The Diffusion of Pulmonary Gases

The Diffusion of Pulmonary Gases

Dalton's Law of Partial Pressures

• Definition: Dalton's Law, also known as the Law of Partial Pressures, states that the total pressure exerted by a mixture of gases is equal to the sum of the pressures exerted independently by each gas in the mixture.

• Partial Pressure: The pressure exerted by each individual gas (its partial pressure) is directly proportional to the percentage of that gas in the total gas mixture.

Application to Atmospheric Gases

• Composition of Earth's Atmosphere: Earth's atmosphere primarily consists of nitrogen (N2), oxygen (O2), carbon dioxide (CO_2), and other trace gases like argon.

• Calculating Partial Pressure: The partial pressure of each atmospheric gas can be determined by multiplying the barometric pressure (P_B) by the percentage concentration of that gas in the atmosphere.

  • Example: Given an approximate oxygen concentration of 21\% (or 0.21) and a normal barometric pressure of 760 mmHg at sea level, the atmospheric partial pressure of oxygen (P{O2}) is calculated as: \text{Atmospheric } P{O2} = 0.21 \times 760 \text{ mmHg} = 159.6 \text{ mmHg}

• Total Atmospheric Pressure: The sum of the partial pressures for nitrogen (P{N2}), oxygen (P{O2}), carbon dioxide (P{CO2}), and trace gases collectively equals the total atmospheric pressure, which is typically 760 mmHg at sea level.

• Effect of Altitude:

  • Atmospheric pressure decreases as altitude increases due to the decreasing density of atmospheric gases.

  • As the density of atmospheric gases decreases, the partial pressure exerted by each gas also decreases (e.g., P{O2} decreases).

  • Important Note: Even though barometric pressure decreases with altitude, the concentration (percentage) of all atmospheric gases remains constant. For instance, oxygen is always approximately 21\% of the atmosphere, whether at sea level or on Mount Everest.

• Effect of Depth (Underwater):

  • Atmospheric pressure increases by 1 atmosphere (760 mmHg) for every 33 feet of descent below sea level in water.

  • Example: At 99 feet below sea level, the total pressure exerted on the body is 4 atmospheres (4 \times 760 \text{ mmHg} = 3040 \text{ mmHg}).

  • Consequently, the partial pressure exerted by each gas increases proportionally. For example, the partial pressure of oxygen increases approximately four times, from 159 mmHg to 636 mmHg (given 159 \times 4 = 636 mmHg).

Gas Movement: Pressure Gradients versus Diffusion Gradients

• Pressure Gradient:

  • This refers to the bulk movement of an entire mixture of gases from an area of high total pressure (or high concentration of the mixture) to an area of low total pressure (or low concentration).

  • It is the primary mechanism responsible for moving air in and out of the lungs during ventilation.

  • In this context, all individual gases within the mixture (N2, O2, CO_2, trace gases) move in the same collective direction, either into or out of the lungs.

• Gas Diffusion (Diffusion Gradient):

  • This describes the movement of individual gas molecules from an area of their own high partial pressure (high concentration) to an area of their own low partial pressure (low concentration).

  • Crucially, each individual gas (e.g., O2, CO2) can continue to move independently from other gases based on its own partial pressure gradient.

Partial Pressures of Gases in the Air, Alveoli, and Blood

• 
  

• The following table (Table 4–1) illustrates the typical partial pressures of gases in different compartments under standard pressure and temperature:
  

  Gases	Dry Air (mmHg)	Alveolar Gas (mmHg)	Arterial Blood (mmHg)	Venous Blood (mmHg)
  P{O2}	159.0	100.0	95.0	40.0
  P{CO2}	0.2	40.0	40.0	46.0
  P{H2O} (water vapor)	0.0	47.0	47.0	47.0
  P{N2} (and other)	600.8	573.0	573.0	573.0
  Total	760.0	760.0	755.0	706.0
  Relationship Between Temperature, Absolute Humidity, and Water Vapor Pressure (Table 4–2, at sea level 760 mmHg):
  Temperature (\text{Celsius})	Absolute (Maximum) Humidity (\text{mg/L})	Water Vapor Pressure (\text{mmHg})
  :----------------------------------	:-------------------------------------------	:----------------------------------
  37°	44.0	47.0
  35°	39.6	42.2
  30°	30.4	31.8
  27°	25.8	26.7
  25°	23.0	23.8
  20°	17.3	17.5
  Ideal Alveolar Gas Equation

  • Purpose: This equation is clinically used to compute the alveolar oxygen tension (P{AO2}).

