VO2 Max in Sports, Physiology, and Health

IV. A. 1. a. Gases have physical properties that are often independent of the identity of the gas; the conceptual understanding of the relationships between these properties is important.

IV. A. 1. c. The quantitative relationships between properties of gases are summarized for most systems using the ideal gas law.

VO_{2 max} is defined as the maximum rate (L/min) of oxygen (O₂) that a person is able to use during exercise. Increasing VO_{2 max} leads to an increase in oxygen consumption and thus an increase in adenosine triphosphate (ATP) production. CO₂ release is directly dependent on the abundance of ATP. VO_{2 max} acts as a good indicator of athletic performance, especially in endurance sports such as distance running, swimming, and cross country skiing. Many of these athletes strive to achieve a higher VO_{2 max} in order to increase their lung capacity and improve their athletic performance, so accurate calculation of VO_{2 max} is necessary. 

 Using concentrations of oxygen (O₂) and carbon dioxide (CO₂) expelled from the lungs, the rate of oxygen uptake can be determined. This maximal uptake value is widely accepted as the best index of cardiorespiratory endurance capacity. Pressure of these exhales is measured in millimeters of mercury (mmHg), the amount of pressure exerted by a column of mercury exactly 1 mm high (1). The combined gas law is defined as:

\[(P_1V_2)/(T_2n_2) = (P_2V_2) / (T_2n_2)\nonumber\]

This equation is used to determine the true amount of oxygen released during an exhale, oxygen expulsion. Similarly, it is also used to determine the number of moles in a known volume of gas (5). Given that PVTn can be considered a constant if the gas is considered ‘ideal’ (gas has negligible volume, particles are equally sized, there are no intermolecular forces acting on the particles, the particles move randomly in agreement with Newton’s Laws of Motion). The ideal gas law, thus can be written as:

\[PV=nRT\nonumber\]

Where P is air pressure (in ATM), V is volume (in L), n is the number of moles, R is the PVTn constant, equal to 8.314 (L/K x mol), and T is temperature (measured in Kelvin)  (2).

All aerobic organisms require oxygen to carry out their metabolic functions. As organisms increase in size, the ratio of surface area to volume decreases, forcing diffusion distances to increase and alternative ways of seizing oxygen to be established (4). Supplying necessary oxygen to the body, thus, is directly dependent on the rate at which oxygen can be absorbed from the surrounding air into the lungs.

In order to measure VO_{2 max},  a stress “max” test must be performed.  This measures the minute ventilation (the amount of air the subject inspires or expires per minute) of the subject and the oxygen and carbon dioxide concentrations of the expired air. In order for a test to be considered “max,” it must contain:

1. A peak or plateau in oxygen uptake (VO₂) while the workload continues to increase

2. A peak or plateau in oxygen uptake (VO₂) while the workload continues to increase

3. An Respiratory Exchange Ratio (RER) (amount of CO₂ produced / amount of O₂ consumed) of >1.10 

4. A rate of perceived exertion (RPE) of >18

The VO_{2 max} calculated here (VO_{2 max}) is a measure of the peak VO₂ in a “max” test (VO_{2 peak}) while attempting to confirm the highest physiologically attainable value of VO₂ simultaneously. VO_{2 peak} is defined as the highest value attained during the “max” test whereas VO_{2 max} is the highest physiologically attainable value of uptake.  This difference is determined by the presence of a VO₂ plateau, a peak in oxygen uptake. Although different, these terms are often used interchangeably in literature. In order to ensure that VO_{2 max} = VO_{2 peak}, the  “max” test criteria outlined above must be met.

A 110 lb female athlete runs on a treadmill then breathes into a balloon, and the gas from the balloon is drawn into oxygen and carbon dioxide meters to determine the concentrations. The volume of the gas is recorded with a Rayfield gas meter. These values are at BTPS (body temperature, pressure, saturated). The recorded values after one minute at max stress are 1.92L O₂, 1.45L CO₂. 15.2%O₂, 4.445% CO₂. Gas temp is 24ºC. Barometric pressure is 735mmHg. P_H2O = 41.0mmHg. 

