Module C: DiffusionModule C: Diffusion

MODULE C – DIFFUSION OF MODULE C – DIFFUSION OF GASESGASES

Dalton’s LawDalton’s LawPartial Pressure of GasPartial Pressure of GasAtmospheric pressureAtmospheric pressureFractional ConcentrationFractional ConcentrationWater Vapor PressureWater Vapor Pressure

Alveolar-Capillary (A-C) structureAlveolar-Capillary (A-C) structureAlveolar Gas EquationAlveolar Gas EquationGas Diffusion across A-C membraneGas Diffusion across A-C membrane

Fick’s LawFick’s LawHenry’s LawHenry’s LawGraham’s LawGraham’s Law

Perfusion-Limit and Diffusion-Limit to gas transferPerfusion-Limit and Diffusion-Limit to gas transferDiffusing Capacity of the Lung (DDiffusing Capacity of the Lung (DLLCOCO))

ObjectivesObjectivesDiagram the alveolar-capillary membrane showing partial Diagram the alveolar-capillary membrane showing partial pressures of Ppressures of POO22, P, PCOCO22, & P, & PHH22OO at the following locations: at the following locations:

AtmosphereAtmosphere AlveoliAlveoli Venous bloodVenous blood Arterial bloodArterial blood

Given a barometric pressure, FGiven a barometric pressure, FIIOO22, P, PaaCOCO22, calculate the , calculate the PPAAOO22 (Alveolar-Air Equation). (Alveolar-Air Equation).Diagram the pathway of gas diffusion across the alveolar Diagram the pathway of gas diffusion across the alveolar capillary membrane.capillary membrane.

Describe the pressure gradients for ODescribe the pressure gradients for O22 and CO and CO22, , responsible for gas diffusion, across the A-C membrane.responsible for gas diffusion, across the A-C membrane.Describe the total transit time for gas diffusion across the Describe the total transit time for gas diffusion across the lung and the amount of time needed for diffusion in a lung and the amount of time needed for diffusion in a normal individual.normal individual.State how exercise affects the total transit time.State how exercise affects the total transit time.

ObjectivesObjectivesState Fick’s Law of diffusion and describe how State Fick’s Law of diffusion and describe how the diffusion constant is calculated.the diffusion constant is calculated.

Explain Henry’s law.Explain Henry’s law. Explain Graham’s Law.Explain Graham’s Law.

Compare and contrast the rate of diffusion Compare and contrast the rate of diffusion across the A-C membrane between COacross the A-C membrane between CO22 and O and O22..

Describe the clinical applications of Fick’s Law.Describe the clinical applications of Fick’s Law.State the test used to determine the DState the test used to determine the DLLCO CO and and state the normal value.state the normal value.Describe how the DDescribe how the DLLCOCO is affected with is affected with obstructive lung diseases and other clinical obstructive lung diseases and other clinical conditions that decrease the rate of diffusion in conditions that decrease the rate of diffusion in the lung.the lung.

ReadingsReadings

Beachey: Chapter 4 (pp. 80-81) & 7Beachey: Chapter 4 (pp. 80-81) & 7

Egan: Chapter 5 (pp. 101-102) & 10 (230-Egan: Chapter 5 (pp. 101-102) & 10 (230-234)234)

Dalton’s LawDalton’s LawIn a mixture of gases, the total pressure is In a mixture of gases, the total pressure is equal to the sum of the partial pressures of equal to the sum of the partial pressures of each individual gas.each individual gas.

Partial PressurePartial Pressure

Def: The pressure exerted by an individual Def: The pressure exerted by an individual gas in a mixture of gases.gas in a mixture of gases. Designated by PDesignated by PGASGAS To determine the partial pressure of any gas, To determine the partial pressure of any gas,

multiply the percentage of that gas by the total multiply the percentage of that gas by the total pressure.pressure.

Example: Oxygen occupies 21% of the atmosphere. Example: Oxygen occupies 21% of the atmosphere. If the total pressure of the atmosphere (i.e. If the total pressure of the atmosphere (i.e. Barometric Pressure) is 760 mmHg, the POBarometric Pressure) is 760 mmHg, the PO22 of the of the

atmosphere is 159.6 mmHg (760 x .21).atmosphere is 159.6 mmHg (760 x .21).

Barometric PressureBarometric PressureApplication of Dalton’s LawApplication of Dalton’s LawPPNN22 + P + POO22 + P + PArAr + P + PCOCO22 = P = PBAROBARO

As altitude increases, barometric pressure falls and the As altitude increases, barometric pressure falls and the partial pressurepartial pressure of the constituent gases decrease of the constituent gases decrease proportionally. proportionally. The percentage of a gas is also expressed as the The percentage of a gas is also expressed as the “Fractional Concentration” or F“Fractional Concentration” or FGASGAS..

