Though there is not a specific syllabus item for the Fick principle in the CICM curricula, as an essential part of cardiac output monitoring it has to be included in any answer to Section G7(iv) of the 2017 CICM Primary Syllabus, which expects the exam candidate to "describe the methods of measurement of cardiac output". Some discussion of this concept is therefore expected in any written question answer or crosstable viva which incorporates cardiac output measurement by thermodilution (eg. PA catheter) or indicator dilution (LiDCO) methods. 

In summary:

  • the Fick Principle, using oxygen as an example:
    • The total uptake of oxygen is equal to the product of the cardiac output and the arterial-venous oxygen content difference.
    • Thus, cardiac output (CO) = VO2 / (Ca - Cv)
    • The principle can be extended to incorporate the uptake or release of any substance, eg. CO2 or marker substances, and can be applied to the whole body or to individual organs and tissues.
  • Direct Fick method of measuring cardiac output
    • Inspired-expired oxygen difference is measured, which gives the VO2
    • CaO2 is calculated from arterial blood gases, where haemoglobin concentration and saturation are measured
    • CvOis calculated from mixed venous blood gases, which must be collected from a pulmonary artery
    • This is the gold standard for measuring cardiac output
  • Indirect Fick methods:
    • These methods are called "indirect" because one or more of the variables from the Fick equation are estimated rather than measured directly.
    • Examples include:
      • Estimation of VO2 on the basis of nomograms
      • Estimation of CaCO2 on the basis of end-tidal CO2
      • Estimation of CvCO2 on the basis of EtCOduring rebreathing  
      • Estimation of CaO2 on the basis of pulse oximetry
  • Limitations of the Fick method of cardiac output measurement:
    • Any estimated indirect values introduce an error into the calculation
      • Nomogram-based estimates are most inaccurate in morbidly obese or metabolically abnormal patients, eg. hypothermia, paralysis, thyrotoxicosis, burns or sepsis.
      • Even without these, the direct Fick method has an error range of around ±8%
    • Pulmonary O2 consumption (eg. in severe pneumonia) can increase the VO2 and therefore produce an overestimate of the cardiac output
    • A steady state is assumed over the period of measurement.
    • VO2 may not be in equilibrium with tissue oxygen consumption
    • Narrow arteriovenous oxygen content difference (eg. in high output states) amplifies any measurement error
    • Intracardiac shunt produces changes in CvO2 and CaO2  which are not due to changes in cardiac output

In terms of published peer-reviewed sources, for something as common and fundamental as this, there is a surprising deficit of quality material, made even more frustrating by some puzzling bibliographic choices on the part of publishers. For instance, wherever you find the words "Fick's Principle" uttered in the literature, it appears to be an incantation to summon the original 1870 version of Adolf Eugen Fick's paper. This is in fact just two pages, in German, and basically represents minuted talking points and quotes from a meeting of the Physical-Medical Society in Würzburg.  To offer this reference is therefore a mistreatment of the reader, as it prioritises giving credit to a dead man over the learning needs of the living. A much better reference would be Gazbarich Boland & Wang (2019), a chapter from a modern textbook of interventional cardiology which dissects this concept using plain language and presents a solid list of references for those who want to dig deeper. 

Fick's principle

The principle can be summarised as follows:

" the total uptake of (or release of) a substance by the peripheral tissues is equal to the product of the blood flow to the peripheral tissues and the arterial-venous concentration difference (gradient) of the substance."

This definition appears in multiple sources and appears to be an agreed-upon restatement, rather than a faithful translation. In his talk, Fick did not put things in such a polished final form; he just described his experiment to his peers and colleagues, where he measured the cardiac output of a dog's heart, and expressed surprise that nobody came to these conclusions sooner:

"It is astonishing that no one has arrived at the following obvious method by which [the amount of blood ejected by the ventricle of the heart with each systole] may be determined directly, at least in animals. One measures how much oxygen an animal absorbs from the air in a given time, and how much carbon dioxide it gives off. During the experiment one obtains a sample of arterial and venous blood; in both the oxygen and carbon dioxide content are measured. The difference in oxygen content tells how much oxygen each cubic centimeter of blood takes up in its passage through the lungs. As one knows the total quantity of oxygen absorbed in a given time one can calculate how many cubic centimeters of blood passed through the lungs in this time. Or if one divides by the number of heart beats during this time one can calculate how many cubic centimeters of blood are ejected with each beat of heart. The corresponding calculation with the quantities of carbon dioxide gives a determination of the same value, which controls the first."

