Alveolar Ventilation

Alveolar ventilation is the exchange of gas between the alveoli and the external environment. It can be measured as the volume of fresh air entering (and leaving) the alveoli each minute. Oxygen from the atmosphere enters the lungs through this ventilation and carbon dioxide from the venous blood returns to the atmosphere. Physicians and biomedical engineers often discuss alveolar ventilation in terms of standard lung volumes. These standard lung volumes are represented graphically in Fig. 3.2.

3.3.1 Tidal volume

Tidal volume (TV) is the volume of ambient air entering (and leaving) the mouth and nose per minute during normal, unforced breathing. Normal tidal volume for a healthy, 70-kg adult is approximately 500 mL per breath, but this value can vary considerably during exercise.

3.3.2 Residual volume

Residual volume (RV) is the volume of air left in the lungs after maximal forced expiration. This volume is determined by a balance between muscle forces and the elastic recoil of the lungs. Residual volume is e m4

Total lung capacity

Total lung capacity

Functional residual Residual capacity volume

Functional residual Residual capacity volume

Figure 3.2 Standard lung volumes as measured by a spirometer.

approximately 1.5 L in a healthy, 70-kg individual. Residual volume is much greater for individuals with emphysema.

3.3.3 Expiratory reserve volume

Expiratory reserve volume (ERV) is the volume of air expelled from the lungs during a maximal forced expiration that begins at the end of normal tidal expiration. The expiratory reserve volume plus the reserve volume combine to make up the functional reserve capacity. Normal ERV for our standard 70-kg individual is approximately 1.5 L.

3.3.4 Inspiratory reserve volume

Inspiratory reserve volume (IRV) is the volume of air that is inhaled during forced maximal inspiration beginning at the end of normal tidal inspiration. This volume depends on muscle forces and also on the elastic recoil of the chest wall and the elastic recoil of the lungs. The IRV of a healthy 70-kg individual is approximately 2.5 L.

3.3.5 Functional residual capacity

Functional residual capacity (FRC) is the volume in the lungs at the end of normal tidal expiration. FRC depends on the equilibrium point at which the elastic inward recoil of the lungs balances the elastic outward recoil of the chest wall. Functional residual capacity consists of the sum of the residual capacity and the expiratory reserve volume and can be represented by Eq. (3.1). The FRC of a healthy 70-kg adult is approximately 3 L.

3.3.6 Inspiratory capacity

Inspiratory capacity (IC) is the volume of air taken into the lungs during a maximal inspiratory effort that starts at the end of a normal tidal volume expiration. Inspiratory capacity is the sum of TV and IRV and can be represented by Eq. (3.2). The IC of our healthy, 70-kg, adult is about 3 L.

3.3.7 Total lung capacity

Total lung capacity (TLC) is the volume of air in the lungs after a maximal expiratory effort. The strength of contraction of inspiratory muscles, the inward elastic recoil of the lungs, and the chest wall determine the total lung capacity. The total lung capacity is also equal to the sum of the inspiratory reserve capacity, the tidal volume, the expiratory reserve capacity, and the reserve volume. Atypical value for total lung capacity of a healthy 70-kg male is about 6 L. An equation representing the total lung capacity may be written by:

3.3.8 Vital capacity

Vital capacity (VC) is the volume of air expelled from the lung during a maximal expiratory effort after a maximum forced expiration. The vital capacity is the difference between the total lung capacity and the reserve volume. Vital capacity in a normal healthy 70-kg adult is about 4.5 L. Equation (3.4) is for vital capacity:

3.4 Ventilation—Perfusion Relationships

Ventilation is the act of supplying air into the lungs and perfusion is the pumping of blood into the lungs. In this book we will use V to represent the air flow rate associated with ventilation and Q to represent the blood flow rate associated with perfusion. The ratio of ventilation to perfusion is important for lung function and is represented as the ventilation/perfusion ratio as shown in Eq. (3.5).

