Physiologic Dead Space

Ventilation-Perfusion Relationships

September 26, 2016 Cardiology, Mechanical Ventilation, Pulmonary Medicine, Respirology No comments , , , , , , , , , , , , , , ,

Gas exchange between the alveoli and the pulmonary capillary blood occurs by diffusion. Diffusion of oxygen and carbon dioxide occurs passively, according to their concentration differences across the alveolar-capillary barrier. These concentration differences must be maintained by ventilation of the alveoli and persusion of the pulmonary capillaries.

Alveolar ventilation brings oxygen into the lung and removes carbon dioxide fro it. Similarly, the mixed venous blood brings carbon dioxide into the lung and takes up alveolar oxygen. The alveolar PO2 and PCO2 are thus determined by the relationship between alveolar ventilation and pulmonary capillary perfusion. Alterations in the ratio of ventilation to perfusion, called the (VA/QC), will result in changes in the alveolar PO2 and PCO2, as well as in gas delivery to or removal from the lung.

Alveolar ventilation is normally about 4 to 6 L/min and pulmonary blood flow (which is equal to cardiac output) has a similar range, and so the V/Q for the whole lung is in the range of 0.8 to 1.2. However, ventilation and perfusion must be matched on the alveolar-capillary level, and the V/Q for the whole lung is really of interest only as an approximation of the situation in all the alveolar-capillary units of the lung. For instance, suppose that all 5 L/min of the cardiac output went to the left lung and all 5 L/min of alveolar ventilation went to the right lung. The whole lung V/Q would be 1.0, but there would be no gas exchange because there could be no gas diffusion between the ventilated alveoli and the perfused pulmonary capillaries.

Consequences of High and Low V/Q

Oxygen is delivered to the alveolus by alveolar ventilation, is removed from the alveolus as it diffuses into the pulmonary capillary blood, and is carried away by blood flow. Similarly, carbon dioxide is delivered to the alveolus in the mixed venous blood and diffuses into the alveolus in the pulmonary capillary. The carbon dioxide is removed from the alveolus by alveolar ventilation. At resting cardiac outputs the diffusion of both oxygen and carbon dioxide is normally limited by pulmonary perfusion. Thus, the alveolar partial pressures of both oxygen and carbon dioxide are determined by the V/Q. If the V/Q in an alveolar-capillary unit increases, the delivery of oxygen relative to its removal will increase, as will the removal of carbon dioxide relative to its delivery. Alveolar PO2 will therefore rise, and alveolar PCO2 will fall. If the V/Q in an alveolar-capillary unit decreases, the removal of oxygen relative to its delivery will increase and the delivery of carbon dioxide relative to its removal will increase. Alveolar PO2 will therefore fall, and alveolar PCO2 will rise.

Consider these three conditions: 1) A normal V/Q ratio; 2) a V/Q ratio equals to 0; and 3) a V/Q ratio of infinite. With a normal V/Q ratio, inspired air enters the alveolus with a PO2 of about 150 mm Hg and a PCO2 of nearly 0 mm Hg. Mixed venous blood enters the pulmonary capillary with a PO2 of about 40 mm Hg (SvO2 of 75%) and a PCO2 of about 45 mm Hg. This results in an alveolar PO2 of about 100 mm Hg and an alveolar PCO2 of about 45 mm Hg. The partial pressure difference for oxygen diffusion from alveolus to pulmonary capillary is thus about 100 to 40 mm Hg, or 60 mm Hg; the partial pressure gradient for CO2 diffusion from pulmonary capillary to alveolus is only about 45 to 40, or 5 mm Hg.

With a V/Q ratio of 0, the airway supplying has become completely occluded. Its V/Q ratio is zero. As time goes on, the air trapped in the alveolus equilibrates by diffusion with the gas dissolved in the mixed venous blood entering the alveolar-capillary unit (If the occlusion persists, the alveolus is likely to collapse). No gas exchange can occur, and any blood perfusion this alveolus will leave it exactly as it entered it.