Example: The FExample: The FOO22 of the atmosphere is 20.95% of the atmosphere is 20.95%

Partial Pressure of Key GasesPartial Pressure of Key GasesOxygen partial pressure is reduced as it goes Oxygen partial pressure is reduced as it goes from the atmosphere to the alveoli secondary to from the atmosphere to the alveoli secondary to “competition” with carbon dioxide and water “competition” with carbon dioxide and water vapor.vapor.

Water Vapor PressureWater Vapor Pressure

Water in the gaseous form is called water vapor.Water in the gaseous form is called water vapor. Water in the molecular form.Water in the molecular form.

The amount of water vapor present can be The amount of water vapor present can be expressed as:expressed as: A partial pressureA partial pressure A maximal amount (Absolute Humidity in mg/L)A maximal amount (Absolute Humidity in mg/L)

The amount of water vapor is temperature The amount of water vapor is temperature dependent.dependent. Inspired gas at 37° C (100% saturated at the Inspired gas at 37° C (100% saturated at the

carina), has a Water Vapor pressure (Pcarina), has a Water Vapor pressure (PHH22OO) of 47 ) of 47 mmHg and an absolute humidity of 44 mg/L.mmHg and an absolute humidity of 44 mg/L.

Temperature - °CTemperature - °C Vapor Pressure, Vapor Pressure, mmHgmmHg

ConditionCondition

00 4.64.6 water freezeswater freezes

2020 17.517.5 room temperatureroom temperature

3737 4747 body temperaturebody temperature

100100 760760 steamsteam

ReviewReviewDalton’s LawDalton’s Law

Sum of the partial pressures of individual gases add up to the Sum of the partial pressures of individual gases add up to the barometric pressure.barometric pressure.

Partial PressurePartial Pressure Denoted with PDenoted with PGAS (e.g. PGAS (e.g. POO22)) Determined by multiplying the “fractional concentration” (i.e. %; Determined by multiplying the “fractional concentration” (i.e. %;

designated by Fdesignated by FGASGAS) by the barometric pressure) by the barometric pressurePPOO22=P=PBaroBaro x F x FOO22

As altitude increases, barometric pressure (and therefore As altitude increases, barometric pressure (and therefore partial pressures) decrease. Fractional concentrations partial pressures) decrease. Fractional concentrations DO NOT change.DO NOT change.As gas is inhaled, the partial pressure of oxygen goes As gas is inhaled, the partial pressure of oxygen goes down because of water vapor pressure (Pdown because of water vapor pressure (PHH22OO)and )and ultimately by the partial pressure of carbon dioxide in the ultimately by the partial pressure of carbon dioxide in the alveolus (Palveolus (PAACOCO22))

The partial pressure of water vapor is ALWAYS 47 mm Hg at The partial pressure of water vapor is ALWAYS 47 mm Hg at body temperature and full saturation.body temperature and full saturation.

Alveolar Gas EquationAlveolar Gas Equation

One of the most important formulae in One of the most important formulae in Pulmonary medicine.Pulmonary medicine.Signified by PSignified by PAAOO22, where “A” is Alveolar., where “A” is Alveolar.

PPAAOO22 = {[P= {[PBAROBARO – P – PHH22OO] * F] * FIIOO22} – (P} – (PaaCOCO22 * 1.25) * 1.25) oror

PPAAOO22 = {[P= {[PBAROBARO – P – PHH22OO] * F] * FIIOO22} – (P} – (PaaCOCO22 / 0.8) / 0.8)

Water vapor pressure must Water vapor pressure must alwaysalways be be subtracted out from the barometric pressure subtracted out from the barometric pressure whenever we are evaluating inspired gases.whenever we are evaluating inspired gases.

Alveolar Gas Equation ExampleAlveolar Gas Equation Example

At a barometric pressure of 747, a patient At a barometric pressure of 747, a patient breathes room air and has an arterial partial breathes room air and has an arterial partial pressure of carbon dioxide of 32 mm Hg. pressure of carbon dioxide of 32 mm Hg. What is the PWhat is the PAAOO22??