Ventilation perfusion ratio = V (3.5)

Pulmonary arterial smooth muscle vasoconstricts the vessels of the pulmonary capillary beds in response to hypoxia, or low oxygen. This type of vasoconstriction is one of the most important parameters that determine pulmonary blood flow. In other capillary beds within the body, smooth muscle vasodilates in response to tissue hypoxia, improving perfusion.

Resting ventilation is about 4 to 6 L/min. Resting pulmonary artery blood flow is about 5 L/min. At rest, therefore, the ventilation/perfusion ratio is about 0.8 to 1.2. Figure 3.3 shows a schematic representing a ventilation/perfusion ratio of 1 with a ventilation rate and perfusion rate both equal to 5 L/min.

Tidal volume 500 ml

Anatomic dead space 150 ml

Alveorlar gas 3 L

Pulmonary capillary blood 70 ml

Tidal volume 500 ml

Alveorlar gas 3 L

Respiration frequency 15 breaths/minute

Alveolar ventilation 5 L/min

Ventilation/perfusion ratio ~1

Pulmonary perfusion 5 L/min

Figure 3.3 Pulmonary volumes and flows showing a ventilation perfusion ratio of 1.

3.5 Mechanics of Breathing

For the normal physiological case of breathing, air flows into the lungs when the alveolar pressure drops below the pressure of the surrounding ambient air. This is known as negative pressure breathing because the pressure in the alveoli must be negative with respect to the surrounding air. This negative pressure in the alveoli is caused by muscle contractions that increase the volume of the lung causing the alveoli to expand.

Transmural pressure gradient is defined by the difference in pressure between atmospheric air and the pressure in the alveoli. As the transmural pressure gradient increases, the alveoli expand.

Intrapleural pressure, which is also known as intrathoracic pressure, is caused by the mechanical interaction between the lung and chest wall. When all muscles of respiration are relaxed, left to themselves the lungs have a tendency to collapse whereas the chest wall tends to expand. This causes the intrapleural pressure to drop and this resulting negative pressure has the effect of holding the lung and the chest wall in close contact.

The primary muscles of breathing are the diaphragm, the external intercostals, and the accessory muscles. The diaphragm is a dome-shaped sheet of muscle with an area of about 250 cm2. The diaphragm separates the abdominal cavity from the thoracic cavity.

During eupnea, or normal quiet breathing, in the supine position the diaphragm is responsible for two-thirds of the air entering the lungs.

3.5.1 Muscles of inspiration

The rib muscles (external intercostals) raise and enlarge the rib cage when contracted. The diaphragm and the rib muscles contract simultaneously during inspiration. If they did not, the contraction of the external intercostals could cause the diaphragm to be pulled upwards.

Accessory muscles are not used in normal quiet breathing. They are used however; during heavy breathing, as in exercise, and during the inspiratory phase of sneezing and coughing. An example of an accessory muscle is the sternocleidomastoid, which elevates the sternum to increase the anteroposterior (front to back) and the transverse (side to side) dimensions of the chest.

3.5.2 Muscles of expiration

Expiration is passive during quiet breathing and no muscle contraction is required. The elastic recoil of the alveoli due to alveolar stiffness is enough to raise the alveolar pressure above atmospheric pressure, the condition required for expiration.

Active expiration occurs during exercise, speech, singing, and the expiratory phases of coughing and sneezing. Active expiration may also be required due to pathologies such as emphysema. Muscles of active expiration are the muscles of the abdominal wall including the rectus abdominis, external and internal obliques, transverse abdominis, and internal intercostals muscles.

3.5.3 Compliance of the lung and chest wall

The slope of the pressure-volume curve of the lung is known as lung compliance. This volume compliance can be written as dV/dP, representing a change in volume per change in pressure. Compliance has the units of m3/Pa and is inversely related to elasticity, or lung stiffness.