With a V/Q ratio of infinite (dead space), the blood flow is blocked by a pulmonary embolus, and the alveolar-capillary unit is therefore completely unperfused. Because no oxygen can diffuse from the alveolus into pulmonary capillary blood and because no carbon dioxide can enter the alveolus is approximately 150 mm Hg and its PCO2 is approximately zero. That is, the gas composition of this unperfused alveolus is the same as that of inspired air. If this condition is due to the fact that the alveolar pressure exceeds its precapillary pressure (pulmonary arterial pressure, Pa), then it would aslo correspond to part of zone 1.

screen-shot-2016-09-21-at-9-11-53-amConditions 2 and 3 represent the 2 extremes of a continuum of ventilation-perfusion ratios. The V/Q ratio of a particular alveolar-capillary unit can fall anywhere along this continuum. The alveolar PO2 and PCO2 of such units will therefore fall between the two extremes shown in the figure: Units wtih low V/Q ratios will have relatively low PO2s and high PCO2s; units with high V/Q ratios will have relatively high PO2s and low PCO2s. This is demonstrated graphically in an O2-CO2 diagram such as that seen in Figure 5-2. The diagram shows the results of mathematical calculations of alveolar PO2s and PCO2s for V/Q ratios between zero and infinity (for inspired air). The resulting curve is known as the ventilation-perfusion ratio line. This simple O2-CO2 diagram can be modified to include correction lines for other factors, such as the respiratory exchange ratios of the alveoli and the blood or the dead space. The position of the V/Q ratio line is altered if the partial pressures of the inspired gas or mixed venous blood are altered.


Evaluation of the Ventilation-Perfusion Mismatch

Physiologic Shunts

Physiologic shunt = Anatomic Shunt + Intrapulmonary shut (absolute + shuntlike)

Anatomic shunts

Anatomic shunts consist of systemic venous blood entering the left ventricle without having entered the pulmonary vasculature. In a normal healthy adult, about 2% to 5% of the cardiac output, including venous blood from the bronchial veins, the besian veins, and the pleural veins, enters the left side of the circulation directly without passing through the pulmonary capillaries. Therefore, the output of the left venticle is normally greater than that of the right venticle in adults.

Absolute intrapulmonary shunts

Mixed venous blood perfusing pulmonary capillaries assocaited with totally unventilation or collapsed alveoli constitutes an absolute shunt (like the anatomic shunts) because no gas exchange occurs as the blood passes through the lung. Absolute shunts are sometimes also referred to as true shunts.

Shuntlike states

Alveolar-capillary units with low V/Q also act to lower the arterial oxygen content because blood draining these units has a lower PO2 than blood from units with well-matched ventilation and perfusion.

The Shunt Equation

The shunt equation conceptually divides all alveolar-capillary units into two groups: those with well-matched ventilation and perfusion and those with ventilation-perfusion ratios of zero. Thus, the shunt equation combines the areas of absolute shunt and the shuntlike areas into a single conceptual group. The resulting ratio of shunt flow to the cardiac output, often referred to as the venous admixture, is the part of the cardiac output that would have to be perfusing absolutely unventilated alveoli to cause the systemic arterial oxygen content obtained from a patient. A much larger portion of the cardiac output could be overperfusion poorly ventilated alveoli and yield the same ratio.

The shunt equation can be derived as follows: Let Qt represent the total pulmonary blood flow per minute (i.e., the cardiac output), and let Qs represent the amount of blood flow per minute entering the systemic arterial blood without receiving any oxygen (the "shunt flow"). The volume of blood per minute that perfuses alveolar-capillary units with well-matched ventilation and perfusion then equals Qt – Qs.

The total volume of oxygen per time entering the systemic arteries is therefore

Qt x CaO2

where CaO2 equals oxygen content of arterial blood in milliliters of oxygen per 100 mL of blood. This total amount of oxygen per 100 mL of blood. This total amount of oxygen per time entering the systemic arteries is composed of the oxygen coming from the well-ventilated and well-perfused alveolar-capillary units:

(Qt – Qs) x CcO2

where CcO2 equals the oxygen content of the blood at the end of the ventilated and perfused pulmonary capillaries, plus the oxygen in the unaltered mixed venous blood coming from the shunt, Qs x CvO2 (where CvO2 is equal to the oxygen content of the mixed venous blood). There is normally a substantial amount of oxygen in the mixed venous blood. That is,

Qt x CaO2 = (Qt – Qs) x CcO2 + Qs x CvO2

After some mathematical rearranagement, the Qs/Qt is expressed as,

Qs/Qt = (CcO2 – CaO2) / (CcO2 – CvO2) [Equation 1]

The shunt fraction Qs/Qt is usually multiplied by 100% so that the shunt flow is expressed as a percentage of the cardiac output.

