Alveolar Ventilation and Arterial pH

With the help of the buffering systems and renal function, the pulmonary system plays an important role in pH homeostasis. In this chapter we will look at how the lungs contribute to the control of pH, and how failure of the pulmonary system or control of breathing can lead to dangerous deviations in pH.

CO₂ and pH

We will start by revisiting the equation dealt with in the previous chapter in the context of four different clinical scenarios.

Case #1, normal: In the normal situation an increase in tissue metabolism leads to a rise in arterial CO₂, pushing the equation to the right and causing a rise in hydrogen ion concentration and a consequent fall in pH. Both the rise in CO₂ and fall in pH stimulate breathing. This increase in alveolar ventilation leads to a fall in arterial CO₂, pushing the equation back left and lowering hydrogen ions back to normal.

Equation 12.1

[latex]CO_2 + H_2O \Leftrightarrow H_2CO_3 \Leftrightarrow H^+ + HCO^-_3[/latex]

Case #2, metabolic acidosis: CO₂ is by no means the only source of hydrogen ions in the system. Most metabolic pathways result in acidic by-products, and the pulmonary, renal, and buffering systems are generally battling to raise blood and tissue pH back from their tendency to turn acidic. The rise in hydrogen ions resulting from metabolic processes is referred to as metabolic acidosis. The fall in pH stimulates an increase in respiration, which in turn causes a fall in CO₂, and the lower CO₂ drives the equation to the left, reducing the number of H⁺ and thereby raising pH back to normal. Here the pulmonary system has compensated for a metabolic process, and this is referred to as respiratory compensation of metabolic acidosis. The patient may now have a normal blood pH, but the CO₂ will be low. In summary, all the pulmonary system has done is get rid of one source of hydrogen ions (carbonic acid derived from dissolved CO₂) to compensate for another source of hydrogen ions it cannot do anything about (most metabolically driven acids are nonvolatile (i.e., do not vaporize into a gas the lungs can get rid of)).

The advantage of the pulmonary system being involved in pH regulation is that it is quick—a few larger breaths and arterial PCO₂ can be dropped significantly. So the pulmonary system is adept at minute-by-minute (or breath-by-breath) regulation of pH that copes admirably with short-term changes in pH. It is worth noting here that metabolic alkalosis can be reversed by reducing or even stopping breathing, allowing CO₂ to accumulate in the arterial blood and lowering pH back to normal.

The disadvantage to using the pulmonary system for compensation is that it can only mediate its effect via CO₂. So any metabolic acids are eventually dealt with by the renal system, which, although much slower, is capable of excreting any nonvolatile metabolic acids. So through a combination of rapid pulmonary CO₂ expulsion and slower but more versatile renal function, pH is normally maintained within a tight range even in the face of large metabolic changes. The kidney also has the advantage of being able to modify bicarbonate levels, which we will see the importance of when we look at the buffering systems in a moment.

Case #3, respiratory acidosis: Given its capability to influence pH, failure of the lung to expel an appropriate amount of CO₂ can lead to deviations in pH. Let us take a case of severe lung disease, say COPD, for example. The disease has diminished the ability of the lung to expel CO₂, so arterial PCO₂ rises, pushing the equation to the right and causing a fall in pH, referred to as respiratory acidosis. This acid must be immediately buffered until kidney function can be modified to begin secreting the excess hydrogen ions and even produce more bicarbonate to replenish the buffering system, a process referred to as metabolic compensation of respiratory acidosis.

Case #4, respiratory alkalosis: Likewise, if ventilation is inappropriately high with respect to CO₂ production, such as during a period of hyperventilation, then too much CO₂ will be lost and pH will fall. The alkalosis must be immediately buffered to avoid deleterious effects. Over the longer term the kidney can lower the raised pH by reabsorbing hydrogen ions and even excreting bicarbonate buffer—again this is termed metabolic compensation—but this time for an alkalosis caused by an inappropriate respiratory response.

Physiological Buffers

Although the lung’s ability to expel CO₂ and the kidney’s ability to excrete or absorb hydrogen ions allow close regulation of pH, their responses alone are not sufficient to prevent immediate local changes in pH at the tissue. This is the role of the buffering systems.

