ASSIG 3

THE AMERICAN JOURNAL OF PHYSIOLOGY

VOL. 146 AUGUST 1, 1946 No. 5

A THEORETICAL STUDY OF THE COMPOSITION OF THE ALVEOLAR AIR AT ALTITUDE1

WALLACE 0. FENN, HERMANN RAHN AND ARTHUR B. OTIS

From the Department of Physiology, The School of Medicine and Dentistry of the University of Rochester, Rochester, N. Y.

Received for publication March 7, 1946

In our studies of high altitude physiology we have found an oxygen-carbon dioxide diagram a very great aid to accurate thinking. It has been useful in so many different problems that we consider it worth while to describe it in this paper so that it can be made available to others.

1. Breathing pure oxygen. In this diagram the alveolar tensions of carbon dioxide are plotted as ordinates against the alveolar tensions of oxygen as abscis- sae as in figure 1, which represents the situation when an aviator ascends to high altitudes breathing pure oxygen. At any altitude, breathing pure oxygen,

pm -I- pa = pm (1)

where ~‘0, refers to the tension of oxygen in the inspired air (BTPS or body temperature, saturated, ambient pressure) and the other tensions refer to al- veolar air (BTPS). This equation gives a family of parallel diagonal lines on the chart each of which represents a given altitude such that B - 47 = ~‘0~. The intercepts of these diagonals on the X axis represent therefore values of B - 47. With the aid of Henderson’s nomogram for the blood of A.V.B. or any other similar data it is possible to assign a given percentage saturation of the arterial blood to every point on the chart. Thus lines of equal arterial satura- tion can be drawn. To indicate the location of such a family of curves the 65, 75, 85 and 95 per cent saturation lines have been drawn. When the saturation becomes less than about 65 per cent the subject is almost certain to lose con- sciousness very soon and this region of the chart has therefore been labelled ‘ ‘anoxia. ”

To show the normal behaviour of an aviator in going to progressively higher altitudes the line marked “alveolar air” has been drawn to indicate the suc- cessive positions of the alveolar air composition as the altitude is increased from ground level to above 43,000 feet. The curve bends downward after passing the 95 per cent saturation line because of the hyperventilation caused by the stimulus of anoxia. Hyperventilation at 43,000 feet moves the alveolar point

1 Th is work was done under a contract recommended by the Committee on Medical Re- search between the Office of Scientific Research and Development and the University of Rochester.

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638 WALLACE 0. FENN, HERMANN RAHN AND ARTHUR B. OTIS

down on the corresponding diagonal so that the pCO2 is decreased about 10 mm. Hg and the ~0, is increased a corresponding amount. If the pC0, is lowered too far by hyperventilation the symptoms of acapnia develop. A line marking this threshold has been drawn on the diagram at 20 mm. Hg although the level varies considerably with different individuals and different durations of exposure.

So long as the rate of CO2 output remains constant alveolar pC02 will vary in- versely with alveolar ventilation. On this assumption a scale of ventilation

Percent )-lbO,

p 02 mm. Hg

Fig. 1. Alveolar pCOz as ordinates plotted against alveolar ~02 as abscissae at dif- ferent altitudes breathing pure oxygen. The average alveolar air line was taken from analyses of alveolar air samples forcibly exhaled beginning at the end of a normal expira- tion. The pCO2 values were 39 mm. at 30,000 ft.; 34.8 mm. at 40,000 ft.; and 32 mm. at 42,000 feet. The figures are averages of 16, 19, and 21 determinations respectively. The scale of alveolar ventilation at the right is calculated by equation 17 on the basis of a rate of CO, output of 315 cc. per minute (S.T.P.).

rates has been indicated at the right of the diagram. The values were cal- culated according to the equation

V / 272 a=

pcoz (2)

where 272 is a constant (see equation 17 and discussion), V,’ is the alveolar ventilation (BTPS) in liters per minute and

V / a = total ventilation (V t> - (dead space X frequency)

Actually of course the COa output does not remain constant at altitudes where hyperventilation occurs because extra CO2 is blown off. Temporarily this will invalidate the equation given above until the R.Q. returns to normal. A rigid derivation of a ventilation equation to take account of this situation will be given below.

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THEORETICAL COMPOSITION OF ALVEOLAR AIR AT ALTITUDE 639

The chart in figure 1 represents the simplest condition. When air instead of oxygen is breathed the diagram is much more complicated but it is for the understanding of these same complications that the diagram is particularly useful.