The arterial and mixed venous oxygen contents can be determined if blood samples are obtained from a systemic artery and from the pulmonary artery (for mixed venous blood), but the oxygen content of the blood at the end of the pulmonary capillaries with well-matched ventialtion and perfusion is, of course, impossible to measure directly. This must be calculated from the alveolar air equation and the patient's hemoglobin concentration.

Physiologic Dead Space

The use of the Bohr equation to determine the physiologic dead space was discussed in detail in thread "Mechanics of Breathing – Alveolar Ventilation" at http://www.tomhsiung.com/wordpress/2015/11/mechanics-of-breathing-alveolar-ventilation/. If the anatomic dead space is subtracted from the physiologic dead space, the result (if there is a difference) is alveolar dead space, or areas of infinite V/Qs. Alveolar dead space also results in an arterial-alveolar CO2 difference; that is, the end-tidal PCO2 is normally equal to the arterial PCO2. End-tidal PCO2 is used as an estimate of the mean PCO2 of all ventilated alveoli. An arterial PCO2 greater than the end-tidal PCO2 usually indicates the presence of alveolar dead space.

Alveolar-Arterial Oxygen Difference

The alveolar and arterial PO2s are treated as though they are equal. However, the aterial PO2 is normally a few mm Hg less than that alveolar PO2. This is normal alveolar-arterial oxygen difference, the (A-a)DO2, is caused by the normal anatomic shunt, some degree of ventilation-perfusion mismatch, and diffusion limitation in some parts of the lung. Of these, V/Q mismatch is usually the most important, with a small contribution from shunts and very little from diffusion limitation. Larger-than-normal differences between the alveolar and arterial PO2 may indicate significant ventilation-perfusion mismatch; however, increased alveolar-arterial oxygen differences also can be caused by anatomic intrapulmonary shunts, diffusion block, low mixed venous PO2s, breathing higher than normal oxygen concentrations, of shifts of the oxy-hemoglobin dissociation curve.

The alveolar-arterial PO2 difference is normally about 5 to 15 mm Hg in a young healthy person breathing room air at sea level. It increases with age because of the progressive decrease in arterial PO2 that occurs with aging. The normal alveolar-arterial PO2 difference increases by about 20 mm Hg between the ages of 20 and 70. A person's age/4 + 4 mm Hg is a good clinical estimate of the normal alveolar-arterial PO2 difference.

Another useful clinical index in addition to the alveolar-arterial oxygen difference is the ratio of arterial PO2 to the fractional concentration of oxygen in the inspired air. The PaO2/FiO2 should be greater than or equal to 200; a PaO2/FiO2 less than 200 is seen in acute respiratory distress syndrome.

Single-Breath Carbon Dioxide Test

The expired concentration of carbon dioxide can be monitored by a rapid-response carbon dioxide meter in a manner similar to that used in the single-breath tests utilizing a nitrogen meter. The alveolar plateau phase of the expired carbon dioxide concentration may show signs of poorly matched ventilation and perfusion if such regions empty asynchronously with other regions of the lung.

Lung Scans After Inhaled and Infused Markers

Lung scans after both inhaled and injected markers can be used to inspect the location and amount of ventilation and perfusion to the various regions of the lung.

Multiple Inert Gas Elimination Technique

A more specific graphic method for assessing ventilation-perfusion relationships in human subjects is called the multiple inert gas elimination technique. This technique uses the concept that the elimination via the lungs of different gases dissolved in the mixed venous blood is affected differently by variations in the ventilation-perfusion ratios of alveolar-capillary units, according to the solubility of each gas in the blood. At a ventilation-perfusion ratio of 1.0, a greater volume of a relatively soluble gas would be the case with a relatively insoluble gas. Thus, the retention of any particular gas by a single alveolar-capillary unit is dependent on the blood-gas partition coefficient of the gas and the ventilation-perfusion ratio of the unit. Gases with very low solubilities in the blood would be retained in the blood only by units with very low (or zero) V/Qs. Gases with very high solubilities in the blood would be eliminated mainly in the expired air of units with very high V/Qs.

