Circulating, multicompartment O2-CO uptake and Hb/Mb binding model based on Erupaka et al. 2010. All table and eq. references are to 2010 paper unless noted. Figures and data referenced here are from Erupaka et al. 2010 paper.

Description

The model written here is described in the Erupaka et al. 2010 paper and is an expansion
of a previous model (Bruce et al 2008). A significant enhancement to the 2008 model is the 
addition of the cardiac compartment. The recirculating model consists of a lung compartment, 
to handle breathing air into alveolar region, lung capillary compartment, to handle exchange 
between lung and blood, artery region, handle blood transport to muscles, Skeletal and 
cardiac muscle, to model O2 consumption, and mixed venous region, to handle blood transport 
back to lungs. CO and O2 mass balance equations were written for all compartments. CO and O2 entering
through the lungs are transported via the major arteries of the arterial blood compartment to 
the vascular compartments of skeletal muscle (bm1, bm2, bm3), cardiac muscle (bc1, bc2, bc3), 
and non-muscle tissue (bot). CO and O2 then diffuse into the tissue compartments 
(m1, m2, c1, c2, ot), driven by pressure gradients. Determining the partial pressures of O2 and
CO, and O2 flux in each blood compartment of the model is done by solving the oxyhemoglobin 
dissociation curve, Haldane’s equation, and blood-to-tissue O2 flux equations, at each time 
step using an iterative approach to calaculate state variables. The Haldane equation describes 
the competition of CO and O2 for hemoglobin (Hb) and Mb binding sites.
 	

Figure 1: Diagram of model, showing basic flow of blood/gases and compartments. Taken from Figure 1a of Erupaka et al. 2010 paper listed below. Please see paper or model code for more details.

Figure 2 (above): Figure taken directly from figure 6 of Erupaka et al. 2010 paper.

Figure 3: JSim model simulation attempting to reproduce figure 6 from Erupaka et al. 2010 and fit data from Benignus et al. 1994.

JSim model implimentation comments

• Currently unable to reproduce difference in bound %HbCO between arterial blood and muscle venous blood See Fig 6 parameter set and plotpage '2010_fig6'.
• Our model behaviour in the Cardiac muscle tissue regarding %MbCO levels is not as pronounced beteen compartment 1 and 2 and Comp 1 and 2 percentages 'cross over'. See fig 6 and fig 7 parameter sets and plots.
• Replaced ep and ec regions of Bruce et al. 2010's model for a compartment called Lcap (Lung capillary compartment) Want a better model of diffusion of gasses from lung to aveolar capillaries. Removed circulatory transport delays. Use ODEs to describe transport of gasses into and out of the lung.
• Added a term to the alveolar gas equations for CAO2 to take into account CO2 (avg term). Use of this maintains a PAO2 of around 100 Torr rather than a partial pressure near PIO2. May need a more detailed aveolar gas equation to take into account large changes in FIO2 and the diluting effect of N2. Going forward we will want to add CO2 equations. Ref: Hlastala and Berger, Physiology of Respiration, 2001, p65-80.
• Model takes approximately 10 min to reach steady-state, Do not make any changes from initial conditions until approx 10 min has elapsed (param sets usually have t.min = -10 min).
• JSim has trouble finding solutions to the implicit equations and changing some parameters by more than 20% may causes 'zero-finder' errors and simulation will be unable to proceed. The model is not robust.

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.