a microcomputer program of pulmonary and tissue gas exchange

Annals of Biomedical Engineering, Vol. 14, pp. 425-435, 1986 0090-6964/86 $3.00 + .00 Printed in the USA. All rights reserved. Copyright �9 1986 Pergamon Journals Ltd.

A MICROCOMPUTER PROGRAM OF PULMONARY AND TISSUE GAS EXCHANGE

J o s e p h B oy l e I I I

Associate Professor Physiology Clinical Assistant Professor Medicine University of Medicine and Dentistry

New Jersey Medical School Newark, New Jersey

A microcomputer program written in BASIC fo r the IBM-PC and compatibles has been developed to analyze the effects o f many parameters on the gas exchange and transport phenomena in the lungs and the tissues. The program is designed f o r use by medical students and residents concerned with gas exchange (anesthesiology, pulmonary diseases, critical care, etc.) to study the steady state effects on blood and tissue oxygen and carbon dioxide levels. The present program consists o f two main subroutines: Pulmonary Gas Exchange and Tissue Gas Exchange. Steady state gas exchange at the lungs can be studied using either a three-compartment model or V/Q relationships. The V/Q subroutine uses single or multiple populations o f V/Q distributions to determine gas exchange using a log-normal distribution o f V/Q ratios. Other variables can be adjusted which determine the arterial and mixed-venous blood gases, These values are then f ed into the second part o f the program to analyze factors which determine tissue 0 2 tension. The Tissue Oxygen Tension subroutine is also subdivided into a modified Krogh-Erlang model, which provides a three- dimensional plot o f theoretical capillary and tissue 0 2 tensions, and a Piiper model which includes the effect o f diffusion shunt on 0 2 tensions and treats the tissue as a well-stirred compartment. Minimal and maximal tissue 02 tensions are calculated using the Piiper model since the intercapillary distance is allowed to vary depending on the 0 e delivery by diffusion. Estimates o f blood and tissue 0 2 tensions, diffusion/perfusion coefficients, amount o f 0 2 delivered and the size o f the active capillary bed are summarized in a table.

Keywords -F ick Principle, Oxygen delivery, Ventilation/perfusion, Shunt f low, Diffusion/per fusion.

I N T R O D U C T I O N

One of the most challenging problems for the cl inician is the eva lua t ion of gas exchange in the lungs and tissues. This is especially true in the intensive care un i t

when dealing with patients with cardiac or respiratory failure. The p rob lem arises

Acknowledgment-This work was supported by a grant from the Foundation of the University of Medi- cine and Dentistry of New Jersey.

Address correspondence to Joseph Boyle III, MD, Department of Physiology, New Jersey Medical School, 100 Bergen Street, Newark, NJ 07103.

425

426 J. Boyle III

because of the large number of interrelated variables that are involved in determining the gas tensions in the lungs and tissues; most of these variables are not meas- ureable clinically. Clinicians have come to rely heavily on measurements of the arterial blood gases (ABG), and more recently on mixed venous blood gases, in order to evaluate oxygen delivery to the tissues [oxygen delivery is defined as the product of the cardiac output (Qr) and the arterial oxygen content (CaO2)]. However, several recent studies indicate that these data still may not accurately reflect the actual tissue PO E (11,18,21).

The program described here was developed to provide physicians and medical students practice in evaluating the gas exchange properties of the cardiorespiratory system by means of a physiological model. The model incorporates all of the major factors involved in determining pulmonary gas exchange and, therefore, can simulate virtually any set of steady state gas exchange conditions. By altering various gas exchange properties of the model and observing the effect on ABG and tissue O2 tensions the user can gain a better insight into the mechanisms involved in limiting gas exchange and be able to evaluate the effect of various treatments.

RATIONALE

The program provides a three-compartment analysis of gas exchange, as proposed by Riley and Cournand (13-15), as well as a ventilation/perfusion (V/Q) analysis. The three-compartment method is mathematically correct but physiologically unreal- istic, while the V/Q analysis is more realistic but undoubtedly less accurate. The two methods of analyzing pulmonary gas exchange are included so that the user can com- pare the more commonly used three-compartment results with the more realistic V/Q data.

The work of Wagner and coworkers (22,23) has shown that the range of V/Q ratios in the lungs usually can be defined by a log-normal population distribution (Fig. 1). This program defines the population of V/Q ratios by four parameters: the number of modes or populations of the V/Q distribution (normally one); the mean V/Q ratio (normal = 0.85-1); the log standard deviation of the V/Q population (normal is 0.2-0.25); and the proportion of total blood flow going to each mode of the distribution [ventilation is automatically defined by the relation between V/Q and cardiac output (Qr)] . Calculations then provide estimates of alveolar PO2 (PALVO2); alveolar PCO2 (PACO2); 02 uptake; and alveolar ventilation for seven points in each V/Q mode. The amount of true shunt can also be varied which makes it possible to simulate the effects of many different conditions on the gas exchange properties of the system.

Conversion between O2 content and P O E is performed by using a regression analysis of a standard dissociation curve using data from Altman and Dittmer (1) and Severinghaus (16). Regression analysis was carried out using a curve fitting program, termed Curfit (17), which includes a linearized version of Hill's equation (4). Regres- sion analysis between actual and predicted hemoglobin saturation data yielded a correlation coefficient of 0.9940, standard error of estimate of 1.94 and an F value of 11,401 for data ranging between a POE of 1 and 700 mmHg for hemoglobin satu- rations of 1 ~ The determination of blood PO2 is performed by calculat- ing a standard PO2 using the derived regression constants and then adjusting the Pso of hemoglobin due to changes in pH, P C O 2 and temperature by use of the Kelman algorithm (5).