Regional V/Q Differences and Their Consequences in the Lung

screen-shot-2016-09-26-at-8-27-08-pmThe regional variations in ventilation in the normal upright lung were discussed in thread "Mechanics of Breathing – Alveolar Ventilation" at http://www.tomhsiung.com/wordpress/2015/11/mechanics-of-breathing-alveolar-ventilation/. Gravity-dependent regions of the lung receive more ventilation per unit volume than do upper regions of the lung when one is breathing near the FRC. The reason for this is that there is a gradient of pleural surface pressure, which is probably caused by gravity and the mechanical interaction of the lung and the chest wall. The pleural surface pressure is more negative in nondependent regions of the lung, and so the alveoli in these areas are subjected to greater transpulmonary pressures. As a result, these alveoli have larger volumes than do alveoli in more dependent regions of the lung and are therefore on a less steep portion of their pressure-volume curves. These less-compliant alveoli change their volume less with each breath than do those in more dependent regions.

The right side of Figure 5-6 shows that the more gravity-dependent regions of the lung also receive more blood flow per unit volume than do the upper regions of the lung, as discussed in thread "Blood flow to the lung – general and pulmonary vascular resistance" at http://www.tomhsiung.com/wordpress/2016/09/blood-flow-to-the-lung-general-and-pulmonary-vascular-resistance/. The reason for this is that the intravascular pressure in the lower regions of the lung is greater because of hydrostatic effects. Blood vessels in more dependent regions of the lung are therefore more distended, or more vessels are perfused because of recruitment so there is less resistance to blood flow in lower regions of the lung.

Regional Differences in the Ventilation-Perfusion Ratios in the Upright Lung

screen-shot-2016-09-26-at-8-39-33-pmSimplified graphs of the differences of ventilation and perfusion from the bottom to the top of normal upright dog lungs are shown plotted on the same axis in Figure 5-7. The ventilation-perfusion ratio was then calculated for several locations.

Figure 5-7 shows that the difference of perfusion from the bottom of the lung to the top is greater than the difference of ventialtion. Because of this, the ventilation-perfusion ratio is relatively low in more gravity-dependent regions of the lung and greater in upper regions of the lung. If pulmonary perfusion pressure is low, for example, because of hemorrhage, or if alveolar pressure is high because of positive-pressure ventilation with positive end-expiratory pressure (PEEP), or if both factors are present, then there may be areas of zone 1 with infinite ventilation-perfusion ratios in the upper parts of the lung.

The Consequences of Regional Ventilation-Perfusion Differences in the Normal Upright Lung

The effects of the regional differences in V/Q on the alveolar PO2 and PCO2 can be seen in Figure 5-8. The lung was arbitrarily divided into 9 imaginary horizontal sections, and the V/Q was calculated for each section. These sections were then positioned on the ventilation-perfusion line of the O2-CO2 diagram, and the PO2 and PCO2 of the alveoli in each section could be estimated. Under normal circumstances the blood in the pulmonary capillaries equilibrates with the alveolar PO2 and PCO2 as it travels through the lung, and so the effects of regional differences in V/Q on the regional gas exchange could be predicted. As can be seen from the figure, the upper sections have relatively high PO2 and low PCO2; the lower sections have relatively low PO2 and high CO2.

Figure 5-7 and 5-8 demonstrate that the lower regions of the lung receive both better ventilation and better perfusion than do the upper portions of the lung. However, the perfusion difference is much steeper than the ventilation difference, and so the ventilation-perfusion ratio is higher in the apical regions than it is in the basal regions. As a result, the alveolar PO2 is greater and the alveolar PCO2 is less in upper portions of the lung than they are in lower regions. This means that the oxugen content of the blood draining the upper regions is greater and the carbon dioxide contnet is less than that of the blood draining the lower regions. However, these contents are based on milliliters of blood, and there is much less blood flow to the upper most sections than there is to the bottom sections. Therefore, even though the uppermost sections have the greatest V/Q and PO2 and the lowest PCO2, there is more gas exchange in the more basal sections.

