OXYGEN EXCHANGE, BLOOD, AND THE CIRCULATION.

A COORDINATED TREATMENT OF THE FACTORS INVOLVED IN OXYGEN SUPPLY ON THE BASIS OF THE

DIFFUSION THEORY.

BY CECIL D. MURRAY AND WILLIAM 0. P. MORGAN.

(From the Physiological Laboratory, Cambridge University, England.)

(Received for publication, June 25, 1925.)

In the transport of oxygen from lungs to tissues and in the local processes of oxygen exchange, several anatomical and func- tional components are involved: lungs, the heart and larger blood vessels, capillaries, and blood itself. It will be realized that the preceding paper (1) deals with two types of interconnections exist- ing among these components. The first type includes relations which are governed, as it were, by well established physicochemical laws conditioned by the known properties of the various elements of the system. This set of relations constitutes the quantitative physicochemical background of the process of oxygen exchange. As will appear later, this process can be described with very fair accuracy as the steady operation of a system with six degrees of freedom. The second type includes relations governed by physio- logical laws, the nature of which are only vaguely perceived, but which are recognized by the further restrictions, perhaps statisti- cally defined, imposed upon the wide physicochemical scheme. These laws not only delimit a physiological “range” upon the general background, but they also determine a correlation between variables which otherwise, from the purely physical point of view, are apparently independent. The distinction between the two types of relations is perhaps only a temporary necessity, but it at least suggests and emphasizes a dominant problem.

The phenomenon of adaptation can well be studied in connec- tion with a quantitative and detailed description of a particular and simple physiological function, which, though complex in its manner of operation, is yet thoroughly investigated. With this

419

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420 Oxygen Exchange, Blood, and Circulation

in mind we have not thought it superfluous to elaborate into a scheme those relations, discussed in the preceding paper, which are of a purely physical and chemical nature. The scheme to be presented includes a few additional variables and describes as far as possible the whole process of oxygen transport in a general- ized and coordinated manner. Whatever may have developed which contributes to purely physiological problems will not be referred to in this paper, for it is our immediate purpose to de- scribe the physically possible variations in the process of oxygen exchange which are available to man and to animals with blood and circulatory systems of the human type. There can follow a study of those variations or particular paths which are actually “chosen” by the organism.

Description of the Oxygen System.

Of the factors involved in the “oxygen function” of the organism many can be dealt with analytically, some however cannot, and therefore, for the time being, the basis of any coordinated treat- ment must be a graphical one. We can begin at once by referring to Fig. 2 of the preceding paper (1). From the method of its construction, it will be noticed that, if a straight line be drawn on this figure from the venous point to the arterial point, it will have a slope which defines a certain hypothetical, “average” head of oxygen pressure between alveolar air and blood of a composition varying from venous to arterial. This “mean” head of pressure (which can be designated Ap’, in contradistinction to Ap, the head at any particular point in time or along the length of a capillary) is equivalent to the sum of the heads of pressure at each small in- terval, multiplied by the fraction of the whole time or length rep- resented by each small interval of time or length. In mathe- matical form

t1 Ap’ X t =

s A\pdt

to

The factor Ap’ has been calculated for certain special cases by Bohr (2) and by Barcroft (3). It is introduced here because it is one of the two important factors which directly determine oxygen exchange across the capillary wall. The other factor is

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C. D. Murray and W. 0. P. Morgan 421

also a complex one which depends on the capillary surface area, the thickness and the permeability to oxygen of the capillary wall, the temperature, etc. This second factor has likewise received some attention in the past, and has been discussed in Barcroft’s report just alluded to. We will adhere, for the present discussion, to the term diffusing capacity, DC, which was used in the pre- ceding paper. The diffusing capacity may be conveniently thought of as being proportional to the active capillary surface, since, as suggested by the work of Krogh (4), physiological varia- tions in this factor are especially significant.

According to a simple application of the law of diffusion

A$ x DC = MR X k (1)

where MR is the amount per minute of oxygen, measured in cc. of dry gas under standard conditions, which passes across a capil- lary wall of diffusing capacity, DC. If Ap’ is measured in mm. of mercury and if k is taken as one, k = 1, the unit’ of DC is thereby arbitrarily defined.

