Physics of respiratory gases and the alveolar gas equation

Respiratory gases (oxygen, CO₂, and nitrogen) can be measured as percent of total volume represented by each gas in the mixture (%) or according to their partial pressure in millimeters of mercury (mmHg) or kilopascals (1 kPa = 7.5 mmHg). Gases dissolve in fluids and diffuse across membranes (e.g., alveolar–capillary membrane) according to their partial pressures [58]. Dalton’s law states that the total partial pressure of a gas mixture equals the sum of the partial pressure of each gas. The partial pressure of each gas is calculated by multiplying the percent volume of each gas in the mixture by the barometric pressure (P_B), that is, the pressure exerted by the atmosphere, and is expressed in mmHg or kPa (Fig. 37.5). Because the degree of collision among gas molecules is influenced by the gravitational forces exerted by the earth, the partial pressure of a single gas or gas mixture will vary according to the altitude in relation to sea level [58]. While the partial pressure of a gas or gas mixture decreases in proportion to the decrease in barometric pressure at higher altitudes, the percent volume of gas in the mixture remains constant with changes in altitude and barometric pressure. As such, F_IO₂ is the same at sea level or the top of Mount Everest (21%), the highest peak on earth (8848 meters above sea level). However, because P_B at Mount Everest is about one‐third of that at sea level (253 mmHg and 760 mmHg, respectively), oxygen partial pressure in inspired gas (P_IO₂) at this altitude will be markedly low (53 mmHg, calculated as F_IO₂ × P_B), leading to a degree of hypoxemia that is incompatible with life. While extremely high altitudes (above 5500 meters or 18,000 feet) generally cannot sustain developed forms of life due to the low P_IO₂, another more realistic example of the impact of altitude on inspired gases is illustrated in Fig. 37.5. Compared to Rio de Janeiro (Brazil), located at sea level, the P_IO₂ in Fort Collins (United States), located 1525 meters above sea level, is reduced from 160 mmHg to 134 mmHg due to altitude. Oxygen partial pressure in alveolar gas (P_AO₂), calculated on the basis of the alveolar gas equation, will be approximately 105 mmHg and 85 mmHg at sea level and an altitude of 1525 meters, respectively. Assuming that the alveolar to arterial oxygen gradient (P(a‐a)O₂) is normally between 5 and 15 mmHg, normal PaO₂ levels in Rio de Janeiro and Fort Collins are estimated to be approximately 95–100 mmHg and 75–80 mmHg, respectively.

The water vapor partial pressure () decreases the P_B and should be subtracted from the altitude‐based barometric pressure if ambient air humidity is elevated. In the presence of water vapor, the sum of the partial pressures of a gas mixture should be equal to P_B minus (Table 37.4). For simplicity, it is typically assumed that water vapor partial pressure is zero in ambient air and the sum of partial pressure of gases equals the barometric pressure at a given altitude (Table. 37.4). While water vapor partial pressure in inspired gas is probably zero in a patient receiving 100% medical oxygen without humidification, this simplification may stray from reality if relative air humidity and ambient temperature are elevated. If the relative air humidity is 51%, water vapor pressure of ambient air is 9 mmHg at 20 °C [58].

The composition of alveolar gas differs from inspired dry air because, in addition to oxygen and nitrogen, it contains saturated water vapor and CO₂ that diffused out of pulmonary capillary blood, according to the alveolar gas equation (Fig. 37.2, Table 37.4):

Where P_AO₂ is oxygen partial pressure in alveolar gas, F_IO₂ is the fraction of inspired oxygen, P_B is the barometric pressure, is the water vapor pressure, P_ACO₂ is the alveolar CO₂ partial pressure, and R is the respiratory quotient. As inspired gases are warmed and humidified after passing through the conducting airways, water vapor partial pressure increases to 47 mmHg at 37 °C (Fig. 37.2, Table 37.4). Carbon dioxide is highly diffusible across the alveolar–capillary membrane; therefore, P_ACO₂ is assumed to be equal to PaCO₂. However, to account for the metabolic rate, P_ACO₂ should be divided by the R, that is, the ratio between CO₂ production per minute (V̇CO₂) and oxygen consumption per minute (V̇O₂), as follows:

The respiratory quotient is influenced by the diet/source of energy metabolism and varies with the percentage of carbohydrates, proteins, and fats being oxidized. Oxidative metabolism of carbohydrates, proteins, and fats results in R values of 1, 0.8, and 0.7, respectively [58]. The reason for this difference is that when oxygen fuels carbohydrate metabolism, one molecule of CO₂ is formed for each molecule of oxygen consumed; during oxidative metabolism of fats, a large share of the oxygen combines with hydrogen atoms from the fats to form water instead of CO₂. In humans consuming a Western diet, R has been determined to be 0.8 while studies in healthy conscious dogs report an R‐value of 0.9 [43]. The respiratory quotient can be altered by species, breed, nutritional state, hormonal circadian rhythm, and level of activity. Because of changes in the energy metabolism, R values ranging from 0.7 to 0.8 have been reported in critically ill dogs [59].