PPAAOO22 = {[P= {[PBAROBARO – P – PHH22OO] * F] * FIIOO22} – (P} – (PaaCOCO22 * 1.25) * 1.25)

PPAAOO22 = {[747 mm Hg – 47 mm Hg] * .21} – = {[747 mm Hg – 47 mm Hg] * .21} –

(32 mm Hg * 1.25)(32 mm Hg * 1.25)

PPAAOO22 = = {700 mm Hg * .21} – 40 mm Hg{700 mm Hg * .21} – 40 mm Hg

PPAAOO22 = 147 mm Hg – 40 mm Hg = 147 mm Hg – 40 mm Hg

PPAAOO22 = 107 mm Hg = 107 mm Hg

Diffusion – Part IIDiffusion – Part II

Alveolar Gas Equation ExampleAlveolar Gas Equation Example

At a barometric pressure of 747, a patient At a barometric pressure of 747, a patient breathes room air and has an arterial partial breathes room air and has an arterial partial pressure of carbon dioxide of 32 mm Hg. pressure of carbon dioxide of 32 mm Hg. What is the PWhat is the PAAOO22??

PPAAOO22 = {[P= {[PBAROBARO – P – PHH22OO] * F] * FIIOO22} – (P} – (PaaCOCO22 * 1.25) * 1.25)

PPAAOO22 = {[747 mm Hg – 47 mm Hg] * .21} – = {[747 mm Hg – 47 mm Hg] * .21} –

(32 mm Hg * 1.25)(32 mm Hg * 1.25)

PPAAOO22 = = {700 mm Hg * .21} – 40 mm Hg{700 mm Hg * .21} – 40 mm Hg

PPAAOO22 = 147 mm Hg – 40 mm Hg = 147 mm Hg – 40 mm Hg

PPAAOO22 = 107 mm Hg = 107 mm Hg

Normal ValuesNormal Values

PPOO22 PPCOCO22

ArterialArterial 80-100 80-100 mm Hgmm Hg

35-45 35-45 mm Hgmm Hg

VenousVenous 40 mm Hg40 mm Hg 46 mm Hg46 mm Hg

Structure of the Alveolar-Capillary MembraneStructure of the Alveolar-Capillary Membrane

Follow the oxygen molecule from alveolus to RBC:Follow the oxygen molecule from alveolus to RBC:1.1. Fluid layer lining the alveolus.Fluid layer lining the alveolus.2.2. Alveolar epitheliumAlveolar epithelium3.3. Alveolar basement membraneAlveolar basement membrane4.4. Interstitial spaceInterstitial space5.5. Capillary basement membraneCapillary basement membrane6.6. Capillary endotheliumCapillary endothelium7.7. Plasma in capillaryPlasma in capillary8.8. Erythrocyte membraneErythrocyte membrane9.9. Intracellular Erythrocyte fluidIntracellular Erythrocyte fluid

2

1

3

4

5

6

7

8

9

Diffusion across the A-C MembraneDiffusion across the A-C MembraneGas moves from alveoli to capillary Gas moves from alveoli to capillary because of a pressure gradient.because of a pressure gradient.

Exercise and DiffusionExercise and Diffusion

• During exercise, the transit time can be reduced to as low as .40 seconds.

• Increased cardiac output, decreased transit time (less time spent in the capillary in front of a alveolus).

• Since we only “need” 0.25 seconds for complete diffusion, we can handle the increased reduced transit time during exercise.

DemonstrationDemonstration

Honeycombing Honeycombing of lung in of lung in

Pulmonary Pulmonary FibrosisFibrosis

Fick’s LawFick’s LawAdolph Fick (1831 – 1879)Adolph Fick (1831 – 1879)

The amount of gas that diffuses The amount of gas that diffuses across a membrane (V) is across a membrane (V) is directlydirectly proportional to (a) the surface area proportional to (a) the surface area (A), (b) the pressure difference from (A), (b) the pressure difference from one side of the membrane to the one side of the membrane to the other (Pother (P11-P-P22), and (c) a diffusion ), and (c) a diffusion constant (D). It is also constant (D). It is also inverselyinversely proportional to the thickness of the proportional to the thickness of the membrane (T).membrane (T).

V = [A * D * (PV = [A * D * (P11-P-P22)] / T)] / T

Diffusion Constant (D)Diffusion Constant (D)As the gas crosses from a gaseous environment (the alveolus) to a liquid one (everything after that), it has to first dissolve into the liquid and then move through the liquid to the hemoglobin in the RBC. The Diffusion Constant (D) in Fick’s law describes both of these and is determined by two other laws: Henry’s Law – How much can be dissolved. Graham’s Law – The rate gas can move

through a liquid..

Henry’s LawHenry’s LawA chemical law stating that the amount of a gas that dissolves in a liquid is proportional to the partial pressure of the gas over the liquid, provided no chemical reaction takes place between the liquid and the gas.

It is named after William Henry (1774–1836), the English chemist who first reported the relationship.

