Gas Diffusion

Defining Diffusion and Respiration

• Respiration is the process occurring at the level of the alveoli where pulmonary capillaries come into contact with the air sacs to facilitate gas exchange.

• In a clinical setting, respiratory therapists often use the term "ventilation" to describe the bulk flow of gases into and out of the lungs, but technically, "respiration" specifically refers to the diffusion of gases across the alveolar-capillary membrane.

• Diffusion is the movement of gas molecules from an area of high concentration to an area of low concentration. It is the result of high-speed, random motion of gas or liquid molecules colliding with each other and vessel walls.

• Diffusion across a membrane or barrier continues until an equilibrium is reached between the partial pressures on either side of the membrane.

Dalton's Law and the Components of Ambient Air

• Sea Level Barometric Pressure ($P_B$): The total atmospheric pressure at sea level is exactly $760\,mmHg$ (also referred to as $760\,torr$).

• Dalton's Law states that each gas in a mixture exerts a partial pressure proportional to its fractional concentration in the total air mixture.

• The the general equation for Dalton's Law is: $P_{gas} = F_{gas} \times P_B$

• Atmospheric Composition of Ambient Air:

  • Nitrogen ($N_2$): Makes up approximately $78\%$ of the atmosphere.
  • Oxygen ($O_2$): Makes up approximately $21\%$ of the atmosphere.
  • Carbon Dioxide ($CO_2$) and other trace gases: Make up the remaining $1\%$.

• Calculation Example for Oxygen at Sea Level: $P_{O_2} = 0.21 \times 760\,mmHg = 159.6\,mmHg$

• Calculation Example for Nitrogen at Sea Level: $P_{N_2} = 0.78 \times 760\,mmHg = 592.8\,mmHg$

The Impact of Altitude and Depth on Gas Pressure

• At higher altitudes (such as mountains), there is less gravitational pull on gas molecules, causing them to be less tightly packed. This results in a lower barometric pressure ($P_B$), even though the fractional concentration ($F_I O_2$) remains at $21\%$.

• Mount Everest Case Study:

  • Altitude: $29,028\,feet$.
  • Barometric Pressure: Approximately $250\,mmHg$.
  • Inspired Partial Pressure of Oxygen ($P_I O_2$): $0.21 \times 250\,mmHg \approx 43\,mmHg$.

• Extreme Altitude Warning: At approximately $65,000\,feet$, the barometric pressure falls below the pressure of water vapor, causing body tissue to begin to boil or vaporize.

• Underwater Diving and Pressure:

  • At sea level, pressure is $1\,ATM$ (atmosphere), which equals $760\,mmHg$.
  • For every $33\,feet$ traveled below sea level, pressure increases by an additional $1\,ATM$.
  • Pressure at $33\,feet$ depth: $2\,ATM \times 760\,mmHg = 1,520\,mmHg$.
  • Pressure at $66\,feet$ depth: $3\,ATM \times 760\,mmHg = 2,280\,mmHg$.
  • The partial pressure of oxygen ($P_{O_2}$) at $66\,feet$ depth would be: $0.21 \times 2280\,mmHg = 478.8\,mmHg$.

Pressure Gradients and Gas Diffusion

• Pressure Gradient: Refers to bulk gas movement from an area of higher pressure to lower pressure. In bulk flow, all gases move together in the same direction on a "bus."

• Diffusion Gradient: Refers to the individual partial pressure differences of a specific gas. Each gas moves independently according to its own gradient.

• Equilibrium: Diffusion occurs from the high-pressure side of the alveolar-capillary membrane to the low-pressure side until the pressures are equal.

Humidity and Water Vapor Pressure

• Molecular Water (Water Vapor): When water exists in a gaseous state, it behaves according to the laws of gases and exerts pressure.

• Alveolar Conditions: The body warms inspired air to a normal body temperature of $37^\circ C$ and humidifies it to $100\%$ relative humidity.

• At $37^\circ C$ and $100\%$ humidity, the Absolute Humidity is $44\,mg/L$.

• Water Vapor Pressure ($P_{H_2O}$): At these conditions, molecular water exerts a constant partial pressure of $47\,mmHg$.

The Alveolar Air Equation ($P_A O_2$)

• The Alveolar Air Equation is used to calculate the partial pressure of oxygen specifically within the alveoli ($P\text{ big A } O_2$). This is distinct from $P\text{ little a } O_2$, which is the partial pressure in arterial blood.

• The formula (using the multiplier of $1.25$ for $CO_2$) is: $P_A O_2 = (P_B - P_{H_2O}) \times F_I O_2 - (PaCO_2 \times 1.25)$

• Key Components:

  • $P_B$: Barometric pressure (usually $760\,mmHg$ at sea level).
  • $P_{H_2O}$: Water vapor pressure (constant at $47\,mmHg$).
  • $F_I O_2$: Fraction of inspired oxygen ($0.21$ for room air).
  • $PaCO_2$: Partial pressure of arterial carbon dioxide (obtained via arterial blood gas; normal is $40\,mmHg$).
  • $1.25$: A factor related to the respiratory exchange ratio (alternatively, one can divide $PaCO_2$ by $0.8$).

• Normal room air sea level calculation: $P_A O_2 = (760 - 47) \times 0.21 - (40 \times 1.25)$$P_A O_2 = (713 \times 0.21) - 50$$P_A O_2 = 149.73 - 50 = 99.73\,mmHg$

The Respiratory Exchange Ratio (RER)

• The Respiratory Exchange Ratio (RER), or Respiratory Quotient, describes the relationship between oxygen uptake and carbon dioxide excretion.

