This example is characteristic of many examples of mathematical modeling in the life sciences. All mathematical models are simplifications of reality. The modeler must therefore decide which features of the biological system to include and which to ignore. The concentration of CO2 in the lungs is affected by many things, including the rate at which CO2 is produced by the body, the rate of respiration, and the depth of each breath.
The model in this example makes the simplifying assumption that the rate of production of CO2 is constant. It also assumes that the total volume of air exchanged by the lungs per minute is constant (this is referred to by physicians as the “ respiratory minute volume”).
Under these assumptions, this example of the textbook shows that the steady state concentration of CO2 in the lungs is a reciprocal function of the respiratory minute volume. Despite the simplifying assumptions that led to this result, this function has been extremely useful in clinical medicine. It is sometimes considered to be one of the four most important equations in clinical practice. The other three are
- the Henderson-Hassellbalch equation for blood pH
- the alveolar gas equation
- the oxygen content equation.
Finally, it is worth noting that this equation for the steady state concentration of CO2 is usually expressed in different units in clinical settings. For simplicity we have expressed it in terms of the concentration of CO2 in mg/mL but it is usually expressed as the partial pressure of CO2 in clinical settings (measured in mmHg). One can convert between the two different units using the ideal gas law (which relates the number moles of a substance to pressure) and the molar mass of CO2 (which gives the mass of CO2 per mole).