and since most CO2 is transported as HCO3- (bicarbonate) 
  via the CO2 hydration (buffering) reaction, the transport and exchange of HCO3- and H+ are 
  also simulated along with that of O2 and CO2. Furthermore, the model accounts for the 
  competitive nonlinear binding of O2 and CO2 with the hemoglobin inside the red blood cells 
  (nonlinear O2-CO2 interactions, Bohr and Haldane effects), and myoglobin-facilitated transport 
  of O2 inside the parenchymal cells. The consumption of O2 through cytochrome-C oxidase reaction 
  inside the parenchymal cells is based on Michaelis-Menten kinetics. The corresponding 
  production of CO2 is determined by respiratory quotient (RQ), depending on the relative 
  consumption of carbohydrate, protein, and fat. The model gives a physiologically realistic 
  description of O2 transport and metabolism in the microcirculation of the organ. Furthermore, 
  because model solutions for tracer transients and steady states can be computed highly efficiently,
  this model may be the preferred vehicle for routine data analysis where repetitive solutions and 
  parameter optimization are required, as is the case in PET imaging for estimating myocardial O2 
  consumption.

Above figure:
Axial concentration of Oxygen in the four tissue regions (pl = capillary, rbc = red blood cells, isf = interstital, pc = parenchymal)

Equations

The equations for this model may 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.