Kinetics of carbon dioxide elimination

The ideal gas exchange between pulmonary capillary blood and the alveoli is illustrated in Fig. 37.2. As the CO₂ in mixed venous blood (CO₂ partial pressure in mixed venous blood [PCO₂]) reaches the pulmonary capillaries, it equilibrates with P_ACO₂. The rate of CO₂ removal from the alveoli to ambient air, and consequently the P_ACO₂ and the CO₂ partial pressure in end‐pulmonary capillary blood (Pc´CO₂), is determined by the volume of air flowing in and out of alveoli over 1 min, that is, V̇_A [9]. The PaCO₂, which averages CO₂ of the end‐capillary blood from all alveoli, indicates the adequacy of V̇_A. It is important to understand the variables that influence CO₂ removal to manage V̇_A and PaCO₂ in the perianesthetic setting.

The flow of gas in and out of the lungs is an essential component of gas exchange between alveoli and the pulmonary capillary blood. As explained before, V̇_E, is determined by the breathing frequency (f ) and by the volume of gas that enters and leaves the mouth or nostrils in each breath, that is the tidal volume (V_T) (Fig. 37.2, Table 37.3).

Gas exchange takes place only at the level of the alveolar–capillary barrier, more specifically in alveoli that are ventilated and perfused. Areas of the respiratory tract that receive ventilation but that do not participate in gas exchange, are referred to as “deadspace.” Because the upper airways and tracheobronchial tree do not participate in gas exchange, the relative volume necessary to fill these structures during tidal breathing is termed “airway deadspace” (). The conducting airways are not the only component of the respiratory system responsible for deadspace ventilation, however, ventilated but not perfused alveoli also contribute to deadspace. The volume of these alveolar units is referred to as “alveolar deadspace” (). “Physiologic deadspace” () is the total deadspace volume, which includes and (Fig. 37.6A):

Although V̇_E is commonly measured to evaluate pulmonary ventilation, the important factor in pulmonary gas exchange is the rate at which alveolar air is exchanged with atmospheric air. Alveolar ventilation per minute (V̇_A) is described by:

The formula above accounts for the volume of gas that enters and leaves the physiologic deadspace per minute (). With the use of volumetric capnography (further discussed below in this section), V̇_A can be measured. Alternatively, the alveolar ventilation equation can be used to quantitate V̇_A. In this equation, V̇CO₂ is CO₂ production per minute, P_ACO₂ is the CO₂ partial pressure in the alveolus, which is assumed to be equal to PaCO₂, and K is a constant:

From this equation, it is evident that V̇_A is inversely correlated with PaCO₂. If V̇_A is reduced by 50%, and V̇CO₂ is unchanged (stable metabolism), PaCO₂ will double and vice versa. Pulmonary ventilation (V̇_E and V̇_A) in the resting state should match the CO₂ production at the basal metabolic rate, which may vary among animal species and breeds [60]. Because energy expenditure and basal metabolic rate are significantly higher at birth and progressively decrease as aging occurs [60], V̇_E and V̇_A are significantly higher in neonatal and pediatric patients than in adult animals. The clinical implication of higher V̇_E and V̇_A in younger patients is that respiratory depression caused by anesthetic agents can rapidly lead to severe hypercapnia and hypoxemia in these individuals.

Based on the second formula above (V̇_A = V̇_E – ), isolating V̇_E on one side of the equation shows that V̇_E is the sum of and V̇_A. However, during a single breath, gas exchange will depend on the fraction of V_T that goes beyond the , and effectively ventilates alveoli that are perfused. While both fractions of a V_T are useful to consider as independent variables, over time, there is some mixing between the gas in the and the alveolar gas due to diffusion of gases, a phenomenon facilitated by the movement created by the beating heart [61]. This “mixing” action probably explains why PaCO₂ levels are usually not all that elevated in smaller dogs or cats showing a very shallow tachypneic breathing pattern wherein V_T must be near . It probably also explains why insufflation of 15 L/min oxygen deep into the trachea in an apneic horse will maintain PaO₂ values in the 50–60 mmHg range (Dr. Wayne McDonell, personal observation).

