Tuesday, September 30, 2008

Mass exhalation

How much bodily mass do we give out through breathing? The chemical reaction for aerobic respiration is

C6H12O6 + 6O2 → 6CO2 + 6H2O

The amount of carbon dioxide we exhale is then

6 mol CO2 / mol glucose = 1.47 g CO2 / g glucose.

Processing of fatty acids yields a different amount of exhaled CO2. For instance, the oxidation of a saturated fatty acid is expressed as

CnH2nO2 + (3n/2 − 1) O2n CO2 + n H2O

yielding

44n/(14n + 32) g CO2 / g CnH2nO2.

This last expression also serves approximately for unsaturated fatty acids, since these are missing only a few lightweight hydrogen atoms with respect to the saturated acid with the same amount of carbon. Assuming most consumed fat is in the form of palmitate, we have a carbon dioxide yield of

2.75 g CO2 / g fat;

Carbohydrates produce 4 kcal per gram, whereas fatty acid processing yields 9 kcal per gram of fat. While at rest, the human body takes 30% of the energy from carbohydrates and 70% from fat; so, this results in a combined production of carbon dioxide of

0.324 g CO2 / kcal.

For a daily energy consumption rate around 2,500 kcal, 810 grams of carbon dioxide are then expelled through breathing. There is a experimental study by the USDA on the subject that unfortunately I haven't been able to find, but some sources cite it as reporting a value beween 445 and 450 liters of CO2 (881-891 g) per day, which is in good agreement with our calculations.

The value calculated is not the answer to our original question about exhaled bodily mass: much of the oxygen in the CO2 produced comes from the air rather than catabolized substances, specially in the case of fat. We will assume that all the oxygen coming from the burned substance goes to CO2: under these conditions, the amount of bodily mass expelled through breathing is

0.933 g / g glucose,
0.875 g / g fat,

or, using the assumed ratios of carbohydrate and fat consumption,

0.138 g / kcal,

which yields 345 g for a typical daily energy consumption of 2,500 calories.

4 comments :

1. However, there are several other compounds that could add to this, despite the striking prevalence of CO2 over them. One way to look towards this would be to include articles like the following include the following:

Moser B. et al, 2005: Mass spectrometric profile of exhaled breath--field study by PTR-MS., Respir Physiol Neurobiol. 2005 Feb 15;145(2-3):295-300.

Needless to say that oxygen and other compounds find their way out in various forms through our nostrils, including CO, NO, H20 vapors and also volatile substances with relatively complicated structure (ketone breath of the diabetic, post-exercise ketosis are some ideas).

Overall, I really liked your post very much! :)

2. However, there are several other compounds that could add to this, despite the striking prevalence of CO2 over them. One way to look towards this would be to include articles like the following include the following:
[...]

Of course the calculation is just an approximation, albeit hopefully a reasonable accurate one.

Alas the source you provide is not free, so I can't have a look at it.

A thing that struck me as odd during the writing of this entry if that I couldn't find any justified answer to the question of how much CO2 do people exhale, besides the quoted but unavailable USDA study and some coarse calculations based on CO2 breath concentration and wild guesses on respiratory frequency --which misses the fact that how much CO2 we exhale depends on what our energy consumption is.

Thank you for your comments,

3. I usually don't trust USDA studies in their generalizations because they end up claiming that a statement like "C++ templates are bad" is true.

It is however more than true that the amount of CO2 and other gases vary not only according to metabolic needs, but also due to physiological processes taking part at the pulmonary alveoli level, where the actual respiration takes place, submitted to higher control from the bulbar respiratory centers etc. This results in a peculiar mixture of CO2 with the other gases that remains constant within a given state of the individual during the alveolar exchange.

Not to mention that CO2 is also "influenced" and "influences" the blood pH and the other blood gases into a twisted game of dependence, which can end up with lowering the breath rate, one of the effects of the so called CO2 narcosis, like it happens in certain pathological states.

In anycase, with the whole organism trying to compensate, there should be a pretty valid mean upon which to base a calculation, provided such a mean is averaged properly taking under consideration the several states we find each others into during the day. The CO2 i/o should follow the classical Gaussian distribution within out physiological everyday states.

Breath analysis (and not just for measuring exhaled body mass) is an extremely valid tool and quite a good programming challenge given the problem and the hardware you are dealing with. Since you show a genuine interest for these things, I lurked through the material freely available as well in order to post back a useful resource.

Here is an interesting link which treats the problem of the different gases exhaled:

Cao & Duan, 2006: Breath Analysis: Potential for Clinical Diagnosis and Exposure Assessment - Clinical Chemistry 52: 800-811, 2006

Another free resource about the control of the respiratory rate can be given by the NIH bookshelf through this link:

http://www.ncbi.nlm.nih.gov/bookshelf/picrender.fcgi?book=cm&&partid=365&blobtype=pdf

I think that your calculation of the exhaled CO2 should be as accurate as logic allows given the input data given. It also shows the logic of C++ programmers over the pythonistas.

Thanks for your reply as well.

4. Oops, pressed the submit before linking to the Cao article here: Breath Analysis

:)