2. The alveolar air equation. To understand the air-breathing diagram it is necessary to develop the alveolar air equation. Let V = a volume of moist inspired air in milliliters

Y = milliliters of moist CO2 added to V in the lungs X = milliliters of moist 02 removed from V in the lungs c = CO2 and 0 = 02 f = the fraction of moist gas in alveolar air (by volumes) pC and p0 = partial pressures of C or 0 in alveolar air in mm. Hg f’ and p’ refer to moist inspired air

Q Y = respiratory quotient as observed = - X

v+y-x= the new volume after transition from tracheal to alveolar air. y = fC (V + y - x) - j’CV x=f’ov-fo(V+y-2)

Substituting $x for y and A! for x Q

X f’OV - jov

= l+fOQ-f0

Y= fCV - j’CV

1- fc+f+

(3)

(4)

Substituting these values of x and y in the equation ’ = $ and solving for f0 X

gives

j. = j’OQ + fCj’O(l - Q) + f’C - fC fW - Q) + Q

Multiplying both sides by (B - 47) to change f to p we have

po = p’o& + pCj’O(1 - Q> + p’C - pc f’C(l - Q) + Q

(6)

This is the complete alveolar air equation but if COz-free gas is inhaled and j’C = 0 it can be simplified to2

PO = p’0 + pCj’O(1 - Q) pC --

Q Q (7)

If pure oxygen instead of air is inhaled and j’0 = 1; or if Q = 1, whatever the value of f’0 then

PO = p’0 - pc (8)

2 This same equation has been given by Boothby in the Handbook of Respiratory Data, (Washington, D. C., 1944) where prior credit is given to several other authors. (See Essay A.)

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640 WALLACE 0. FENN, HERMANN RAHN AND ARTHUR R. OTIS

Since equation 8 is identical with equation 1 used for the altitude diagonals in figure 1 it is evident (1) that this chart is applicable to oxygen-breathing alti- tudes regardless of the RQ and (2) that if the R.Q. = 1.0 the chart is also ap- plicable to the problems involved in the breat)hing of air.

3. Breathing air. Equation 7 represents the condition where C&free air is inhaled which is practically true of ordinary air. The application of this equa- tion to the oxygen-carbon dioxide diagram is illustrated in figure 2. The alti- tude of 10,000 feet is now represented by a family of diagonals all radiating from a PO’, value of 100 mm. Hg, this being the oxygen tension in the moist inspired air. There is a different diagonal for each R.Q. value and at each altitude there

Percent Hbq, 65 75 85 95

-4 .

p 0, mm. Hg

Fig. 2. Alveolar &‘O, and ~02 at different altitudes breathing air. Families of diagonals for 4 different altitudes are shown. Each line represents a certain R.Q. value as indicated on the graph and was calculated from equation 7. The scale of alveolar vent’ilation at the right is calculated by equation 17 on the arbitrary assumption that the rate of CO2 output is 315 cc. per minute (S.T.P.). The average alveolar air line is based upon analyses of large numbers of samples exhaled forcibly beginning at the end of a normal expiration. Data will be published elsewhere.

is a similar set of diagonals. Four such sets of 0 diagonals have been drawn in figure 2 for four different altitudes. The position of the alveolar air on any one of these diagonals will depend upon the rate of breathing and the rate of CO2 output. The scale on the right indicates the alveolar ventilation for each pCOz level on the assumption that the COa output is constant at 315 cc. per minute. This value was arbitrarily selected. For other values the ordinates are changed in proportion.

It is obvious that the diagonals of one altitude intersect some of the diagonals of a slightly higher or lower altitude. At one of these points of intersection therefore the subject might be at 20,000 feet with an R.Q. of about 1.4 due to

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THEORETICAL COMPOSITION OF ALVEOLAR AIR AT ALTITUDE 641

overventilation and a lowered pC’O2 or he might be at 15,000 feet with an R.Q. of about 0.8. This illustrates the difficulty of calculating what altitude is equiv- alent to a given low-oxygen nitrogen mixture. Strictly speaking it is impoa- sible to calculate such equivalent altitudes without specifying the rate of breath- ing and the R.Q. (See also fig. 5.)

