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
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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.
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.
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.
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- Dash 2010 Blood HbO2 and HbCO2 Dissociation Curves.
- Dash 2006 O2-CO2 BTEX model
- Dash 2016 Simplified blood HbO2 and HbCO2 Dissociation Curves.
- Lung O2-CO2 transport and exchange between 3 compartment lung and lung capillary.
- Dash compartmental model of recirculating O2-CO2 in the alveolus, pulmonary and tissue capillaries.
- Christmas 2016 O2, CO2 solubility coefficient curves.
BTEX, PDE, Cardiac grid, Oxygen, CO2, pH, Solubility, tissue exchange, gas exchange, Haldane Hemoglobin binding, MPC
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Model development and archiving support at physiome.org 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.