Full Answer Section

1.1 The Henderson-Hasselbach Equation: A Chemical Equilibrium Perspective

The Henderson-Hasselbach equation (HHE) describes the relationship between pH, pKa (acid dissociation constant), and the ratio of the conjugate base ([A-]) to the undissociated acid ([HA]) in a weak acid-base system (Henderson, 1908). In the context of blood acid-base balance, carbonic acid (H2CO3) acts as the weak acid, and bicarbonate ([HCO3-]) is its conjugate base. The equation can be expressed as:

pH = pKa + log ([HCO3-] / [H2CO3])

However, due to the low solubility of CO2 in blood, the equation is often written in terms of PaCO2, the partial pressure of CO2:

pH = pKa + log ([HCO3-] / (α x PaCO2))

where α is the solubility coefficient of CO2 in blood.

The HHE highlights the importance of the bicarbonate buffer system in regulating blood pH. Changes in the ratio of [HCO3-] to PaCO2 directly affect blood pH. For example, an increase in [HCO3-] (respiratory compensation for metabolic acidosis) or a decrease in PaCO2 (hyperventilation) will raise blood pH (alkalosis). Conversely, a decrease in [HCO3-] (metabolic acidosis) or an increase in PaCO2 (respiratory acidosis) will lower blood pH (acidosis).

1.2 The Davenport Diagram: A Graphical Representation of Buffering

The Davenport diagram is a graphical representation of the HHE, depicting the relationship between blood pH and [HCO3-] at various PaCO2 levels (Fig. 1) (Davenport, 1974). The diagram typically includes a series of sloping lines representing different PaCO2 values. The vertical axis represents blood pH, while the horizontal axis represents [HCO3-].

The buffer line, a non-horizontal portion of the curve, reflects the buffering capacity of the blood. Steeper slopes represent weaker buffering capacity, while gentler slopes indicate stronger buffering. In the normal physiological range, the blood acts as a strong buffer, minimizing significant pH changes despite fluctuations in PaCO2 or [HCO3-].

Citations

• Davenport, H. W. (1974). The ABC of Acid-Base Chemistry (6th ed.). Chicago: University of Chicago Press.
• Henderson, L. J. (1908). Concerning the relationship between the strength of an acid and its capacity to hydrolyse salts. Journal of the American Chemical Society, 30(7), 1762-1773.

1.3 Conclusion

The Henderson-Hasselbach equation and the Davenport diagram provide valuable tools for understanding and interpreting blood pH, PaCO2, and [HCO3-] levels. The HHE offers a quantitative framework, while the Davenport diagram presents a visual representation of buffering capacity. Together, they facilitate diagnosis and treatment of acid-base disorders in clinical settings.

2. Davenport Diagram in Excel

An Excel spreadsheet can be used to create a simple model of the relationship between blood bicarbonate concentration ([HCO3-]), blood pH, and CO2 tension (PaCO2) based on the Henderson-Hasselbach equation.

Here’s how you can create the model:

1. Set up Data:
   • Create columns for:
     • pH
     • [HCO3-] (mM)
     • PaCO2 (mmHg)
     • pKa (of carbonic acid, assumed to be 6.1)
     • α (Solubility coefficient of CO2 in blood, assumed to be 0.03)
2. Calculate pH using HHE:
   • In a separate column, enter the formula: =6.1 + LOG10(B2/(α*C2)) (Replace B2 and C2 with cell references for [HCO3-] and PaCO2, respectively).

Plotting the Data:

1. Select the data range for [HCO3-] and pH.
2. Insert a scatter chart.
3. Add separate trendlines for different PaCO2 values by right-clicking on a data point and selecting “Add Trendline.”