Pulmonary Gas Exchange and the ABG

 

Understanding the physiology of pulmonary gas exchange is difficult for most of us.  In spite of clear presentations in classic textbooks (6), many of us have only a qualitative grasp of the determinants of hypoxemia and hypercarbia.  Although we may understand the relationship of shunt to hypoxemia, and ventilation to PCO2, the more complicated dependence of the arterial blood composition on oxygen consumption, carbon dioxide production, cardiac output, and the distribution ventilation-perfusion ratios in the lung is far more difficult.  One reason for this difficulty is the fairly complex inter-relationship of these factors to the final arterial blood gas, which makes it hard to guess the relative effects when several factors change simultaneously.

 

A better understanding may come from a quantitative analysis of pulmonary gas exchange.  Begin by picturing yourself standing in the left atrium.  You look about and see streams of blood draining onto you from the pulmonary veins and mixing to form the arterial blood.  After your initial shock has passed, you observe that the color of the blood coming from different pulmonary veins is different.  Veins carrying blood from the apex of the lung which is evidently well oxygenated is bright red, while veins carrying blood from the more poorly oxygenated areas of the lung is a bit more blueish.  You then observe that the final color of the mixture of blood swirling around you is in between these two extremes;  indeed it is the color you would get if you mixed a blood sample from each pulmonary vein in proportion to its contribution to the mixture, namely its fractional perfusion.  Since the color of the blood is related to its oxygen saturation and thus to its oxygen content, evidently the final arterial blood gas is can also be constructed by mixing together the oxygen contents (and carbon dioxide contents) of the various pulmonary veins in proportion to their respective fractional perfusions.

 

Let us see if we can make this a bit more precise by quantitatively considering the fundamental determinants of arterial blood gas composition.  We begin with the single respiratory unit.  This is the volume of lung within which gas composition is uniform due to diffusive mixing.  In humans, the respiratory unit appears to be the distal alveolar duct (2, 1) which subtends approximately 1000 alveoli.  In a steady state, the rate at which oxygen (or any other gas) enters the unit from the atmosphere is the same as the rate at which oxygen leaves the unit in the capillary blood.  We can write this down as an equation:

 

                        Rate of O2 entering unit = Rate of O2 leaving unit

                        VI * FIO2   -  VA * FAO2  = Q * CCO -  Q * CVO2

 

 

where VI and VA are the inspired and alveolar ventilations; FIO2 and FAO2 are the inspired and alveolar fractional oxygen concentrations;  Q is the blood flow to and from the unit; and CVO2 and CCO2 are the mixed venous and capillary oxygen contents in the blood flowing into and out of the unit.  Here is a schematic of the single unit.

 Graph

  Notice, the rate at which oxygen enters the blood from the atmosphere is simply the difference between the amount of oxygen inspired (VI * FIO2 ) and the amount expired (VA *FAO2 ) in each minute, since not all the oxygen in the inspired air is absorbed in each breath; some oxygen remains in the expired air.  Similarly, the net addition of oxygen to the blood is the amount of oxygen exiting the unit in the capillary blood (Q * CCO2  ) minus the amount entering the unit in the mixed venous blood (Q * CVO2  ), since the mixed venous blood generally still has some oxygen remaining in it after perfusing the tissues.

 

Identical statements can be written down for the other gases present in the unit, namely carbon dioxide and nitrogen.  It is helpful to put all three equations side by side so that we can see the similarities:

 

            for O2:            VI * FIO2 - VA * FAO2  = Q * CCO2  - Q * CVO2        (1)

            for CO2:                      - VA * FACO2  = Q * CACO2  - Q * CVCO2                (2)  

            for N2:             VI * FIN2  - VA * FAN2  = Q * CCN2  - Q * CVN2                      (3)

 

These equations are nonlinear, coupled, implicit, and simultaneous.  Their complete solution requires a computer.  However, for purposes of discussion only, we can make a simplifying assumption that VI and VA are approximately the same (V) and then rearrange these equations algebraically to show the O2 and CO2 contents in the blood flowing from the unit.

 

                                    CCO2 = CVO2 + V/Q * (FIO2 - FAO2)

                                    CCCO2 = CVCO2 - V/Q * FACO2

 

Notice, the gas contents in the blood coming from the unit depend upon only three things: the mixed venous composition entering the unit, the inspired O2 fraction, and the ratio of ventilation to perfusion of the unit.   Of course, to calculate the corresponding PO2 and PCO2, we must also know several additional details, namely the blood hemoglobin concentration, the oxyhemoglobin dissociation curve, and the relationship between CO2 content and PCO2, (the carbon dioxide solubility curve).  This mathematical approach explicitly reveals the fundamental importance of the mixed venous composition and the V/Q ratio to the final arterial blood gas. 

