# 2.3: Respiratory Regulation of Acid-Base Balance

## 2.3.1: How is the Respiratory System Linked to Acid-base Changes?

Respiratory regulation refers to changes in pH due to pCO2 changes from alterations in ventilation. This change in ventilation can occur rapidly with significant effects on pH. Carbon dioxide is lipid soluble and crosses cell membranes rapidly, so changes in pCO2 result in rapid changes in [H+] in all body fluid compartments.

A quantitative appreciation of respiratory regulation requires knowledge of two relationships which provide the connection between alveolar ventilation and pH via pCO2. These 2 relationships are:

• First equation - relates alveolar ventilation (VA) and pCO2
• Second equation - relates pCO2 and pH.

The two key equations are outlined in the boxes below:

### First Equation: Alveolar ventilation - Arterial pCO2 Relationship

Relationship: Changes in alveolar ventilation are inversely related to changes in arterial pCO2 (& directly proportional to total body CO2 production).

paCO2 is proportional to [VCO2 / VA]

where:

• paCO2 = Arterial partial pressure of CO2
• VCO2 = Carbon dioxide production by the body
• VA = Alveolar ventilation

Alternatively, this formula can be expressed as:

$paCO_{2} = 0.863 \times \frac {V_{CO_{2}}} {V_{A}}$

(if VCO2 has units of mls/min at STP and VA has units of l/min at 37°C and at atmospheric pressure.)

### Second Equation: Henderson-Hasselbalch Equation

Relationship: These changes in arterial pCO2 cause changes in pH (as defined in the Henderson-Hasselbalch equation):

$pH = pKa + \log \frac {[HCO_{3}^{-}]} {0.03 \times pCO_{2}}$

or more simply: The Henderson equation:

$[H^{+}] = 24 \times \frac {pCO_{2}} {[HCO_{3}^{-}]}$

The key point is that these 2 equations can be used to calculate the effect on pH of a given change in ventilation provided of course the other variables in the equations (eg body's CO 2 production) are known.

The next question to consider is how all this is put together and controlled, that is, how does it work?

## 2.3.2: Control System for Respiratory Regulation

The control system for respiratory regulation of acid-base balance can be considered using the model of a simple servo control system. The components of such a simple model are a controlled variable which is monitored by a sensor, a central integrator which interprets the information from the sensor and an effector mechanism which can alter the controlled variable. The servo control means that the system works in such a way as to attempt to keep the controlled variable constant or at a particular set-point. This means that a negative feedback system is in operation and the elements of the system are connected in a loop.

Control systems in the body are generally much more complex than this simple model but it is still a very useful exercise to at first attempt such an analysis.

### Control System for Respiratory Regulation of Acid-base Balance

Control Element

Physiological or Anatomical Correlate

Comment

Controlled variable

Arterial pCO2

A change in arterial pCO2 alters arterial pH (as calculated by use of the Henderson-Hasselbalch Equation).

Sensors

Central and peripheral chemoreceptors

Both respond to changes in arterial pCO2 (as well as some other factors)

Central integrator

The respiratory center in the medulla

Effectors

The respiratory muscles

An increase in minute ventilation increases alveolar ventilation and thus decreases arterial pCO2 (the controlled variable) as calculated from 'Equation 1'(discussed previously). The net result is of negative feedback which tends to restore the pCO2 to the 'setpoint'.