Experimentally, has been evaluated in animals using several techniques that are influenced to varying degrees by pulmonary ventilation and perfusion abnormalities (V̇_A/Q̇ mismatch and shunt). As clinicians and researchers, it is important to consider the methodology and the factors influencing the measurement as it may alter the interpretation of the results [62–64]. Initial studies in humans measured using the single‐breath nitrogen washout test (Fowler’s technique), which involves plotting the partial pressure of nitrogen in expired gas of a single breath after a maximal voluntary inspiration of 100% oxygen [9,65]. However, the Fowler technique is technically challenging to perform in conscious animals due to the need for voluntary maximum inspiration.

Physiologic deadspace to tidal volume ratio (/V_T), which is the proportion of V_T that does not contribute to gas exchange, has been determined through application of the Bohr equation:

In this equation, P_ACO₂ represents mean alveolar CO₂ partial pressure and P_ECO₂ is the average CO₂ partial pressure in mixed expired gas collected during a single breath. Effectively, the greater the amount of gas from alveolar units that are ventilated and non‐perfused () that is added to the exhaled breath, the greater the reduction of P_ECO₂ below P_ACO₂, thereby indicating a greater proportion of deadspace ventilation in relation to V_T. However, before the advent of volumetric capnography, measurement of P_ACO₂ required complex methodology applicable only to the research setting (for example, multiple inert gas elimination technique) [25,66]. Therefore, PaCO₂ has been substituted for P_ACO₂ in the calculation (Bohr–Enghoff equation) as follows:

The presence of perfused non‐ventilated alveoli (shunt) or alveoli with low ventilation‐to‐perfusion (V̇_A/Q̇) ratio does not increase true ; however, the calculated /V_T ratio using the Enghoff modification of the Bohr equation is impacted by ventilation‐to‐perfusion inequalities caused by shunt and areas of low V̇_A/Q̇ ratio as these abnormalities will add CO₂‐rich mixed venous blood to arterial blood, increasing PaCO₂, and resulting in greater overestimation of /V_T by the Bohr–Enghoff equation. Specifically, any calculation that replaces P_ACO₂ with PaCO₂ will artificially increase the deadspace determination in the presence of poorly ventilated (low V̇_A/Q̇ ratio) and non‐ventilated alveoli (shunt) due to rising PaCO₂ levels, assuming constant V_T [62–64]. In patients with lower‐than‐expected PaO₂ values in relation to the F_IO₂, the impact of shunt and low V̇_A/Q̇ regions on gas exchange should be considered when applying these calculations to patient ventilatory management.

In addition to the Bohr–Enghoff /V_T, the alveolar deadspace fraction (/V_T), that is the fraction of V_T that ventilates non‐perfused alveoli, has been proposed to be estimated by replacing P_ECO₂ with P_ETCO₂ [67]:

Calculation of /V_T as described above will result in a significantly smaller deadspace value as it reflects only a fraction of total (physiologic) deadspace [62–64]. Under normal circumstances, P_ETCO₂ is up to 5 mmHg lower than PaCO₂ because of dilution of alveolar gas, which contains CO₂, with gas from deadspace which does not contain CO₂. As a simplification of the formula above, is considered to be increased if the arterial to end‐tidal CO₂ gradient (P(a‐ET)CO2) is abnormally high. In this case, because P_ACO₂ is replaced by PaCO₂, /V_T and P(a‐et)CO₂ will also increase in the presence of V̇_A/Q̇ mismatch caused by shunted flow and a low V̇_A/Q̇ ratio leading to oxygenation impairment, in a similar way as the Bohr–Enghoff /V_T [68]. Therefore, in the presence of the above‐described conditions, an increase in /V_T and P(a‐et)CO₂ reflects an increase in the scatter of V̇_A/Q̇ mismatch in the lung rather than only an increase in .

In the research setting, /V_T can be determined by collecting arterial blood gas samples to measure PaCO₂ as an equivalent to P_ACO₂ as well as collecting exhaled gases in a mixing chamber, or Douglas bag, to measure CO₂ in mixed expired gas (P_ECO₂) in large animals (horses and cows) and dogs [25,69]. More recently, with the introduction of volumetric capnography for monitoring patients during mechanical ventilation, /V_T can be more practically and reliably measured in intubated small animals [70]. Volumetric capnography is the graphic representation of expired CO₂ versus expired V_T measured using a capnograph and a pneumotachometer (device that measures flow over time) placed at the end of an endotracheal tube.

The diagram in Fig. 37.6A shows the composition of deadspace and its relationship with alveoli presenting different ventilation‐to‐perfusion ratios. If alveoli present an ideal ventilation‐to‐perfusion ratio (V̇_A/Q̇ = 1), an equilibrium is established between deoxygenated (mixed venous) blood with higher CO₂ content entering the pulmonary capillary and alveolar CO₂ (P_ACO₂). The mixed expired CO₂ in each tidal breath reflects the average CO₂ from alveoli that are effectively ventilated and perfused over a range of V̇_A/Q̇ ratios, which contribute to CO₂ elimination, and alveoli that are ventilated but not perfused (), which do not contribute to CO₂ elimination. An increase in , lowers CO₂ in mixed expired gas (P_ECO₂) and increases the gradient between P_ACO₂ (or PaCO₂ according to the Bohr–Enghoff equation) and P_ECO₂ [62–64].

