Re: Exact mathematics in energy consumption

Hi Shishir,

I’m not an expert on the devices and methods used to measure oxygen metabolism, but I looked around and I found some information about what seem like some good examples for you. I am providing references which you can review for more information. You can also try searching the internet for some of the terms discussed below.

Metabolic oxygen consumption (also known as volume of O2 consumed or VO2) can be measured through a process called indirect calorimetry. This process measures the difference between the oxygen inhaled and exhaled by a person. One method of indirect calorimetry involves collecting all of the exhaled gas in a large (100 Liter) container called a Douglas Bag. The number of breaths taken and the time that transpires during the collection are noted so that the oxygen consumption rate can be calculated. The O2 and CO2 compositions of the contents of the bag are then analyzed using gas flow analyzers and CO2 analyzers. This process is described in greater detail in this PDF file. The VO2 is calculated using a formula known as the Haldane transformation . Other methods of determining VO2 involve the use of a water- sealed spirometer or a Deltarrac gas-exchange system. I found one estimate of the resting VO2 value for men as 310 ml O2 consumed per minute, and 260 ml of O2 / minute for women (Smith and McNaughton, below).

We can use our knowledge of the biochemistry of oxidative phosphorylation to calculate the metabolic energy generated when O2 is consumed. This has already been discussed to a certain extent in our archives; you should review this answer, this answer and this answer, describing the relationship beween metabolism and ATP consumption. In general, 686 kcal are released when 1 mole of glucose is completely oxidized to 6 moles of H2O and 6 moles of CO2. This is the nutritional Caloric value that is associated with carbohydrates. However, we know that 30 moles of ATP are generated for each mole of glucose metabolized and that 6 moles of O2 are consumed in this process. The energy of the gamma phosphate bond in ATP is 7.2 kcal (or 30.1 kJ) per mole, so about 216 kcal (or 903 kJ) of metabolic energy are generated for every 6 moles of O2 consumed**. This is about 1/3 (0.31) of the total caloric value of the oxidation of a mole of glucose. The remaining 470 Kcal (or 1966 kJ) per mole of glucose are "lost" as heat.

So, we know that about 114 kcal (478 kJ) are released per mole of O2 consumed. 1/3 of this (35 kcal or 148 kJ) is captured in the form of ATP, and the remainder is "lost" as heat. The next thing we need to know is, how we can relate moles of O2 to the VO2? For this, we can turn to the ideal gas law, represented as PV = nRT, where P = pressure (in atmospheres), V = volume (in liters), n = number of molecules (in moles), R = the ideal gas constant or 0.08206 liter atmospheres / moles kelvin, and T = temperature (in kelvin). The ideal gas law tells is that at 1 atmosphere pressure and 273.15 degrees kelvin (aka Standard Temperature and Pressure, or STP), the molar volume of any gas will be 22.4 liters per mole. So, one liter of O2 at STP will contain 0.0446 moles of O2, which corresponds to 5 kcal (or 21 kJ) if all of that oxygen is used to oxidize glucose. Remember, only 1/3 of those kcal will be captured as ATP.

Now, one of the papers I cite below (Ballal and MacDonald) suggests that the energy expenditure estimated from their study of VO2 is approximately 4.8 kcal (20.08 kJ) per liter of O2 consumed (presumably at STP). This is pretty close to the value that we calculated here. Hurray for biochemistry, the ideal gas law, and math! Using our numbers, one mole (180 grams or 6.3 ounces) of glucose will be oxidized by 134.5 liters of O2, yeilding 30 moles of ATP. The basal metabolic requirement for an adult human is approximately 2000 kcal per day. This very nicely corresponds to just about 3 moles (525 grams or 1.1 pounds) of glucose, and of this, one third is captured as ATP, while the rest is "lost" as heat.

Finally, lets take a look at the resting VO2 values from the Smith and McNaughton paper. If a female consumes 260 ml of O2 per minute resting, then it will take about 517 minutes (or 8.6 hours) to oxidize one mole of glucose. This means that 2.8 moles (24/8.6) of glucose will be consumed in a day (or 3.3 moles for a male consuming 310 ml of O2 per minute), which is pretty close to our estimate of 3 moles of glucose for a 2000 kcal per day diet.

Here are some references that you might find useful for obtaining more information.

Oxygen consumption measurement systems :

L. Donaldson, S. Dodds and T. S. Walsh (2003) Clinical evaluation of a continuous oxygen consumption monitor in mechanically ventilated patients Anaesthesia 58: 455

TF Fok, J-S Gu, CN Lim, PC Ng, HL Wong, KW So (2001) Oxygen consumption and resting energy expenditure during phototherapy in full term and preterm newborn infants Arch Dis Child Fetal Neonatal Ed 85 :F49-F52

Ronco, JJ, Phang, PT, Walley, KR, Wiggs, B, Fenwick, JC, & Russel, JA (1991) Oxygen consumption is independent of changes in oxygen delivery in severe adult respiratory distress syndrome. Am Rev Respir Dis 143 :1267-1273

MA Ballal and IA Macdonald (1982) An evaluation of the Oxylog as a portable device with which to measure oxygen consumption Clin Phys Physiol Meas. 3:57-65.

Resting VO2 values in men and women:

Smith J, McNaughton L. (1993) The effects of intensity of exercise on excess postexercise oxygen consumption and energy expenditure in moderately trained men and women. Eur J Appl Physiol Occup Physiol. 67:420-5.

You can find more information about glucose metabolism in any college-level biochemistry textbook, and more information about the ideal gas law in any college-level chemistry textbook.