To convert the gas volume from nonstandard conditions (BTPS) to standard conditions (STPD), a conversion factor must be calculated. This takes into account the conversion from Celsius to Kelvin, the water vapor pressure in exhaled air, and saturated gas to standard density (3). 

STPD conversion factor: [273.15 x (P_B) - P_H2O ]/[(273 + T_gas)735]

= [273.15 x (735mmHg)- P_H2O ]/[(273 +24)760]

= [204862 K mmHg - P_H2O ] / 445360

.8398 is the conversion factor. 

To find the total volume of gas (in ATPS, as measured from the meter), the volume of exhaled oxygen is divided by the fraction of oxygen in the air. 

1.92LO₂/.152= 12.63L (ATPS).

To convert from the measured volume to standard volume, the conversion factor is multiplied by the measured volume. The ideal gas law governs this reaction, as seen below. Pressure times volume equals moles times R (constant) times temperature (in Kelvin). The conversion factor is forcing the non-ideal gas into ideal parameters, which makes it equivalent to (P₂T₁/T₂P₁) (3). 

PV=nRT, and the moles of each gas and R values are the same in non-standard and standard.

 P₁V₁/T₁= P₂V₂/T₂, so V₁=V₂(P₂T₁/T₂P₁)

VE (STPD) = VE (ATPS) (STPD factor)

VE (STPD) = 12.63 L (.8398)=10.61L

Therefore, the equivalent to 10.61L of gas was exhaled in ideal conditions. 

Next, the calculation of oxygen uptake must be performed, a crucial component of calculating VO_{2 max}.  Calculation of the oxygen uptake in L/min is done by taking the volume of exhaled air, multiplying it by the fraction of N₂ in the air and .265, then subtracting the fraction of exhaled O₂ to account for the amount that was not used. The fraction of N₂ exhaled is simple because breath is made up of mainly nitrogen, oxygen, and carbon dioxide. Any small amount of argon or other gas is unknown (3). 

FEN₂ = 1- [FEO₂ + FECO₂]= .804

Then, the rate of oxygen uptake is calculated using the FEN₂ value: 

VO₂(L/min) = VE (STPD) X [(FEN₂ X .265) - FEO₂

VO₂(L/min) = 10.61L (.804*.265)- .152= 2.11 L/min.

Finally, the athlete’s weight must be taken into consideration, and the final units must be calculated. VO_{2 max} is written in terms of mL/min/kg. 

2.11L/min *1000mL/1L= 2110mL/min

She is 110 pounds, and that must be converted to kilograms:

110lbs*0.4536kg/lb = 49.90kg. 

Finally, O₂ uptake per kg is calculated:

2110L/min/49.90kg = 42.3L/min/kg

Her VO_{2 max} is 42.3L/min/kg. 

References

1. Alviar-Agnew, M., & Agnew, H. (2022a). The Combined Gas Law- Pressure, Volume, Temperature. In: LibreTexts. https://chem.libretexts.org/Bookshel...nd_Temperature 

2. Alviar-Agnew, M., & Agnew, H. (2022b). The Ideal Gas Law- Pressure, Volume, Temperature, and Moles. In: LibreTexts. https://chem.libretexts.org/Bookshel...ture_and_Moles

3. Buckenmeyer, P. (2004). VO2 at Rest and in Progressive Exercise. Retrieved 10/28/2022 from https://web.cortland.edu/buckenmeyer...04/labvo2.html 

4. LibreTexts. (2019). Respiration and Gas Exchange. In: LibreTexts. https://chem.libretexts.org/Sandboxe...d_Gas_Exchange

5. Zumdahl, S. S., & DeCoste, D. J. (2017). In Chemical Principles (8th ed., online). Cengage Learning. (2013), 132-145.