This page will look better in a graphical browser that supports web standards, but is accessible to any browser or internet device.

Served by Samwise.


Four region, recirculating model for the O2-CO2 transport, exchange and metabolism. Based on Dash 2006 paper. Computes dissolved O2 and CO2 from total O2 and CO2 (TO2 and TCO2) using Dash et al. 2016 routine and Christmas 2017 O2/CO2 solubility algorithm. Gas exchange with 3 compartment lung used. Incorporates calculations for temperature changes based on consumption of O2 in parenchymal tissue region.

Model number: 0405

Run Model: 
    Help running a JSim model.
Java runtime required. Web browser must support Java Applets.
(JSim model applet may take 10-20 seconds to load.)


 Four region, recirculating model for the O2-CO2 transport, exchange and metabolism. Based on 
 Dash et al 2006 and 2010 papers. Computes dissolved O2 and CO2 from total O2 and CO2 (TO2 and TCO2) 
 through numerical inversion method using Dash et al. 2016 routine. O2 and CO2 gas solubility change with 
 time and position based on Christmas et al. 2017 O2/CO2 solubility algorithm that incorporates temperature
 and density (or water space) into its solubility calculations. Gas exchange with simple 3 compartment 
 lung is used. Incorporates calculations for temperature changes (time and position dependent) based on 
 consumption of O2 generating heat in parenchymal tissue region and releasing heat through lung exchange.

Download JSim model project file

Model layout

Figure 1: Layout of model and flow of gases (O2, CO2). Flow of gases in the lung is governed by ordinary differential equations (ODEs) with time domain (Air to Alveolus regions). The recirculating blood and tissue exchange equations are governed by partial differential equations (PDEs) with time and axial spatial domains (Lung capillary to Arteries to Tissue to Veins). See Figure 2 below for details of tissue-exchange. Lung capillary sub-region has just blood (RBC and plasma) with a water film region as the interface between it and the Alveolus. The Veins and Arteries just have the blood region (RBC and plasma).

Figure 2: Muscle blood-tissue-exchange (BTEX) region. All four sub-regions: RBC, plasma, interstitial fluid (ISF), parenchymal cell (PC) have separate solubility coefficients for O2 and CO2 (αO2, αCO2), and separate O2, CO2, HCO3-, H+ concentrations. All variables have time and one spatial dimension along the axis of the capillary. The consumption of oxygen occurs in the PC which produces carbon dioxide and heat which raises the temperature in the PC. Temperature of RBC and plasma sub-regions are assumed to be the same. Blood flow (Fblood), RBC flow (Frbc), and plasma flow (Fpl) are different based on hematocrit and measured relative velocity differences between plasma and RBCs. Binding of O2 and CO2 to hemoglobin (Hb) occurs in the RBC and O2 to myoglobin occurs in the PC.

Model Simulation Plots

Figure 3: Axial profiles of the partial pressures of O2 and CO2, pH, and HCO3- concentrations in the four sub-regions of the tissue region. Plot occurs at end of simulation run at near steady-state. Note: consumption of O2 as the partial pressure diminishes along the capillary while CO2 increases. For all plots: Initial pO2 in blood vessels = 100 mmHg, pCO2 = 40 mmHg, pO2 in isf and pc = 50 mmHg, CO2 in isf and pc = 50 mmHg. pH in the plasma = 7.4. Partial pressure of O2 in air = 150 mmHg, CO2 = 0 mmHg.

Figure 4: Axial profiles of the partial pressures of O2 and CO2, pH, and HCO3- concentrations in the three sub-regions of the lung region. pO2Pul_isf and pCO2Pul_isf correspond to the partial pressures of O2 and CO2 in the thin water film sub-region. Plot occurs at end of simulation run at near steady-state. Note: O2 partial pressure increases along the capillary while CO2 decreases as they equilibrate with the lung.

Figure 5: O2 and CO2 hemoglobin saturations in each of the four regions (SHbO2, SHbCO2). Top two plot Hb saturation as a function of time while the bottom plots Hb saturation as a function of distance along the blood vessels.

Figure 6: Temperature in the the seven sub-regions as a function of time (Top) and as a function of blood vessel position (Bottom). Heat is produced in the tissue region (TempTis_pc) and released through the veins (TempVen_cap) and lung (TempPul_cap).


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.

Model Feedback

We welcome comments and feedback for this model. Please use the button below to send comments:


 Allen TH, Krzywicki HJ, Roberts JE. J. Appl. Physiol 1959;14:1005. [PubMed: 13792786]
 Allen TH, Welch BE, Trujillo TT, Roberts JE. J. Appl. Physiol 1959;14:1009. [PubMed: 13792787] 

 Austin W, Lacombe E, Rand PW, Chatterjee M. Solubility of carbon dioxide in serum from
 15 to 38 c. Journal of Applied Physiology 18: 301–304, 1963.

