Relationship Between pH and [H⁺]

It is important to understand the relationship between [H⁺] and pH, however, because it is not a simple direct one. Because the pH is the negative log of the free hydrogen ion concentration, the relationship between pH and [H⁺] is inverse. An increase in pH reflects a decrease in [H⁺], whereas a decrease in pH is associated with a increase of hydrogen ions.

Also, because the relationship is logarithmic, a relatively large change in hydrogen ion concentration only slightly alters the numeric value of pH. For example,doubling of the normal [H⁺] only results in a 0.3 unit decrease in pH.²

Bases

All hydrogen ions released in solution, however, do not remain free. Many hydrogen ions are attracted to and combine with other chemical substances that are present in the blood. Any substance capable of combining with or accepting a hydrogen ion in solution is called a base.

Thus, from a chemical standpoint,the blood pH is a result of the balance of acids and bases (i.e., acid-base balance) at any given moment.

Acid Homeostasis

Normal body metabolism tends to result in an accumulation of excess acid. Thus, it is important that the body excrete acid at a rate equivalent to its production to maintain pH homeostasis.

Base Homeostasis

Like acids, the bases in the bloodstream must also be maintained in a constant balance. The organ responsible for the regulation of blood bases is the kidney. The plasma bicarbonate concentration [HCO₃] is the major blood base of clinical significance. The [HCO₃] is carefully controlled in the nephron, which is the functional unit of the kidney.

Carbonic Acid Production

Based on the law of mass action, the CO₂ that builds up at the tissues leads to a parallel increase in carbonic acid and ultimately hydrogen ions (Fig. 8-1). Thus, there is an increase in the amount of carbonic acid present in the blood as it passes the tissues and CO₂ enters. Venous blood has more CO₂ and carbonic acid than arterial blood. In fact, that is why venous blood is slightly more acidic (pH = 7.38) compared with arterial blood (pH = 7.40). Actually, the difference in pH would be more substantial were it not for the many effective buffer systems in the blood.

Carbonic Acid Excretion

When the venous blood reaches the lungs, the increased CO₂ and carbonic acid that entered the blood at the tissues must be excreted. This is precisely the role of the lungs in acid-base balance: to excrete CO₂ and carbonic acid at the same rate that it is being produced. Figure 8-2 shows that as CO₂ diffuses into the alveoli, the law of mass action forces the hydrolysis reaction to the left. The net effect of this action is a reduction in carbonic acid and a decrease in the number of hydrogen ions in the blood. Thus, as CO₂ is excreted via the lungs, the body is functionally excreting H₂CO₃.

CO₂Production

CO₂ production depends on both the quantity and the nature of metabolism. The quantity of metabolism varies directly with body temperature. Metabolism increases as an individual’s body temperature increases. The nature of metabolism depends on the type of foodstuff (e.g., fat, protein, carbohydrate) being metabolized. For example, carbohydrate metabolism produces more CO₂ than does fat metabolism.

In normal humans, increases in CO₂ production, such as during exercise, are balanced physiologically by increasing alveolar ventilation proportionately. Sometimes, however, increases in CO₂ production cannot be offset by increased ventilation. This finding may occur when CO₂ production is high (e.g., patients with burns, total parenteral nutrition, sepsis) or when the ventilatory system is compromised.

Large increases in metabolism and CO₂ production sufficient to result in PaCO₂ elevation may occur occasionally in patients with sepsis (blood infection) or massive burns. Also, an increase in blood PaCO₂ can occur after intravenous administration of the drug sodium bicarbonate (NaHCO₃) to a patient who is unable to increase alveolar ventilation.³⁶⁵ Because bicarbonate is one of the factors in the hydrolysis reaction, its presence in increased quantities pushes the reaction to the left, which, in turn, has the effect of increasing dissolved CO₂ and H₂CO₃ levels in the blood.

The individual with a normal respiratory system responds to the increased CO₂ with a parallel rise in alveolar ventilation and CO₂ excretion. The inability to increase alveolar ventilation may be seen, however, when central nervous system ventilatory control mechanisms are not intact or when the respiratory muscles are paralyzed. Paralysis of the ventilatory muscles may occur after trauma or pharmacologic intervention for control of mechanical ventilation. Thus, in these situations the clinician should try to minimize CO₂ loading in the blood or to provide the patient with some type of ventilatory support to aid in excretion of the additional CO₂ load.