It is also desirable to introduce the oxygen capacity of blood as a variable to be considered. Let Hgb, therefore, refer to the oxygen capacity of the blood in volumes per cent; i.e., to the cc. of O2 (standard) contained in 100 cc. of blood in equilibrium with a partial pressure of oxygen, pOz = 145 mm. With this additional variable the term specific diffusing capacity, SDC, must be ex- tended to mean: the diffusing capacity of a given capillary region, per liter of flow per minute, BF, of blood of a certain total. oxygen capacity, Hgb. The definition and the units2 are implicit in the following equation.

SDC = Dc BF X Hgb

The term specific diffusing capacity emphasizes the adjustment of diffusing capacity to the product BF X Hgb-a product we

1 The unit of DC is here twenty times greater than the unit for diffusing capacity as calculated in the preceding paper (1).

2 The unit of SDC is here the same as that used in the preceding paper. It will be seen that the introduction of the factor Hgb (which had the value of 20 in the case discussed in the previous paper) has necessitated a corre- snonding change in the unit of DC.

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422 Oxygen Exchange, Blood, and Circulation

may designate by the name hemoglobin flow and t,he abbreviation HF. The reciprocal of the specific diffusing capacity may well be called the speciJic hemoglobin flow, SHF, thus emphasizing the adjustment of hemoglobin flow t.o diffusing capacity. Thus we can write

SHF = s+C = BF X Hgb HF

DC =E (3)

The slight amplifications of what is implicitly contained in Fig. 2 of the preceding paper (1) have now been defined, and it will be obvious that similar reasoning applies equally t.o Figs. 3 and 5 of that paper. The purpose of the present additions will be more apparent later. A discussion of some underlying assump- tions and simplifications is also reserved for the end.

In order to provide data which can be applied to all ordinary physiological conditions, data which will yield immediately the desired quantitative relations for any observed case, we have made fifteen constructions similar to Fig. 2, and six similar to Fig. 3 of the preceding paper. Among these twenty-one pre- liminary constructions (not reproduced here) are three sets, each set corresponding to a certain oxygen dissociation curve. The three curves used are chosen from those published by Bock, Field, and Adair (5), and further treated in the paper by Hender- son, Bock, Field, and Stoddard (6). Their curves are given under t.he headings pCOZ = 80, 40, and 20 mm., indicating that in the determination of each curve the partial pressure of carbon dioxide was kept constant at the value stated. For the purpose of general- izing these curves, however, it is necessary, though perhaps not altogether sufficient, to define them by the hydrogen ion activity of the serum rather than by the carbon dioxide pressure. This point will be referred to again. Actually we have, as it were, relabelled these curves as corresponding sufficiently closely to curves for pH, = 7.25, 7.45, and 7.65-values obtainable from the two papers cited. With each of the three selected oxygen dissociation curves we

have made constructions to cover the conditions where the pressure of oxygen in alveolar air assumes the values: ~02 alveolar air = 110, 100, 90, 70, and 50 mm., and where the oxygen pressure of tissues assumes the values: ~02 tissues = 0 and 20 mm. Thus

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C. D. Murray and W. 0. P. Morgan 423

we have chosen twenty-one conditions, and for each has been calculated series of values to cover practically all combinations of arterial and venous points. Fifteen of the constructed curves begin at a venous point where V per cent = 0, and six begin at an arterial point, A per cent = 100. From one such curve-for instance for the case: p02 alveolar air = 110, pH, =7.45, and V per cent = O-values for Ap’ are calculated by dividing the dif- ference in percentage saturation between arterial and mixed ve- nous bloods, AO, per cent, for successively chosen arterial points, by the value of XDC as determined graphically at thf se points. The scale is selected so that

10 A$ X SDC = A 02 ‘j&, or 10 Ap’ = A 02 70 X SHF (4)

Calculations for V per cent = 10 (and each subsequent venous point) with successive arterial points are then easily made with the aid of the tabulated data obtained from the curve beginning at V per cent = 0. Data thus obtained from one construction, including values of Ap’ and AOz per cent for combinations of ar- terial and venous points, can then be recast in graphic form yield- ing a chart, the rectangular coordinates of which measure Ap’ and A.02 per cent. Twenty-one of these charts (the term chart will now be used to refer to one of this series) designated by Ro- man numerals, and arranged according to the following scheme, are presented here.