The pressure-volume curve for the lung is different for inspiration than it is for expiration. The difference in volume for a given pressure upon inspiration versus the same pressure upon expiration is known as hysteresis. At low lung volumes, the lung is stiffer (has a lower compliance) during inspiration than during expiration. At high lung volumes, the lung is less stiff (has a higher compliance) during inspiration.

3.6 Work of Breathing

The rate and depth at which one breathes, under normal circumstances is managed to minimize the amount of work that is done. If you try to breathe rapidly and shallowly for an extended period of time, you can transfer the necessary oxygen, but will rapidly grow tired from the effort. Work for a system that executes a cyclic process with only expansion and compression can be modeled by Eq. (3.6):

In Eq. (3.6), W represents the work done between points a and b. P represents the pressure inside the system (in this case the lung). The volume of the system is represented by V. Figure 3.4 shows a typical pressure-volume curve during breathing. The work term can be thought of as an area under the pressure-volume curve.

For example, one part of the work done by the diaphragm on the lungs due to inspiration can be thought of as the work needed to overcome the elastic resisting forces of the chest wall and diaphragm. This work done to overcome elasticity can be represented by the area under the line AB as shown in Fig. 3.5.

The total work done by the diaphragm on the lungs due to inspiration can be thought of as the work needed to overcome the elastic resisting forces of the chest wall and diaphragm, plus the work done to overcome the resistance to flow. This total work of inspiration can be represented by the area under the inspiration curve as shown in Fig. 3.6.

During expiration, the elasticity of the lungs and chest wall help provide the stored energy so that diaphragm work is not necessary. The energy stored in these elastic tissues can be partially recovered during expiration. The work done to overcome resistance to flow cannot be overcome. The total work of one total breathing cycle,

Volume above FRC, L

Figure 3.4 Shows intrapleural pressure versus lung volume for inspiration and expiration.

Volume above FRC, L

Figure 3.4 Shows intrapleural pressure versus lung volume for inspiration and expiration.

Figure 3.5 Pressure-volume curves showing the work done to overcome elasticity during inspiration.

Figure 3.6 Pressure-volume curve showing the total work done by diaphragm due to inspiration.

Volume above FRC, L

Figure 3.6 Pressure-volume curve showing the total work done by diaphragm due to inspiration.

Figure 3.7 Work done by the diaphragm during one breath cycle.

including inspiration and expiration, can be shown as the cross-hatched area in Fig. 3.7.

Clinical features. An important cause of respiratory failure is fatigue of the muscles of respiration. When the diaphragm and respiratory muscles cannot carry out the work of breathing the result is a progressive fall in oxygenation and/or rise in carbon dioxide concentration.

3.7 Airway Resistance

Although the air that flows through your trachea is not very massive or very viscous, there is a noticeable hydraulic resistance to the flow. This resistance results in a pressure drop along the airway. This pressure decreases along the airways, in the direction of flow. This pressure drop is also dependent on the flow rate in the tube, the viscosity of the fluid, and the pattern of flow. There can be no flow along a tube unless there is a pressure difference, or pressure gradient, along the tube.

As explained in Sec. 1.4.1 fluid particles move along streamlines during laminar flow. When air flows at low rates in relatively small diameter tubes, as in the terminal bronchioles, the flow is laminar. Turbulent flow is a random mixing flow. When air flows at higher rates in larger diameter tubes, like the trachea, the flow is often turbulent.

In Chap. 1, we also saw that a dimensionless parameter, termed the Reynolds number, Re, could be used to predict whether flow is turbulent or laminar. The number is defined in Eq. (3.7):

In Eq. (3.7) p is fluid density in kg/m3, Vis fluid velocity in m/s, D is pipe diameter in m, and m is fluid viscosity in Ns/m2. Physically the Reynolds number represents the ratio of inertial forces to viscous forces.