Mechanics of Breathing – Alveolar Ventilation

November 17, 2015 Physiology and Pathophysiology, Pulmonary Medicine No comments , , , , , , , , , , , , , , , ,

Important Measurements of Lung Functions

The tidal volume (VT) is the volume of air entering or leaving the nose or mouth per breath. It is determined by the activity of the respiratory control centers in the brain as they affect the respiratory muscles and by the mechanics of the lung and the chest wall. During normal, quiet breathing the VT of a 70-kg adult is about 500 mL per breath, but this volume can increase dramatically, for example, during exercise.

The residual volume (RV) is the volume of gas left in the lungs after a maximal forced expiration. It is determined by the force generated by the muscles of expiration and the inward elastic recoil of the lungs as they oppose the outward elastic recoil of the chest wall. Dynamic compression of the airways during the forced expiratory effort may also be an important determinant of the RV as airway collapse occurs, thus trapping gas in the alveoli. The RV of a healthy 70-kg adult is about 1.5 L, but it can be much greater in a disease state such as emphysema, in which inward alveolar elastic recoil is diminished and much airway collapse and  gas trapping occur. The RV is important to a healthy person because it prevents the lungs from collapsing at very low lung volumes. The collapsed alveoli would require very great inspiratory efforts to reinflate.

The expiratory reserve volume (ERV) is the volume of gas that is expelled from the lungs during a maximal forced expriation that starts at the end of a normal tidal expiration. It is therefore determined by the difference between the functional residual capacity (FRC) and the RV. The ERV is about 1.5 L in a heathy 70-kg adult.

The inspiratory reserve volume (IRV) is the volume of gas that is inhaled into the lungs during a maximal forced inspiration starting the end of a normal tidal inspiration. It is determined by the strength of contraction of the inspiratory myscles, the inward elastic recoil of the lung and the chest wall, and the starting point, which is the FRC plus the VT. The IRV of a normal 70-kg adult is about 2.5 L.

The functional residual capacity (FRC) is the volume of gas remaining in the lungs at the end of a normal tidal expiration. The FRC consists of the RV plus the ERV. It is therefore about 3 L in a healthy 70-kg adult. FRC=RV+ERV

The inspiratory capacity (IC) is the volume of air that is inhaled into the lungs during a maximal inspiratory effort that begins at the end of a normal tidal expiration. It is therefore equal to the VT plus the IRV. The IC of a normal 70-kg adult is about 3 L. IC=VT+IRV

The total lung capacity (TLC) is the volume of air in the lungs after a maximal inspiratory effort. It is determined by the strength of contraction of the inspiratory muscles and the inward elastic recoil of the lungs and the chest wall. The TLC consists of all 4 lung volumes: the RV, the VT, the IRV, the ERV. The TLC is about 6 L in a healthy 70-kg adult. TLC=RV+ERV+VT+IRV

The vital capacity (VC) is the volume of air expelled from the lungs during maximal forced expiration starting after a maximal forced inspiration. The VC is therefore equal to the TLC minus the RV, or about 4.5 L in a healthy 70-kg adult. The VC is also equal to the sum of the VT and IRV and ERV. It is determined by the factors that determine the TLC and RV. VC=TLC-RV=VT+IRV+ERV


Physiologic Dead Space

The volume of air entering and leaving the nose or mouth per minute, the minute volume, is not equal to the volume of air entering and leaving the alveoli per minute. Alveolar ventilation is less than the minute volume because the last part of each inspiration remians in the conducting airways and is not expelled from the body. No gas exchange occurs in the conducting airways for anatomic reasons: The walls of the conducting airways are too thick for mucn diffusion to take place; mixed venous blood does not come into contact with the air. The conducting airways are therefore referred to as the anatomic dead space. A reasonable estimate of anatomic dead space is 1 mL of dead space per pound of ideal body weight.

Besides the anatomic dead space, there is another form of wasted ventilation, where the alveoli are ventilated but not perfused with venous blood. No gas exchange occurs in these alveoli for physiologic, rather than anatomic, reasons. A healthy young person has little or no alveolar dead space, but a person with a low cardiac output might have a great deal of alveolar dead space. The anatomic dead space plus the alveolar dead space is known as the physiologic dead space.