The kinetics of CO₂ elimination assessed by the volumetric capnography curve has three distinct phases (Fig. 37.6B). Phase I represents exhaled gas from the upper airways, which does not contain CO₂. Phase II represents expired gas from the lower portions of the airways mixed with CO₂‐rich alveolar gas, which causes a rapid rise in CO₂. Phase III is the expired volume that represents pure alveolar gas as the CO₂ curve flattens and plateaus. The slope of phase III reflects the emptying of alveoli with different time constants. In patients with small airway disease/bronchoconstriction, or with lung disease, resistance to gas flow may differ substantially among alveolar units [71]. During expiration, alveoli where the conducting airways offer low resistance to gas flow empty first (“fast” alveoli), whereas poorly ventilated alveolar units due to increased resistance to gas flow take longer to empty. Because alveoli with different time constants differ in the speed they are emptied during expiration, the slope of phase III increases [71]. The area under the CO₂ curve represents the total amount of CO₂ exhaled during a single breath (V_TCO_2,br). The CO₂ eliminated per minute, which is assumed to be equivalent to CO₂ production per minute (V̇CO₂), is calculated by multiplying the respiratory rate (f) by the V_TCO_2,br.

The airway–alveolar interface, identified as the inflection point of phase II, is the limit between exhaled gas from lower conducting airways (bronchioles) and CO₂‐rich alveolar gas (Fig. 37.6C). The expired volume below and above the inflection point represents the airway deadspace () and the alveolar tidal volume (), respectively. The CO₂ level at the midpoint of phase III slope, starting at the inflection point and ending at the end‐tidal partial pressure of CO₂ (P_ETCO₂), represents the average CO₂ of all alveolar units (P_ACO₂) [64,66,72]. Studies measuring P_ACO₂ by the multiple inert gas elimination technique have validated P_ACO₂ measured by volumetric capnography [66,72].

The area above the volumetric capnography curve, which reflects deadspace ventilation, shows that ( + ) calculations based on the Bohr equation (Fig. 37.7A) are overestimated when PaCO₂ is used to replace P_ACO₂ in the Enghoff modification of the original formula (Bohr–Enghoff equation) (Fig. 37.7B).

In heathy individuals, is representative of as is negligible. In normal conscious humans at rest, is approximately 2 mL/kg (150 mL) and V_T is 6–7 mL/kg of ideal body weight (assuming a V_T of 450–500 mL in a 75 kg adult human), resulting in a /V_T ratio of approximately 30% [65]. Veterinary species in general have significantly larger deadspace volumes (indexed to body weight) than humans. Under normal conditions, remains relatively constant, however, V_T can change for a variety of reasons (e.g., thermoregulation, excitement, and acid–base disturbances) and therefore alter the relative amount of deadspace per V_T. As such, it is important to consider the deadspace volume as well as V_T indexed to ideal body weight, particularly as it relates to both anesthetic equipment and mechanical ventilation settings. In an experimental setting, unsedated normal tracheostomized dogs breathing quietly through a standard endotracheal tube had a of 5.9 mL/kg [17]. In conscious healthy horses and cows breathing through a face mask, the Bohr–Enghoff (calculated using a correction factor for the added deadspace represented by the facemask) was about 5.2 and 3.7 mL/kg [25]. Recent observations in anesthetized dogs receiving mechanical ventilation have confirmed that estimated by volumetric capnography is substantially larger in the canine species (6.5–7.6 mL/kg) than the calculated using the single‐breath nitrogen washout test (Fowler’s method) in humans (2 mL/kg) [65,69,70]. Although some of the measured differences in deadspace between humans and animals can be attributed to the use of the Bohr–Enghoff equation, which overestimates the /V_T ratio, the use of this method likely did not have a major influence because measurements were obtained under conditions where alveolar deadspace, shunt, and V̇_A/Q̇ mismatch were minimal (standing horses and cows, healthy conscious and anesthetized dogs) [73]. Because of differences in between animal species and humans, V_T settings during mechanical ventilation cannot be directly extrapolated from humans to animals, as discussed further in Chapter 38.