Buffering systems are chemicals within tissue and the blood that have the ability to absorb either hydrogen ions and/or hydroxyl ions. Once these ions are removed from solution (albeit temporarily) then their effect on pH is diminished. We will deal with buffers in the context of acids, as this is the most common physiological situation.

If you need an analogy for the function of buffers, imagine them as a chemical mop—they soak up the hydrogen ions and stop them from making a cellular mess, but the hydrogen ions, although contained, remain in the system. It is the role of the lungs and kidneys to “rinse the mop” and get rid of the hydrogen ions from the system.

There are three major chemical buffering groups in the body:

1. the bicarbonate system,
2. the phosphate system, and
3. intra- and extracellular proteins.

We will deal with the bicarbonate system as it involves the respiratory system and is also the major extracellular buffer.

Bicarbonate buffering: A buffering system consists of a weak base capable of absorbing a strong acid and a weak acid capable of absorbing a strong base. As such, the bicarbonate system involves two components: sodium bicarbonate (a weak base) and carbonic acid (a weak acid). Let us look at how it works and put it in the context of the lungs.

First let us see how a weak acid (carbonic acid) deals with a strong base, in this example, sodium hydroxide (equation 12.2).

Buffering a strong base using a weak acid:

Equation 12.2

[latex]NaOH = \color{red}{H_2CO_3}[/latex]

Sodium hydroxide is a strong base as it rapidly dissociates into a hydroxyl ion and a sodium ion.

Equation 12.3

[latex]{{Na^{+}}\atop{\color{red}{OH}^{-}}} + \color{red}{H_2CO_3}[/latex]

The hydroxyl ion is the potential threat to physiological function so must be buffered. This is achieved by the carbonic acid dissociating into a hydrogen ion and bicarbonate (a process you are familiar with).

These dissociated ions now bind to form new partnerships as water and sodium hydroxide (a weak base) (equation 12.4).

Equation 12.4

[latex]{{Na^{+}}\atop{\color{red}{OH}^{-}}} + {{HCO_{3-}}\atop{{H}^{+}}} \rightarrow H_2O + \color{blue}{NaHCO_3}[/latex]

So there are a couple of things to notice here beyond watching the ions move and form new components. First, the buffering process has taken a situation with the threat from a strong base (NaOH) and toned it down to a situation with a weak base (NaHCO₃); the problem has not gone away, it has just been reduced (or buffered). Second, you will see that both of the components of the bicarbonate system, carbonic acid and sodium bicarbonate, appear in the equation—we have just shifted from one to the other.

Let us look at the opposite situation to see what happens when the buffering system is faced with a strong acid. This time a strong acid (hydrochloric acid) is faced with our weak base (sodium bicarbonate) (equation 12.5).

Buffering a strong acid using a weak base:

Equation 12.5

[latex]HCl + \color{blue}{NaHCO_3}[/latex]

The hydrochloric acid rapidly dissociates into a hydrogen ion and a chloride ion. The hydrogen ion now threatens physiological function and must be buffered.

Our weak base dissociates into sodium and bicarbonate ions. Again our ions recombine, this time to produce harmless sodium chloride and carbonic acid (equation 12.6).

Equation 12.6

[latex]{{\color{red}{H}^{+}}\atop{{Cl}^{-}}} + {{HCO_{3-}}\atop{{Na}^{+}}} \rightarrow NaCl + \color{red}{H_2CO_3}[/latex]

Notice again we have reduced but not removed the threat as we have gone from the presence of a strong acid to a weak one. Also notice that our two components in the bicarbonate system appear in the equation, and we have switched from one to the other. This should now make you realize that these two components are part of a reversible equation, and this reversible equation, even after the addition of sodium to one end, should look rather familiar (equation 12.7).

Equation 12.7

[latex]CO_2 + H_2O \leftrightarrow {\color{red}{H_2CO_3}} \leftrightarrow H^+ + HCO_{3-} + Na^+ \leftrightarrow \color{blue}{NaHCO_3}[/latex]

As CO₂ is at one end of the equation you should appreciate how alveolar ventilation can influence the bicarbonate buffering system.