  • Equation: The ideal alveolar gas equation is given by: P{AO2} = [PB - P{H2O}] F{IO2} - P{aCO_2} (1.25)

    • Where:

      • P{AO2} = Alveolar partial pressure of oxygen (mmHg)

      • P_B = Barometric pressure (mmHg)

      • P{H2O} = Water vapor pressure (typically 47 mmHg at 37°C)

      • F{IO2} = Fractional inspired oxygen concentration (e.g., 0.21 for room air)

      • P{aCO2} = Arterial partial pressure of carbon dioxide (mmHg)

      • 1.25 = A respiratory quotient factor, often approximated as \frac{1}{0.8}

  • Clinical Example:

    • Given: Patient receiving an F{IO2} of 0.40, barometric pressure (PB) is 755 mmHg, and arterial P{CO2} (P{aCO_2}) is 55 mmHg.

    • Calculation:
      P{AO2} = [755 \text{ mmHg} - 47 \text{ mmHg}] \times 0.40 - 55 \text{ mmHg} \times 1.25
      P{AO2} = [708 \text{ mmHg}] \times 0.40 - 68.75 \text{ mmHg}
      P{AO2} = 283.2 \text{ mmHg} - 68.75 \text{ mmHg}
      P{AO2} = 214.45 \text{ mmHg}

  • Simplified Equation: When the arterial P{CO2} (P{aCO2}) is less than 60 mmHg and the patient is receiving oxygen, a simplified equation can be used:
    P{AO2} = [PB - P{H2O}] F{IO2} - P{aCO_2}

  Fick's Law of Gas Diffusion

  • Fick's Law describes the rate of gas diffusion across the alveolar-capillary membrane.

  • The law states that the rate of gas diffusion is:

    • Directly proportional to the surface area (A) available for diffusion and the partial pressure gradient (P1 - P2) of the gas.

    • Inversely proportional to the thickness (T) of the membrane.

  • Formula (General concept, specific formula not provided in slide text): The rate of diffusion (V{gas}) can be conceptually represented as: V{gas} = \frac{A \times D \times (P1 - P2)}{T}

    • Where D represents the diffusion coefficient, which incorporates factors like gas solubility and molecular weight (not explicitly detailed in provided slides).

  Clinical Applications of Fick's Law

  • Area (A) Component:

    • Verification: This component is confirmed when a decreased alveolar surface area (e.g., caused by alveolar collapse or alveolar fluid) reduces the ability of oxygen to enter the pulmonary capillary blood.

  • Pressure Gradient (P1 - P2) Component:

    • Verification: This portion of the law is confirmed when a decreased alveolar oxygen pressure (P{AO2} or P_1) reduces the diffusion of oxygen into the pulmonary capillary blood. Such a decrease can be caused by high altitudes or alveolar hypoventilation.

  • Thickness (T) Component:

    • Verification: This factor is confirmed when an increased alveolar tissue thickness (e.g., caused by alveolar fibrosis or alveolar edema) reduces the movement of oxygen across the alveolar-capillary membranes.

  Perfusion-Limited Gas Flow

  • Definition: Perfusion-limited gas flow describes a scenario where the transfer of gas across the alveolar wall is primarily dependent on, or limited by, the amount of blood flow (perfusion) passing the alveoli.

  • Relevance (as per learning objective): Nitrous oxide (N_2O) is an example of a gas typically classified as perfusion-limited. This means that gas uptake is limited by the amount of blood available to transport it away, rather than by the rate at which it can diffuse across the membrane. Once the partial pressures equilibrate across the membrane, further uptake relies on more blood arriving to pick up the gas. This is often due to the very high solubility of the gas in blood or a very efficient diffusion across the membrane.