PH.3

Lung charts. p02 alveolar air.

110 100 00 70 50

7.25 I 11 III IV V 7.45 VIII IX X XI XII 7.65 xv XVI XVII XVIII XIX

Tissue charts. ~02 tissues.

0 20 -.-

VI VII XIII XIV

xx XXI

The scale for Ap’, in mm. of mercury, is numbered at the top of each chart. A02 per cent, the scale of ordinates, is measured downward. On each of the lung charts is a set of curves, num- bered at their lower extremities according to the arterial percent- age saturations, A per cent which they represent. These lines are crossed by a few venous lines, and limited by the curve V per cent = 0. The limit of arterial saturation is given by the num-

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424 Oxygen Exchange, Blood, and Circulation

bers in brackets (near the numeral designating the number of each chart), and this limit is properly represented by the vertical line, Ap’ = 0. On the tissue charts the general positions of the arterial and venous lines are reversed, and the limit of reduction of the blood is given as before in brackets, which limit also is represented by the line Ap’ = 0.

It will be noticed that, since A02 per cent is determined by part of the coordinate system, the set of arterial lines necessarily deter- mines the set of venous lines on the same chart, and vice versa.

The lines denoting specific hemoglobin flow, SHF, could have been drawn on these charts in accordance with Equation 4.

An example of the method of using the charts is as follows: Given pO2 alveolar air = 95, pH, = 7.35, A per cent = 95, and V per cent = 65; to find Ap’ and SHF by double interpolation. First, reference is made to Chart II (~02 = 100 and pH, = 7.25), and here the intersection of the line AOz per cent = 30 with the curve A per cent = 95 yields the value Ap’ = 39. Similarly, readings are made on three other charts as indicated in the following tabulation.

PH8 PO2 = 100 po2=90 @A=95

7.2 II : 39 III : 26 32.5 7.45 IX : 51 x : 40 45.5

7.35 45 33 39.0

The required value for Ap’ is 39 mm.; and SHF = ~ (39 x 10) = 13

30

The choice of A02 per cent and Ap’ as the variables to be rep- resented by the rectangular coordinates was made largely be- cause of the simplicity of the following relations, the first two of which have already been stated.

Ap’X DC = MR (1) 10 A$ = SHF X AO, 010 (4) AOz y0 X Hgb = 10,000 AOz cc. (5) lOOOA0,cc.X BF = MR (6)

Equation 1 follows from the diffusion theory; the constant was taken to be one, and is omitted here. Equation 4 follows from

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4’ ill 20 30 40 50 60 70 80

10

20

30

1 40 \s\ \

V-50 _̂ \J// \ \

\

80

CHART I. ~0, alveolar air = 110 mm.; pH, = 7.25.

AP’

80

CHART IT. p02alveolar air = 1OOmm ;pII, = 7.25. 425

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A,’ 10 x0 37 40 ' 50 60 7J

10

20

30

40

50

60

70

80

90

100 I4 III 5.71

CHART III. ~02 aleveolar air = 90 mm. : n,H, = 7.25.

CHART IV. pOz alveolar air = 70 mm.; pH. = 7.25. 426

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CHART V. p02 alveolar air = 50 mm.; pH, = 7.25.

CHART VI. ~0, tissues = 0 mm.; pH, = CHART VI. ~0, tissues = 0 mm.; pH, = 7.25. 7.25.

427 427

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AP’ 30 ‘10 50 60 70 80 90 100

10

80

CHART VII. ~0, tissues = 20 mm.; pH, = 7.25.

AP’ -n 0

in .- .-- 30 -. 40 so 60 70 80 90 100

10

20

30

40

50

7 0 60

\ 70 \\\\v

\ no

ED

SO

CHART VIII. pO1 alveolar air = 110 mm.; pH. = 7.45. 428

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80

30

100 CIIART IX. ~01 alveolar air = 100 mm.; pH, = 7.45.

4’ ,,o 10 ZD 30 40 so 60 70 80 90 103

\ ’ \I \ AAY\\I\A

10 \

\/ 1, \ v\\\uv V*80 \,

20

\ 20

CHART X. p02 alveolar air = 90 mm.; pH, = 7.45.

429

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CHART XI. pOz alveolar air = 70 mm.; pH, = 7.45.