A full set of altitude diagonals for 20,000 feet breathing air is shown in figure 3. If equation 7 is solved for 0

Q PC0 - f’0) = p’0 - po - f’opc

Liters/ min. (Vd) 5 IO 2.0 30 50 06

\ \ \ \\\ \\\\\\ \ 1

I I I I I I

0 IO z-0 30 40 so 60 70

(9)

p U, mm. Hg

Fig. 3. Alveolar air diagram for 20,000 feet breathing air. Each diagonal line starting at PO2 = 63 represents a given R.Q. as indicated on the diagram and was calculated from equa- tion 7. The nearly vertical parallel lines represent points of equal alveolar ventilation cal- culated by equation 15 on the arbitrary assumption that the rate of oxygen consumption, X0, equals 315 cc per min. The average alveolar air line is the same as that in figure 2. The R.Q. = 00 and Va = 00 lines are identical and have a reciprocal slope of 0.2093 = f’0. For points A, B and C see text p. 646.

Obviously Q = 00 when the denominator = 0 or when p’0 - p0 = f’OpC. The negative (reciprocal) slope of the @ = 00 diagonal is therefore f’o. The iso-ventilation lines which are also included in figure 3 will be discussed later.

It is instructive to inquire what happens to the R.Q. diagonals when the percentage of oxygen in the inspired air increases. For the sake of simplicity it may be assumed that the barometric pressure is so adjusted that at all per- centages the tension of oxygen in the inspired air (X intercept) remains con- stant. This assumption however is immaterial to the argument because slopes of the R.Q. diagonals are identical at all values of p’0 for the same value of f’0.

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642 WALLACE 0. FENN, HERMANN RAHN AND ARTHUR B. OTIS

From figure 4 it can be seen that when j’0 (i.e., the fraction of 02 in the inspired air) increases, the R.Q. diagonals come closer together until when j’0 = 1.0 they all coincide with the R.Q. = 1 .O diagonal. Thus when pure 02 is breathed the alveolar air must lie along a single diagonal regardless of the R.Q. On the graphs in figure 4 two special alveolar points are indicated by circles: (1) at pm = 40 and & = 0.8 and (2) at $02 = 25 and & = 1.5. Point 1 is a normal and point 2 is one that could easily be reached temporarily by overventilation without danger of serious hypocapnia. It is significant that the gain in ~02 in this process is 33 mm. Hg at 6 per cent, 31 mm. at 21 per cent, 24 mm. at 60

Fig. 4. R.Q. diagonals at different altitudes (pressures) and breathing gas mixtures of different oxygen percentages so that the inspired ~02 = 63 mm. Hg in each case. Each line is calculated according to equation 7. The spread diminishes as the oxygen percentage increases. See text for discussion of points marked by circles.

per cent, 20 mm. at 80 per cent 02 and only 15 mm. at 100 per cent 02. At air-breathing altitudes therefore the immediate benefit (in terms of ~0, gain) derived from overventilation may be twice as great in terms of alveolar oxygen tension as at oxygen-breathing altitudes and this difference depends upon the spreading of the R.Q. diagonals.

4. Equivalent altitudes. The difficulty involved in calculating what mixture of O2 and Nz is equivalent to a given altitude is illustrated by figure 5. The solid lines represent R.Q. diagonals at 20,000 feet breathing air. The same inspired p’Oz can be obta.ined by an 8.83 per cent 02 + 91.17 per cent N, mixture

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THEORETICAL COMPOSITIOK OF ALVEOLAR AIR AT ALTITUDE 643

at sea level but the R.Q. diagonals on such a mixture differ appreciably as in- dicated by the dotted lines. At equal rates of ventilation therefore the alveolar air would not be the same under the two conditions unless the R.Q. = 1.0. Furthermore at the same R.Q. (except when 62 = 1) it would be impossible to breathe in such a wav that the alveolar composition would be the same at ground level on low 0,‘ as at altitude on air. This is obvious because the R.Q. diagonals for the two conditions do not cross except at infinite ventilation rates (i.e., at pC = 0). This illustrates convincingly the possible fallacies involved in the common expedient of simulating high altitude conditions by low oxygen mixtures.

- 20,OOOft.on air ground 8.83 @fd3,

0’ I

IO tfo I 30 410

I 50 66 : Q

p O2 mm. Hg

Fig. 5. Difference between 20,000 feet breathing air (solid lines) and an 8.85 per cent oxy- gen mixture in nitrogen at ground level having the same inspired ~02 . The dotted and solid R.Q. diagonals diverge more and more as the R.Q. becomes greater or less than 1.0. This illustrates the problem of calculating equivalent altitudes. See text. Each line is calcu- lated according to equation 7.