The relationship between V̇_E, V̇_A, and is critical to understanding the kinetics of CO₂ in both health and disease. Clinically, an increase in total deadspace volume () can be due to a change in (either physiologic due to bronchodilation or iatrogenic with artificial airways/apparatus deadspace) and/or . An increase in f with a reduction in V_T, and therefore the creation of a higher /V_T ratio, is extremely common in conscious animals for a variety of reasons, including thermoregulation. In healthy animals, V̇_A and as a result, PaCO₂ are maintained within physiological limits through central and peripheral chemoreceptor stimulation as previously discussed. In disease states, increases in commonly occur with low pulmonary perfusion pressures secondary to a low cardiac output (CO), pulmonary thromboembolism, severe airway disease, and acute respiratory distress syndrome (ARDS) [74–77]. An increase in does not necessarily impair arterial oxygenation (PaO₂) if the capillary flow that bypasses ventilated alveoli is perfusing well‐ventilated lung areas. PaCO₂ levels can also be maintained within normal levels when there is an increase in by increasing f or V_T to maintain V̇_A. Arterial blood gases (PaO₂ and PaCO₂) may therefore be maintained within normal ranges in awake spontaneously breathing animals with increases in . In patients with underlying disease and patients under general anesthesia, a compensatory increase in V̇_A in the face of increased may not occur. In these instances, PaCO₂ will rise due to a reduction in V̇_A. In addition to impacting PaCO₂ values, decreases in V̇_A associated with an increase in may also have an impact on a patient’s oxygenation by lowering the P_AO₂ if inspired gases are not enriched with oxygen (Table 37.5).

Pulmonary mechanics

Fluctuating pressure gradients between the airway opening and the alveoli cause air to flow in and out of the lungs. The factors that contribute to these pressure gradients and the measurement of their magnitude are referred to as “pulmonary mechanics.” During spontaneous breathing, a negative pressure gradient between the airway opening (mouth, nostrils, or the interface between the breathing circuit and the endotracheal tube) and the alveoli/pleural cavity is responsible for the inflow of gas to the lungs. In anesthetized patients, a mechanical ventilator is commonly used to create a positive pressure gradient between the airway opening (endotracheal tube) and the alveoli to generate flow of gases into the lungs during inspiration. Factors that influence the development of a pressure gradient between the airway opening and the alveoli include the elasticity of the lungs, thoracic cage, and diaphragm (chest wall), in addition to the resistance to flow between these two regions. These properties determine the normal distribution of airflow within the lung and the energy expended to achieve optimal ventilation (work of breathing). Both anesthesia and disease can alter the elastic properties and resistance of the respiratory system, impacting the ability to achieve adequate alveolar ventilation. While pulmonary physical characteristics are generally measured on the whole lung in the clinical setting, regional differences in physical properties are also important in determining normal distribution of ventilation.

Pressures measured in the respiratory system are illustrated in Fig. 37.8. By convention transpulmonary pressure (P_L) is the difference in pressure across the entire respiratory system, from the pressure at the airway opening (P_ao) to the pleural pressure (P_pl); however, intensive care specialists and anesthesiologists often define P_L as the difference between alveolar and pleural pressures (P_alv−P_pl), creating some confusion in the literature [10,78]. The pressure gradient from atmospheric pressure (taken as P_ao) to the pleural space (P_pl) is responsible for the movement of air to and from the lungs during spontaneous breathing. The P_ao is always 0 cmH₂O at 1 atmosphere throughout the respiratory cycle in non‐instrumented, conscious, and spontaneously breathing animals. With initiation of inspiration, as active muscular effort enlarges the pleural cavity through expansion of the thoracic wall and contraction of the diaphragm, P_pl becomes more negative and causes P_alv to become slightly sub‐atmospheric (negative). The slightly negative pressure gradient between P_ao (0 cmH₂O) and P_alv (e.g., −1 cmH₂O) drives airflow from the mouth/nostrils to the alveoli, and lung volume increases. In contrast to inspiration, expiration is normally passive and depends on the elastic recoil of the lungs, diaphragm, and intercostal muscles, which causes P_pl to become less negative and returns the lungs to a resting position, that is, to FRC. The horse is a notable exception in that abdominal muscle contraction plays a part in normal expiratory activity, producing a biphasic mode of exhalation. As the P_pl becomes less negative, P_alv may slightly increase above atmospheric pressure. Reversal of the pressure gradient during expiration (P_alv > P_ao) causes air to flow from the alveoli to the airway opening/atmosphere [49,79].

The pressure difference between the airway opening and the pleural space, P_L (Fig. 37.8), can be measured using a differential pressure transducer connected to the airway opening to measure P_ao (face mask or endotracheal tube) and to an esophageal balloon placed in the thoracic esophagus to provide a surrogate measure of P_pl. The change in lung volume (or V_T) can be measured using a spirometer, a body plethysmograph, or a pneumotachometer [10].

