L4: Steady State and Equilibrium

  • Fundamental Basis: The Fick principle is fundamentally grounded in the physical principle of the conservation of mass. This means that in a closed system, mass cannot be created or destroyed; it can only change forms. This concept is essential in understanding how substances move through different systems, such as in the human body.

  • Core Concept: Broadly stated, the amount of a substance added to a flowing stream will result in an increase in the concentration of that substance in the outflow stream compared to the inflow stream. Simply put, if you put more of something into a moving flow (like water or air), the amount of that substance will be higher in what comes out than what goes in.

  • Mass Balance: The mass of the substance added to the system is quantitatively equal to the difference in concentration between the outflow and inflow streams, relative to the flow rate. This is a key point because it helps us understand how changes in one part of a system can affect the rest. If more substance is added, the concentration increases accordingly, which can be observed and measured.

  • Steady State vs. Non-steady State:

    • Steady State: This is the primary focus of respiratory physiology review. In a steady state, the concentrations of the substance remain unchanging in both the inflow and outflow streams over time. It’s like a stable balance where everything remains consistent unless something changes in the system.

    • Non-steady State: This condition occurs when the concentration of the substance in the outflow stream changes with respect to time (e.g., during thermal dilution). This involves more complex mathematics and is not the initial focus of this discussion. In a non-steady state, the amounts of substances can change frequently, which makes it more complicated to track and calculate.

Mathematical Expressions of the Fick Principle in the Steady State

  • Theoretical Model: Imagine a tube with fluid or gas flowing through it.

    • [x]i: Concentration of substance xx on the inflow side. This concentration represents how much of the substance is present in the fluid entering the system.

    • [x]o: Concentration of substance xx on the outflow side. This concentration shows how much of that substance is present when it exits the system.

  • Relating Mass and Flow: The relationship between flow, mass added, and concentration differences assumes that no additional flow enters or exits the system between the measured inflow and outflow points. This means that the calculations we perform are based on the same amount of flow that was originally measured, which keeps things simple.

  • Calculation of Flow Rate (QQ): The volume flow rate can be calculated if the mass of the substance added per unit time and the concentration difference are known:

Q=mass of x added per unit time[x]0˘01fo−[x]0˘01fiQ = \frac{\text{mass of } x \text{ added per unit time}}{[x]\u001fo - [x]\u001fi}
This formula shows that to find the flow rate (how quickly something is moving), we need to know how much of a substance is added and how much of it there is when it goes in and out.

  • Arteriovenous Difference: In physiological contexts, this is often expressed as the difference between arterial and venous concentrations (A−VA - V difference). This difference helps us understand how much oxygen or nutrients are being transported in the blood from the heart to the rest of the body and how much is being returned after the tissues have used it.

Application to Cardiac Output and Systemic Oxygen Consumption

  • Calculating Cardiac Output: The most common clinical and physiological application of the steady-state Fick principle is the calculation of cardiac output based on oxygen consumption (\text{\dot{V}O}_2). Cardiac output is a critical measure of how well the heart is pumping blood and getting oxygen to the body.

  • Measuring Oxygen Consumption (\text{\dot{V}O}_2): This represents the amount of oxygen removed by systemic tissues. It is measured by comparing the amount of oxygen entering the lungs versus the amount leaving the lungs per unit time. Essentially, we look at how much oxygen our body is using versus how much is being taken in.

  • Standard Values for a Normal Human (60 kg60\,kg):

    • Oxygen Consumption (\text{\dot{V}O}_2): Approximately 250 mL/min250\,mL/min of oxygen. This is a typical value for a healthy adult at rest, indicating how much oxygen the body uses in one minute.

    • STPD: Oxygen volumes are expressed as Standard Temperature Pressure Dry (STPDSTPD). This ensures that when we measure gases, we do so under standardized conditions so that our values are comparable.

    • Arterial Oxygen Content (CaO2CaO_2): Approximately 200 mL O2/L blood200\,mL\,O_2/L\,blood. This value assumes the individual is at sea level, has a normal hemoglobin concentration, and is breathing normal atmospheric air (approximately 21% O221\%\,O_2). Hemoglobin is a protein in our blood that carries oxygen, so this gives us an idea of how much oxygen is available to our tissues when the blood is pumped out from the heart.

