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Understanding Acid-Base Physiology: The Henderson-Hasselbach Equation and the Davenport Diagram

Abstract

Acid-base balance is a critical physiological parameter for optimal cellular function. This paper explores the theoretical basis of the Henderson-Hasselbach equation, a fundamental equation used to describe the relationship between blood pH, bicarbonate concentration ([HCO3-]), and partial pressure of carbon dioxide (PaCO2). Furthermore, we discuss the Davenport diagram, a graphical representation of the buffering system, which helps visualize the interplay between these factors. Understanding these concepts is crucial for interpreting arterial blood gas measurements and diagnosing acid-base disturbances.

The Henderson-Hasselbach Equation: A Theoretical Basis

The Henderson-Hasselbach equation (HHE) describes the relationship between blood pH, pKa (the dissociation constant of a weak acid), [HCO3-], and the conjugate acid (H2CO3, carbonic acid) concentration [1]. In the context of blood, carbonic acid acts as a weak acid, dissociating into bicarbonate ion (HCO3-) and hydrogen ion (H+).

HHE can be expressed as:

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

However, due to the low concentration of dissolved CO2 in plasma compared to bicarbonate, [H2CO3] can be approximated by the PaCO2 divided by a constant (α), which represents the solubility of CO2 in plasma.

Full Answer Section

Therefore, the commonly used form of the HHE is:

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

This equation highlights the key factors influencing blood pH:

• Bicarbonate Concentration ([HCO3-]) : An increase in [HCO3-] shifts the equilibrium towards the left, leading to a higher pH (alkalosis). Conversely, a decrease in [HCO3-] shifts the equilibrium towards the right, resulting in a lower pH (acidosis).
• Partial Pressure of Carbon Dioxide (PaCO2) : An increase in PaCO2 (respiratory acidosis) increases the concentration of H2CO3, driving the reaction towards the right and lowering pH. Conversely, a decrease in PaCO2 (respiratory alkalosis) reduces H2CO3 formation, shifting the equilibrium towards the left and elevating pH.

The pKa of the carbonic acid system is approximately 6.1 at 37°C. When the ratio of [HCO3-] to (α * PaCO2) is 1:1 (log of 1 = 0), the pH equals the pKa (6.1), representing a neutral state. Deviations from this ratio due to changes in [HCO3-] or PaCO2 lead to acidosis (pH < 6.1) or alkalosis (pH > 6.1).

The Davenport Diagram: A Graphical Representation

The Davenport diagram is a graphical representation of the HHE, used to visualize the relationship between pH, [HCO3-], and PaCO2 [2]. It typically features axes representing blood pH and [HCO3-]. Isopleths, or lines of constant PaCO2, are superimposed on the graph.

The theoretical basis for the Davenport diagram lies in rearranging the HHE equation to isolate [HCO3-]:

[HCO3-] = α * PaCO2 * 10^(pH - pKa)

This equation demonstrates a linear relationship between [HCO3-] and pH at a constant PaCO2 value. Therefore, isopleths on the Davenport diagram represent straight lines with a slope dependent on the pKa and α of the carbonic acid system.

The Davenport diagram provides a valuable tool for:

• Visualizing Acid-Base Disturbances: Deviations from the normal range of [HCO3-] and pH on the diagram can indicate the presence of metabolic or respiratory acid-base disturbances.
• Understanding Compensation: The body attempts to compensate for primary acid-base disturbances through physiological mechanisms. The Davenport diagram can show the compensatory changes in [HCO3-] in response to a change in PaCO2.

Citations

1. Forster, R. E., & Murphy, P. M. (2010). Acid-base balance: A physiologic approach (4th ed.). Elsevier Saunders.
2. Astrup, P. (1984). Acid-base disturbances in intensive care medicine. Lancet, 2(8402), 1018-1022. doi:10.1016/S0140-6736(84)91099-9