The pressure gradient between the alveoli and the pleural cavity (P_alv−P_pl) is traditionally defined as elastic recoil pressure of the lung (P_el(L)) (Fig. 37.8 and 37.9) [78]. In spontaneously breathing subjects, P_el(L) measured at the end of inspiration provides an estimate of the lung’s ability to deflate/return to its resting position (FRC). In anesthetized individuals receiving positive‐pressure ventilation, P_alv−P_pl provides an assessment of the positive pressure applied to the lung tissue per se, excluding the effects of the chest wall and abdomen [80].

In spontaneously breathing animals, the relationship between change in pleural pressure (∆P_pl) and the resultant change in lung volume (∆V) is known as “respiratory system compliance” (C_RS) or “total compliance” [9,61].

As shown by the formula above, C_RS describes the ability of the lungs to distend in response to a change in pleural pressure. Compliance provides a measure of how stiff the lung is and is inversely correlated with elastance, that is, the force causing the lungs to recoil to FRC. C_RS is also known as “total compliance” because both the lungs and chest wall (thoracic wall and diaphragm) provide an elastic resistance to lung expansion on inspiration. However, in spontaneously breathing animals, the contribution of the latter to the total respiratory system compliance is not captured when intrapleural pressures are measured due to the effort exerted by the inspiratory muscles. When the chest wall and diaphragm are partially or completely relaxed (and do not contribute any effort to breathing), however, as often occurs during general anesthesia, they become an important contributor to the elastic resistance to inspiration and total compliance (C_RS). During general anesthesia, the relationship of C_RS to the individual compliance of the lungs (C_L) and chest wall (C_CW) is additive, because the lungs and chest wall are arranged concentrically and can be expressed as:

During positive‐pressure ventilation, the pressure gradient that drives gas into the lungs is no longer negative and is determined by the difference between airway pressure measured at end‐inspiration and end‐expiration (∆P_aw). Therefore, in anesthetized patients receiving mechanical ventilatory support, C_RS is measured as the ratio between change in lung volume ∆V (that is the V_T delivered by the ventilator) and the change in airway pressure (∆P_aw) during a mechanical breath:

Prior to the advent of spirometry, in anesthetized patients receiving positive‐pressure ventilation, airway pressures at end‐inspiration and end‐expiration were used for pressure determinations, and ventilator settings (volume displaced by the bellows) were used for volume calculations. As further described in Chapter 38, with the use of modern anesthesia ventilators incorporating built‐in flow sensors (built‐in spirometry) or with the use of stand‐alone multiparameter monitors incorporating flow sensors that are placed between the endotracheal tube and the breathing circuit (near patient spirometry), more accurate determination of changes in volume and pressure can be obtained during mechanical ventilation [81,82]. The difference in how C_RS is measured in spontaneously breathing versus animals receiving positive‐pressure ventilation is an important concept for the veterinary clinician as the contribution of the different components (lung and/or chest wall) to total compliance needs to be considered when interpreting values and when implementing ventilatory support strategies.

Compliance is further characterized as either dynamic, static, or quasistatic. In spontaneously breathing animals, dynamic compliance describes changes in lung volume per unit change in pleural pressure in the presence of airflow. If the patient is receiving mechanical ventilation in a volume‐controlled mode without an inspiratory pause (period of zero flow at the end of inspiration), then dynamic compliance is measured as the change in lung volume per unit change in airway pressure (peak inspiratory pressure minus end‐expiratory pressure) (Fig. 37.10A). Dynamic C_RS is altered by changes in the elastic properties of the respiratory system and by changes in airway resistance (R_aw). Static and quasistatic C_RS describes changes in lung volume per unit change in pressure during a brief pause at end‐inspiration (zero airflow). Because patient cooperation is required, static compliance measurements are often performed in anesthetized animals receiving mechanical ventilatory support with an inspiratory pause (Fig. 37.10B) [30,83–85]. The pause at end‐inspiration, before passive expiration begins, must be long enough to allow airflow to equilibrate between alveoli with faster and slower filling rates, the latter reflective of areas with heightened resistance to airflow that may be increased during pathological conditions (e.g., bronchitis/pneumonia in small animals and small airway disease in horses) [84,85]. If the duration of the inspiratory pause is between 0.5 and 2 s, frictional resistance imposed by the airways may impact measurements in humans; therefore compliance measurements are better defined as quasistatic [84,85]. Once gas flow distribution has been completed, that is, the resistive properties of the respiratory system are overcome, the ratio between V_T and the change in airway pressure (plateau minus end‐expiratory pressure) reflects solely the elastic properties of the respiratory system (static or quasistatic C_RS) (Fig. 37.10C). Lungs develop low static compliance (become stiffer) with a reduction in lung volume, such as occurs with regional atelectasis, pulmonary edema, or fibrosis. In the case of dynamic compliance, increases in R_aw can contribute to decreases in compliance measurements. For example, asthma (heaves, recurrent airway obstruction) in horses and asthma (bronchopulmonary disease) in cats decreases dynamic lung compliance via increased R_aw [86,87].