 

To transfer these conclusions to the real lung, notice that there are about half a million respiratory units in the lung (8), each with its own V/Q ratio, but fortunately each receiving the same mixed venous blood and the same FIO2.  Thus, all of the respiratory units in the lung share two of the three determinants of gas exchange.  The blood from each unit drains ultimately into the left atrium where the contributions from all of the units mix in proportion to their perfusion to form the final mixed arterial blood.  So, the determinants of arterial blood gas composition in the lung are identical to those of the single unit, with the V/Q distribution taking the place of the V/Q ratio.

 

At this point we can get closer to the real lung by joining a set of individual respiratory units in parallel:

Graph

Notice, the individual compartments each receive the same mixed venous blood and inspire the same FIO2, and each contributes to the final arterial mixture in proportion to its perfusion, just like the real lung.  If we specify a different V/Q ratio for each compartment, we can solve equations 1-3 above exactly for the oxygen and carbon dioxide content of each compartment, using a computer (10).  (If you would like to learn the techniques used to solve these equations exactly, see me.)     If we then mix the compartment contents together in proportion to the fractional perfusion of each compartment, we get the mixed arterial O2 and CO2 contents.  We can then use the hemoglobin dissociation curve and the CO2 solubility curve to lookup the corresponding PO2 and PCO2 of the mixed arterial blood.  That is all there is to it.

 

For  example, here is the VQ distribution from a normal 23 year old medical student at rest sitting in a chair:

Graph

Notice it is relatively narrow and is centered about an average V/Q ratio of 1.  If we use this distribution to construct a 10 compartment model and compute the PO2 and PCO2 and capillary blood contents for each compartment using a normal mixed venous composition (and the computer program) we get:

  

V/Q

%cardiac output

pH

PO2

PCO2

CcO2

CcCO2

0

0.0

7.38

40.0

45.0

13.9

51.8

0.05

0.0

7.37

49.9

46.1

16.2

51.6

0.1

0.0

7.37

52.9

45.9

16.7

51.3

0.3

2.7

7.37

67.0

44.7

18.1

50.3

0.5

18.7

7.38

81.2

43.1

18.8

49.3

1.0

69.0

7.41

103.8

39.2

19.3

47.3

2.0

8.4

7.45

121.6

33.2

19.5

44.1

3.0

1.3

7.49

129.1

29.1

19.6

41.7

6.0

0.0

7.57

137.8

21.5

19.9

36.8

10

0.0

7.65

141.8

16.3

20.0

32.9

 

To calculate the mixed arterial O2 content we add up the compartment O2 contents in proportion to their fractional perfusions.  Since there are only five perfused compartments, the mixture will look like this:

 

arterial O2 content =  2.7%*18.1 + 18.7%*18.8 + 69%*19.3 + 8.4%*19.5

              + 1.3%*19.6

 

This equals 19.2 mls O2 per 100 mls blood.  If we do the same thing for CO2  we will find that the arterial CO2 content is 47.4 mls CO2 per 100 mls blood.  The final step is the get the arterial blood gas from the contents.  For O2 we use the hemoglobin dissociation curve :

Graph

An O2 content of 19.2 corresponds to a PO2 of 100.  Doing the same thing with the CO2 content curve would show that a CO2 content of 47.4 would correspond to a PCO2 of 40 :

 

Graph

For a normal bicarbonate concentration, the corresponding pH can be obtained from the Henderson Hasselbach equation and is 7.41 

 

So, that is how the arterial blood gas actually comes about.  A few fine points should be mentioned.  First, we saw above that the arterial blood gas depends fundamentally on the mixed venous composition.  In a living patient however, the mixed venous composition itself depends upon the total oxygen consumption and carbon dioxide production of the body and by the position and breadth of the V/Q distribution itself.  Consequently, the basic determinants of arterial composition are actually interdependent!   This interdependence is a source of significant confusion, which can be relieved interactively working through several case studies using the computer simulation associated with this web page ( click here).  I encourage you to simply play around by varying aspects of the V/Q distribution, varying the O2 consumption and CO2 production requirements, introducing an anemia, etc, and observe the final effect on the arterial blood gases, until you feel comfortable with your overall understanding of pulmonary gas exchange.  By varying parameters step-wise, you can observe the effect of each parameter independently on the final blood gas values.