CO₂Excretion

In the clinical setting, increased CO₂ production is usually balanced by increasing alveolar ventilation. Furthermore, most clinical changes in PaCO₂ are a result of changes in alveolar ventilation. Nevertheless, it is becoming increasingly clear that changes in CO₂ production can also lead to PaCO₂ alterations.

To show the inverse relationship between alveolar ventilation and PaCO₂, Proportion 8-1 is sometimes simplified to the form shown in Proportion 8-2. In this proportion, CO₂ is considered to be a constant and the number one is substituted in the numerator. The proportion becomes simply an inverse relationship between PaCO₂ and alveolar ventilation.An increase in alveolar ventilation results in a decreased PaCO₂. Conversely, a decrease in alveolar ventilation causes an increased PaCO₂.

SIMPLIFIED CO2 HOMEOSTASIS1V˙A=PaCO2 Proportion 8-2

Proportion 8-2

Minute Ventilation

The amount of gas moving in and out of the lungs with each breath is called the tidal volume (VT). The number of breaths taken each minute is often referred to as the frequency or respiratory rate (RR). Exhaled minute ventilation (E) can be calculated as shown in Equation 8-5.

SIMPLIFIED CO2 HOMEOSTASIS1V˙A=PaCO2 Equation 8-5

VT×RR=E Equation 8-5

Minute ventilation, however, is not a very reliable index of the adequacy of ventilation. The drawback of minute ventilation is that it does not tell us if the lungs are excreting CO₂ in correct proportion to its production. To assess the adequacy of ventilation one must get an arterial blood gas and evaluate the PaCO₂. The PaCO₂ is the best index available to assess the adequacy of ventilation relative to CO₂ production. If the lungs are maintaining CO₂ homeostasis, the PaCO₂ is maintained within the normal range (i.e., PaCO₂35 to 45 mm Hg).

Alveolar Ventilation

As shown in Proportion 8-2, PaCO₂ is inversely proportional to alveolar ventilation. Alveolar ventilation differs from minute ventilation in that only the gas that reaches functional (i.e., perfused) alveoli is considered alveolar ventilation; in other words, deadspace volume (VD) (see Chapter 6) is subtracted from the tidal volume (VT) to determine alveolar ventilation (A). The formula for calculation of alveolar minute ventilation is shown in Equation 8-6.

SIMPLIFIED CO2 HOMEOSTASIS1V˙A=PaCO2 Equation 8-6

A=(VT-VD)×RR Equation 8-6

One can readily see that any increase in tidal volume or RR (or a decrease in deadspace) increases alveolar ventilation, assuming of course that all other variables remain constant. An increase in alveolar ventilation, in turn, lowers PaCO₂. Conversely, a fall in RR or tidal volume (or an increase in deadspace) decreases alveolar ventilation and increases PaCO₂. When a change in PaCO₂ is seen clinically, Equation 8-6 should be analyzed to determine what variable has resulted in the change in the patient’s ability to excrete CO₂.

Minute Ventilation versus Alveolar Ventilation

Table 8-1 shows three sets of parameters where the minute ventilation is the same (6000 mL/min); however, alveolar ventilation and CO₂ excretion are grossly different.Figure 8-3 similarly illustrates how alveolar ventilation and deadspace ventilation would be impacted by the breathing patterns inTable 8-1. During normal breathing (seeFig. 8-3,A), most ventilation is effective alveolar ventilation. If minute volume remains constant, alveolar ventilation will increase with larger tidal volumes and a slower respiratory rate (seeFig. 8-3,B). Finally, if breathing is very rapid and shallow, deadspace ventilation can actually exceed alveolar ventilation (seeFig. 8-3,C) despite a constant minute ventilation.