As previously mentioned in this section, for gas to flow into the lungs, a pressure gradient must be developed to overcome, in addition to the elastic resistance, the nonelastic resistance of the respiratory system. The relationship between the pressure gradient and gas flow illustrated in Fig. 37.11A is analogous to a fundamental principle of physics, referred to as Ohm’s law, wherein voltage (equivalent to pressure gradient along a tube) is proportional to current (equivalent to gas flow) multiplied by resistance [88].

Or in terms of gas flow:

Rearranging Ohm’s law to determine resistance:

According to the Hagen–Poiseuille equation, laminar gas flow through an unbranched straight tube is proportional to the pressure gradient across the tube and the fourth power of the radius of the tube, and inversely proportional to the viscosity of the gas and length of the tube:

By combining Ohm’s law and the Hagen–Poiseuille equation (substituting Hagen–Poiseuille’s determinants of flow into Ohm’s law), the resistance to laminar gas flow can be established:

Resistance to laminar flow therefore increases with an increase in the tube length or a reduction in tube radius. The significance of this equation for the anesthetist is the impact of the diameter of a patient’s airway on the resistance to gas flow. An increase in resistance can result from a variety of conditions such as bronchospasm, congenital or acquired anatomic abnormalities in the airway, and/or the presence of mucus, exudates, foreign bodies, or tumors within the airway lumen [89,90]. If a narrow endotracheal tube is used in a patient with an already increased airway resistance due to respiratory disease (e.g., tracheal collapse or brachycephalic airway syndrome), there may be a dramatic increase in resistance to airflow during anesthesia with spontaneous ventilation. For example, if the diameter of the upper airway is reduced by 50% due to pathology or secondary to the placement of a small endotracheal tube, the R_aw goes up 16‐fold. Of note, with laminar flow, viscosity is the only gas property to influence resistance.

While the above relationship between gas flow, pressure gradient, and resistance is valid during laminar flow, when flow rate exceeds a critical velocity, it becomes turbulent as gas molecules swirl and turn in a chaotic pattern rather than in an orderly manner. In this circumstance, the relationship between the pressure gradient as gas flows through a straight tube (∆P) and the flow rate is no longer linear. Fig. 37.11B shows the physics of turbulent flow. In this case, ∆P will depend on gas density and the squared flow as follows [89,90]:

With turbulent flow, the change in pressure is inversely proportional to the fifth power of the radius of the tube (Fanning equation); therefore, airway radius has an even greater impact on air flow than with laminar flow [91]. In a straight unbranched tube, the transition from laminar flow to turbulent flow can be estimated by the Reynold number (Re), a nondimensional number that is derived from gas velocity, tube diameter, gas density, and gas viscosity.

As the Reynolds number increases above 2000, air flow becomes progressively more turbulent. While airway resistance and its determinants are generally explained in terms of laminar flow, the structure of airways results in a mix of laminar and turbulent flow in the major airways. In addition to the variables included in calculating the Reynolds number, branching and/or irregularities in the tube predispose to turbulent flow. In general, resistance to gas flow is significantly greater with turbulent flow relative to laminar flow and turbulent flow is dependent on gas density and not viscosity. Because flow may become turbulent during pathological conditions that include narrowing/partial obstruction of the airways, incorporating helium, a gas with less density relative to oxygen or air, as a carrier gas with oxygen (mixture of 70% helium and 30% oxygen) may reduce resistance to gas flow [92,93]. As gas flow is usually laminar in the distal airways (and therefore not influenced by gas density), helium, which has a viscosity similar to air, may be less useful in animals with mild‐to‐moderate bronchoconstriction of the distal airways but it may have a positive impact in the presence of severe bronchospasm affecting the whole bronchial tree, as gas flow is likely turbulent under these circumstances [89]. In anesthetized horses, an alveolar recruitment maneuver with a mixture of 70% helium and 30% oxygen increased dynamic C_RS and improved pulmonary oxygen exchange (decreased P(a‐a)O₂) when compared to 100% oxygen [93]. However, dynamic C_RS is altered by the resistive and elastic properties of the respiratory system, and it remains to be demonstrated that the use of helium as a carrier gas would improve pulmonary mechanics by reducing resistance to gas flow in horses [93].