Because of their critical role in maintaining blood pH, bicarbonate ions are routinely measured along with arterial blood gases. Knowing what the blood pH, arterial CO₂, and bicarbonate levels are provides a very powerful and commonly used diagnostic measure allowing us not only to determine the pH status of the patient, but also the source of the problem and whether the renal or pulmonary systems are achieving compensation. Because of its power and common use, we are going to go through some fundamentals, and I am afraid that means looking at the bane of many a medical student: the Henderson–Hasselbalch equation. For those with a background in chemistry you might skip the next section, but for the rest of us, we are going to go through this step-by-step.

The Henderson–Hasselbalch Equation

What we will see is how the balance of bicarbonate and hydrogen ions determines pH, and how both of these ions can be influenced by the kidneys and lungs to keep pH constant.

First, we will take the central and most important part of the infamous equation, discarding the more innocuous ends.

Equation 12.8

[latex]H_2CO_3 \leftrightarrow H^+ + HCO_{3-}[/latex]

This central portion describes the dissociation of carbonic acid into hydrogen and bicarbonate ions. But because carbonic acid is a weak acid, this dissociation is incomplete—some carbonic acid staying whole, some dissociating into the ions. The level of dissociation is described by the dissociation constant (K’), which really is the ratio of the concentrations of dissociated components to carbonic acid (equation 12.9).

Equation 12.9

[latex]K' = \displaystyle\frac{{H}^{+} \times {HCO}_{3}-}{H_2CO_3}[/latex]

Because we are interested in calculating the pH, however, we are more interested in the amount of hydrogen ions, so rearranging this equation for hydrogen ion concentration we see the hydrogen ion concentration is the dissociation constant, multiplied by the ratio of carbonic acid and bicarbonate (equation 12.10).

Equation 12.10

[latex]H^+ = K' \times \displaystyle\frac{H_2CO_3}{HCO_3-}[/latex]

This equation theoretically would allow us to now determine hydrogen concentration and therefore pH, but there are some practical problems for us, the first of which is that the instability of carbonic acid means we cannot measure its concentration. So we have to use a proxy measure. The amount of carbonic acid is determined by the amount of carbon dioxide, as can be seen in the equation that is so familiar to you—the greater the amount of CO₂, the more carbonic acid.

Equation 12.11

[latex]CO_2 + H_2O \leftrightarrow H_2CO_3 \leftrightarrow H^+ + HCO_3-[/latex]

So after accounting for the dissociation constant of carbonic acid and CO₂ and water, we can simply replace carbonic acid concentration with concentration of CO₂ (equation 12.12).

Equation 12.12

[latex]H^+ = K' \times \displaystyle\frac{CO_2}{HCO_3}[/latex]

We then bump into our next practical problem: our equation now has CO₂ concentration in it, but clinically we do not measure CO₂ as a concentration (as in mmols), but as a partial pressure. So our next and nearly final step is to convert CO₂ concentration to CO₂ partial pressure, and we do this by multiplying the partial pressure (our measured value) by the solubility coefficient of carbon dioxide, which happens to be 0.03 mmol/mmHg. Our equation thus now can be completed using our adjusted PCO₂ (equation 12.13).

Equation 12.13

[latex]H^+ = K' \times \displaystyle\frac{0.03 \times PCO_2}{HCO_3-}[/latex]

Our equation as it is now allows us to calculate hydrogen ion concentration, but we need pH, so we have to make a conversion. Because pH is the negative logarithm of hydrogen concentration, we express everything in the negative log form. And because the negative log of the dissociation constant is referred to as pK, then we can simplify our equation one more step (equation 12.14).

Equation 12.14

[latex]pH = pK - log \displaystyle\frac{0.03 \times PCO_2}{HCO_3-}[/latex]

To make our equation simple to use, we now get rid of the negative log, and so get the following (equation 12.15):

Equation 12.15

[latex]pH = pK + log \displaystyle\frac{HCO_3-}{0.03 \times PCO_2}[/latex]

We know that the pK of the bicarbonate system happens to be 6.1, so substituting this into the equation we end up with the Henderson–Hasselbalch equation (equation 12.16).

