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 SchoolMay 14, 2004

James BaileyAppalachian State University

Sean LavertyMillersville University

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

Biological Background

Discussion of:

Respiration and Circulation

Constraints on Systems

Ventilation

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

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

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

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.

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

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

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

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

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

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

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

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

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

Acknowledgements

Project Advisor - Dr. Thomas Hillen

PIMS Participant ProfessorsLaboratory Assistants

Keener and Sneyd

PIMS Participant Students