Exchange of gas in external air into a non-linearly compliant lung with calculation of concentration of material in lung over a series of breaths and transport into the pulmonary capillary blood and subsequent loss into a "body" composed of blood in exchange with a tissue region where consumption occurs.
OneAlvLung.ExchBody.proj (Physiome # 206) Inflowing solute gas in the inspired air is transported by passive diffusion across the alveolar-capillary membrane from the alveolar space to the pulmonary capillary blood, resulting in "consumption" of alveolar gas as the blood flows away to the body. The alveolar transmembrane conductance is PSO2lung ml/(min) permeability times membrane surface area, which has the units of a flow. The blood flow through the lung is the cardiac output (or flow of plasma), Fblood, to the body. The "body" is here represented by a blood pool exchanging with a volume of body tissue with the conductance between them being PSO2tiss, ml/min. In the tissue there is consumption Gtiss, ml/min. Cyclic breathing leads to a pseudo-steady-state in which the alveolar partial pressure, PO2lung is less than in the outside air, PO2atmos, that is, there is no equilibration, and the concentration in the alveolus fluctuates with each breath. At very low capillary blood flows, the PO2atmos, PO2lung, and blood very nearly equilibrate. (New features: Passive transmembrane transport, PS, flow in a second region, the capillary blood, and the dissolution of a gas into a fluid medium.) With PS set to zero, consumption must cease and alveolar gas concentrations will equilibrate with outside air. With PS > 0 but Fair = 0, there will also be equilibration, but with a lag time taken for the blood in the lung capillary to equilibrate. With both PS >0, Fair>0, and Gtiss =0, there is complete equilibration PO2atmos = PO2lung = PO2pulcap = PO2tisscap = PO2tiss, as required. Some of the code for this model is identical to that in OneAlvLung.xxx. The parts that are different are the additional code for calculating a concentration of a substance in the lung and the non-linear compliance which decreases at high and low volumes causing the pressure in the lung to rise or decrease respectively relative to a constant compliance. The verification correctly calculates the concentration once every six seconds when R*Com<=0.5 sec, when PSO2lung = 0 so no material is lost from the lung. The model includes three additional regions as stirred tanks: lung capillary blood, Vpulcap, blood circulating in the body, Vbl, and tissue of volume, Vtiss, exchanging with Vpulcap with conductance PSO2tiss. Main assumptions are the same as found in model Lung_RC. GENERAL RESULTS: The ventilator, using a driving pressure of 20 mmHg gives an approximately normal tidal volume. Normally of course, the driving force is provided by expansion of the chest, creating a negative pressure in the intrapleural space, just the oppposite of a positive pressure ventilator. When R*Com<0.5, Concentration in Lungs follows an exponential decay to ambient (air) concentrations. The non=linear compliance is similar to that portrayed by Levistsky p 30. Loops to set Pscalar to 100 and -50 serve to reveal the whole P_V curve. Second level loops show effects of a1 and A2 on compliance curve (= slope of P_V curve).
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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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.