Henry’s LawHenry’s LawThe amount of gas that can be dissolved by 1 ml of a given liquid at standard pressure (760 mm Hg) and at a specified temperature is called the solubility coefficient.

The solubility coefficient varies inversely with temperature.

For oxygen at 37° C the coefficient is 0.0244 ml/mm Hg/mL H2O.

For carbon dioxide it is 0.592 ml/mm Hg/mL H2O. In a liquid medium (like the blood and interstitial space),

carbon dioxide is 24 times more soluble.

Graham’s LawGraham’s Law

Thomas Graham (1805-1869)Thomas Graham (1805-1869) ““The rate of diffusion of a gas through a The rate of diffusion of a gas through a

liquid is inversely proportional to the liquid is inversely proportional to the square root of the gram molecular weight square root of the gram molecular weight (GMW) of the gas.”(GMW) of the gas.”

GMW of Oxygen – 32GMW of Oxygen – 32

GMW of Carbon Dioxide - 44 GMW of Carbon Dioxide - 44

66

65

44

32

of

2

2

2

2

.

.

COGMW

OGMW

OofDiffusionRate

COofDiffusionofRate

Diffusion ConstantDiffusion ConstantFrom Henry’s law we get:From Henry’s law we get:

Diffusion is directly proportional to the solubility coefficientDiffusion is directly proportional to the solubility coefficient

From Graham’s law we get:From Graham’s law we get: Diffusion is inversely proportional to the gram molecular weightDiffusion is inversely proportional to the gram molecular weight

Combining them together we see that diffusion is Combining them together we see that diffusion is proportional to the solubility of the gas and inversely proportional to the solubility of the gas and inversely proportional to how heavy it is.proportional to how heavy it is.

Carbon Dioxide diffuses 20 times more than oxygen (i.e. Carbon Dioxide diffuses 20 times more than oxygen (i.e. has a diffusion constant that is 20 times greater).has a diffusion constant that is 20 times greater).

ratio 1:20 a roughly or 20.5916104

31523

024466

592065

Ot Coefficien SolubilityCO

COt Coefficien SolubilityO

O of

CO of

22

22

2

2

.

.

..

..

GMW

GMW

Diffusion

Diffusion

Clinical Application of Fick’s LawClinical Application of Fick’s LawAs the surface area (A) available for As the surface area (A) available for diffusion decreases (with lung disease), the diffusion decreases (with lung disease), the amount of gas that diffuses also decreases.amount of gas that diffuses also decreases.As the pressure difference (PAs the pressure difference (P11-P-P22) between ) between the alveolus and the capillary decreases (as the alveolus and the capillary decreases (as would occur at an elevated altitude), the would occur at an elevated altitude), the amount of gas that diffuses also decreases.amount of gas that diffuses also decreases.As the thickness of the alveolar-capillary As the thickness of the alveolar-capillary membrane increases, the amount of gas membrane increases, the amount of gas that diffuses also decreases.that diffuses also decreases.

Perfusion & Diffusion LimitingPerfusion & Diffusion Limiting

When the amount of oxygen that is diffused across When the amount of oxygen that is diffused across the A-C membrane is restricted by the amount of the A-C membrane is restricted by the amount of blood flow present (only so much blood can be blood flow present (only so much blood can be oxygenated) we say this is a oxygenated) we say this is a perfusion limitationperfusion limitation.. This is what occurs in normal individuals.This is what occurs in normal individuals.

When the amount of diffused is limited by the When the amount of diffused is limited by the thickness of the A-C membrane or the loss of thickness of the A-C membrane or the loss of alveolar surface area (as occurs in lung disease) alveolar surface area (as occurs in lung disease) we say this is a we say this is a diffusion limitationdiffusion limitation..

Diffusing Capacity of the LungDiffusing Capacity of the LungThe DThe DLLCOCO measures the amount of carbon monoxide measures the amount of carbon monoxide (CO) that moves across the alveolar-capillary membrane.(CO) that moves across the alveolar-capillary membrane.

Carbon monoxide is an ideal tracer gas.Carbon monoxide is an ideal tracer gas.

Normal DNormal DLLCOCO for healthy adults is 25 (20-30) for healthy adults is 25 (20-30) ml/min/mmHgml/min/mmHgMeasurement affected by body size, age, lung volume, Measurement affected by body size, age, lung volume, exercise, body position, and hemoglobin concentration.exercise, body position, and hemoglobin concentration.Decreased if:Decreased if:

Lung surface area is reduced Lung surface area is reduced EmphysemaEmphysema

Alveolar-capillary distance is increasedAlveolar-capillary distance is increasedPulmonary FibrosisPulmonary FibrosisCongestive Heart FailureCongestive Heart Failure