    • Mixed Venous Oxygen Content (CvO2CvO_2): Approximately 150 mL O2/L blood150\,mL\,O_2/L\,blood for blood returning from the systemic circulation. This tells us how much oxygen is left in the blood after it has delivered oxygen to the tissues.

  • Sample Calculation:

Cardiac Output=250 mL O2/min200 mL O2/L−150 mL O2/L=25050=5 L/min\text{Cardiac Output} = \frac{250\,mL\,O_2/min}{200\,mL\,O_2/L - 150\,mL\,O_2/L} = \frac{250}{50} = 5\,L/min
This calculation shows how we can determine the heart's output based on the oxygen consumption and the difference in oxygen content before and after blood circulates through the body.

Calculating Oxygen Delivery to Specific Tissues

  • Oxygen Delivery: It is critical in respiratory physiology to determine if enough oxygen is reaching vital organs (e.g., coronary circulation, kidneys, liver, brain) to support metabolism. This is important because if any of these organs do not receive enough oxygen, they cannot function properly.

  • Expressing Tissue Flow: Flow is historically and conventionally expressed per 100 g100\,g of tissue. This standardization allows for easier comparison across different tissues and helps in clinical assessments.

  • Example Calculation for Oxygen Delivery:

    • Tissue Blood Flow: 0.18 L blood/100 g tissue/min0.18\,L\,blood/100\,g\,tissue/min (equivalent to 180 mL blood/100 g tissue/min180\,mL\,blood/100\,g\,tissue/min). This shows how much blood flows to each 100 grams of tissue in a minute.

    • Arterial Oxygen Content: 200 mL O2/L blood200\,mL\,O_2/L\,blood. This indicates how much oxygen is carried by the blood.

    • Formula: Oxygen Delivery=Blood Flow×Arterial Oxygen Content\text{Oxygen Delivery} = \text{Blood Flow} \times \text{Arterial Oxygen Content}. This equation helps us calculate the total amount of oxygen reaching the tissues based on blood flow and oxygen content.

    • Result:

Oxygen Delivery=0.18 L blood/100 g/min×200 mL O2/L blood=36 mL O2/100 g tissue/min\text{Oxygen Delivery} = 0.18\,L\,blood/100\,g/min \times 200\,mL\,O_2/L\,blood = 36\,mL\,O_2/100\,g\,tissue/min
This calculation tells us how much oxygen is actually delivered to each 100 grams of a given tissue per minute, which is crucial for understanding how well that tissue is oxygenated.

Broad Physiological Applications and Bottom Line

  • Versatility of the Principle: The Fick principle can be used to calculate various physiological parameters, including:

    • Hormone secretion rates from specific glands. Hormones are chemicals that help regulate many functions in our bodies, so understanding their release is critical.

    • Consumption rates of metabolites like glucose. Glucose is a primary energy source for our cells, and knowing how much is used helps assess metabolic activity.

    • Production rates of carbon dioxide (CO2CO_2). As our cells use oxygen, they produce CO_2, which needs to be properly managed by our respiratory system.

  • Required Variables: To calculate consumption or secretion in the steady state, one requires the inflow concentration, the outflow concentration, and the flow rate. Gathering these measurements is crucial for accurately using the Fick principle in practice.

  • The Bottom Line: The mass of a measured substance entering the blood at a specific point must equal the mass of the substance leaving the blood at that point in the steady state. This is a fundamental concept of the Fick principle and helps ensure that our measurements and calculations are consistent and reliable.

  • Steady State Oxygen Balance:

([O2]arterial×Blood Flow)=([O2]venous×Blood Flow)+Oxygen Consumption by tissue([O_2]_{arterial} \times \text{Blood Flow}) = ([O_2]_{venous} \times \text{Blood Flow}) + \text{Oxygen Consumption by tissue}
This equation illustrates how the oxygen delivered to tissues can be calculated based on the amount of oxygen in arterial blood compared to that in venous blood. The difference tells us how much oxygen the tissues are utilizing.

Historical Perspective and Reading

  • Reference: For a deeper historical context and modern utility of the Fick principle, refer to the work of Gabriel Laszlo. Understanding its historical development helps us appreciate the advancement in physiological sciences.

  • Article Details: "The Fick Principle" by Gabriel Laszlo, based in Bristol, published in the Journal of Applied Physiology (circa 2004/2005). This article provides a historical perspective on the principle's development and its continuing relevance in contemporary medicine and physiology. Reading about its application reinforces the significance of the Fick principle in understanding human health and function.