Basic Ventilation Model

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Lung The ventilatory function of the lung can be explained already in a very simplified (1) model. Oxygen (O2) has to be transported from the outside air to the blood, and carbon dioxide (CO2) the other way, thereby passing airways and alveoli. The latter are the locations where gases are exchanged with the blood, and are taken together as Alveolar Space (VA), the remaining part is (physiological) Dead Space (VD). The conditions are, fixed values of O2 and CO2 (2) partial pressure in the outside air, PO2,in and PCO2,in respectively, and fixed values of oxygen uptake (˙VO2) and carbon CO2 production (˙VCO2) of the body.
Breathing is, by intaking and exhaling a Tidal Volume (VT) at a frequency fR mostly measured in per minute. Then, the process is simple and can be explained without mathematics. For oxygen, this is show in the figure below. The inhaled air does not reach the alveolar space instantly but first has to pass through the dead space. Then, oxygen pressure P is increased until inspiration ends, after which it decreases due to uptake by the blood. The amounts must be equal, but below that will be explained for CO2 since it is easier. Lung

Modelling gas transport is based on the gas law PV=nRT but since RT is a constant in the body, it is done based on P×V being the "amount of gas". As to a gas mixture, there are two equivalent possibilities:
 – PTotVX – Total gas pressure times relative volume of the gas X
 – PXVTot – Partial pressure of gas X times total volume
Then, for CO2 – of course the formulas are also for volume per time:

PTot˙VCO2 = PE,CO2 fR (VT − VD)
where the End-Expiratory CO2 Pressure PE,CO2 is what was in the lung. This formula is used to determine VD. But there is a considerable pitfall in calculations with gases, due to the fact that circumstances can be very different. In physics, dry gases at 0°C are considered, which is indicated by STPD (Standard Temperature and Pressure, Dry), in lung function body conditions BTPS (Body Temperature and Pressure, Saturated with water vapour), 37°C. Standard Pressure is 101.3 kPa but in the body 6.3 kPa is 'taken away' by the water vapour so that only 95 kPa remains for the gases. Simple math then learns, that the difference is considerable, about 20%.
(1) In particular in patients, the lung can be much more complicated.
(2) At sea level, there is about 20% O2 but only 0.04% CO2 so that in physiology PCO2≅0.

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