Chapter 3

## Gas Exchange

## Zoheir Bshouty

### Chapter Overview

Gas exchange involves the exchange of gases between the lung and the blood. The gases of interest are oxygen and carbon dioxide. The general objectives behind this chapter are to leave you with enough basic physiological knowledge that would enable you to identify derangements in gas exchange based on the interpretation of arterial blood gases and to try to identify the mechanism(s) leading to these derangements.

Although pH plays a certain role in interpreting arterial blood gases, when dealing with gas exchange, emphasis is on interpreting derangements in the partial pressure of arterial oxygen (P_{a}O_{2}) and the partial pressure of arterial carbon dioxide (P_{a}CO_{2}).

To help with these, some key equations will be used. The derivation of these equations is beyond the scope of this chapter but the principles used in deriving these equations will be mentioned. Equations that are useful in clinical practice are boxed.

The chapter will start with derangements in carbon dioxide followed by derangements in oxygen. The reason for this order, as you will see later, is that derangements in carbon dioxide can directly lead to derangements in oxygen, while derangements in oxygen do not affect carbon dioxide. The goal is to keep the topic as simple as possible and at the same time clinically relevant. Often, learners fail to understand the link between theory and clinical applicability; therefore, the chapter starts with two clinical scenarios that will be referred to occasionally to help maintain this link.

In this chapter and in pulmonary physiology in general, V indicates volume. Subscripts are used to identify the various types of volumes (e.g., V_{D} for dead space). When written with a diacritic period such as V it indicates volume measured over a period of one minute (e.g., V_{E} for minute ventilation).

### The Problem

** Case 1**. An elderly man is brought to the Emergency Department by his daughter. He tells the resident that his chronic cough and shortness of breath have become worse in the last few days, during which time he has had periods of drowsiness and confusion. The patient is drowsy and uncooperative, blue and in obvious respiratory distress. The resident decides to take an arterial blood gas sample on room air.

** Case 2**. An elderly woman presents to the outpatient clinic complaining of increased fatigue and shortness of breath on exertion that were insidious in nature and have gradually progressed over the past five years. As part of her investigation an arterial blood gas on room air is drawn with the following results:

** Analyzing P_{a}O_{2} and P_{a}CO_{2} and identifying the mechanism(s) for the gas exchange disturbances in the earlier context is the topic of this chapter**.

### Normal values for arterial blood gases

Textbooks often reference the following normal ranges for arterial blood gases,

In some ways, however, it is difficult to define **“normality”** particularly for P_{a}O_{2}, which may vary with body position, age, and smoking history, to mention the more important factors. Also, as you will see later, the three variables are linked physiologically. A normal P_{a}O_{2} of 80 mmHg at a normal P_{a}CO_{2} of 45 mmHg will be abnormal at a P_{a}CO_{2} of 35 mmHg. Similarly, a normal P_{a}CO_{2} of 45 mmHg at a of 24 mEq/L will be abnormal at a of 15 mEq/L.

The lungs are the first link in the O_{2} transport chain to the tissues (for metabolism) and the last link in the CO_{2} transport chain (by-product of metabolism). There is no doubt that both patients have a problem getting O_{2} into their blood. In addition, the first patient has a problem getting rid of CO_{2}.

As mentioned earlier, we will refer back to these two cases as new concepts are learned to maintain the link between theory and clinical practice.

**Anatomic dead space (V _{Danat})** is the volume of all non-gas-exchanging airways from the nose (or mouth, during mouth-breathing) down to the respiratory bronchioles Fig. 1.

**Alveolar dead space (V _{Dalv})** is the volume of inspired air that is delivered to alveoli in which there is no gas exchange or gas exchange is incomplete. V

_{Dalv}is primarily the result of under perfusion of the affected alveoli Fig 1. V

_{Dalv}is too small to be measured in healthy subjects, particularly young people, but can become large enough to interfere with alveolar ventilation (V

_{A}) in patients who have certain lung diseases, in spite high V

_{E}.

**Physiologic dead space (V _{D})** is the sum of V

_{Danat}and V

_{Dalv}. V

_{D}defines the portion of each inspiration that does not equilibrate with gas pressures of the pulmonary capillary blood Fig. 1.

In the lungs, not all alveoli are ventilated and perfused at ideal proportions. For a given perfusion rate, some alveoli are underventilated (or hypoventilated), while others are overventilated (or hyperventilated) with respect to the ventilation required to accomplish adequate gas exchange. The same is true for blood perfusion (i.e., for a given V_{A} some areas are underperfused, while others are overperfused). The ratio between ventilation (V) and perfusion (V) is referred to as the ventilation to perfusion ratio (V/Q). This concept and the concept of V/Q mismatch will be discussed in detail at the end of the chapter. Despite the existence of a wide spectrum of V/Q ratios, dead space and shunt (see later) are calculated under the assumption that the lung consists of:

1.Alveoli that are optimally and equally ventilated and perfused (with complete equilibration of gas pressures between alveoli and capillary blood, V/Q = 1, Fig. 2 compartment 1).

2.Alveoli that are optimally ventilated but not perfused at all (“V_{Danat}”, V/Q Fig. 2 compartment 2 = ∞)

3.Alveoli that are optimally perfused but not ventilated at all (contributing to “shunt”, V/Q Fig. 2 compartment 3 = 0)

**Thus, V _{D} is a theoretical rather than an actual volume**.

### Factors affecting V_{Danat}

**Size of subject**. V_{Danat} is highly dependent on body size. A good estimate is based on *body height* (rather than body weight), a relationship that holds true for both children and adults.

**Age**. V_{Danat} increases slightly with age. This increase is probably due to loss of elasticity (i.e., increased compliance) of airways.

