Davenport Diagram - Derivation

Derivation

When a sample of blood is exposed to air, either in the alveoli of the lung or in an in vitro laboratory experiment, carbon dioxide in the air rapidly enters into equilibrium with carbon dioxide derivatives and other species in the aqueous solution. Figure 1 illustrates the most important equilibrium reactions of carbon dioxide in blood relating to acid-base physiology:

Note that in this equation, the HB/B- buffer system represents all non-bicarbonate buffers present in the blood, such as hemoglobin in its various protonated and deprotonated states. Because many different non-bicarbonate buffers are present in human blood, the final equilibrium state reached at any given P_CO2 is highly complex and cannot be readily predicted using theory alone. By depicting experimental results, the Davenport Diagram provides a simple approach to describing the behavior of this complex system.

Figure 2 shows a Davenport Diagram as commonly depicted in textbooks and the literature. To understand how the diagram is to be interpreted, it is helpful to understand how the diagram is derived in the first place. Consider the following experiment. A small sample of blood is taken from a healthy patient and placed in a chamber in which the partial pressure of carbon dioxide (P_CO2) is held at 40 mmHg. Once equilibrium is reached, the pH and bicarbonate concentration are measured and plotted on a chart as in Fig. 3.

Next, the P_CO2 in the chamber is held constant while the pH of the blood sample is changed, first by adding a strong acid, then by adding a strong base. As pH is varied, a titration curve for the sample is produced (Fig. 4). Notice that this titration curve is valid only at a P_CO2 of 40 mmHg, because the chamber was held at this partial pressure throughout the experiment.

Next, imagine that the experimenter obtains a new, identical blood sample from the same patient. However, instead of placing the sample in a chamber with a P_CO2 of 40 mmHg, the chamber is reset to a P_CO2 of 60 mmHg. After equilibration, a new point is reached, indicating a new pH and a new bicarbonate concentration (Fig 5). Note that the bicarbonate concentration at the new, higher P_CO2 is larger than in the first measurement, whereas the pH is now smaller. Neither result should come as a surprise. Increasing the P_CO2 means that the total amount of carbon dioxide in the system has increased. Because the gaseous carbon dioxide is in equilibrium with the carbon dioxide derivatives in the solution, the concentrations of carbon dioxide derivatives, including bicarbonate, should also increase. The fall in pH is also not surprising, since the formation of a bicarbonate molecule is concomitant with the release of a proton (see Fig. 1).

If this same experiment is repeated at various partial pressures of carbon dioxide, a series of points will be obtained. One can draw a line through these points, called the buffer line (Fig. 6).

The buffer line can be used to predict the result of varying the P_CO2 within a range close to the experimentally determined points. Additionally, for each experimental point, a titration experiment can be performed in which pH is varied while P_CO2 is held constant, and titration curves can be generated for each of the partial pressure of carbon dioxide (Fig. 7). In the Davenport Diagram, these titration curves are called isopleths, because they are generated at a fixed partial pressure of carbon dioxide.

A key concept in understanding the Davenport Diagram is to note that as P_CO2 is increased, the magnitude of the resulting change in pH is dependent on the buffering power of the non-bicarbonate buffers present in the solution. If strong non-bicarbonate buffers are present, then they will quickly absorb the vast majority of protons released by the formation of bicarbonate, and pH will change very little for a given rise in bicarbonate concentration. The result will be a buffer line with a very steep slope (Fig. 8). On the other hand, if only weak non-bicarbonate buffers are present (or if no non-bicarbonate buffer is present at all), then a much larger change in pH will be observed for a given change in bicarbonate concentration, and the buffer line will have a slope closer to zero.

It is instructive to note that the slope of the bicarbonate line will never actually reach zero (i.e. will never be horizontal) under equilibrium conditions, even in the complete absence of non-bicarbonate buffers. This is because the production of protons resulting from an increase in P_CO2 is concomitant with the production of bicarbonate ions, as mentioned previously. Thus, a decrease in pH resulting from increased P_CO2 must always occur with some minimal increase in bicarbonate concentration. Likewise, an increase in pH for similar reasons must occur with some minimal decrease in bicarbonate concentration.