L5: Nonsteady State: Rebreathing Methods

The Fick principle serves as the primary mathematical framework for calculating the flow of a fluid through a system by observing the behavior of a known substance within that fluid. It is especially useful in fields such as medicine and biology to understand how substances move in and out of different areas in the body.

• General Mechanism: As a fluid flows through a tube or vessel, a known substance is added to it at a specific rate. For example, think about a water pipe through which we are pouring some food coloring. The addition of food coloring results in an increase in the concentration of that coloring in the fluid leaving the tube compared to the fluid entering it. This leads us to understand how much fluid is flowing through the tube based on the difference we observe in the concentration of the substance.

• Variable Requirements: To calculate flow using this principle, three primary variables are required:

  • The amount of mass added to the system per unit of time ($\text{mass/time}$). This means how much of the substance we add, like grams of a dye per minute.

  • The concentration of the substance at the point of entry (upstream concentration). This is the level of the substance before it enters the tube or vessel.

  • The concentration of the substance at the point of exit (downstream concentration). This concentration is what we measure after the substance has passed through the tube. For instance, we can think of measuring how much food coloring is in the water at the exit compared to at the entry.

• Flow Calculation Logic: Knowing the concentration difference between the ends of the tube (the arteriovenous difference, which is a fancy term for measuring how much of the substance has been absorbed or removed) and the mass added per unit time allows for the simple calculation of flow ($Q$). This equation helps us figure out how quickly the fluid is moving based on our observations.

Non-Invasive Carbon Dioxide Application

• A non-invasive version of the Fick method utilizes Carbon Dioxide ($CO\text{2}$) to calculate flow through the lungs (specifically, the amount of blood that the heart pumps out, also called cardiac output). In simpler terms, we can find out how well the heart is working based on how much $CO\text{2}$ is being released by our body.

• Endogenous Production: Unlike methods that require injecting a tracer (which is a measurement tool), this method uses $CO\text{2}$ produced naturally by the body's metabolism. This means that instead of adding something artificial to the body to measure flow, we are using what our body already produces.

• Measurement of Production Rate: The production rate of $CO\text{2}$ ($\text{ }\bullet\text{V}\text{CO}_2$) can be accurately measured by collecting the alveolar gas (gas exchanged in the lungs) expired over a specific period of time. So, by breathing into a device, we can measure how much $CO\text{2}$ is being exhaled.

• Atmospheric Context: It is noted that there is negligible $CO\text{2}$ present in the normal atmosphere. This is important because it simplifies the assessment of the volume of $CO\text{2}$ added to the blood as it passes through the lungs, making our calculations easier to conduct without external interference.

• Physiological Trick: The method relies on "gas equilibration" to determine the arteriovenous difference for $CO\text{2}$ without requiring invasive arterial or venous blood sampling. This means that we can measure the difference without needing to take blood samples, which is less comfortable for patients.

Arterial and Venous PCO2 Estimation via Equilibration

• Estimation of Arterial CO2 ($P\text{ }a\text{ }CO_2$):

  • Under normal conditions where a subject is breathing room air, the alveolar gas (the air located in the lungs that participates in gas exchange) is assumed to be in equilibrium with the blood leaving the pulmonary capillaries (the tiny blood vessels in the lungs).

  • Consequently, the alveolar blood $CO_2$ after equilibration is assumed to be equal to the end-expiratory partial pressure of carbon dioxide ($P_{e t}CO_2$). This means that as we breathe out, the $CO_2$ level is basically balanced in our blood.

  • This value is further assumed to be equal to the systemic arterial blood partial pressure of carbon dioxide ($P\text{ }a\text{ }CO_2$). In simpler terms, we assume the $CO_2$ level in the blood after we've breathed out is the same as that in our arteries, which makes it easier to estimate.

• Estimation of Mixed Venous CO2 ($P_{\bar{v}}CO_2$):

  • To find the venous side of the equation, a specific rebreathing technique is used. This means when we want to measure $CO_2$ in the veins, we can have the person breathe from a bag.

  • The subject breathes into a bag or vessel containing a known concentration of $CO_2$. This concentration is typically set at a level that is non-zero but not excessively high—generally close to the expected mixed venous $P_{CO_2}$. So, we use a concentration that we can accurately measure without it being too overwhelming.

  • As the subject rebreathes this gas, the partial pressure of $CO_2$ in the gases exiting the lungs is measured. This helps us to see how much $CO_2$ is in the blood from the veins.

  • Over time, the measured $P_{CO_2}$ will "asymptote" (gradually approach) the partial pressure of mixed venous carbon dioxide ($P_{\bar{v}}CO_2$). This means that as they continue to breathe, the $CO_2$ levels stabilize and help us get an accurate reading.

Practical Application and Assigned Reading

• The principles discussed are applied in the clinical evaluation of hemodynamics (the study of blood flow), specifically for calculating cardiac output in high-acuity (very critical) settings. This is essential information for doctors and nurses in hospitals to monitor how well a patient’s heart is functioning.

• Reference Paper: The assigned reading to support this lecture is titled "Evaluation of $CO_2$ and rebreathing cardiac output method in seriously ill patients." This paper discusses the method we just learned about in more detail.

• Contextual Note: Although the paper was published "a long time ago," the speaker emphasizes that the underlying physiology remains constant and relevant for modern clinical practice. This means that even though the study is older, the basic principles are still useful and accurate today.

Theoretical Review for Students

Students are expected to master several key physiological relationships mentioned in the transcript to fully comprehend the rebreathing method:

• Equilibration Dynamics: Understanding why, after equilibration while breathing room air, the end-expiratory alveolar partial pressure of carbon dioxide ($P_{A}CO_2$) is considered equal to the arterial partial pressure ($P_{a}CO_2$). This relationship is crucial for understanding how gases exchange in the lungs.

• Rebreathing Asymptote: Understanding the biophysical reasons why the alveolar partial pressure of carbon dioxide ($P_{A}CO_2$) approaches the levels found in mixed venous blood ($P_{\bar{v}}CO_2$) when a subject rebreathes expired gas. This concept helps students grasp the idea of gas exchange and how we can measure it effectively.

• Calculation of Flow: Integrating these two estimated values ($P_{a}CO_2$ and $P_{\bar{v}}CO_2$) into the Fick equation to determine the volume of blood flowing through the lungs per minute. This conclusion is what allows us to use the Fick method to monitor and evaluate heart function and lung performance.