60

70

80

A-85 90

100 CHART XII. ~0, alveolar air = 50 mm.; pH. = 7.45.

430

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CHART XIII. ~02 tissues = 0 mm.; pH, = 7.45.

CHART XIV. ~02 tissues = 20 mm.; pH. = 7.45.

431

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70

80

90

100 CHART XV. ~OS alveolar air = 110 mm.; pH, = 7.65.

AP' 0 0

10

i PO

\\ v\

, I

30

\:

30

40

I \ \\\/ 40

\ \ ,I %

60

70

80

9D

100 CHART XVI. 170~ alveolar air = 100 mm.; pII, = 7.65.

43 2

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60 70 80 90 AP'

u

10

20

30

40

50

9 * 60

70

80

30

100

50

A O&Z 60

80

CHART XVII. ~02 alveolar air = 90 mm.; pH. = 7.65.

API 10 20 30 40 53 60 70 80 90 100

CHART XVIII. pO* alveolar air = 70 mm.; pH, = 7.65.

433

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CHART XIX. ~0% alveolar air = 50 mm. ; pH, = 7.65.

3 CHART XX. ~01 tissues = 0 mm.; pH, = 7.65.

434

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C. D. Murray and W. 0. P. Morgan 435

Equations 1, 5, and 6, and the definition: SHF = BF X Hgb

DC *

Equation 5 introduces a term, A02 cc., which is the difference in actual oxygen content (in cc. of 02 contained per cc. of blood) between arterial and mixed venous bloods. The relation ex- pressed is sufficiently obvious. Equation 6 is equally obvious. Throughout, it must be kept in mind that MR, DC, and BF re-

A 9 % 60

80

90 90 XXI

100 100 [501

90 100

10

20

30

40

CHART XXI. ~02 tissues = 20 mm.: pH, = 7.65.

fer to corresponding values for the specified anatomical region considered in any case, whether this be a single capillary, a single organ, or the lungs as a whole, or the tissues (other than lungs) as a whole. In the last two cases MR would represent the total oxygen consumption of the individual per minute, in short, the metabolic rate; and similarly BF would be the total blood flow

per minute, and DC would be the total diffusing capacity of lungs

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436 Oxygen Exchange, Blood, and Circulation

or tissues, according to which portion of the circulation was u consideration.

0,CONSUMPTlON

rider

FIG. 1.

Now each of the equations just given can be expressed in simple graphic form, and the fact that some variables occur twice makes

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C. D. Murray and W. 0. P. Morgan 437

it possibIe to arrange four adjoining graphs in such a way that there will be but two sets of ordinates (for M‘R and A02 per cent) and two sets of abscissa: (for Ap’ and AO, cc.). The arrangement will be seen in Fig. 1 of this paper-to be spoken of as the figure in contradistinction to the charts already described. It will be noticed that the lower right quadrant of the figure has the same coordinate background as that of the charts, and hence any one of these charts can be expanded into the form of Fig. 1, or a specific chart may be thought of as placed in the lower right quadrant of the figure. In this quadrant, the rectangular co- ordinates being A02 per cent and Ap’, SHF is represented by radi- ating coordinates as indicated by Equation 4. Lines for SHF could also have been drawn on the charts. The lower left quad- rant will be seen to correspond with Equation 5, Hgb being repre- sented by radiating lines. The upper left quadrant corresponds to Equation 6, with BF represented by the radiating lines. Lastly, the upper right quadrant corresponds to Equation 1, with DC represented by radiating lines.

On such a figure, which defines, in part at least, the physico- chemical background of the process of oxygen transport, the ac- tual precise conditions prevailing may be delineated for any ob- served case. By way of recapitulation, the actual procedure for conditions in the lung may be briefly detailed, an example from the previous paper being chosen.

In bhe beginning it was mentioned that the function of oxygen transport would be described in terms of the operation of a sys- tem with six degrees of freedom. From an experimental point of view the first six variables to be mentioned may be selected as t,he independent ones, and the system defined as follows: First find

(1) p0~ alveolar air = 110 mm. (2) pH, = 7.45

These two determinations indicate the proper chart to refer to -in this case Chart VIII.