- Translation by Leroy & Fox, 1998

To rewrite this into a form easily understood by an early school-age child, 

  • Blood flows through organs and tissues
  • These organs and tissues consume oxygen
  • The venous blood returning from these organs and tissues therefore has less oxygen
  • Therefore, there is a difference between arterial and venous oxygen content, in terms of mls of oxygen per litre of blood.
  • This difference in content is key: if you know how much oxygen was consumed in total, and how much the content per litre has changed, you can work out how much blood had to flow through the organs to produce the observed oxygen content difference.
  • This an example of applying the principle of mass conservation

In other words:

VO2 = (CO × Ca) - (CO × Cv)

where:

VO2 is the total oxygen consumption, as a volume per unit time (eg. L/min)

CO is the cardiac output, also as volume per unit time (L/min)

Ca and C are the arterial and venous oxygen content (eg. ml/L)

To rearrange things:

CO = VO2 / (Ca - Cv)

The "direct" Fick method of measuring cardiac output

In order to measure the cardiac output with the abovementioned equation, you need to know the arterial oxygen content,  venous oxygen content, and the total oxygen consumed by the organism. The former can be determined from arterial and mixed venous blood gases, and the latter can be determined by comparing the oxygen content of inhaled and exhaled alveolar gas. To represent this concept with some childish artwork:

a picture which tries to explain the Fick principle

All of the abovementioned variables can be measured directly:

VO2 is measured by comparing an inhaled oxygen volume with an exhaled oxygen volume (traditionally, using all sorts of collection bags or hoods); it is usually around 3.5 ml of O2 per kg per minute, or around 250ml/min for a normal-sized person. 

The oxygen content of blood can be measured by collecting an arterial blood gas together with a mixed venous sample, and it is calculated by using the following (very familiar) equation:

Total blood oxygen content = (sO2 × ceHb × BO) + (PaO2 × 0.03)

Where:

  • ceHb = the effective haemoglobin concentration
  • PaO2 = the partial pressure of oxygen in arterial gas
  • 0.03 = the content, in ml/L/mmHg, of dissolved oxygen in blood
  • BO the maximum amount of Hb-bound O2 per unit volume of blood (normally 1.39)
  • sO2 = oxygen saturation

Thus, plugging in common values (eg. Hb 140g/L) you get a CaO2 of around 200ml/L and a CvO2 of around 150ml/L, i.e an arteriovenous oxygen content difference of 50ml/L. How many litres of blood, then, would it take to produce the observed VOof 250ml? It is really quite simple:

CO =  250ml / (200ml – 150ml)

= 250 / 50

= 5 L/min

In case a visual learner happens upon this page, they will probably benefit from a diagram which incorporates these values:

Fick principle version 2

And there you have it. That is the "direct" Ficks method for measuring cardiac output, so called because the VO2 is measured directly by collecting exhaled oxygen (eg. into a Douglas bag).  Oxygen is not the only possible gas, of course, and variations of this method have been developed which use CO2

CO = VCO2 / (CaCO2 - CvCO2)

 It is such a simple concept that one might ask, why don't we use this all the time? Indeed: it is considered the gold standard in the measurement of cardiac output. Or, at least, wherever authors discuss cardiac output, they tend to throw out a line about how the direct Fick method is a gold standard. They are also usually quick to follow this with a statement about how impractical it is, eg. "however, it is rarely performed given the need for special equipment and technical skills". The method is theoretically sound, and works well in the lab, but it is difficult to apply in any real-world situation, as there are many practical problems to overcome.

Caveats to the direct Fick method of cardiac output measurement

First, some practical concerns, which might seem like trivial complaints. For example, the need to collect and measure the quantity of expired oxygen. This requires time; most sources recommend at least one minute of measurement if not longer. Fiddling around with bags is certainly cumbersome, and there is a risk of bag gas equilibrating with atmospheric air through multiple connections and disconnections which would inevitably take place, potentially producing an over-estimate of cardiac output. Alternatively, the subject can be instructed to breathe through a mouthpiece which is attached to an oxygen detector and flowmeter, estimating the oxygen volume from the product of concentration and flow. This requires some training and is obviously unsuitable for the uncooperative delirious patient, or one which is hypoxic and struggling for breath, or somebody who has been midazolated to the point where they can't follow basic instructions.

