Models two compartments, fluid and air, for a soluble gas passively exchanging between the volumes, V1 liquid, V2 air, with buffering site in V1, forming a closed system. Assumes constant volumes, dry air. Simple model of alveolar-capillary gas exchange.
Simple two compartment model of gas exchange between fluid and gas compartments with buffering of gas in water compartment. Emphasis is on mass exchange as the mass flux of gas across a phase boundary can be confusing. For this model the compartment volumes and temperature are held constant and the system is closed so that the total mass in the system is constant. Depending on the overall rate constants for the buffering reaction, the total CO2 in the system changes but the total amount of CO2 plus the buffering substrates still remains constant. To check that the ODE for CO2 in water compartment reduces to the analytical expression for pCO2w, just set the forward buffer reaction constant, kp1, to zero.
Figure: Partial pressure in the two compartments as a function of time with buffering on (kp1 = 0.4 sec^-1) and off. pCO2w (black) is the partial pressure, mmHg, in the water compartment and pCO2alv (red) is the partial pressure in the air/gas compartment. Green line is the analytical solution for pCO2w when buffering is off. Note that when buffering is on, the partial pressure increases in the water compartment and it takes much longer (>200 sec) for the partial pressures between the two compartment to equilibrate. The buffering increases the availablity of CO2 to the system.
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.
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Christmas KM and Bassingthwaighte JB. Equations for O2 and CO2 solubilities in saline and plasma: Combining temperature and density dependences. J Appl Physiol 122: 1313-1320, 2017. Dash, R.K. and Bassingwaighte, J.B., Simultaneous Blood-Tissue Exchange of Oxygen, Carbon Dioxide, Bicarbonate, and Hydrogen Ion, Ann Biomed Eng 34(7): 1129-1148 2006. Dash RK and Bassingthwaighte JB. Erratum to: Blood HbO2 and HbCO2 dissociation curves at varied O2, CO2, pH, 2,3-DPG and Temperature Levels. Ann Biomed Eng 38(4): 1683-1701, DOI: 10.1007/s10439-010-9948-y PMC2862600, 2010 Hills BA, Gas Transfer in the Lung (Book), Cambridge University Press, London, 1974 Comroe J, Lung (Book), YEAR BOOK MEDICAL, Second Edition edition (1965) https://www.imagwiki.nibib.nih.gov/physiome/Models/tutorial
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The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.
Model development and archiving support at https://www.imagwiki.nibib.nih.gov/physiome 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.