Work, Power, and Energy Expenditure in the Respiratory System

In simple intuitive terms, the variable that best sums up the function of a muscle-powered pump is the mechanical load that the contraction of the powering muscles must overcome with each pump cycle. Over time, mechanical load translates into power (the product of work by the time that it takes to carry it out) and energy expenditure. Accordingly, whether the respiratory muscles can carry a given mechanical load is ultimately determined by their ability to generate work from the limited amount of energy that they receive from their blood supply. The first law of thermodynamics stipulates that when a certain amount of energy is added to a closed system by an external source (in this case the metabolism of fuels supplied by the circulation to the respiratory muscles), the resultant change in the system’s internal energy may either be applied to perform external work (W) over a period of time (t) or is dissipated as heat (Q). Implicit in this statement is the fact that only a portion of the energy that the respiratory muscles derive from metabolic substrates is transformed into respiratory work. This proportion varies depending on the system’s efficiency (E), defined as:

(1)

Thus workload and efficiency define the demands that the contractile machinery of the respiratory muscles must meet and therefore are the relevant variables in the analysis of the mechanical function of the respiratory system.

Determinants of Respiratory Work

Every high school physics student learns to calculate the external work done to move an object between two points as the product of the force needed to overcome all resistances to the movement by the distance between the points. Because the force may change along the way, the same student may learn at some point that it is more precise to break the movement into many elementary components and then add up all the work components by integration, as shown in Figure 42-1, A.

Figure 42–1 A. The amount of work that a force (F) must perform to move an object over a linear distance s is equivalent to the product F × s. If the force varies during the displacement, then it is more precise to integrate the product of F by the change in s (ds). B. The work needed to produce a volume displacement V in a syringe, a better analogy for the respiratory pump, is determined as the integral of the product of the pressure inside the pump (the tridimensional analog of F) by dV (the tridimensional analog of ds).

The calculation of the external work during breathing follows the same general principle, with one caveat: allowances must be made for the fact that the lungs and the chest wall move in all the dimensions of space. In other words, their displacements are measured in terms of volume, not distance, and determined by pressure, not force.

The mathematical subtleties of this distinction may become a little clearer if we compare the breath to the action of a syringe, where, by pushing or pulling on the plunger, we create a pressure (P), positive or negative, that has the effect of changing the volume contained in the barrel (V). The work done in this process can be determined by integrating the product P · dV, as shown in Figure 42-1, B. The obvious corollary is that the work done by the respiratory muscles and, by extension, the energy that must be supplied to these muscles are both defined by the volume-pressure relationships of the lungs and the chest wall.

Volume-Pressure Relationships

Before analyzing the volume-pressure behavior of the various components of the respiratory system, it is helpful to clarify the terminology. Throughout this chapter, the term “thorax” is used in reference to all the moving components of the respiratory system, including the walls of the thoracic cavity (the skeletal rib cage and its soft attachments), the abdomen, and the lungs themselves. Similarly, the term “chest wall” is used to indicate all the structures that form the enclosure of the lungs, including the thoracic wall, the diaphragm, the abdominal wall, and the abdominal organs.

The volume changes of the respiratory system can be easily measured with the help of devices such as spirometers or plethysmographs. For any breath, the thorax (defined by the suffix TH), the lungs (L), and the chest wall (W) all undergo the same change in volume, or:

(2)

The reason for this identity is the existence of a noncompressible and nonexpandable boundary, the pleural space, which links lungs to chest wall and prevents them from changing volume independently of each other.

The pressures needed to inflate the thorax, the lungs, and the chest wall are, however, different from each other. Respiratory physiologists have traditionally approached the analysis of these pressures by taking an imaginary walk from the mouth down the airways to the alveolus, across the lung tissue and visceral pleura to the pleural space, and finally across the chest wall to the surface of the chest (Figure 42-2). The difference between the pressures measured at two consecutive stops is the driving pressure needed to cause or maintain a certain volume displacement:

Figure 42–2 Schematic representation of the thorax demonstrating the relevant pressure gradients generated during breathing (these are the gradients that one would encounter during an imaginary walk from the mouth, through the airways, and across the walls of the lungs and the chest wall). The difference (P_AW) between the pressure at the mouth (P_M) and the pressure at the alveoli (P_A) drives gas flow between the airspaces and the atmosphere. The transpulmonary pressure (P_L) is the pressure that distends the lungs and is calculated as the difference between P_A and pleural pressure (P_pl). The transmural pressure of the chest wall (P_W) is the effective pressure distending the rib cage and abdomen defined as the difference between P_pl and atmospheric pressure (P_B). The transmural pressure of the thorax as a whole (P_TH) is the difference between P_A and P_B.