As an analogy, imagine the ratio of the momentum of a vehicle (mass X velocity) to the frictional braking force available (force). A person walking on dry pavement has a relatively small mass, relatively low velocity, and relatively low ratio of momentum to stopping force. For comparison, imagine a very large truck moving at high velocity on an icy street. This second combination of truck on ice has a very high ratio of momentum to stopping force and is a highly unstable situation in comparison to the first. Analogously to the person walking on pavement, low mass air flows with low Reynolds numbers are more stable and more likely to be laminar in comparison to denser flows at high velocity with higher Reynolds numbers.

In the lungs, fully developed laminar flow probably occurs only in very small airways with low Reynolds number. Flow in the trachea may be truly turbulent. Much of the flow in intermediate sized airways will be transitional flow in which it is difficult to predict if the flow will be laminar or turbulent.

In Chap. 1 we also developed Poiseuille's law, which describes laminar flow in rigid tubes. Poiseuille's law applies to air flow, just as it does to blood flow, when the flow is laminar. Recall that:

8m dx where Q = the flow rate

R = the airway radius m = the air viscosity dP/dx = the pressure gradient along the airway

Resistance to flow can be thought of as the driving pressure divided by the flow. Poiseuille's law can be rearranged to solve for the resistance as shown in Eq. (3.9).

Figure 3.8 Showing a forced expiration versus time curve for a patient with normal airway resistance.

Time, s

Figure 3.8 Showing a forced expiration versus time curve for a patient with normal airway resistance.

Figure 3.9 The volume versus time curve for forced expiration in a patient with chronic obstructive pulmonary disease shows a great resistance to expiratory flow.

Time, s

Figure 3.9 The volume versus time curve for forced expiration in a patient with chronic obstructive pulmonary disease shows a great resistance to expiratory flow.

Although the resistance to flow associated with the tube is inversely related to the fourth power of the radius, the resistance contributed by airways is not predominantly in the smallest diameter airways. As airways branch they become narrower, but also more numerous. The major site of airway resistance is the medium—sized bronchi. Small bronchioles contribute relatively little resistance because of their increased numbers.

Most resistance in airways occurs up to the seventh generation of branching vessels. Less than 20 percent of the resistance is attributable to airways that are less than 2 mm in diameter because of the large number of vessels. Twenty-five to 40 percent of total resistance is in the upper airways including the mouth, nose, pharynx, larynx, and trachea.

One way to assess expiratory resistance is to begin by measuring the forced vital capacity (FVC) of the lung, using a spirometer. The patient starts by making a maximal inspiratory effort to total lung capacity. After a short pause, the patient makes a maximal forced expiratory effort.

We may define forced expiratory volume (FEVj), as the volume of air expired in 1 s during a forced expiratory effort. The ratio of FEV1 to FVC is a good index of airway resistance. In normal, healthy subjects, FEV1/FVC is greater than 0.80, or 80 percent.

Forced expiratory flow rate between time t1 and time t2 can be defined as the average flow rate between times t1 and t2, as measured during a forced expiration. The rate can be represented graphically as the slope of a line drawn between two points on the forced expiration curve.

In Fig. 3.8, point A represents the point on when the lung volume is equal to 25 percent of the vital capacity. A second point, B, is drawn on the curve representing the point when lung volume is equal to 75 percent of vital capacity. The slope of the line AB is the forced expiratory flow rate,

FEF25-75%.

Figure 3.8 represents a normal, healthy patient and Fig. 3.9 represents a patient with an airway obstruction. Note the steep slope corresponding to a high forced expiratory flow rate in the healthy patient in Fig. 3.8 and the shallow slope corresponding to a low forced expiratory flow rate in Fig. 3.9.

3.8 Gas Exchange and Transport

In the next section of this book, we will consider how oxygen moves from ambient air into the tissues of the body. Diffusion of a gas occurs when there is a net movement of molecules from an area with a high partial pressure to an area with a lower partial pressure. Only 50 years ago, it was still believed by some scientists that the lung secreted oxygen into the capillaries. That would mean that oxygen would move from the atmosphere to a relatively higher concentration inside the lung by an active process. More accurate measurements have now shown that gas transport across the alveolar wall is a passive process.