During spontaneous ventilation, the relationship between the pressure gradient across the respiratory system during inspiration, that is, the pressure at the airway opening (P_ao) minus the pleural pressure (P_pl) and the rate of inspiratory airflow (usually expressed in liters per second, L/s) is known as R_aw (expressed in cmH₂O/L/s) [61,79].

Airway resistance can be calculated during mechanical ventilation if using a volume‐controlled mode with an inspiratory pause during anesthesia (Fig. 37.10D). Considering that plateau pressure (P_plat) recorded at the end of an inspiratory pause is the pressure that reflects the elastic properties of the respiratory system, while peak inspiratory pressure (P_peak) is the pressure that is necessary to overcome both the frictional resistance imposed by the airways (resistance) and the elastic properties of the respiratory system, R_aw is calculated as the gradient between P_peak and P_plat, divided by the flow rate [84,85]:

In conscious animals, measurement of R_aw can be obtained by simultaneous determination of instantaneous airflow with a pneumotachometer connected to the airway opening (mouth or nostrils) via a facemask and of the gradient between P_ao and P_pl (estimated by an esophageal balloon catheter), using a differential pressure transducer. The upper airways including the nasal cavity, pharynx, and larynx are major determinants of resistance to airflow within the respiratory system, generally contributing over 50% of the total R_aw [79]. Due to the extensive branching of the airways and dramatic increase in total airway area toward the periphery of the lung, despite the narrow radius, airflow velocity in bronchioles is very low and follows a laminar pattern. Therefore, the relative contribution of the small airways and bronchioles to total R_aw is low (< 10%) unless marked lower airway disease/bronchospasm is present [79]. As with lung compliance, resistance to airflow changes with lung volume. As lung volume decreases, R_aw increases, with dramatic increases occurring at lung volumes below FRC.

Presence of turbulent flow and increased R_aw directly impact the work of breathing, which is the energy spent by respiratory muscles (measured in joules) for air to flow in and out of the lungs. Work of breathing is measured as the product of pressure changes across the respiratory system (P_ao − P_pl in spontaneously breathing animals) and the volume of gas moved (V_T) [89,90]. Because inspiration is an active process that involves contraction of the diaphragm and chest wall muscles, most of the work done occurs during inspiration [89,90]. Respiratory work is further divided into elastic work (required to overcome the recoil of the lung) and resistive work (required to overcome the frictional opposition or resistance to airflow) [89,90]. As is discussed in Chapter 38, turbulent flow and increased R_aw are likely to be present in dogs with brachycephalic airway syndrome or collapsed trachea and horses with severe bronchospasm secondary small airway disease (heaves). The consequent increase in the respiratory work may lead to fatigue of inspiratory muscles, therefore, mechanical ventilatory support may be required in these patients.

Distribution of ventilation

The distribution of inspired gases during inspiration is not completely homogenous throughout the lung, with gravity playing a major role in regional pulmonary ventilation. Specifically, due to the weight of the lung in the thorax, P_pl is more negative (sub‐atmospheric) in the uppermost part of the thorax relative to the lowermost portion and the negative pressure gradient between the alveoli and the pleural cavity (P_alv − P_pl) is greater in dorsal lung compared to ventral lung areas. Therefore, the average alveolar size is larger in the uppermost areas and smaller in the lowermost areas of the lung at end‐expiration (Fig. 37.12A) [94,95]. Since larger alveoli have lower compliance (they are less distensible), they expand less on inspiration, and air preferentially enters the more compliant lowermost alveoli (Fig. 37.12B), producing a vertical gradient of ventilation distribution in standing animals breathing quietly [96–98]. This tendency for preferential ventral ventilation in the lung may also be associated with regional chest wall and diaphragmatic movement. During anesthesia, the distribution of ventilation becomes more uneven and may even reverse so that the uppermost lung of a laterally recumbent horse is receiving most of the ventilation.

Local resistance to air flow and compliance are the two major determinants of regional distribution of ventilation [79] (Fig. 37.13). Alveoli within regions with normal resistance and compliance completely fill during slow and fast tidal breathing, while alveoli that are poorly complaint due to inflammation/fluid accumulation in the interstitium (e.g., in pneumonia) only partially fill during inspiration. If there is increased resistance to airflow due to narrowing of the small airways caused by mucus, bronchoconstriction, or foreign material, these alveolar units take longer to fill and empty during tidal breathing and are referred to as “slow” alveoli. Slow alveoli also tend to be under‐distended during inspiration (less ventilated than perfused), especially at faster respiratory frequencies [79]. Slow alveoli contrast with alveoli that completely fill regardless of the breathing pattern (“fast alveoli”). Uneven distribution of ventilation, leading to areas of low V̇_A/Q̇ and gas exchange impairment (lower‐than‐expected PaO₂ values) occur in lung disease due to areas with poor compliance or increased resistance to airflow.