 Beek JHGM van, Supandi F, Gavai AK, Graaf AA de, Binsl TW, Hettling H.
 Simulating the physiology of athletes during endurance sports events: Modelling human energy
 conversion and metabolism. Philosophical Transactions of the Royal Society of London A: Mathematical,
 Physical and Engineering Sciences 369: 4295–4315, 2011.

 Bassingthwaighte JB, Yipintsoi T, and Harvey RB. Microvasculature of the dog left ventricular
 myocardium. Microvasc Res 7: 229-249, 1974.

 Bassingthwaighte JB and Vinnakota KC. The computational integrated myocyte.
 A view into the virtual heart. In: Modeling in Cardiovascular Systems.
 Ann. New York Acad. Sci. 1015:, edited by Sideman S. and Beyar R. 2004, pp 391-404.
 Brozek J, Grande F, Anderston JT, and Keys A. Densitometric analysis of body composition: 
 revision of some quantitative assumptions. Ann NY Acad Sci 110: 113–140, 1963.

 Christmas KM, Bassingthwaighte JB. Equations for O2 and CO2 solubilities in saline and plasma: 
 Combining temperature and density dependences. Journal of Applied Physiology 122:1313–1320, 2017.

 Dash RK and Bassingthwaighte JB (2006), "Simultaneous Blood--Tissue Exchange of Oxygen, Carbon Dioxide, 
 Bicarbonate, and Hydrogen Ion", Annals of Biomedical Engineering., Jul, 2006. Vol. 34(7), pp. 1129-1148.

 Dash RK and Bassingthwaighte JB (2010), "Erratum to: Blood HbO2 and HbCO2 Dissociation Curves at Varied 
 O2, CO2, pH, 2,3-DPG and Temperature Levels", Annals of Biomedical Engineering., Apr, 2010. Vol. 38(4), 
 pp. 1683-1701.

 Dash RK, Korman B and Bassingthwaighte JB (2016), "Simple accurate mathematical models of blood HbO2 
 and HbCO2 dissociation curves at varied physiological conditions: evaluation and comparison with other 
 models", European Journal of Applied Physiology., Jan, 2016. Vol. 116(1), pp. 97-113.

 Effros RM and Chinard FP. The in vivo pH of the extravascular space of the lung. 
 J Clin Invest 48: 1983–1996, 1969. (for water content of RBC)

 Gonzalez F and Bassingthwaighte JB. Heterogeneities in regional volumes of distribution and
        flows in the rabbit heart. Am J Physiol Heart Circ Physiol 258: H1012-H1024, 1990.

 Haurowitz, F. Chemistry and Biology of Proteins. New York: Academic Press; 1950. (for rho protein) 

 Hill EP, Power GG, Longo LD. A mathematical model of carbon dioxide transfer in the placenta 
 and its interaction with oxygen. American Journal of Physiology 224: 283–299,1973.

 Jardine B, Raymond GM, and Bassingthwaighte JB. Semi-automated modular program constructor for 
 physiological modeling: Building Cell and organ models. F1000 Research 4: 1461 
 (doi: 10.12688/f1000research.7476.3) 12pp., 2016. PMID:28698795 PMCID:PMC5488124 

 Kaminsky DA, Whitman T, Callas PW. DLCO versus dlco/va as predictors of pulmonary gas exchange. 
 Respiratory Medicine 101: 989–994, 2007.

 Kelman G. Digital computer procedure for the conversion of pco2, into blood co2 content. 
 Respiration Physiology 3: 111–115, 1967.

 Stolwijk J. A mathematical model of physiological temperature regulation in man. Washington, DC, USA: 
 National Aeronautics Space Administration, 1971.

 Vinnakota K and Bassingthwaighte JB. Myocardial density and composition: A basis for calculating 
 intracellular metabolite concentrations. Am J Physiol Heart Circ Physiol 286: H1742-H1749, 2004.
 Yipintsoi T, Scanlon PD, and Bassingthwaighte JB. Density and water content of dog ventricular
        myocardium. Proc Soc Exp Biol Med 141: 1032-1035, 1972.

 Ypma TJ. Historical development of the newton–Raphson method. SIAM Review 37: 531–551, 1995.

Related Models

Key Terms

BTEX, PDE, Cardiac grid, Oxygen, CO2, pH, Solubility, tissue exchange, gas exchange, Haldane Hemoglobin binding, MPC

Model History

Get Model history in CVS.

Posted by: BEJ


Please cite in any publication for which this software is used and send an email with the citation and, if possible, a PDF file of the paper to:
Or send a copy to:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.

[This page was last modified 14Mar18, 3:17 pm.]

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.