Similar difficulties are encountered if the condition of breathing air at 20,000 feet is simulated by inhaling pure 02 at 100 mm. Hg where the inspired p02 is again the same. In this case the alveolar air must lie along the Q = 1 diago- nal regardless of the actual value of Q, and the discrepancies between the two conditions are therefore still larger than in the previous comparison. In order to simulate 20,000 feet breathing air by pure O2 at a higher altitude it is neces- sary to select an altitude for pure 02 such that the B - 47 value is equal to pC + p0 for the alveolar air at 20,000 feet. If then the R.Q. and CO2 output can be assumed to remain the same at both altitudes, the alveolar air will be t.he same provided the vent,ilation is so regulated that the alveolar pC02 is also the same.

5. l’he ventilation equ,ation. The intercept of one of these R.Q. diagonals on the x axis represents the oxygen tension of the moist inspired air. When the air enters the alveoli the oxygen tension diminishes and the carbon dioxide ten-

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644 WALLACE 0. FENN, HERMANN RAHN AND ARTHUR B. OTIS

sion increases and the point on the chart which represents the composition of the alveolar air moves up to the left along one of these diagonals. If the rate of breathing is very fast it will not move very far up the diagonals because the air will not remain long in contact with the alveolar walls. If the rate of breath- ing is “normal” the pCOz will be “normal” and the alveolar air composition will lie along the average alveolar air line shown in the chart (fig. 2 or 3). If the rate of breathing is infinitely fast the alveolar air will have the same com- position as the inspired air. It should be possible, therefore, to draw a series of lines across the chart which represent equal rates of ventilation. The deriva- tion of equations for plotting these lines must now be considered. ing altitudes this is somewhat more complicated than it is for

At air breath- pure oxygen.

The problem is much simplified in the beginning if only alveolar ventilations are concerned. The total ventilation can always be obtained by adding the dead space ventilation which is equal to the product of dead space volume and the frequency of breathing. Let Y and X = rates of CO2 output and O2 intake respectively in cubic centimeters per minute at BTPS.

X 0 = 02 intake in cc. per minute at OOC. dry, 760 mm. Hg Y 0 = CO2 output in cc. per minute, at OOC. dry, 760 mm. Hg V a = Alveolar ventilation in cc/min at BTPS, Vt = total and Vd = dead

space ventilation. Vt = Va + Vd. V /

a = alveolar ventilation in liters per min. at BTPS.

Now Y = VafC

fC Y Y =v+y-z=v+y-Y -

Q

Substituting (11) in (10)

Y - -v Y - - v+; -Y or y = QVY

QV a-QY+Y - Q

Putting this value of y equal to that in equation 4 and solving for Va

V = Y(Q + f’C(l - &)I a

= X(Q + f’W - Q)) QCfC - f’C> fC -f’c

Now

X 0 = x273 x B - 47 310 - 760

V a = 1000 v:

(10)

(11)

(12)

fC PC P’C - -- B - 47

and f’C = B-7

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THEORETICAL COMPOSITION OF ALVEOLAR AIR AT ALTITUDE 645

Substituting these values for X, V,, and (in the denominator) fC and f’C in equation 12 we have

V / 0.864X0(& + f’C(1 - Q))

a =

pc - p’C (13)

The equation is more useful when expressed in terms of X0 because this may reasonably be assumed to remain constant while Y, varies with the rate of breathing. While this equation expresses the ventilation in terms of CO2 tension it can also be expressed in terms of O2 tension by the same method. Thus in equation (11)

fC Y QX =v+~-x= V+Qx-x (14)

This value of fC is substituted in (10) and solved for x. The resulting equation is combined with (3) and solved for Va to obtain

V / 0.864 X0(1 - f’O(1 - Q)) a =

p’0 - po If f’0 = 1, then f'C = 0 and from (15)

V I 0.864 Xo Q a= p’0 - po WV

1f fV = 0 then from (13)

Jr’ = 0.864 Xo Q 0.864 Yo a

pc = pc (17)

If Y, = 315 cc. COz per minute equation 17 is identical with equation 2. Thus, when the CO2 output is assumed constant and p’C = 0, the lines of constant ventilation of the pCOz-pOz chart are parallel to the X axis for all altitudes, according to the scale shown in figure 1.