(3) A per cent = 96 (4) V per cent = 75

These two findings now fix a. point on Chart VIII, and conse- quently a point in the lower right quadrant of Fig. 1. From this

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438 Oxygen Exchange, Blood. and Circulation

point on the figure two lines arc drawn, one vertically upward, the other horizontally to the left. Now the determination of

(5) Hgb = 20 ~01s. per cent

serves to fix, by the inters&ion of the radial line Hgb = 20 with the horizontal line just drawn, a point in the lower left quadrant. From this point another vertical line is drawn upward. Finally, the determination of the oxygen consumption

(6) MR = 210 cc. of 02 per minute

completes the description of the system. The following variables can now be obtained by simple calcula-

tion or graphical inspection.

(7) Ap’ = 53 mm. (8) AOn per cent = 21 per cent (9) SHF = 25, or SDC = 0.040 (10) A& cc. = 0.042 (11) BF = 5 liters per minute (12) DC = 4.0

The dotted rectangle, which can be called the “lung rectangle,” represents the above case as it would appear on Fig. 1. The figure should be labelled with the appropriate values for ~0, alveolar air and for pH,.

If it were possible to determine the oxygen pressure of t,he tis- sues, and if this pressure were uniform, the original experimental determinations mentioned above (with a value for p03 tissues sub- stituted for ~0, alveolar air) could be applied to the greater cir- culation. As it is, the best that can be done in practice is to assume some standard arbitrary value for ~0~ tissues. Thus rela- tivc values can be obtained for the other factors which might. bc of interest. For instance, to continue with the special case just discussed, assuming pOZ tissues = 0, and neglecting for the mo- ment, the small difference in pH, between arterial and venous bloods, one refers to Chart XIII. Then, utilizing values already stated above, one finds for the tissues:

(13) Ap’ = 51 mm. (14) SZZF = 24 (15) DC = 4.1

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C. D. Murray and W. 0. P. Morgan 439

Other variables, represented by the left portion of the rectangle are identical for lungs and tissues in any given steady state. The only difference between the lung and tissue rectangles lies in the position of the line forming the right side of each rectangle.

If the oxygen pressure of the tissues were uniform, regardless of its actual value, the whole process of oxygen exchange and transport in lungs and tissues together could be described fairly accurately as the operation of a system with seven degrees of freedom. It is interesting to observe that when the conditions prevailing in the lung have been defined, all but one of the theo- retically independent variables are approximately determined for the tissues as a whole.

Although forming no essential part of the present paper, it may be pointed out that the determination of the variables al- ready mentioned leads to certain other factors which amplify the general description of the circulation. For example, if BF be multiplied by the systolic blood pressure, a good estimate of the effective mechanical work of the heart is obtained. Similarly, BF divided by the pulse rate yields a value for the volume output of each ventricle per beat. The blood flow, the blood pressure, and the viscosity of blood, taken together can lead to valuable information concerning the peripheral vessels and circulation.

DISCUSSION OF THE CHARTS WITH PARTICULAR REFERENCE TO

THE ASSUMPTIOSS INVOLVED.

It is now necessary to examine the conditions which must be fulfilled in order that application of the charts and the figure may be rigorous, and to examine the errors which are apt to occur as conditions depart from the ideal. The method of construction of the Ap’-AO, per cent charts suffers from the limitations of any graphical procedure, but besides there may arise slight errors from three known sources.

1. Although it is supposed that the oxygen dissociation curve of hemoglobin is primarily determined by the pH and the tempera- ture, other factors, such as the salts of the red blood corpuscle and the concentration of hemoglobin itself, may be involved, and es- pecially in connection with the relation pH,-pH, (7). Thus the PI-I, values assigned to the charts are subject to future modi-

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440 Oxygen Exchange, Blood, and Circulation

fication, or to the ‘substitution of some other more significant variable such as pH,, the activity of the hydrogen ion in the red blood corpuscle.

