Model number


Translate original model from Matlab into JSim mml. Four compartment ODE model consisting of Systemic capillary and tissue, Pulmonary capillary, and alveolus compartments. Uses an iterative approach to calculating partial pressures of O2 and CO2 in the capillaries using Dash et al. 2016 simplified calculations for O2 and CO2 binding to Hb.


 Recirculating 4-compartment model for O2-CO2 transport and exchange between the lungs 
 and a systemic organ, say heart. Instantaneous equilibrium binding of O2 and CO2 with 
 the hemoglobin (Hb) inside red blood cells (RBCs) is considered. The subscripts "Alv", 
 "PulCap", "SysCap", and "SysTis" indicate the four comaprtments "alveoli", "pulmonary 
 capillary", "systemic capillary", and "systemic tissue", respectively. The model solves
 the dynamics of four state variables (O2, CO2, HCO3M, HP) in the four compartments. The
 aleveoli compartment does not have HCO3M and HP, resulting in 14 mass conservation ODEs 

 Developed by: Ranjan K. Dash, Ph.D. (Matlab code last modified: 02/29/2016)
 Department of Physiology and Biotechnology and Bioengineering Center
 Medical College of Wisconsin, Milwaukee, WI-53226

pO2pCO2plot fig1
Figure: Partial pressures of O2 and CO2, pH and concentration of HCO3 as a function of time in the various compartments. Alv: Alveoli, PulCap: pulmonary capillary, SysCap: systemic capillary, SysTis: systemic tissue.



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.

Download JSim model project file


Help running a JSim model.

   Dash RK, Korman B, and Bassingthwaighte J. Simple accurate mathematical models of blood HbO2 and 
   HbCO2 dissociation curves at  varied physiological conditions: evaluation and comparison with 
   other models. Eur J Appl Physiol 115(8): 97-113, DOI: 10.1007/s00421-015-3228-3, 2015.

   Bassingthwaighte JB, Jardine B, and Dash RK. A Dynamical Computational Model of Circulating Blood Gases,
   Hemoglobin Binding, and pH Regulation in the Microcirculation. F1000Research EB16-7571 (poster), 2017.

   Bassingthwaighte JB, Dash RK, Beard DA, and Nolan M. The pathway for oxygen: Tutorial modelling 
   on oxygen transport from air to mitochondrion. Adv Exp Med Biol 876 
   Oxygen Transport to Tissue XXXVII 876: 103-110, 2015.

   Dash RK, Bassingthwaighte JB (2010) Erratum to: blood HbO2 and HbCO2 dissociation curves at varied 
   O2, CO2, pH, 2,3-DPG and temperature levels. Ann Biomed Eng 38:1683–1701

   Dash RK, Bassingthwaighte JB (2006) Simultaneous blood-tissue exchange of oxygen, carbon dioxide, 
   bicarbonate, and hydrogen ion. Ann Biomed Eng 34:1129–1148	
Key terms
O2-CO2 transport
carbon dioxide
HbO2 binding
HbCO2 binding
compartmental modeling

Please cite in any publication for which this software is used and send one reprint to the address given below:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.

Model development and archiving support at provided by the following grants: NIH U01HL122199 Analyzing the Cardiac Power Grid, 09/15/2015 - 05/31/2020, NIH/NIBIB BE08407 Software Integration, JSim and SBW 6/1/09-5/31/13; NIH/NHLBI T15 HL88516-01 Modeling for Heart, Lung and Blood: From Cell to Organ, 4/1/07-3/31/11; NSF BES-0506477 Adaptive Multi-Scale Model Simulation, 8/15/05-7/31/08; NIH/NHLBI R01 HL073598 Core 3: 3D Imaging and Computer Modeling of the Respiratory Tract, 9/1/04-8/31/09; as well as prior support from NIH/NCRR P41 RR01243 Simulation Resource in Circulatory Mass Transport and Exchange, 12/1/1980-11/30/01 and NIH/NIBIB R01 EB001973 JSim: A Simulation Analysis Platform, 3/1/02-2/28/07.