Estimation of energy expenditure by the reverse Fick method

This is a technique of invasively measuring the consumption of oxygen and the production of CO₂ in a living human organism. It requires the use of a PA catheter. The technique relies on the reversal of the normal Fick method of estimating cardiac output.

The college has asked about the reverse Fick method in several past paper SAQs, including the following:

• Question 7 from the first paper of 2015
• Question 7.4 from the first paper of 2014
• Question 25.4 from the second paper of 2010
• Question 28 from the second paper of 2007

Usually, the questions either ask about the generic methods of calculating or measuring energy expenditure (in which case only a superficial knowledge is required) or to explain why the indirect calorimetry measurement is different from the reverse Fick method (spoiler: the latter fails to measure oxygen consumption in the lung).

Reversal of the Fick Method for measuring cardiac output

The Fick equation for measuring cardiac output normally collects data avout the VO₂ and the DO₂ to arrive at a cardiac output.

Fick teaches us that VO₂ (oxygen extraction) is determined by the following equation:

We can rearrange that to form an equation which calculates cardiac output on the basis of oxygen extraction:

\(CO = {VO_2 \over Ca - Cv}\)

So, in a normal person, with a body surface area of 2m2 and thus with a VO2 of 250ml per minute,

\(CO = {250ml\over 200ml - 150ml} = 250/50 = 5L/min\)

Thus, knowing this equation, we can collect the cardiac outut data, and use the difference in venous and arterial oxygen content to calculate the oxygen extraction by the organism, and thus calculate its rate of metabolism - because oxygen utilisation in metabolic processes is correlated to the metabolic rate.

Of course, this takes arterial blood from the systemic circulation and compares it to the mixed blood in the pulmonary artery, which neglects the oxygen consumption of the lung.

This means that when it is compared to indirect calorimetry, the reverse Fick method typically underestimates the total body energy expenditure, though not by a lot (on average it seems to be about 88kcal/day). Obviously, when the energy expenditure of the lung is massively increased (eg. in ARDS) this method will be much more inaccurate.