Fick's Principle of cardiac output measurement

To rearrange things:

CO = VO₂ / (C_a - C_v)

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:

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 × BO₂ ) + (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
• BO₂ =  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 VO₂ of 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:

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 / (C_aCO₂ - C_vCO₂)

 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).

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 CO₂ measurement 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):
  
  
   
• 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:

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:

 VCO_2,1 / (C_aCO_2,1 - C_vCO_2,1) = VCO_2,2 / (C_aCO_2,2 - C_vCO_2,2)

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

Rearranging to solve for CO,

CO =  (VCO_2,1 -VCO_2,2 ) / (C_aCO_2,1 - C_aCO_2,2) - (C_vCO_2,1 - C_vCO_2,2)

Assuming that there is no change in mixed venous CO2 content during this change in minute volume, C_vCO_2,1 = C_vCO_2,2  and therefore:

  CO =  (VCO_2,1 -VCO_2,2 ) / (C_aCO_2,1 - C_aCO_2,2)

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)