Table 8-1

Minute Ventilation Versus Alveolar Ventilation

VT (mL)	RR (bpm)	VD (mL)	(mL/min)	A (mL/min)	PaCO2 (mm Hg)
500	12	150	6000	4200	40
250	24	150	6000	2400	80
1000	6	150	6000	5100	30

On Call Case 8-1   ABGs and Critical Thinking

You are the only person available to care for this patient. You must assess the patient/situation and act accordingly.

A 52-year-old patient with acute respiratory distress syndrome is being mechanically ventilated in the control mode in the critical care unit. The patient is being pharmacologically paralyzed to facilitate mechanical ventilation. Previous blood gases had shown a normal PaCO₂ and PaO₂ with a severe metabolic acidosis (pH 7.12) secondary to renal failure. Two ampules of sodium bicarbonate are administered IV to correct the metabolic acidosis and the following blood gas is obtained.

ARTERIAL BLOOD GASES

SaO2	70%
pH	7.10
PaCO2	56 mm Hg
PaO2	52 mm Hg
[HCO3]	16 mEq/L
FIO2	0.50

ASSESSMENT

Abnormalities: List abnormal data and other noteworthy information. Classify ABG.

Explanation: List possible diseases, pathology, or other situations that may have led to this patient’s condition.

INTERVENTION

Importance: Prioritize concern(s) of treatment in order of urgency and/or seriousness as you see the overall situation.

Note likewise that the PaCO₂ varies inversely with the alveolar ventilation. The inadequacy of minute ventilation as an index of the adequacy of ventilation is clearly shown in Table 8-1 and Figure 8-3. The PaCO₂ is the only reliable index of the adequacy of ventilation.

It should also be noted that inTable 8-1 and Figure 8-3, deadspace is considered a constant 150 mL/breath. In these sets, changes in alveolar ventilation are due to alterations in VT and RR. In many disease states, deadspace varies considerably from this value. Thus, even when tidal volume and RR are known, the blood gas and specifically the PaCO₂ are necessary to assess the adequacy of A and the ability of the body to maintain CO₂ homeostasis.

Dissolved CO₂

As described in Chapter 3, gases dissolve in liquids in direct proportion to their partial pressures. Furthermore, the volume of gas dissolved in a given liquid depends on the solubility coefficient of that gas in that particular fluid. The solubility coefficient of CO₂ in blood is approximately 0.072 vol%/mm Hg, which, of course, is much higher than the solubility coefficient of O₂(0.003 vol%/mm Hg). Given a normal PaCO₂ of 40 mm Hg, the normal volume of dissolved CO₂ in the arterial blood is approximately 2.9 vol%.

In comparison with O₂, however, CO₂ is sometimes reported in units of mEq/L. The solubility coefficient of CO₂ in units of mEq/L is 0.03 mEq/L/mm Hg. Thus, given a normal arterial PCO₂ of 40 mm Hg, the normal volume of dissolved CO₂ in the plasma is (40 mm Hg × 0.03 mEq/L/mm Hg) 1.2 mEq/L. Dissolved CO₂ transport accounts for only approximately 8% of the total volume of CO₂ transported from the tissues to the lungs. The factor for converting CO₂ in vol% to mEq/L is (vol%/2.23 = mEq/L).

Carbonic Acid

As shown previously in Equation 8-1, the concentration of carbonic acid [H₂CO₃] in the blood varies directly with the quantity of dissolved CO₂, because these two substances are related directly via the hydrolysis reaction. The amount of actual H₂CO₃ in the blood, however, is minute (0.006%) in comparison with total CO₂ transport.

The reason for this unbalanced relationship is that the chemical equilibrium point of the reaction is such that the ratio of dissolved [CO₂] to [H₂CO₃] is approximately 340 to 1 (see Equation 8-1).³⁶⁴ In other words, the reaction is shifted far to the left. Thus, although the quantitative relationship between dissolved CO₂ and H₂CO₃ is very important from an acid-base perspective, the volume of CO₂ being transported in the form of H₂CO₃ is negligible.

In some texts, H₂CO₃ is excluded as a mechanism of CO₂ transport because of its nominal role. Nevertheless, it is included here for completeness and to reinforce understanding of the direct relationship between the quantities of dissolved CO₂ and H₂CO₃.