At face value, these are obviously not insurmountable disadvantages. In fact they sound like the complaints of a lazy technician, i.e one might say that if you really wanted to measure cardiac output with this method, you would perfect the technique and do it properly with minimal inaccuracy. To make a counterargument, one might point out that any method of measurement, no matter how accurate, would be consigned to the animal laboratory if it were too impractical to use routinely in human clinical practice. The direct Fick method definitely suffers from this problem.

Apart from limitations related to the pragmatic application of the Fick Principle, there are serious physiological sources of inaccuracy, which are discussed in greater detail by Visscher & Johnson (1953) and  Venkateswaran (2014)

  • Inaccuracies in measuring VO2:
    • Pulmonary O2 consumption may be nontrivial: If the lung itself is consuming a large amount of oxygen (eg. in ARDS or pneumonia), the exhaled oxygen content will be lower, but not lower due to systemic oxygen consumption, i.e. the cardiac output will be overestimated. Light (1988), in an experimental model of pneumonia, was able to demonstrate a 13-15% difference due to the oxygen consumption by the infected lung.
    • Steady state is assumed: The oxygen uptake by the tissues is thought to be in equilibrium with the oxygen uptake by the lungs, but it does not have to be. An extreme example of this would be cardiac arrest, where the oxygen uptake in the tissues is high, but the oxygen extraction by the lung is low (or nil). Practically, one can eliminate this concern by measuring VO2 during some sort of "steady state" where oxygen consumption is stable for a sustained period.
    • Poor flow and poor ventilation: from the above, it follows that if ventilation is poor or blood flow is poor, the measurement of VO2 by exhaled gas will not be reflective of the tissue oxygen consumption.
  • Inaccuracies in measuring CaO2 and CvO2
    • If the arteriovenous oxygen content difference is narrow, the method becomes more unreliable, as small measurement errors are amplified by the equation. 
    • The presence of an intracardiac shunt completely destroys any vestige of accuracy in CvO2 measurement; for instance, it can be diluted by left atrial blood (raising the CvO2); or alternatively, the CaO2 can be artificially depressed by the admixture of venous blood in a right-to-left shunt. Either way, the end result is the same: the CaO2-CvO2 difference would not be due to the rate of systemic oxygen extraction. 

Accuracy and reproducibility of the direct Fick method

So, from a practical standpoint, how accurate and reproducible is this "gold standard" method? One might think this should be a relatively difficult question to answer, considering the Fick method being the gold standard, realistically there ought to be no higher standard to measure it against. Fortunately, Seely et al (1950) found a cardiac output measurement technique which was even more gold standard-er than the Fick method. They opened the chests of several dogs and diverted the main pulmonary artery into an optical rotameter (thus avoiding the common error of aortic flow measurement, where the flowmeter fails to account for coronary blood flow).

Seelys method of measuring cardiac output by a main pulmonary artery rotameter

The image here is from an earlier paper by Seely & Gregg (1950), in which they detailed their experiment design. All cardiac output from the right heart would therefore have to pass through the flow measurement device in order to reach the rest of the circulation. The honest physiologist would have to admit that this setup is in fact the "gold standard" against which all other measurement techniques should be calibrated. In case one is still interested, the direct Fick method agreed with the rotameter within about ±8%, which was described by the authors as "high accuracy, excellent agreement" even though it would equate to a cardiac output range from 4.6-5.4L/min, or a cardiac index range of 2.5-3.0. Similarly, Thomasson (1957), using a more realistic setup (intact humans, specifically "volunteers, members of the hospital staff or the Stockholm city police force") looked mainly at the reproducibility of measurements carried out during steady-state conditions and also found an error margin of around 0.46 L/min, or about 7.2% of the cardiac output.