6. Oxygen isoventilation lines (when X, is constant). Equations 13 and 15 express the alveolar ventilation in terms of the R.Q. On a chart like that in figure 2 they would permit the calculation of the alveolar ventilation which would be necessary to reach a given pCOz value (equation 13) or a given ~02 value (equation 15) on a specified R.Q. diagonal at any altitude. In order to draw an isoventilation line on such a chart it is necessary to combine these two equations with the elimination of @ This results in the following

V L

0.864 X0(1 - f’o - f’c> = (1 - f’C)(p’O - PO) - f’O(pC - p’C>

Or, rearranging,

(18)

PO= -- p’o + f’OP’C 0.864 X,( 1 - f'0 - f'C) f ‘OPC 1 - f’C w Vi(l -f’c> - iqv ’

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646 WALLACE 0. FENN, HERMANN RAHN AND ARTHUR B. OTIS

In equation 19 all the terms refer to the composition of the inspired air at a given altitude except p0, PC, X0 and Va’. The equation gives therefore the composition of the alveolar air which would be expected from a given set of con- ditions if the rate of oxygen consumption and the alveolar ventilation are known. If p0 and pC are the only variables then this is the equation of a straight line of

reciprocal slope equal to - f0 GC (in the last term) and the intercept on the X

axis is given by the first 3 terms on the right side of the equation. When CO2 is absent from the inspired air, equation 19 may be simplified to

PO = p'0 - 0+64X0(1 - j'0) _ j,OpC Va I (20)

When in addition, j’0 = 1 the equation becomes p0 = p’0 -PC. This means that in pure O2 the alveolar air is always somewhere on this diagonal regardless of the values of V,‘, X, , or Q.

A set of isoventilation lines plotted from equation 20 for a subject breathing air at 20,000 feet is shown in figure 3. All the lines are parallel and have a negative slope of 0.209 which is the fraction of oxygen in the inspired air (j’0). The line for Va’ = 00 is seen to coincide with the line for Q = 00.

The beneficial effect of high R.Q. due to overventilation at altitude is well illustrated by figure 3. Point A indicates that a subject at this altitude with a rate of oxygen consumption of 315 cc. per min. and an R.Q. of 0.8 who is breath- ing so as to provide 5 liters per minute of alveolar ventilat,ion will have an al- veolar pCOz of 42 mm. (This is slightly higher than normal but will illustrate the principle.) If now the alveolar ventilation is increased to 10 liters per min- ute the alveolar CO2 tension will decrease and the R.Q. will increase possibly to 1.4 so that the alveolar air will be represented by point B, the p02 being 22 mm. greater than at A. If the same ventilation rate is maintained for a half hour or more the R.Q. will gradually fall as excess CO2 is blown off until it returns to the normal value of 0.8 as represented by point C.

It is important to note that this temporary gain in pOz due to hyperventilation is largely dependent upon the presence of nitrogen in the air. If pure O2 had been inhaled the point B would have been on the same diagonal as points A and C (i.e., the & = 1 diagonal) each point being at the same pCO2 level as in figure 3; and the gain in ~02 would have been correspondingly less as shown in figure 4. The greater the oxygen percentage, the more nearly the R.Q. diagonals and the O2 isoventilation lines coincide with the Q = 1 line and the less the temporary gain in ~0, with hyperventilation.

Another way to explain this R.Q. effect is as follows. When pure O2 is in- haled the CO2 which escapes into the lung must displace 02 in equal amounts so that a 10 mm. increase in pCO2 leads to a 10 mm. decrease in ~02. When air is inhaled however an increase of 10 mm. pCO2 in the lungs leads approxi- mately to a decrease of pN2 of 7.9 mm. and a decrease of p02 of only 2.1 mm. The slope of the 02 isoventilation lines in figure 3 indicates a loss of 2.1 mm. of ~02 for a gain of 10 mm. of pCO2. Thus when overventilating with inspired

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THEORETICAL COMPOSITION OF ALVEOLAR AIR AT ALTITUDE 647

air the resulting high R.Q. and increased CO2 output has the advantage that it maintains the pC0, at a comfortable level without appreciably diminishing the gain in pOz.

Or conversely, it may be said that in air, the same gain in ~02 is obtained with less increase in ventilation than in pure 02. After the high R.Q. due to anoxic hyperventilation has returned to normal (point C, fig. 3) there is little differ- ence between pure 02 and air in this respect. For a fall of 10 mm. in the pCO2 there is a (permanent) gain of 10 mm. in pOz when pure oxygen is inhaled and a gain of about 12 mm. ~0, in air if the R.Q. is 0.8. It is well known that this initial R.Q. effect is a very important factor in the maintenance of conscious- ness for short periods at extreme altitudes in air. The principle is not new but is here demonstrated in a novel way.