**Breathing pattern**. V_{Danat} increases with increasing tidal volume (V_{T}). This is due to the increase in distending pressure that parallels the increase in V_{T} which stretches the elastic airways as well as the lungs.

### Factors affecting V_{Dalv}

**Pulmonary embolism**. Occlusion of pulmonary vessels creates a situation where alveoli continue to be ventilated yet unperfused, hence contributing to an increase in V_{Dalv}.

**Mechanical ventilation with high Positive End-Expiratory Pressure (PEEP)**. Similar situation to pulmonary embolism except that pulmonary vessels are occluded by the high alveolar pressure.

The increase in V_{Danat} is usually not enough to cause a disturbance in gas exchange. Diseases that affect gas exchange through their effect on dead space do so by increasing V_{Dalv} which, in turn, leads to an increase in V_{D}. So, it suffices to calculate V_{D} in order to determine whether it is contributing to a gas exchange derangement.

### Calculation of V_{D}

Why is it important to calculate V_{D}? The answer is very simple, Dead Space ventilation (V_{D}) is considered wasted ventilation. The larger the dead space volume, V_{D} (or ventilation, V_{D}) the less volume is available for adequate gas exchange (termed alveolar volume, V_{A}, or ventilation, V_{A}, Eq. 3.3). And, as you will see later, V_{A}, and in turn V_{A}, have a large impact on carbon dioxide elimination.

**V _{E}**. The total amount of gas that is moved in and out of the lung per minute and is equal to the product of V

_{T}and respiratory frequency (f):

**V _{D}**. The amount of gas that moves in and out of the dead space of the lung per minute and is equal to the product of V

_{D}and f:

**V _{A}**. The volume of gas that is introduced into the gas-exchanging regions of the lung per minute. It is equal to V

_{E}minus V

_{D},

**Bohr equation**. The Bohr Equation enables us to estimate V_{D} (as a proportion of V_{T}) using a sample of CO_{2} in mixed expired gas (P_{ME}CO_{2}) and P_{a}CO_{2}. The derivation of this relationship is based on the laws of conservation of mass for CO_{2},^{}1

Going back to *Case 1*, if the patient’s P_{ME}CO_{2} was 36 mmHg, given a P_{a}CO_{2} of 80 mmHg, the proportion of the total ventilation that is being wasted in dead space is (applying Eq. (3.4)):

Indicating that over half of his V_{T} is wasted on dead space. Under normal condition, at rest, V_{D}/V_{T} is approximately 0.3 (30%).

One of the factors that has a large impact on the distribution of ventilation between dead space and gas exchanging alveoli is breathing pattern. Consider the patient in *Case 1*, when assessed he was noted to having rapid shallow breathing. His respiratory frequency was 40 per minute and his estimated V_{T} was approximately 200 mL. As his V_{D}/V_{T} was 0.55, his V_{D} would have been 200 · 0.55 = 110 mL. The subject’s V_{E} was 40 · 0.2 = 8 L/minute, V_{D} = 40. 0.11 = 4.4 L/minute, and V_{A} = 8 − 4.4 = 3.6 L/minute. If V_{E} were to remain the same (8 L/minute) and his breathing pattern were to change to slower and deeper, for example f = 20 and V_{T} = 400 mL. In this latter case V_{D} would be 20 · 0.11 = 2.2 L/minute and compartment V_{A} would be 8 − 2.2 = 5.8 L/minute. What impact will this have on his gas exchange? This is the topic of the next section.

### V_{A} and CO_{2}

### Relation between V_{A} and P_{a}CO_{2}

During steady state conditions of ventilation and perfusion, the rate of CO_{2} production (V_{CO2}), at the tissue level, is constant and equals the rate of CO_{2} elimination at the lung. Alveolar CO_{2} concentration is directly related to CO_{2} production (V_{CO2}) and inversely related to CO_{2} elimination which is controlled by V_{A}. This relationship is also derived using the laws of conservation of mass for carbon dioxide,^{}2 :

where P_{B} is barometric pressure and 47 is water vapor pressure at 37°C.

Conventionally, P_{A}CO_{2} is expressed in mmHg, V_{A} in L/minute at BTPS (Body Temperature Pressure Saturated) and V_{CO2} is expressed in mL/minute at STPD (Standard Temperature Pressure Dry). To account for P_{B}, the difference in units between V_{A} (L/minute) and V_{CO2} (mL/minute), and to standardize BTPS conditions with STPD one needs to multiply the right-hand side of the equation by a correction factor *k* (equals 0.863). Also, since CO_{2} is a very diffusible molecule across biologic membranes P_{a}CO_{2} can be substituted for P_{A}CO_{2} and the equation can be written in the following form:

This equation expresses a very important core concept as it relates effective breathing (as represented by V_{A}) to the metabolic rate of CO_{2} production (V_{CO2}). Thus, the measurement of P_{a}CO_{2} expresses whether V_{A} is adequate for the metabolic needs of the body without measuring either V_{A} or V_{CO2}. If normally P_{a}CO_{2} is 40 mmHg, then a doubling to 80 mmHg means that V_{A} is only half of what is normally required for the body’s CO_{2} output. In other words, at a given metabolic rate, P_{a}CO_{2} is inversely proportional to V_{A}.

Going back to *Case 1*, at the end of the last section, we wondered what would happen to the patient’s gas exchange if he were to change his breathing pattern.

From Eq. (3.6), substituting 80 for P_{a}CO_{2}, 0.863 for *k*, and 3.6 for V_{A}, gives a V_{CO2} of 333 mL/minute. Using the same equation, by changing V_{A} from 3.6 to 5.8 L/minute, and assuming that V_{CO2}