(3)

(4)

(5)

where P_AW is the pressure gradient across the airways, P_M the pressure measured at the mouth (or, for that matter, at the connector of an endotracheal tube), P_L the lung transmural pressure or transpulmonary pressure, P_W the chest wall transmural pressure, P_A the alveolar pressure, P_pl the average pressure at the pleural surface, and P_B the atmospheric pressure (conventionally considered to be zero or reference).

Consider first a situation in which the lungs undergo passive distention, without participation of the respiratory muscles. This is what happens during positive airway pressure ventilation, when the pressure drive for inflation of the thorax is provided by P_M. By performing a series of substitutions in equations 3through 5 and assuming P_B = 0, we can easily arrive to the following equality:

(6)

which reveals that, from a mechanical point of view, the components of the respiratory system form a series arrangement, whereby the total pressure needed to generate a movement is the sum of the pressures generated in the airways, the lungs, and the chest wall. Respiratory physiologists have often borrowed from electrical theory, assuming, perhaps to the dismay of many readers, that the black and white simplicity of electrical circuitry is less intimidating than the complexities of Newtonian mechanics. When speaking of electrical circuits, the term series indicates that every element in the circuit experiences the same current as the circuit as a whole, but the total voltage across the circuit is the sum of the voltages across the individual elements. Because current is the electrical analog of flow (volume per unit of time) and voltage is the analog of pressure, it is easy to see how Equations 2 and 6 justify the overall electrical analogy, even though many readers may be less impressed by how much conceptual clarity it sheds for them.

The mechanical behavior of the airways and the lungs does not change substantially during muscle-powered breathing. The behavior of the chest wall, on the other hand, is greatly influenced by the contraction of the respiratory muscles. Because the muscles not only act on the wall but are also part of the wall itself, any attempt to define mathematically the behavior of the chest wall during a spontaneous breath becomes a futile exercise. For our purposes here, however, it may suffice to say that, during spontaneous breathing, equation 6 can be modified as:

(7)

where P_mus represents the pressure generated by the muscles’ contraction, inclusive of the effects that this contraction has on the behavior of the chest wall itself. Thus every time we take a breath, the neural output to the respiratory muscles is adjusted to overcome as precisely as possible the opposing pressures generated by the respiratory system.

Nature of the Mechanical Forces Acting on the Respiratory Pump

Volume changes within the respiratory system are dictated primarily by the body’s need to take up oxygen and eliminate carbon dioxide and therefore are determined by factors such as physical activity or metabolic rate, which are relatively independent of the condition of the lungs and chest wall. Pressure changes, on the other hand, depend on physical processes that take place in the respiratory system’s constituents. For instance, elastic pressures result primarily from the tendency of tissue components such as collagen and elastin fibers to recover their original shape after being stretched during lung inflation. Airway resistive pressures relate to friction and overcome the adherence of the moving gas molecules to the airway walls (viscous pressures) and, to a lesser extent, compensate for the loss in gas kinetic energy at points where the movement and direction of the gas vary randomly (turbulence). Tissue-resistive pressures are applied primarily to produce molecular rearrangements in the tissue and at the gas/liquid alveolar interface as the lungs inflate and deflate. Finally, inertial pressures derive from the acceleration and deceleration of the gas and tissue contained in the thorax during breathing. (Inertial pressure losses are negligible in children during normal breathing and therefore need no more than a passing reference here.)