Li tera/min. (Va’) if X, = 3C 0 5 to- 5 IO 20 5000

\ \

Q=l Q=l

I I I I I I 40 60 80 100 IZLD M=o

- a I 160

p UL mm. Hg

Fig. 6. Lines of equal alveolar ventilation at three different values of f’0 or oxygen frac- tion in the inspired air. The right side of the figure represents the situation when air is inhaled, the left side, the case for pure oxygen, and the family of lines in the middle repre- sents 80 per cent oxygen. (See text .)

It has been shown in figure 4 that the R.Q. diagonals approach the Q = 1 line when f'0 approaches 1.0. The same is true of the oxygen ventilation lines calculated from equation 15 or 19 when X, is constant. This result is illustrated graphically in figure 6 where 3 sets of diagonals are plotted for f'0 = 0.21, 0.8 and 1.0. These are plotted arbitrarily at different ~‘0, values but this makes no difference because the slopes of the lines are not influenced by the absolute pOz but only by the 02 percentage, f'0 as shown by equation 20. In this graph the points of intersection of the iso-ventilation lines and the diagonal Q = 1.0 are marked by circles. For the same ventilation rate these intersections are all at the same pC0, value at all altitudes. Thus as f’0 approaches 1.0 these iso- ventilation lines rotate anticlockwise about these marked intersections until at f'0 = 1 .O in pure oxygen they coincide with the Q = 1.0 diagonal.

7. Carbon dioxide isoventilation lines (i.e., when Y, is constant). The iso- ventilation lines shown in figure 3 were derived on the assumption that the rate of oxygen consumption is constant. Passing along one of these lines from low

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648 WALLACE 0. FENN, HERMANN RAHN AND ARTHUR B. OTIS

to high CO2 tensions it is found that the p0 gradually diminishes as the R.Q. increases. The reason for this is that at the higher R.Q. values the rate of CO2 output is greater for the same amount of 02 taken out. As more CO2 comes into the lungs from the blood per minute the volume of air that comes into the lungs from the trachea is correspondingly diminished because there is less decrease in volume due to oxygen absorption. Hence the oxygen in the alveoli is not renewed so rapidly and the oxygen tension falls.

When the rate of carbon dioxide output is assumed to be constant a very different set of isoventilation lines results. This can be shown by replacing

OJmin. if Va’= 10 l/min.

60 80 loo p OL mm. Hg

160 ”

Fig. 7. Alveolar air chart for 20,000 feet (left) and ground level (right) breathing air showing R.Q. diagonals 0.5,l.O and 2.0 for each altitude. The chart shows the relationship between isoventilation lines (nearly vertical) when the O2 intake is assumed constant and those (horizontal) when the CO% output is constant.

X, by YO/Q in equations 13 and 15, and then combining them as before with the elimination of Q. This results in the following

rl’ - 0.864 Yo(l - f’C - j’0) - (PC - p'C)(l -f'O) -jv(p'O - PO)

or, rearranging

PO = P’O + p'C(1 - f'0)

jlc + 0.864 Y,(l - f’C - j’0) - 1 - f’OpC (22j

vyc I fC

Evidently these equations are very similar in form to equations 18 and 19. Whenf’O = 1 or when f’C = p’C = 0 equation 21 reduces to equations 16 or 17.

The two sets of isoventilation lines given by equations 18 and 21 may be called for convenience the oxygen and the carbon dioxide isoventilation lines respec- tively. The relation between them can be shown most simply when there is no COz in the inspired air as illustrated in figure 7. In this graph R.Q. diagonals for Q = 0.5, 1.0 and 2.0 are drawn for two different altitudes breathing air. The oxygen isoventilation lines are drawn from equation 20 assuming that X = 300 cc. per min. and the carbon dioxide isoventilation lines, parallel to the X axis, are drawn from equation 17 assuming that Y = 300 cc. per minute.

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THEORETICAL COMPOSITION OF ALVEOLAR AIR AT ALTITUDE 649

When Q = 1.0 both Y, and X0 = 300 and both the O2 and CO2 5 lit/min ventilation lines intersect at both altitudes on the Q = 1.0 lines. The same is true for the 10 and 20 lit/min lines. When however Q = 2.0 the 10 lit/min O2 line intersects the 5 lit/min CO2 ventilation line. But this is a 5 lit/min line only when Y, = 300. Since Q = 2.0, Y, in this case = 600 so the ventilation is really 10 lit/min at this point if X0 = 300 as indicated by the O2 line. Con-

.6 .8 1.0 I.4 2.l

50-

k \ \\- 42qa 21 40 ml \ \ \\\\\

.