• Alveolar $CO_2$ Excretion: Normally $250\,mL/min$.

• Blood Oxygen Uptake: Normally $200\,mL/min$.

• RER Ratio Calculation: $R = \frac{250\,mL/min\,CO_2}{200\,mL/min\,O_2} = 1.25$

• Conversely, when looking at oxygen uptake relative to carbon dioxide production, the ratio is $0.8$. These numbers provide the constants used in the alveolar air equation.

Anatomy of the Alveolar-Capillary Membrane (ACM)

• The total path length an oxygen molecule must travel to bind with hemoglobin is approximately $0.2$ to $2.5\,microns$.

• The oxygen molecule must traverse nine distinct layers:

  1. Surfactant-containing fluid layer (lining the alveolus).
  2. Alveolar epithelium.
  3. Alveolar basement membrane.
  4. Interstitial space (functional potential space containing fluid).
  5. Capillary basement membrane.
  6. Capillary endothelium (vessel wall).
  7. Plasma (liquid portion of the blood).
  8. Red blood cell (erythrocyte) membrane.
  9. Intracellular erythrocyte fluid.

Transit Time and Diffusion Dynamics

• Normal Transit Time: The total time it takes for a red blood cell to travel through the pulmonary capillary bed is approximately $0.75\,seconds$.

• Normal Diffusion Time: Under resting, healthy conditions, gas equilibrium (reoxygenation) is reached in only $0.25\,seconds$.

• Safety Cushion: In a healthy individual, only about "one-third" of the available transit time is utilized for gas exchange. This provides a buffer for when blood flow increases (exercise) or if the membrane becomes diseased.

• Effects of Exercise: During exercise, cardiac output increases, and blood flow speeds up. This decreases the transit time to perhaps $0.25\,seconds$. In healthy lungs, equilibrium is still achieved because oxygenation is so rapid.

• Effects of Disease: If the membrane is thickened, it may take the full $0.75\,seconds$ to reach equilibrium. If this person then exercises and the transit time drops to $0.25\,seconds$, they will exit the capillary before being fully reoxygenated (hypoxia).

Fick's Law of Diffusion

• Fick's Law summarizes the factors determining the rate of gas transfer across a sheet of tissue: $\text{Rate of Diffusion } \propto \frac{A \times D \times (P_1 - P_2)}{T}$

• Relationships:

  • Directly Proportional: Diffusion increases if Surface Area ($A$) or the Partial Pressure Gradient ($P_1 - P_2$) increases.
  • Inversely Proportional: Diffusion decreases if the Thickness ($T$) of the membrane increases.
  • Diffusion Constant ($D$): Stays the same for specific gases like $O_2$ and $CO_2$.

Henry's and Graham's Laws

• Henry's Law: The amount of gas dissolving in a liquid is proportional to the partial pressure of the gas. Carbon dioxide ($CO_2$) is $24\,times$ more soluble than oxygen ($O_2$).

• Graham's Law: The rate of diffusion of a gas through a liquid is inversely proportional to the square root of the gram molecular weight (GMW).

• Combined Effect: When solubility and GMW are combined, $CO_2$ diffuses through the alveolar-capillary membrane $20\,times$ faster than $O_2$. Because $CO_2$ diffuses so rapidly, the ACM is almost never a limiting factor for $CO_2$ excretion; hypoxia (oxygen issues) always appears first in membrane disease.

Clinical Terms and Conditions

• Hyperbaric Oxygen Therapy: Delivering oxygen at pressures greater than $1\,ATM$ (using chambers). This widens the pressure gradient ($P_1 - P_2$) to drive more oxygen into the blood. It stimulates angiogenesis (new blood vessel growth) to repair chronic wounds or diabetic foot injuries.

• Oxygen Toxicity: Occurs when breathing high concentrations ($F_I O_2 > 50\%$) for long periods. Can lead to chest pain, CNS tremors, convulsions, and absorption atelectasis (where washing out nitrogen causes alveoli to collapse).

• Pulmonary Edema: Characterized by frothy white or pink secretions. Treated with diuretics and CPAP (continuous positive airway pressure) to drive fluid back and improve oxygenation.

Perfusion-Limited vs. Diffusion-Limited Flow

• Perfusion-Limited: Gas transfer depends solely on the amount of blood flowing past the alveoli. Oxygen is normally perfusion-limited in healthy lungs. Nitrous oxide ($N_2O$) is used to test this.

• Diffusion-Limited: Gas transfer depends on the integrity/thickness of the ACM. Carbon Monoxide ($CO$) is a diffusion-limited gas because blood has a high affinity for it ($210\,times$ more than oxygen). Oxygen becomes diffusion-limited only in disease states like pulmonary fibrosis or emphysema.

Questions & Discussion

• Q: What does normal arterial $PO_2$ and $PCO_2$ look like?

• A: Arterial $PaO_2$ is normally $80$ to $100\,mmHg$ (though $95-100$ is the target). Arterial $PaCO_2$ is $35$ to $45\,mmHg$.

• Q: What does venous blood look like?

• A: Venous blood ($PvO_2$) is typically $40\,mmHg$ and $PvCO_2$ is $46\,mmHg$.

• Q: What is a shunt?

• A: A pulmonary shunt is blood flow without ventilation. Blood moves from the right side of the heart to the left side without picking up oxygen, often due to collapsed alveoli (atelectasis).