Disease induces alterations in these physical processes and therefore also in the forces and pressures that result from them. To relate these alterations to the disease’s clinical manifestations, it is helpful to classify both processes and pressures into nondissipative and dissipative, depending on whether the energy consumed stays in or leaves the system. For instance, elasticity is typically a nondissipative process because the energy needed to produce elastic deformation during inspiration is accumulated in the tissues and then used to empty the lungs during expiration. In contrast, all resistive processes are dissipative: the energy liberated by the friction of the gas against the airway walls or by the molecular interactions within the tissue is transformed into heat and transported outside of the system by the blood or the expired gas.

Nondissipative Phenomena: Elastic Behavior of the Respiratory System

Elastic pressures result from the tendency of the components of the lungs and chest wall to recover their original shape after undergoing deformation. Because this tendency increases proportionally to the magnitude of the deformation, elastic pressures are volume-dependent. Thus they are most easily studied when the volume of the thorax is kept constant, a situation in which the absence of movement renders all resistive pressures irrelevant. This can be accomplished by inflating the lungs passively to the desired level or by asking the subject to inspire to a given volume and then to close the glottis while relaxing the respiratory muscles (something that a trained individual can do). In such circumstances, P_AW = 0, and

(8)

By obtaining measurements at various volumes and then plotting volume against P_A, P_L, and P_W, we can compare the volume-pressure relationships of the thorax as a whole with those of the lungs and the chest wall. Not unexpectedly given the heterogeneous composition of the structures involved, the relationships are complex and cannot be described in a simple mathematical equation (Figure 42-3). In all three cases, the plotted curve has a sigmoidlike shape, with pressure increasing rapidly relative to volume at low and high volumes and more slowly at middle volumes.¹

Figure 42–3 Idealized representation of the static volume-pressure relationships of the thorax (TH), lungs (L), and chest wall (W). Pressure, on the abscissa, represents the pressure across the thorax as a whole (P_TH = P_A – P_B), lungs (P_L = P_A – P_L), and chest wall (P_W = P_pl – P_B; see Figure 42-2). The arrows indicate the magnitude and direction of the pressures acting on the thorax and its components at two volumes: (1) the relaxation volume of the thorax, where the recoils of the lung and the chest wall neutralize each other; and (2) an arbitrary volume where the recoils of the lungs and the chest wall act both in the direction of reducing thoracic volume. Inset: Detail of the same curves, indicating the elastic work done on the thorax as a whole and each of its components for a volume displacement starting at a volume A (the relaxation volume of the thorax) and ending at a volume C. The work done on the thorax as a whole is represented by the area A-B-C; the work done on the lungs by A-A_L-B_L-C; and the work done on the chest wall by A_W-A-B_W-C. A portion of the work done on the chest wall (the triangular area in purple between A_W and the ordinate axis) is contributed by the recoil of the chest wall, which between those points facilitates the action of the respiratory muscles.

Being a continuous function, each volume-pressure relationship has a defined slope at any given volume (dV/dP). This slope defines the compliance of the thorax, lungs, or chest wall for that particular volume, depending on whether dP is replaced by dP_A, dP_L, or dP_W. Although a cursory examination of Figure 42-3 reveals that both the lung and chest wall compliances defined in this manner vary markedly over the entire range of volumes, on closer inspection, the ratio dV/dP is relatively constant at normal breathing volumes. Thus for these volumes, it is safe to write:

(9)

where ΔP_el represents the change in elastic recoil pressure of the thorax (ΔP_A), lungs (ΔP_L), or chest wall (ΔP_W) for a lung volume excursion ΔV, and C is the compliance of the corresponding component. As lung volume decreases or increases beyond this linear range, dV/dP starts to decrease in a volume-dependent manner, and the respiratory muscles must generate progressively larger pressures to produce the same volume change. Disease frequently causes the lungs to operate outside of their linear volume-pressure range, thereby increasing both the work of breathing and the energy needed to do it.