60-

0 ;L co 2

I - -

I I I I I I I I I I

0 ’ lb zb 3b 4b 50 60 70 8-O so IC

0 0% mm. Hg Fig. 8. The effect of adding CO2 and 02 to the inspired air. Three sets of R.Q. diagonals are shown for three

different mixtures. All are calculated according to equation 6 for an altitude of 29,815 feet. The isoventila- tion lines traversing the R.Q. diagonals are calculated according to equation 22 assuming that the CO* output, YO = 315 cc per minut,e. As the pCOz increases in the inspired air these lines deviate from t,he horizontal. Figures on these lines indicate the alveolar ventilation in liters per minut’e.

versely these ventilation lines may be regarded as lines of equal Y, or X0 if the alveolar ventilation = 10 lit/min. The numerical values appropriate to this interpretation have been inserted in the figure. Thus the two 600 cc/min lines intersect on the diagonal Q = 1.0 but the 300 cc. X, and the 600 cc. Y, lines intersect on the Q = 2.0 diagonal.

8. Ventilation when inspired air contains CO:!. When the inspired air con-

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650 WALLACE 0. FENN, HERMANN RAHN AND ARTHUR B. OTIS

tains a certain amount of CO2 the carbon dioxide ventilation lines plotted from equation 22 are not parallel to the X axis but they have a reciprocal

1 -f’O. slope equal to - I

fC This is illustrated in figure 8 where three sets of R.Q.

diagonals are represented for different mixtures of 02 and CO2 at 29,815 feet. The effect of adding 20 mm. of COz to the inspired air is to raise the origin of the R.Q. diagonals by 20 mm. Breathing COz-free air in the lower left the COz isoventilation lines are parallel to the Xaxis as in figures 6 and 7 and are drawn from equation 17 assuming that Y = 315 cc/min. In a 10.5 per cent COZ, 31.4 per cent O2 mixture the isoventilation lines have a s1igh.t slope to them and

p Oz mm. Hg

Fig. 9. Alveolar air chart illustrating the advantages of adding CO2 to the inspired air at an altitude of 20,000 feet. Two sets of R.Q. diagonals are represented breathing air and air plus 6.6 per cent COZ. Dotted lines represent isoventilation lines calculated by equation 19 on the assumption that the rate of oxygen intake, X0 , is constant at 315 cc/min. See text for the significance of the marked points.

this is more marked when the oxygenand the CO2 are both still further increased. It may also be observed that as the nitrogen percentage decreases, the R.Q. diagonals come closer together as they did in figure 4 for oxygen alone. When the nitrogen percentage = 0 the COz isoventilation lines coincide with the Q = 1 diagonal just as the O2 isoventilation lines do. This can be seen from equation 22. When f ‘0 = 1, then f’C = 0 and this equation reduces to p0 = p’0 - pC which is the equation for the Q = 1 diagonal.

9. Advantages of inspired CO2 at altitude. It has been shown that a high R.Q. is advantageous at altitude because it permits a high ventilation rate and con- sequently a high alveolar p02 without serious hypocapnia. The same is true of COa added to the inspired air. The benefit in other words is the same whether the CO2 is exogenous or endogenous.

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THEORETICAL COMPOSITION OF ALVEOLAR AIR AT ALTITUDE 651

The advantage gamed from adding CO2 to the inspired air is shown in figure 9. Two sets of altitude diagonals are drawn for 20,000 feet. The lower set applies to the case where COZ-free air is breathed. If now CO2 is added to air at this altitude until the CO2 tension is 20 mm., the CO2 percentage will be 6.62 per cent and the oxygen will have been diluted to 19.5 per cent. The total dry pressure (B - 47) = 302 mm. The broken lines in figure 9 are 02 isoventilation lines drawn from equation 19. With this particular CO2 mixture made by dilut- ing air the equation for the ventilation is the same whatever the amount of CO2 added but this is a special case selected both because of its simplicity and be- cause it is the most practical way of producing such a mixture for experimental purposes. If a subject goes to 20,000 feet without changing his rate of CO2 output or his ventilation he would have an alveolar air composition represented by point A (assuming an R.Q. of 0.8). Due to the stimulus of anoxia he would increase his ventilation rate from 5.6 to perhaps 11.6 liters per minute and would move approximately to point C where his R.Q. is 1.4. If however he were to use a 6.6 per cent COz mixture he would be at point B for the same rate of ventilation or at about point E if his ventilation were increased to 20 liters per minute. Both points C and E are only temporary because if the ventilation were to continue at the same rate the R.Q. would eventually return to 0.8 and the alveolar air would move to points D and F respectively. Point D would have the higher arterial saturation but it has the disadvantage of a considerable amount of hypocapnia. The performance would certainly be better at F than at D and probably better at E than at C. Point B is better than C because it can be maintained indefinitely but the arterial saturation is only about 67 per cent while at D it is about 90 per cent (see fig. 2 for saturation lines). At F however the saturation is 85 per cent and the pCOz is high enough for normal performance. Comparing points A and B it is evident that the addition of 20 mm. of CO2 has increased the oxygen tension 20 mm. without decrease in the pm l