Let us put this in context.

First, the equation shows that if CO₂ rises then pH falls, and because CO₂ is under the influence of alveolar ventilation, this explains how the alveolar ventilation can now control pH. It also shows that if bicarbonate increases then pH increases, and equally if bicarbonate falls then pH falls. Because the bicarbonate concentration can be modified either way by the kidneys, the equation also shows how the kidneys can modify pH (equation 12.16).

Equation 12.16

Role of kidneys (numerator) / Role of lungs (denominator)

[latex]pH = 6.1 + log \displaystyle\frac{HCO_3-}{0.03 \times PCO_2}[/latex]

The involvement of these two major physiological systems in this equation make the bicarbonate system a very powerful buffer, particularly when considering that there is an unlimited source of CO₂ and therefore bicarbonate supplied by the metabolism.

But more importantly it shows that pH is actually determined by the ratio of bicarbonate and CO₂ and that both are equally important. This fact is critical to appreciate as it forms the basis of understanding the compensation mechanisms we dealt with earlier. This is why I put you through this derivation. So for example, if a rise in CO₂ (such as in lung disease) is accompanied by an equal rise in bicarbonate (generated by the kidney), then the ratio between the two remains the same and therefore pH remains the same. Likewise, if during a fall in CO₂ the kidneys excrete bicarbonate, then pH can be kept constant. So before we finish, let us show you that the equation actually works by plugging in some numbers.

Example #1: Let us start with normal values, a PCO₂ of 40 mmHg and a bicarbonate of 24, and plug these into the equation. This comes to 6.1 plus the log of 20, which is 6.1 plus 1.3, or 7.4 (i.e., normal arterial pH).

Equation 12.17

[latex]pH = 6.1 + log \displaystyle\frac{24}{(0.03 \times 40)} = 6.1 + log(20) = 6.1 + 1.3 = 7.4[/latex]

Example #2: Now let us look at a case of acute lung failure that has caused a rise in arterial PCO₂, but has not persisted long enough for the kidney to respond and compensate. PCO₂ has risen to 50 mmHg, and bicarbonate has not changed. Our calculation now goes to 6.1 plus the log of 16, which is 6.1 plus 1.2, and pH has fallen to 7.3.

Equation 12.18

[latex]pH = 6.1 + log \displaystyle\frac{24}{(0.03 \times 50)} = 6.1 + log(16) = 6.1 + 1.2 = 7.3[/latex]

We now have three numbers that can give a meaningful clinical interpretation. The low pH indicates the patient is in acidosis. The raised PCO₂ suggests that this is respiratory acidosis, and the unchanged bicarbonate suggests no metabolic compensation has taken place.

Example #3: Now let us return to our patient thirty-six hours later when we have given the kidney a chance to respond. The patient’s PCO₂ remains at 50 because of the persistent lung problem, but the kidney has raised the bicarbonate to 30. Now our equation becomes 6.1 plus the log of 20, or 6.1 plus 1.3, and pH is 7.4—apparently normal.

Equation 12.19

[latex]pH = 6.1 + log \displaystyle\frac{30}{(0.03 \times 50)} = 6.1 + log(20) = 6.1 + 1.3 = 7.4[/latex]

But when we look at all three numbers we see that the patient is far from normal: the pH is okay only because the kidneys have raised bicarbonate to match the raised CO₂ and keep the ratio the same. So we now have a respiratory acidosis with metabolic compensation.

Summary

So although it has been a long journey through this chapter you should now be able to interpret blood gas values to determine whether a patient is in acidosis or alkalosis and whether or not compensation is present. I strongly recommend writing the Henderson–Hasselbalch equation as a formula in Excel so that you can plug in CO₂ and bicarbonate values and see what happens to pH. By repeatedly interpreting blood gas values and pH, determining the status of a patient will rapidly become second nature.