At any given volume, the lungs, the chest wall, and the thorax each generate a certain elastic pressure or recoil. This recoil can act to increase or decrease volume (as indicated by the direction of the arrows in Figure 42-4). By definition, elastic recoil drives the thorax and its individual components to adopt a volume, known as the relaxation volume, at which recoil itself is extinguished. The relaxation volumes of the lungs and the chest wall are the volumes that each of these components would adopt if all the mechanical constraints imposed by their mutual attachments and interactions were removed. The relaxation volume of the thorax, in contrast, is defined by the mechanical interaction of the lungs and the chest wall. It coincides with the point at which the opposing elastic recoils of these two components neutralize each other (as shown by the equal magnitude but opposite pressure vectors in Figure 42-4).

Figure 42–4 Idealized volume pressure relationships illustrating the differences in the elastic behaviors of the infant and adult thoraxes (normalized for vital capacity). The difference between the two points (labeled 1) highlights the effect of maturation on the relaxation volume of the thorax. In the infant the chest wall is considerably more compliant than in the adult and, as a result, the opposite recoils of the lungs and the chest wall neutralize each other at a lower relaxation volume. Thus infants tend to have a lower functional residual capacity (FRC) than do adults. At volumes higher than the relaxation volume of the chest wall, the recoils of the lungs and the chest wall act in the same direction, opposing further increases in volume (as highlighted here at vital capacity, labeled 2).

In the adult, the relaxation volume of the lungs is lower than the residual volume (the volume of gas contained in the lungs at the end of a forced expiration). The relaxation volume of the chest wall, by contrast, exceeds 50% of the vital capacity (the maximal volume of gas that can be inhaled from residual volume). This discrepancy in the relaxation volumes of the lungs and chest wall has three important consequences. First, it forces the relaxation volume of the thorax as a whole to occupy a position intermediate between the relaxation volumes of the lungs and the chest wall (at approximately 35% of vital capacity). Under most circumstances, this volume coincides with the functional residual capacity (FRC), which is the volume contained in the lungs at the end of a tidal expiration. Second, as the thorax starts to rise above its relaxation volume during inspiration, the outward recoil of the chest wall contributes to the expansion of the lungs, thereby reducing the work that the respiratory muscles need to perform during normal breathing (see Figure 42-3, inset, where the work done by the chest wall at the beginning of a breath is represented by W_W). Finally, at normal breathing volumes, the opposing actions of the lungs and chest wall recoils create a negative pressure at the boundaries of the lung tissue with the chest wall and the other intrathoracic structures. This negative pressure is an important contributor to the return of venous blood to the chest. The static volume-pressure relationships of the lungs and chest wall vary depending on their state of maturation and health (see Figure 42-4). In the infant, the chest wall generates remarkably little outward recoil within the normal range of breathing volumes.^2–5 Because the inward recoil of the lungs varies little with respect to lung size and age during development,^6–8 the relaxation volume of the infant’s thorax is proportionally smaller than that of the adult (as shown in Figure 42-4 by the lower intercept of the volume-pressure relationship of the thorax and the ordinate axis). If, as occurs in the adult, the FRC coincided with this relaxation volume (15% of vital capacity compared with 35% in the adult), then the infant would be at a definite disadvantage in terms of alveolar stability and oxygenation. The newborns of most mammalian species, however, have developed physiologic strategies to maintain their FRC above the relaxation volume of the thorax.⁹ These strategies are generally directed at interrupting expiratory flow before expiration is complete and include shortening of the expiratory time,¹⁰ contraction of adductor muscles of the glottis to retard exhalation,^11,12 and persistence of the tonic activity of the inspiratory muscles during expiration.¹³ Being so dependent on the pattern of breathing, the FRC of the newborn and small infant is very vulnerable to changes in muscle coordination and tone. As an example, the decrease of tonic activity of the respiratory and laryngeal muscles associated with rapid eye movement sleep¹³ may cause a substantial reduction in thoracic lung volume at these ages. Similarly, muscle weakness, anesthesia, deep sedation, and central nervous system depression in general tend to lower FRC below levels compatible with alveolar stability. Under such circumstances, alveoli close, and both the shunt fraction and the work of breathing increase.

In addition to its effects on the FRC, the reduced outward recoil of the chest wall in the infant reduces the chest wall’s contribution to lung expansion. It also limits the amplitude of the pleural pressure variations as the lungs expand, an effect that helps to explain the surprising cardiovascular tolerance of many infants to the application of high levels of positive airway pressure.