Comparing points B and D it is evident that at the same rate of ventila- tion the addition of 20 mm. of CO2 to the inspired air has raised the alveolar pCOz 21 mm. with a loss however of 5 mm. of ~02 .

The & = 1 diagonal for 6.6 per cent CO2 has been continued as a broken line to the X axis which it intersects at 79 mm. This represents the oxygen tension of the inspired air at an altitude of 15,137 feet. It may be said therefore as an approximation that the addition of this amount of CO2 has lowered the equiv- alent altitude 4 or 5 thousand feet.

10. Survival limits on the COZ-02 diagram. Finally it seems worth while to call attention to figure 10 which represents a COZ-02 diagram on a much larger scale to include the lethal limits in all directions. The shaded area up to about 1 atmosphere of pOz, represents the normal or physiological area. It is bounded on the top by the CO2 narcosis level at about 50 mm. on the bottom by the acap- nia threshold at about 20 mm. pC02 and on the left by anoxia at altitudes > 40,000 feet or tensions of O2 < 100 mm. The corners of this shaded area are rounded off indicating that the effects of anoxia are additive to both high CO2 and low COZ. At an air pressure above 5 atmospheres the disorienting effects of high nitrogen concentration become noticeable (Behnke et al., 1935) and at

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652 WALLACE 0. FENN, HERMANN RAHN AND ARTHUR B. OTIS

10 atmospheres or diving depths under water of 200 feet this nitrogen narcosis becomes severe. At 3 atmospheres of 02 pressure oxygen poisoning becomes evident in some 2 hours of exposure and this effect is more severe at the higher CO2 tensions. Thus high CO2 is additive in its effects to both high 02 and high nitrogen. The combination of high COz with still higher O2 pressures may

-- - CO2 Narcosis

c

c

b

l

.

.

.

c

O *

m

Inspirrd I Air 2

pOi-Atmospheres

Fig. 10. An alveolar air diagram to illustrate schematically the relation of the normal range of pOz and pCO2 to the abnormal regions characterized by too much or too little of either gas. Abscissae represent oxygen tensions in atmospheres. If these same partial pressures of O2 are reached by breathing air at pressures indicated on the middle horizontal scale there is the additional complication commonly ascribed to nitrogen poisoning. The

lowest scale on the axis of abscissae represents the corresponding altitude in feet breathing O2 or the depth under water breathing air which would give the same O2 pressure. Exact

positions of the lines are not well established.

result in collapse within a minute as reported by Case and Haldane 1941. Many details of this diagram are still most uncertain as for example the alveolar pC0, level at high oxygen pressures and the effect of combining acapnia and high nitrogen or high oxygen. It seems a fair guess that these effects will also be additive so that at high pressures acapnia will occur at higher pCOa levels than

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THEORETICAL COMPOSITION OF ALVEOLAR AIR AT ALTITUDE 653

under normal conditions. Figure 10 is presented only as a simple means of utilizing this diagram for the demonstration of a large number of physiological effects of respiratory gases.

No originality is claimed for any of the physiological facts reported in this paper. The method of presenting the facts and parts of the mathematical treatment are new and bring out the relationships in a clear and quantitative way which should be helpful in both teaching and research.

SUMMARY

Equations are developed for calculating the alveolar air composition in terms of the altitude, the composition of the inspired air, the alveolar ventilation volume, the rate of oxygen consumption and the R.Q. These equations are illustrated graphically in a series of charts in which pC0, is plotted as ordinates aga.inst ~0% as abscissae. The important physiological consequences of these equations are pointed out. The paper represents a theoretical treatment of certain known facts of high altitude physiology.

REFERENCES

BEHNKE, A. R., R. M. THOMPSON AND E. P. MOTLEY. This Journal 112: 554,1935. CASE, E. W. AND i. B. S. HALDANE. J. Hyg. 41: 225, 1941.

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