Indirect Fick method of measuring cardiac output

So far, we have been referring only to the "direct" Fick method, implying that there must also be an "indirect" method. That is in fact correct, as it would be insane if there wasn't. The indirect method is a modification of the original which cuts a few corners. Unfortunately, a precise definition of which exact corners which end up being cut seems to be difficult to pin down, but the basic theme of these "indirect" techniques is the desire to avoid having to collect some sample or another, usually the mixed venous blood. On the basis of this, one could concoct an informal definition, as follows:

"A direct Fick method relies on measurements of gas content taken from arterial blood, mixed venous blood, and the expired gas volume.

The indirect Fick method relies on an estimate of one or more of these variables."

Every author who has ever published on this topic seems to promote their own variant of the indirect Fick method, apparently depending on what instrument was not available in their immediate laboratory environment. For example, the first use of this term can actually be traced back all the way to Loewy & Schrötter (1905) or Plesch (1909), who really had no mechanism of sampling mixed venous blood,  as pulmonary artery catheters weren't going to be invented for another fifty years. These authors came up with different methods of estimating the CvO2 or CvCO2 on the basis of the fact that alveolar gas, if given enough time, will end up equilibrating its gas content with the mixed venous blood.

In other words, if the venous blood and alveolar gas are allowed to mingle freely for long enough, the partial pressure of the alveolar gas in the system equilibrates with the venous blood, making it possible to estimate the arteriovenous oxygen content difference without having to obtain a mixed venous sample. Loewy & Schrötter came up with an idea which involved blocking a distal bronchus with a special flexible silver tube (the alveoli distal to the tube therefore providing the gas sample); Plesch (1909) described a less invasive method where the same thing can be achieved by instructing the patient to rebreathe their exhaled gas mixture out of a small bag until the blood returning into the lung is in equilibrium with the lung-bag system.  Fortunately, even in the darkest timeline the CICM trainees can be reasonably confident that this sort of historical trivia will not be expected from them. However if they are still interested when the exams are behind them, they can actually track down the original articles by Loewy & Schrötter and Plesch, in their original German, or review p.99-104 from Circulation of the Blood : Men and Ideas by Fishman & Richards (1982).

The modern modification of these rebreathing equilibrium techniques is best described by Haryadi et al (2000). In short: 

  • First, the patient is made to breathe spontaneously through an end-tidal CO2 monitor.
  • The end-tidal COmeasurement therefore corresponds to the arterial PaCO2, and can be used to calculate the CaCO2.
  • Moreover the end-tidal CO2 monitor can estimate the total VCO2 over a minute of breathing by measuring both the expired volume and CO2 concentration.
  • Then, the bag is attached, and the patient is instructed to rebreathe their gas mixture.
  • During the period of rebreathing, the end-tidal CO2 measured from the bag will rise gradually, asymptotically approaching the CO2 concentration in the mixed venous blood. To borrow the first depiction of this from Defares et al (1961):

    EtCO2 use for the indirect Fick method, from Defares et al (1961)
     
  • At the same time, as the CO2 content of the expired gas mixture approaches the CO2 content of venous gas, the CO2 exchange at the alveolus approaches zero, i.e. the VCO2 trends towards zero with a long enough period of rebreathing. 
  • Without asphyxiating the patient completely, the curve of this trend can be extrapolated from a short series of measurements, and the CvCO2 can be calculated.

Hoping that a diagram might clarify this process (it didn't), one could represent these steps as follows:

indirect Fick method

This is what's called a "total" rebreathing method, and from the description one can immediately tell that it is going to be useable only in a small proportion of carefully briefed fully cooperative patients who have nothing whatsoever wrong with their brains, hearts or lungs. In short, a group whose cardiac output measurement no intensivist could possibly ever care about.

A "partial" indirect Fick method is also described, which is somewhat more suited to sedated ventilated patients. Instead of rebreathing gas, the patient's ventilation is changed to transiently increase their minute volume, and two sets of variables are collected:

 VCO2,1 / (CaCO2,1 - CvCO2,1) = VCO2,2 / (CaCO2,2 - CvCO2,2)

where variables subscripted 1 and 2 are from separate sets of measurement. 

