The acid load excreted by the lungs can be expressed as
where VC02 is the C02 excreted, VA is the alveolar ventilation, PaC02 is the partial pressure of C02 in arterial blood, and K is a factor converting pressure to volume fraction.
Equation (3) shows that, to maintain a normal PaC02 (and pH) when the volatile acid load VC02 is increased, the alveolar ventilation must rise by the same
proportion. If the alveolar ventilation cannot increase, the same acid load is eliminated at the cost of higher PaC02. In the steady state (i.e. unmodified PaC02), the V CO2 excreted by the lung equals the metabolic CO2 produced.
However, CO2 excretion is a function not only of alveolar ventilation, but also of cardiac output. According to Fick's law
where Q is the cardiac output, and CvCO2 and CaCO2 are respectively the CO2 contents of mixed venous and arterial blood. Assuming, for simplicity, that the relationship between CO2 content and partial pressure is linear in the range of physiological interest, and combining and rearranging eqn.(3) and e,qn„...(.4.), it follows that
This equation shows that PaCO2 (which affects the acid-base status of the blood) for a given acid load and PvCO2 increase when cardiac output increases and decrease when alveolar ventilation increases. E.q.ua.t.i.o,Q,(.5.) emphasizes the importance of the transport Q of the acid load from the tissues to the lungs. In fact, for a given acid load, which primarily affects PvCO2, if Q decreases and VA remains constant, PaCO2 (and the arterial acid-base status) may be normal or even decrease, but PvCO2 will increase substantially, resulting in large PaCO2 - PvCO2 and pH gradients. In some circumstances, often encountered in critically ill patients (e.g. low flow states), arterial sampling may not give an accurate assessment of the acid-base status, and sampling of mixed venuous blood is mandatory ( Weil §L§.L 198.6).
In summary, the respiratory component of the acid-base status, i.e. PaCO2, is a function of the acid load, the alveolar ventilation, and the cardiac output.
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