Lungs/Chest Wall Interactions

Although, considered in isolation, the lungs and the chest wall have different volume-pressure relationships, their mechanical linkage at the pleural space prevents them from changing volume independently. By sharing a common boundary, the lungs and chest wall are also influenced simultaneously by variations in the pressure at this boundary. The resultant interplay is well illustrated by the effects of a pneumothorax, a complication that is quite familiar to readers who practice intensive care medicine. When a certain volume of air enters the pleural space, the most immediate effect is an increase in the pleural pressure (ΔP). This increase causes the effective transmural pressures of the lungs and chest wall to change by the same absolute amount, but in opposite direction: transpulmonary pressure (P_A − P_pl) decreases by -ΔP, whereas chest wall transmural pressure (P_pl) increases by ΔP. No longer held together by a rigid boundary, the lungs and the chest wall respond to the change in transmural pressure by decreasing and increasing volume along their respective volume-pressure relationships (Figure 42-5). Consequently, one could say that the volume of air originally introduced in the pleural cavity is partitioned into two components, one the volume by which the lungs collapse and the other the volume by which the chest wall expands. The relative sizes of the lung collapse and the chest wall expansion are dictated by the volume-pressure relationships of the lungs and chest wall. If the compliance of the chest wall exceeds the compliance of the lungs (as is usually the case in the infant), then the chest wall expands more than the lungs collapse. The difference is even greater when lung compliance is reduced by disease (Figure 42-5, B). Then the chest wall absorbs the majority of the volume change while the lungs barely decrease their volume. This simple analysis explains why noncompliant lungs show surprisingly little collapse when a pneumothorax develops, a finding that is often mistakenly attributed to the “stiffness” of the lung parenchyma. It also provides an opportunity to point out that the magnitude of the chest wall expansion, although frequently overlooked in radiographs, relates more directly to the true malignancy of a pneumothorax (compression of vascular structures) than does the usually more apparent collapse of the lungs.

Figure 42–5 A, The effects of a pneumothorax are used here to illustrate the interdependence between the elastic recoils of the lungs and the chest wall. Pressures, on the abscissa, represent the transmural pressures of the lungs (L, P_A – P_pl, see Figures 42-2 and 42-3) and chest wall (W, P_pl – P_B). The introduction of a volume of gas into the pleural space raises pleural pressure by a magnitude ΔP, which changes both transmural pressures by the same absolute magnitude, but in opposite directions. Lungs and chest wall respond to the change in transmural pressure by decreasing (C→D) and increasing their volume (A→B) along their respective volume-pressure relationships. The volume of the pneumothorax is thus partitioned between the lungs and the chest wall according to their relative compliances. B, When lung compliance is decreased by disease, the volume pressure relationship of the lungs is displaced to the right and has a lower slope. Under these circumstances, the chest wall is forced to accommodate the majority of the volume change introduced by the pneumothorax (AB >> C’D’), giving perhaps the wrong impression that the stiffness of the lungs prevents them from collapsing further.

One important idea to emerge from these considerations is that, respiratory muscle activity aside, the pressure inside the pleural space is really determined by the elastic recoil of the chest wall and the volume of the thoracic contents. As long as lung volume is not forced above its normal range and chest wall compliance is unaltered by disease, pleural pressure (and thus the pressure around the major vessels and the heart) remains low, regardless of the airway pressures. Conversely, excessive lung distension (e.g., in asthma) is always associated with a high pleural pressure and is, for that reason, less well tolerated from a cardiovascular point of view. The dependence of pleural pressure on chest wall compliance explains why premature infants and newborns, who have very large chest wall compliance, have limited changes in this pressure during positive pressure ventilation, even if physiologic lung volumes are exceeded. Disease-induced reductions in chest wall compliance, on the other hand, always increase pleural pressure and reduce venous return to the heart. This is one reason why patients with abdominal distension typically have low cardiac output and why relief of the distension (e.g., by paracentesis in patients with ascites) reduces pleural pressure and increases cardiac output.

Dissipative Forces