a carbon dioxide driven model for the alveolar lung
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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Dr. Thomas Hillen:Please sit on your hands for the next
thirty minutes.
We’ll take you out for coffee later if you
listen
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A Carbon Dioxide Driven Model for the Alveolar Lung
PIMS Summer SchoolMay 14, 2004
James BaileyAppalachian State University
Sean LavertyMillersville University
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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
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Biological Background
Discussion of:
Respiration and Circulation
Constraints on Systems
Ventilation
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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
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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
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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
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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.
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Properties of Capillary Diffusion
ePP
vv
vAgcga
L
L
L
LPDvAQ
dxtxqptLAutAudxtxuAt
s
1)((
),(),(),0(),(000
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
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The Gas Exchange Model:[The Mackey-Glass Equation]
'Vαxλdt
dx
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
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The Hill Equation
xx
nn
n
mVV
'
Where:- Vm is the maximum tidal volume per breath- θ influences the rate of breathing- n influences the maximum CO2 level
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The Oxygen Concentration Equation:
[The Bailey-Laverty Equation]
R
αxVλiOdt
bO PdP '
2
2
Where:- PbO2
is the partial pressure of blood O2
-PiO2 is the partial pressure of inspired O2
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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
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Hold your breath, we’re almost there...
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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
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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
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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
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Acknowledgements
Project Advisor - Dr. Thomas Hillen
PIMS Participant ProfessorsLaboratory Assistants
Keener and Sneyd
PIMS Participant Students