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A Carbon Dioxide Driven Model for the Alveolar Lung

Dr. Thomas Hillen: Please sit on your hands for the next thirty minutes. We’ll take you out for coffee later if you listen. A Carbon Dioxide Driven Model for the Alveolar Lung. PIMS Summer School May 14, 2004 James Bailey Appalachian State University Sean Laverty Millersville University.

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A Carbon Dioxide Driven Model for the Alveolar Lung

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  1. Dr. Thomas Hillen:Please sit on your hands for the next thirty minutes.We’ll take you out for coffee later if you listen

  2. A Carbon Dioxide Driven Model for the Alveolar Lung PIMS Summer SchoolMay 14, 2004 James BaileyAppalachian State University Sean LavertyMillersville University

  3. Problem Statement Build a simple model of the breathing process, describing the concentration of oxygen within the lung during regular breathing. Consider the following: • Different breathing mechanisms • Environmental conditions • Presence of toxic chemicals

  4. Biological Background Discussion of: Respiration and Circulation Constraints on SystemsVentilation

  5. Respiration and Circulation • Respiration – Function: To provide oxygen [O2] to the blood and remove excess carbon dioxide [CO2] from the blood • Circulation – Function: A system responsible for transporting materials throughout the body via blood and respiratory pigments

  6. Constraints of diffusion • Diffusion is extremely slow!While it works for unicellular organisms, it does not provide sufficient O2 to larger organisms • A breath-taking example: A one centimeter organism with a 100ml O2/kg/hr demand [less than half that of a resting human] would need an atmospheric pressure of 25 atms to rely on diffusion

  7. Ventilation • The process beginning with the movement of atmospheric air into the alveoli, where gas exchange occurs, and the expulsion of the air from the body • To depend on gas exchange by diffusion, the human lung contains roughly 300 million individual alveoli with a total surface area of nearly seventy square meters

  8. Capillary-Alveolar Transport The flow of gas by diffusion depends on: • the diffusion coefficient – which itself depends on the size and solubility of the gas molecules • the alveolar surface area through which diffusion occurs • the length of the path to the alveoli • the partial pressure gradient across the membrane.

  9. Properties of Capillary Diffusion • Where:- A is the capillary cross-sectional area • - L is the capillary length • - v is the blood velocity • u is the gas concentration • p is the capillary surface area • q(x,t) is the flux per unit area across the capillary wall • Q is the total flux across the capillary wall • σ is the solubility of the gas in blood • Pgi is the partial pressure of the gas in its respective location • Ds is the diffusion coefficient of the gas

  10. The Gas Exchange Model:[The Mackey-Glass Equation] Where:- x is the partial pressure of blood CO2-λ is the rate of production of CO2 -α assumes that change in x varies linearly with the concentration -V’ is the ventilation rate described by the Hill equation

  11. The Hill Equation Where:- Vm is the maximum tidal volume per breath- θ influences the rate of breathing- n influences the maximum CO2 level

  12. The Oxygen Concentration Equation:[The Bailey-Laverty Equation] • Where:- PbO2is the partial pressure of blood O2 • PiO2 is the partial pressure of inspired O2

  13. Ventilation-Perfusion Ratio:For Hypo- and Hyperventilation R relates the volume of CO2 eliminated from the blood to the oxygen uptake through the lungs, and is equal to V’/Q as defined above

  14. Hold your breath, we’re almost there...

  15. Figures to Follow • Rapid Breathing • Blood Level Carbon Dioxide • Blood Level Oxygen • Blood Level Gases with Increasing Metabolic Rate • -Carbon Dioxide • -Oxygen • Blood Level Oxygen with Increasing Altitude • -With No Exertion • -With Exertion • Presence of Environmental Toxins

  16. Suggestions for Further Study • Incorporate complexities which arise from the branching structure of the lung • - Our model assumes that the flow of the gas through the lung, and the flow of blood through capillary mesh surrounding the alveoli are both constant • The model should incorporate pulmonary branch diameters, branching angles, and gravitational angles and the corresponding effects on the flow and distribution of gas

  17. Suggestions for Further Study • Incorporate complexities which arise from environmental variations • - This model ignores variations in partial pressures of inspired inert gases • The model ignores changes in humidity of inspired air • The model ignores molecular mass and atomic structure of inspired gases and the effects on deposition

  18. Acknowledgements Project Advisor - Dr. Thomas Hillen PIMS Participant ProfessorsLaboratory Assistants Keener and Sneyd PIMS Participant Students

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