Physiologic dead space = anatomic dead space + alveolar dead space [Bohr equation]

The Bohr equation makes use of a simple concept: Any meaurable volume of carbon dioxide found in the mixed expired gas must come from alveoli that are both ventilated and perfused because there are negligible amounts of carbon dioxide in inspired air. Inspired air remaining in the anatomic dead space or entering unperfused alveoli will leave the body as it entered (except for having been heated to body temperature and humidified), contributing little or no carbon dioxide to the mixed expired air:

FEco2 X VT = FIco2 X VDco2 + FAco2 X VA,

FEco2 X VT is volume of CO2 in mixed expired air

FIco2 X VDco2 is volume of CO2 coming from dead space

FAco2 X VA is volume of CO2 coming from alveoli

F means fractional concentration

E means mixed expired

I means inspired

A means alveolar

VDco2 is dead space for CO2 (physiologic dead space)

FAco2 is fractional concentration of CO2 in alveoli that are both ventilate and perfused

Since FIco2 is approximately equal to zero, the FIco2 X VDco2 term drops out. Substituting (VT – VDco2) for VA:

FEco2 X VT =  FAco2 X (VT – VDco2)

VDco2 X FAco2 = VT X (FAco2 – FEco2)

After these mathematic processes, we can calcuate the dead space for CO2/physiologic dead space by the following equation:

VDco2 = VT x (PAco2 – PEco2)/PAco2

The Pco2 of the collected mixed expired gas can be determined with a CO2 meter. The CO2 meter is often also used to estimate the alveolar Pco2 by analyzing the gas expelled at the end of a normal tidal expiration, the "end-tidal CO2". But in a person with significant alveolar dead space, the estimated alveolar Pco2 obtained in this fashion may not reflect the Pco2 of alevoli that are ventilated and perfused because some of this mixed end-tidal gas comes from unperfused alveoli. This gas dilutes the CO2 coming from alveoli that are both ventilated and perfused.

Because there is an equilibrium between the Pco2 of perfused alveoli and their end-capillary Pco2, so that in patients without significant venous-to-arterial shunts, the arterial Pco2 represents the mean Pco2 of the perfused alveoli. Therefore, the equation above could be rewritten as:

VDco2 = VT x (Paco2 – PEco2)/Paco2

If the Paco2 is greater than the mixed alveolar Pco2 determined by sampling the end-tidal CO2, then the physiologic dead space is probably greater than the anatomic dead space; that is, a significant arterial-alveolar CO2 difference means that there is siginifcant alveolar dead space. Situations in which alveoli are ventilated but not perfused include those in which portions of the pulmonary vasculature have been occluded by blood clots from the venous blood (pulmonary emboli), situations in which there is low venous return leading to low right ventricular output, and situations in which alveolar pressure is high (positive-pressure ventilation with positive end-expiratory pressure).


Alveolar Ventilation and Alveolar Oxygen and Carbon Dioxide Levels

The levels of oxygen and carbon dioxide in the alveolar gas are determined by the alveolar ventilation, the pulmonary capillary perfusion, the oxygen consumption of the body, and the carbon dioxide production of the body. Alveolar gas is composed of the 2.5 to 3 L of gas already in the lungs at FRC and the approximately 350 mL per breath entering and leaving the alveoli. About 300 mL of oxygen is continuosusly diffusing from the alveoli into the pulmonary capillary blood per minute at rest and is being replaced by alveolar ventilation. Simiarly, about 250 mL of carbon dioxide is diffusing from the mixed venous blood in the pulmonary capillaries into the alveoli per minute and is then removed by alveolar ventilation.

PS: normal PAO2 is 104 mm Hg and normal PACO2 is 40 mm Hg.

The alveolar PO2 increases by 2 to 4 mm Hg with each normal tidal inspiration and falls slowly until the next inspiration. Similarly, the alveolar PCO2 falls 2 to 4 mm Hg with each inspiration and increases slowly until the next inspiration.

The concentraton of carbon dioxide in the alveolar gas is dependent on the alveolar ventilation and on the rate of carbon dioxide production by the body (and its delivery to the lung in the mixed venous blood). The volume of carbon dioxide expired per unit of time (VECO2) is equal to the alveolar ventilation VA times the alveolar fractional concentration of CO2 (FACO2). No carbon dioxide comes from the dead space: VECO2 = VA X FACO2. Simarily, the fractional concnetration of carbon dioxide in the alveoli is directly proportional to the carbon dioxide production by the body (VCO2) and inversely proportional to the alveolar ventilation: FACO2 is directly proportional to VCO2/VA.