2. By expressing actual dissociation curves in the percentage saturation form (taking the total oxygen capacity to include the free dissolved oxygen, and calling this 100 per cent saturation), the fact that variations in the hemoglobin content alter the shape of the curve is neglected. There is thus an error, which in the extreme case assigns to pure serum an oxygen dissociation curve typical of ordinary whole blood instead of the simple straight line relation between p02 and dissolved Oz. With blood poor in hemo- globin, the values of pOz, at a given total content of oxygen, would actually be greater than the values of pOz used in the calculation of the charts. In anemia, then, Ap’ in the lungs would be actually less, and Ap’ in the tissues would be greater, than the correspond- ing values calculated from the charts; and conversely in poly- cythemia. To avoid this error much additional labor would be required and many more charts; fortunately, since the amount of dissolved oxygen is small in comparison with the combined oxygen in cases within the range of hemoglobin content compatible with life, the error from this source is insignificant.

3. In the integration of the amount of oxygen passing across the capillary wall, it is assumed that blood follows a path, or goes through changes, expressed by the oxygen dissociation curve, in other words that the oxygen content of the blood is determined by the equilibrium oxygen pressure of the blood (and vice versa), and moreover that this relation is sufficiently accurately expressed by the oxygen dissociation curve at constant pCO2 of blood.3 Obviously pCOz varies during the passage of blood through a capillary, and so does pH,; but reference to Figs. 111 and 112 of Henderson’s paper (6) will show that the theoretical path of the blood in the lung is very close to the oxygen dissociation curve at a constant pH, or at a constant pCOz if the arterial values of these factors are taken. In the tissues the path followed is very close to the curve at the pH, or $0, of the venous blood. This pre- sumptive fact, as Hendersoh showed, is due to the exchange of C’Oz being much more rapid than the exchange of 02. The values

3 This slight inconsistency has been avoided in the preceding paper.

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C. D. Murray and W. 0. P. Morgan

of Ap’, as obtained from the charts, will be too high as a result of neglecting this factor, but only in exceptional cases will the error be greater than about 1 mm., and usually it will be much less. The three sources of error so far mentioned may lead to a combined error of about 5 per cent in the value of Ap’ as calculated.

We come now to more indefinite sources of error. If the re- action between dissolved oxygen and hemoglobin is slow, or if the diffusion of oxygen into the red corpuscle is slow, compared to the process of diffusion across the capillary wall-a consideration suggested by the recent work of Hartridge and Roughton (8)- the path of the blood in a capillary will not fohow the oxygen dissociation curve. At any point along a capillary in the lung, ~02 of blood will be higher than the oxygen content would lead us to suppose, hence Ap’, as calculated, will be too high. In the tis- sues, ~02 of blood will be lower than we should suppose, and hence Ap’ will again, as calculated, be too high. For the present, until the possible error involved can be properly corrected, we can only assume that the magnitude of this effect will be relatively constant.

The last question to be raised in respect to the underlying as- sumptions in our calculations concerns the extension of results, based on the theoretical properties of blood in a given capillary, to cover the lung as a whole or the tissues as a whole. The prob- lem of the tissues is beset with difficulties. In the first place the oxygen pressure of the tissues cannot be accurately determined. Secondly, the oxygen pressure in the tissues along a capillary is probably not uniform, but higher at the end which receives the arterial blood. Thirdly, the mixed venous blood, derived from various organs in which pOz may be very different, offers scant information in respect to the precise prevailing conditions. How- ever, marked variations, characteristic of the tissue circulation as a whole or of a significant portion of it, will be reflected in the composition of the mixed venous blood. Thus comparative data may be obtained, and for this purpose it may be useful to select the arbitrary value ~02 = 0 as a reference standard for the oxygen pressure of the tissues.

In contrast to the diversity of conditions presented by the rest of the body, the lung offers a condition of relative uniformity. The oxygen pressure of the alveolar air can be obtained with con- siderable accuracy, and this pressure is presumably uniform along

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442 Oxygen Exchange, Hood, and Circulation

the length of a capillary. In the lung there is practically only one case which cannot be accurately described from data on the mixed arterial blood; namely, a condition of partial stagnation. After a quantity of blood has nearly reached equilibrium with alveolar air, it may travel through any additional length of capil- lary without further detectable change in composition. If a con- siderable quantity of such blood mixes with blood which is not in equilibrium with alveolar air, the mixed blood will not reveal the existence of the superfluous length of capillary through which the first portion has passed. The values of Ap’, as determined by the data on such mixed arterial blood, will be too high, and conse- quently the values of the diffusing capacity will be too low. The superfluous capillary area will not be discovered unless other signs or symptoms suggest its existence.