3.8.1 Diffusion

Gases like oxygen and carbon dioxide move across the blood-gas barrier of the alveolar wall by diffusion. You might ask, "What parameters affect the rate of transfer?" The rate of gas movement across the alveolar wall is dependent on the diffusion area, the driving pressure, and the wall thickness.

The diffusion area is the surface area of the alveolar wall, or blood-gas barrier. That surface area is proportional to the rate of diffusion. The driving pressure that pushes gasses across the alveolar wall is the partial pressure of the gas in question. The driving force that pushes oxygen into the blood stream is the difference between the partial pressure of oxygen in the alveoli and the partial pressure of oxygen in the blood, DPO2. The rate of diffusion of oxygen into blood stream is proportional to DPO2.

The rate of diffusion of oxygen into the blood stream is inversely proportional to the thickness of the alveolar wall. A thicker wall causes the oxygen diffusion to decrease and a thinner wall makes it easier for oxygen to flow into the blood stream.

The blood gas barrier in the lung has a surface area of about 50 to 100 m2 spread out over 750 million alveoli. This huge diffusion area is available to a relatively small volume of blood. Pulmonary capillary blood volume is only about 60 mL during resting and about 95 mL during exercise.

Carbon dioxide diffuses about 20 times more rapidly than oxygen through the alveolar wall. The much higher solubility of carbon dioxide is responsible for this increased diffusion rate.

3.8.2 Diffusing capacity

One might wonder if oxygen transfer into the blood is limited by how fast the blood can flow through the lungs, or by how fast oxygen can diffuse through the blood-gas barrier. It turns out that under normal physiological circumstances, oxygen diffusion through the alveolar wall is sufficient and the limiting factor for oxygen uptake is perfusion, or the rate of blood flow through the capillaries. An erythrocyte spends an average of about 0.75 to 1.2 s passing through a pulmonary capillary under normal resting conditions.

Under some circumstances oxygen diffusion rates through the wall may also limit the oxygen transfer rate. During extreme exercise, an ery-throcyte may stay in the capillary as little as 0.25 s. Even this very short time would be enough time for oxygen to diffuse into the capillaries at normal atmospheric oxygen partial pressures. However, during extreme exercise at high altitude, or in a patient with thickening of the alveolar wall due to pulmonary fibrosis, oxygen flow rate may switch from a perfusion limited to a diffusion limited process.

3.8.3 Resistance to diffusion

So far, we have considered the blood gas barrier as the only source of resistance to diffusion of gases from the alveoli into the blood stream. In fact, there is a second important component. The uptake of oxygen occurs in two stages. The first is diffusion through the alveolar wall, and the second is the reaction of oxygen with hemoglobin.

The diffusing capacity through the alveolar wall is defined by the flow rate of the gas divided by the partial pressure difference that is driving the flow. Diffusing capacity of a gas can be written as Da in Eq. (3.10).

In Eq. (3.10), Vgas represents the flow rate of some gas from the alveoli into the capillary. Pa represents the partial pressure of that gas in the alveoli and Pc represents the partial pressure of the same gas in the capillary.

If we think of the electrical analogy in which resistance is equal to voltage divided by current, we can see that it is possible to think of 1/Da as a resistance to diffusion.

The rate of reaction of oxygen with hemoglobin can be represented by U. The units on U are ml O2/min per mL blood per mmHg partial pressure of O2. If Vc represents the volume of pulmonary capillary blood, then U X Vc will have the units of mL O2/min/mmHg, or flow divided by pressure. Once again, the inverse, pressure/flow is analogous to resistance.

Resistanceo2#Hgb = (3.12)

u Vc

The total resistance to the flow of oxygen into the blood stream is the combination of the resistance to diffusion caused by the blood gas barrier plus the resistance to flow due to the oxygen-hemoglobin reaction.

The resistances can be added together as shown in Eq. (3.13). 1/DL is the total resistance to the flow of oxygen due to the lung.

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