Since FACO2 X (PB – PH2O) = PACO2, then PACO2 is directly proportional to VCO2/VA.

After these mathematic proving, we got the following formula to estimate the PACO2:

PACO2 is in directly proportional to VCO2/VA

where PACO2 is the alveolar CO2 pressure, VCO2 is the carbon dioxide production by the body, and the VA is the alveolar ventilation. In healthy people, alveolar PCO2 is in equilibrium with PaCO2. Thus, if alveolar ventilation is doubled, then the alveolar and arterial PCO2 are reduced by one-half. If alveolar ventilation is cut in half, near 40 mm Hg, then alveolar and arterial PCO2 will double.

For O2, it is evident that as alveolar ventilation increases, the alveolar PO2 will also increase. Doubling alveolar ventilation, however, cannot double PAO2 in a person whose alveolar PO2 is already approximately 104 mm Hg because the highest PAO2 one could possibly achieve (breathing air at sea level) is the inspired PO2 of about 149 mm Hg.

After some mathematic calculation, we got the following formula to estimate the PAO2:

PAO2 = PiO2 – PACO2/R + F

where, R= respiratory exchange ratio, VCO2/VO2, which represents the whole body carbon dioxide produced per time divided by the whole body oxygen consumption per time. It is primarily dependent on the foodstuffs metabolized by the cells of the body. In a person with a typical mixed diet, it is approximately 0.8; a person consuming a diet consisting of mainly carbohydrates or proteins would have an R of approximately 1.0; a person consuming a diet consisting of mainly fat would have an R of approximately 0.7.

As alveolar ventilation increases, the alveolar PCO2 decreases, bringing the alveolar PO2 closer to the inspired PO2.


Regional Distribution of Alveolar Ventilation

As previously discussed, a 70-kg person has about 2.5 to 3 L of gas in the lungs at the FRC. Each eupneic breath brings about 350 mL of fresh gas into the alveoli and removes about 350 mL of alveolar air from the lung. Although it is reasonable to assume that the alveolar ventilation is distributed fairly evenly to alveoli throughout the lungs, this is not the case. Studies performed on normal subjects seated upright have shown that alveoli in the lower regions of the lungs receive more ventilation per unit volume than do those in the upper regions of the lung.

Explanation

screen-shot-2016-09-16-at-9-03-21-pmPrecise measurements made of the intrapleural surface pressures of intact chests in the upright position have shown that intrapleural surface pressure is not uniform throughout the thorax: The intrapleural surface pressure is less negative in the lower, gravity-dependent regions of the thorax than it is in the upper, nondependent regions. There is a gradient of the intrapleural surface pressure such that for every centimeter of vertical displacement down the lung (from nondependent to dependent regions) the intrapleural surface pressure increses by about +0.2 to +0.5 cm H2O. This gradient is apparently caused by gravity and by mechanical intereactions between the lung and the cehst wall.

Because the difference in intrapleural surace pressure throughout the lung, the transmural pressure of the alveoli between nondependent and dependent lung areas at FRC are not the same. The left side of Figure 3-12 shows that alveolar pressure is zero (equals to atmophere) in both regions of the lung at the FRC. Since the intrapleural pressure is more negative in upper regions of the lung than it is in lower regions of the lung, the transpulmonary pressure (alveolar minus intrapleural) is greater in upper regions of the lung than it is in lower regions of the lung. Because the alveoli in upper regions of the lung are subjected to greater distending pressures than those in more dependent regions of the lung, they have greater volumes than the alveoli in more dependent regions.

It is this difference in volume that leads to the difference in ventilation between alveoli located in dependent and nondependent regions of the lung. This can be seen on the hypothetical pressure-volume curve shown on the right side of Figure 3-12. This curve is similar to the pressure-volume curve for a whole lung, except that this curve is drawn with the pressure-volume characteristics of single alveoli in mind. The abscissa is the transpulmonary pressure. The ordinate is the volume of the alveolus expressed as a percent of its maximum.

