Modified Fick's Principle For The Non Invasive Estimation of Cardiac OutPut: Explained

Fick's Principle and Cardiac Output

Fick's principle is a fundamental concept in cardiovascular physiology for calculating cardiac output, which is the volume of blood (not the amount of blood) the heart pumps per unit of time. The principle is a statement of the conservation of mass, stating that the total uptake or release of a substance by an organ is the product of the blood flow to the organ and the difference in the concentration of the substance between the arterial and venous blood.

The classic equation for calculating cardiac output (CO) using Fick's principle is:

$CO = \frac{V O _{2}}{C _{a} O _{2} - C _{v} O _{2}}$

Where:

$V O_{2}$ is the oxygen consumption rate of the body.
$C_{a} O_{2}$ is the oxygen content of the arterial blood.
$C_{v} O_{2}$ is the oxygen content of the mixed venous blood.

Modified Fick's Principle for Non-Invasive Cardiac Output

The traditional Fick method is invasive, requiring the collection of blood samples from both an artery and the pulmonary artery to measure oxygen content. The modified Fick's principle aims to estimate cardiac output non-invasively. While there are various non-invasive methods, some Fick-derived techniques calculate oxygen consumption ( $V O_{2}$ ) based on respiratory quotient and the measurement of carbon dioxide ( $C O_{2}$ ) exchange. Other modern non-invasive methods, such as thermodilution and Doppler ultrasound, have largely replaced the Fick method in clinical practice.

The modified Fick principle, or more accurately, indirect Fick methods, substitute direct measurements with estimations to make the process non-invasive. While the direct method is the most accurate, its invasiveness and technical demands have led to the development of these alternative techniques for a safer and more practical clinical application.

Amount vs. Volume

In a medical context, amount and volume are related but distinct concepts. Volume is the three-dimensional space occupied by a substance, typically measured in units like liters (L) or milliliters (mL). It is a measure of the space an object or substance takes up. Amount refers to a quantity of a substance, which can be measured in various units depending on the substance, such as grams (g), moles (mol), or in the case of blood, as a volume. However, the term "amount" is more general. For instance, you could talk about the amount of hemoglobin in the blood, which is a mass, or the amount of blood coming out of the heart, which is a volume (cardiac output).

How Does the Law of Mass Conservation Apply to Fick's and Modified Fick's Principles?

The law of conservation of energy

The law of conservation of energy states that energy cannot be created or destroyed, only transferred or transformed from one form to another. In any isolated system, the total amount of energy remains constant

The Law of Conservation of Mass is the fundamental principle underpinning both the classic and modified Fick's principles. Simply put, it states that what goes in must come out, or be accounted for. In the context of cardiac output, this law is applied to the exchange of respiratory gases, oxygen ( $O_{2}$ ) and carbon dioxide ( $C O_{2}$ ).

For Oxygen ( $O_{2}$ ): The total amount of $O_{2}$ a person consumes from the air they breathe in ( $\dot{V} O_{2}$ ) must be equal to the amount of $O_{2}$ the blood has picked up from the lungs and delivered to the body. The amount of $O_{2}$ delivered by the blood is a product of the blood flow (cardiac output) and the difference in $O_{2}$ concentration between the blood leaving the lungs (arterial blood) and the blood returning to the lungs (venous blood).
.For Carbon Dioxide ( $C O_{2}$ ): The same logic applies, but in reverse. The amount of $C O_{2}$ the body produces through metabolism ( $\dot{V} C O_{2}$ ) must equal the amount of $C O_{2}$ the blood carries away from the tissues and releases into the lungs. This amount is the product of cardiac output and the difference in concentration between the venous blood and the arterial blood.

How is metabolic CO₂ taken to the alveoli?

Carbon dioxide is a waste product of cellular metabolism. After being produced in the body's tissues, it diffuses into the bloodstream. The majority of this $C O_{2}$ travels to the lungs in one of three ways:

Dissolved in plasma (a small amount).
Bound to hemoglobin (forming carbaminohemoglobin).
Converted into bicarbonate ions (HCO₃⁻) in red blood cells.

When the blood reaches the tiny capillaries surrounding the alveoli in the lungs, these processes reverse. $C O_{2}$ unbinds from hemoglobin and is released from bicarbonate, diffusing from the blood into the alveoli to be exhaled.

The Breath-Holding Maneuver: Achieving Equilibrium

The breath-holding maneuver, typically for about 20 seconds, is a clever way to non-invasively estimate the concentration of $C O_{2}$ in mixed venous blood. When you hold your breath, you create a closed system in your lungs. During this time:

The $C O_{2}$ in the blood returning to the lungs no longer has an outlet to be exhaled.
This causes the partial pressure of $C O_{2}$ in the alveoli ( $P_{A} C O_{2}$ ) to rise and equilibrate with the partial pressure of $C O_{2}$ in the blood coming from the pulmonary artery ( $P_{\overset{v}{ˉ}} C O_{2}$ ).
At this equilibrium point, the $C O_{2}$ concentration in the alveolar gas is a very close approximation of the mixed venous $C O_{2}$ concentration.

Why is Oxygen Not a Factor During Equilibrium?

While $C O_{2}$ is building up, you are not taking in any new oxygen. However, the oxygen that was already in your lungs and blood continues to be consumed by the body. The goal of this maneuver is not to measure oxygen uptake but to create a stable concentration of $C O_{2}$ to measure the arteriovenous difference. The initial oxygen in the lungs and blood is sufficient to sustain the body for the 20-second period, but it is not a part of the calculation for cardiac output using the $C O_{2}$ rebreathing method.

What is the arteriovenous difference?

The arteriovenous difference is essential to both Fick's principles.

It indicates the amount of a substance (such as $O_{2}$ or $C O_{2}$ ) that has been exchanged between the blood and the body's tissues.

For $O_{2}$ , it's the difference between the high concentration in arterial blood and the low concentration in venous blood.
For $C O_{2}$ , it's the difference between the high concentration in venous blood and the lower concentration in arterial blood.

This difference reveals how much of the substance is being consumed or produced per unit of blood flow.

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