Rearranging to solve for CO,

CO =  (VCO2,1 -VCO2,2 ) / (CaCO2,1 - CaCO2,2) - (CvCO2,1 - CvCO2,2)

Assuming that there is no change in mixed venous CO2 content during this change in minute volume, CvCO2,1 = CvCO2,2  and therefore:

  CO =  (VCO2,1 -VCO2,2 ) / (CaCO2,1 - CaCO2,2)

All sorts of sub-variations on this theme also exist, ranging from crude methods where you change the respiratory rate up and down, to more sophisticated methods where extra dead space is added to the circuit (such as the proprietary system described by Haryadi et al in 2000). The fact that you have never heard of the NICO cardiac output monitoring device from Novametrix Medical Systems Inc. is telling, as is the deadness of their corporate profile link. All we can deduce from the URL is that they got bought out by Respironics at some stage. In short, this method is not exactly mainstream.

To summarise, depending on which variables you decide you don't feel like measuring, the indirect Fick method has multiple permutations, of which the most common are:

  • Estimating the mixed venous gas content:
    • by rebreathing of CO2 (total rebreathing method)
    • by comparing changes in CaCO2 and VCO2 with changes in ventilation (the partial rebreathing method)
  • Estimating the arterial gas content:
    • by measuring the end-tidal CO2 instead
    • by measuring the oxygen saturation using a pulse oximeter
  • Estimating the VO2
    • by using nomograms based on age, weight and sex
    • by using common equations, of which there are several largely unsatisfactory choices (Bergstra et al, 2004)

References

Gazibarich, Gary J., John Edward Boland, and Louis W. Wang. "Analysis and interpretation of Fick and thermodilution cardiac output determinations." Interventional Cardiology and Cardiac Catheterisation: The Essential Guide (2019): 221.

Fick A. Uber die messung des Blutquantums in den Hertzvent rikeln.Sitzber Physik Med Ges Wurzburg July 9th: 36, 1870

That is not a link to a pdf file or article, but rather to a site which is selling the original printed article, bound together with the rest of that years issues of Verhandlungen der Physikalisch-Medicinischen Gesellschaft in Würzburg.

Vandam, Leroy D., and John A. Fox. "Adolf Fick (1829–1901), Physiologist A Heritage for Anesthesiology and Critical Care Medicine." Anesthesiology: The Journal of the American Society of Anesthesiologists 88.2 (1998): 514-518.

Kendrick, A. H., et al. "Direct Fick cardiac output: are assumed values of oxygen consumption acceptable?." European Heart Journal 9.3 (1988): 337-342.

Visscher, M. B., and J. A. Johnson. "The Fick principle: analysis of potential errors in its conventional application." Journal of Applied Physiology 5.10 (1953): 635-638.

Venkateshwaran, S. "Principle of Fick–utilities and limitations." Kerala Heart Journal 4.2 (2014).

Light, R. BRUCE. "Intrapulmonary oxygen consumption in experimental pneumococcal pneumonia." Journal of Applied Physiology 64.6 (1988): 2490-2495.

Thomasson, B. "Cardiac Output in Normal Subjects Under Standard Basal Conditions the Repeatability of Measurements by the Fick Method." Scandinavian journal of clinical and laboratory investigation 9.4 (1957): 365-376.

Seely, Robert D., WILLIAM E. NERLICH, and Donald E. Gregg. "A comparison of cardiac output determined by the Fick procedure and a direct method using the rotameter." Circulation 1.6 (1950): 1261-1266.

Seely, Robert D., and Donald E. Gregg. "Technic for Measuring Cardiac Output Directly by Cannulation of the Pulmonary Artery." Proceedings of the Society for Experimental Biology and Medicine 73.2 (1950): 269-270.

Plesch, Johann. "Hämodynamische Studien." Zeitschrift für experimentelle Pathologie und Therapie 6.2 (1909): 380-618.

Loewy, Adolf, and H. V. Schrötter. "Untersuchungen über die Blutcirculation beim Menschen." Zeitschrift für experimentelle Pathologie und Therapie 1.2 (1905): 197-311.

Haryadi, Dinesh G., et al. "Partial CO2 rebreathing indirect Fick technique for non-invasive measurement of cardiac output." Journal of clinical monitoring and computing 16.5-6 (2000): 361-374.

Defares, J. G., M. E. Wise, and J. W. Duyff. "New indirect Fick procedure for the determination of cardiac output." Nature 192.4804 (1961): 760-761.

Bergstra, A., et al. "Validation of Fick cardiac output calculated with assumed oxygen consumption: a study of cardiac output during epoprostenol." Netherlands Heart Journal 12.5 (2004): 208.