The alveolus in the upper, nondependent region of the lung has a larger transpulmonary pressure than does the alveolus in a more dependent region because the intrapleural pressure in the upper, nondependent regions of the lung is more negative than it is in more dependent regions. Because of this greater transpulmonary pressure, the alveolus in the upper region of the lung has a greater volume than the alveolus in a more gravity-dependent region of the lung. At the FRC, the alveolus in the upper part of the lung is on a less steep portion of the alveolar pressure-volume curve in Figure 3-12 than is the more compliant alveolus in the lower region of the lung. Therefore, any change in the transpulmonary pressure during a normal respiratory cycle will cause a greater change in volume in the alveolus in the lower, gravity-dependent region of the lung than it will in the alveolus in the nondependent region of the lung, as shown by the arrows in the figure. Because the alveoli in the lower parts of the lung have a greater change in volume per inspiration and per expiration, they are better ventilated than those alveoli in nondependent regions (during eupneic breathing from the FRC).

A second effect of the intrapleural pressure gradient in a person seated upright is on regional static lung volume, as is evident from the above discussion. At the FRC, most of the alveolar air is in upper regions of the lung because those alveoli have larger volumes. Most of the ERV is also in upper protions of the lung On the other hand, most of the IRV and IC are in lower regions of the lung.

Alterations of Distribution at Different Lung Volumes (low volumes/RV, high volumes/)

Most of the air inspired during a tidal breath begun at the FRC enters the dependent alveoli. If a slow inspiration is begun at the RV, however, the initial part of the breath (inspiratory volume less than the ERV) enters the nondependent upper alveoli, and dependent alveoli begin to fill later in the breath. The intrapleural pressure gradient from the upper parts of the lung to the lower parts of the lung is also the cause of this preferential ventilation of nondependent alveoli at low lung volumes.

Positive intrapleural pressures are generated by the expiratory muscles during a forced expiration to the RV. This results in dynamic compression of small airways. At the highest intrapleural pressures these airways close, and gas is trapped in their alveoli. Because of the graident of intrapleural pressure found in the upright lung, at low low lung volumes the pleural surface pressure is more positive in lower regions of the lung than it is in upper regions. Also, alveoli in lower lung regions have less alveolar elastic recoil to help hold small airways open because they have smaller volumes than do the alveoli in upper regions. This means that airway closure will occur first in airways in lower regions of the lung. The expiratory effort has ended and the inspiratory effort has just begun. Airways in the lowest regions of the lung are still closed, and the local pleural surface pressure is still slightly positive. No air enters these alveoli during the first part of the inspiratory efforts until sufficient negative pressure is generated to open these closed airways.

In contrast to the situation at the FRC, at the RV the alveoli in the upper regions of the lungs are now on a much steeper portion of the pressure-volume curve. They now have a much greater change in volume per change in transpulmonary pressure – they are more compliant at this lower lung volume. Therefore, they receive more of the air initially inspired from the RV.

It has already been noted that even at low lung volumes the upper alveoli are larger in volume than are the lower gravity-dependent alveoli. They therefore constitute most of the RV.

Patients with emphysema have greatly decreased alveolar elastic recoil, leading to high FRCs, extremely high RVs, and airway closure in dependent parts of the lung even at high lung volumes. They therefore have relatively more ventilation of nondependent alveoli.


Reference Range of Critical Parameters

Dry Atmospheric Gas at Standard Barometric Pressure

PO2 = FiO2 X Ptot = 0.2093 X 760 mm Hg = 159 mm Hg

PCO2 = FiCO2 X Ptot = 0.0004 X 760 mm Hg = 0.3 mm Hg

Inspired Gas at Standard Barometric Pressure

PO2 = FiO2 X (PB – PH2O) = 0.2093 X (760 – 47) mm Hg = 149 mm Hg

PCO2 = FiCO2 X (PB – PH2O) = 0.0004 X (760 -47) mm Hg = 0.29 mm Hg

Alveolar Gas at Standard Barometric Pressure

PAO2 = 104 mm Hg, PACO2 = 40 mm Hg, PAN2 = 569 mm Hg, PAH2O = 47 mm Hg

Mixed Expired Air at Standard Barometric Pressure

PEO2 = 120 mm Hg, PECO2 = 27 mm Hg, PEN2 = 566 mm Hg, PEH2O = 47 mm Hg