 

Here is a typical clinical case for practice.  An elderly man with underlying obstructive pulmonary disease and advanced congestive heart failure is admitted to the intensive care unit in respiratory failure.  He is intubated and placed on mechanical ventilation and is deeply sedated.  He is found to have pneumonia and is wheezing diffusely.  Based on these findings, one can assume his V/Q distribution is abnormal and is composed of a combination of shunt, low V/Q and high V/Q ratios (3).  His arterial blood gas is pH 7.44, PCO2 36, PO2 65 on 30% inspired oxygen.  Later that evening, he develops a fever (39 oC), rigors, and hypoxemia.  Reevaluation reveals his chest x-ray is unchanged, he remains sedated, and there is no evidence of any other complication.  His ABG is now pH 7.25, PCO2 74, PO2 56.  What has happened ? (Clue: what do fever and shivering do to the patients O2 consumption and CO2 production (4,11) ?)

 

Solution:  Using the program (VO2.htm), create an abnormal V/Q distribution containing perfusion of shunt, low V/Q and high V/Q ratios and set the FIO2 at 0.30.  Since the patient is sedated, use default values of O2 consumption, CO2 production, and cardiac output, and then calculate the arterial blood gas.  Vary the V/Q distribution until the initial blood gas values are approximated.  At his point, raise body temperature from 37oC to 39oC and re-compute the ABG.  Paradoxically, the PO2 rises by about 6 mmHg.  Why? This is the Bohr effect, which is confirmed by noting that the total arterial oxygen content has not increased, in spite of the higher PO2, implying a shift to the right of the hemoglobin dissociation curve.  Next, double O2 consumption and CO2 production to 500 ml/min and 400 ml/min respectively and recalculate the ABG. This reveals the development of hypoxemia and hypercarbia. Why?

 

The output of the calculation shows that because of the higher oxygen consumption, the mixed venous oxygen content declines significantly.  Since areas of shunt and low V/Q ratios are present, the lower mixed venous content in turn drives the mixed arterial oxygen content lower, resulting in hypoxemia.  The converse applies to carbon dioxide. 

 

A few other teaching points can be made.  First, since our patient has become hypercarbic, evidently he is too sedated to increase his minute ventilation and return his PCO2 to normal.  How does increased total minute ventilation affect the V/Q distribution?  If the distribution of ventilation remains unchanged, increasing total ventilation will raise the V/Q ratio of each compartment and increase the total V/Q ratio of the lung.  This will decrease the arterial PCO2.  Second, because of heart failure, he cannot increase his cardiac output adequately in response to an increased metabolic demand.  If he could, what would the effect be on his blood gases?  Increasing his cardiac output from 5 L/min to 7 L/min increases his PO2 back to 64, and decreases his PCO2 to 53.  Examination of the mixed venous composition again reveals the mechanism.

 

 

References

1.  Ciurea D, Gil J.  Morphometric study of human alveolar ducts based on serial sections. J App Physiol  67: 2512-2521, 1989.

 2.  Felici, M, Filoche M, Sapoval B. Diffusional screening in the human pulmonary acinus. J Appl Physiol 94: 20102016, 2003.

 3.  Gea J, Roca J, Torres A, Agusti AGN, Wagner PD, Rodriguez-Roisin R.  Mechanisms of abnormal gas exchange in patients with pneumonia.  Anesthesiology 75:782-789, 1991.

 4.  Manthous CA, Hall JB, Olson D, Singh M, Chatila W, Pohlman A, Kushner R, Schmidt GA, Wood LD.  Effect of cooling on oxygen consumption in febrile critically ill patients.  Am J Respir Crit Care Med  151: 10-14, 1995.

 5. Ochs M, Nyengaard JR, Jung A, Knudsen L, Voigt M, Wahlers T, Richter J, Gundersen HJG.  The number of alveoli in the human lung. Am J Respir Crit Care Med 169: 120-124, 2004.

 6. West JB.  Respiratory Physiology- the Essentials, Baltimore, MD : Williams and Wilkins, 2004.

 7.  West JB, Wagner PD.  Pulmonary gas exchange. In: Bioengineering Aspects of the Lung, edited by West JB. New York, NY : Marcel Dekker, 1977.

 8.  Zwischenberger JB, Kirsh MM, Dechert RE, Arnold DK, Bartlett RH.

Suppression of shivering decreases oxygen consumption and improves hemodynamic stability during postoperative rewarming. Ann Thor Surg  43: 428-431, 1987.