Many abnormalities of the lung may be examined from a func- tional standpoint by means of the charts which have been given. Hypothetical examples, for instance examples characterizing a short-circuited circulation or a case of obstructed bronchus, may be chosen, and the consequences of these conditions may be esti- mated. In every case it will be found that lack of uniformity involves a loss of efficiency: either there is a superabundance of capillaries, or an unduly large blood flow through ill ventilated regions of the lung, or both. The problem suggested here will not be further discussed in this paper.

SUMMARY.

A general physicochemical background, over which the process of oxygen transport and diffusion runs its course, has been de- scribed quantitatively in terms of the operation of a system with six independent degrees of freedom.

The process has been studied as a function of (1) the metabolic rate, (2) the oxygen capacity of the blood, (3) and (4) the per- centage saturations of arterial and mixed venous bloods, (5) the hydrogen ion activity of the serum, and (6) the oxygen pressure of the alveolar air (or the tissues). Certain other variables might, however, be substituted in this list.

More particularly, the relations between the coefficient of utili- zation, the capillary area across which diffusion takes place, the arterial and venous percentage saturations, and the “mean”

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C. D. Murray and W. 0. P. Morgan

head of oxygen pressure across the capillary wall have been given for a range of combinations of values for the hydrogen ion activity of the serum and the oxygen pressure of the alveolar air and of the tissues.

A new term, the specific hemoglobin flow, has been introduced to emphasize the important physiological adjustment of the prod- uct, blood flow times oxygen capacity, to capillary area. This derived factor is the reciprocal of the equally significant factor, specific diffusing capacity.

In that the discussion and the treatment of the various factors aim at giving a fairly complete description of the conditions for the diffusion and transport of oxygen in the body, it is hoped that this description may afford a basis fo.r testing the physiological

rale of the diffusion process, and the distribution of physiological

function among the various factors under all sortsof environmental and pathological states.

BIBLIOGRAPHY.

1. Henderson, L. J., and Murray, C. D., J. Biol. Chem., 1925, lxv, 407. 2. Bohr, C., Skand. Arch. Physiol., 1909, xxii, 221. 3. Barcroft, J., Binger, C. A., Bock, A. V., Doggart, J. H., Forbes, H. S.,

Harrop, G., Meakins, J. C., and Redfield, A. C., Phil. Tr. Roy. Sot. London, 1922. ccxi, 351-480.

4. Krogh, A., The anatomy and physiology of the capillaries, New Haven and London, 1922.

5. Bock, A. V., Field, H., Jr., and Adair, G. S., J. Biol. Chem., 1924, lix, 353.

6. Henderson, I,. J., Bock, A. V., Field, H., Jr., and Stoddard, J. I,., J. Lliol. Chem., 1924, lix, 379.

7. Barcroft, J., Rock, A. V., Hill, A. V., Parsons, T. R., Parsons, W., and Shoji, It., J. Physiol., 1922, lvi, 157.

8. Hartridge, H., and Roughton, F. J. W., Proc. Roy. Sot. London, Series A, 1923, civ, 395.

Some Methods.

(a). Van Slyke, D. D., and Neill, J. M., The determination of gases in blood and other solutions by vacuum extraction and manometric measurement. I., J. Biol. Chem., 1924, lxi, 523.

(5). Hastings, A. B., and Sendroy, J., Jr., J. Biol. Chem., 1924, lxi, 695. (Calorimetric pH determination of blood without the use of buffer standards.)

(c). Burwell, C. S., and Robinson, G. C., J. Clin. Inu., 1924, i, 47.

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444 Oxygen Exchange, Blood, and Circulation

(d). Field, H., Jr., Bock, A. V., Gildea, E. F., and Lathrop, F. L., J. CEin. Inu., 1924, i, 65.

(e). Murray, C. D., and Taylor, H., J. Physiol., 1925, lix, p. Ixvii. (The last three references describe methods for the determination of the mixed venous composition of blood.)

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Cecil D. Murray and William O. P. MorganTHEORY

THE BASIS OF THE DIFFUSION INVOLVED IN OXYGEN SUPPLY ON

TREATMENT OF THE FACTORS COORDINATEDTHE CIRCULATION: A

OXYGEN EXCHANGE, BLOOD, AND

1925, 65:419-444.J. Biol. Chem. 

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