Pulmonary and Tissue Gas Exchange

6

427

FLO~

3

L/M]

tr~rr 0 I I

I I ,,,,,,,,, i I I I

SHIINI" . 0 0 1 . 0 1 .1 1 U/O

10 1 0 0

FIGURE 1. This is a plot of the V/Q distribution which is drawn from data input by the user. The data represented by this graph are a bimodal V/Q distribution with means of 0 .01 and 0 . 9 5 and standard deviations of 0 .4 and 0 .23 , respectively, and a true shunt f low of 1 L/rain (circle). The data represented by this graph would then be fed into the program to determine values for arterial and mixed venous blood gases.

The Fick Principle is essential when analyzing the relationship between blood flow and 02 content in the arterial and venous blood. The Fick Principle is an expression o f the conservation of mass and can be written

VO2 = Qr(CaO2 -- CVO2) , (1)

where V O 2 is the oxygen consumption, Qr is blood flow, CaO2 is the arterial O2 content and CVO2 is the venous 02 content.

If total body 02 consumption is considered then Qr represents cardiac output and CVO2 is the mixed venous blood which should be sampled from the pulmonary artery.

Rearranging Eq. 1 gives

C V O 2 = C a O 2 - - V O 2 / Q T �9 (2)

This relationship has been used for years to evaluate the 02 delivery system for the entire body since if 02 consumption rises or blood flow decreases then the venous P O 2 ( P V O 2 ) decreases. P V O 2 is a function of CVO2 as defined by the hemoglobin dissociation curve. The Fick relationship holds true for each organ as well so that VOz for any organ can be calculated from the organ blood flow and the respective arterial and venous 02 contents. When PVO2 falls below a critical level this gener- ally indicates that 02 delivery is inadequate and that tissue anoxia is present (10). The intracapillary PO2 is also important since as it falls the pressure head causing diffusion to occur is lost. Thus even though blood f l o w m a y be the primary factor

428 J. Boyle III

in limiting 02 delivery it eventually leads to an inadequate capillary 0 2 tension so that diffusion limitation may also play a role in producing anoxic or hypoxic conditions. It is important to differentiate between conditions leading to anoxia because of inadequate blood flow or to diffusion limitation since each one requires a different approach. Anoxia due to inadequate perfusion may be treated with vasodilators, cardiac stimulants or volume infusion, whereas diffusion impairment may be cor- rected by supplemental O2 administration. A formula derived by Haab (3) is used to calculate a diffusion/perfusion ratio which estimates whether 02 delivery in the tissues is limited by diffusion (a low ratio) or perfusion (a high ratio) conditions. Under normal conditions the ratio ranges between 1 and 4 so that 02 delivery is determined by both diffusion and perfusion conditions. Three estimates of tissue P O 2 a r e provided by the program: An average P O E is calculated from the Krogh-Erlang (7) model and minimal and maximal PO 2 are calculated from the Piiper model (12). These latter two values arise since the intercapillary distance varies depending on the capillary P O 2 and the diffusion rate of O2.

DESCRIPTION OF THE PROGRAM

The program is written in BASICA and utilizes standard graphics commands for the IBM-PC or PC-compatible microcomputer; a color graphics board is also required. Table 1 shows an outline of the program with the various options that are available. The program is completely menu driven so that the user needs to have only minimal computer expertise to run the program. Following a brief introduction the user can select either a three compartment or V/Q model of gas exchange. A list of parameters is presented (Table 1) any of which can be altered to observe the effect on pulmonary gas exchange depending on whether the user has selected the three- compartment or V/Q analysis. After the initial conditions are set the resultant ABGs are calculated for the steady state condition and displayed as a graphic of the Fick equation (2). Figures 2-4 are examples of this graphic which are generated by the program. Variables have been named according to the standard nomenclature as much as possible within the constraints of the BASIC language in order to make the

TABLE 1 Listing of adjustable parameters available in program.

1. Number of V/Q modes 2, Mean V/Q ratio 3, V/Q standard deviation 4. Fraction of cardiac output 5, Tidal volume 6. Dead space 7, Respiratory rate 8, 02 concentration 9, 02 consumption

A. Pulmonary gas exchange

B. Tissue gas exchange 1. 02 consumption 2. Blood f low 3. Capillary density 4. Shunt f low

10. Respiratory exchange ratio 11. Cardiac output 12. Pulmonary blood volume 13. Shunt f low 15. Pulmonary diffusion capacity 15. Hemoglobin concentration 16. Base excess 17. Temperature

Pulmonary and Tissue Gas Exchange 429

C U 0 2 10

(UOLZ)

2 0 . F R = 2 0 1 6 1 2 I N I T I A L U R L B E S Q= 6 4 3

P a 0 2 = 9 7 ........ ...... ...... P a C 0 2 = 3 9 ....... ...... ...... pH = 7 , 4 2 ...... ...... ......

15, HC03 = 24 ......... ...... ...... PU02 = 37 ~ ...... , .......

A L U . U E N T = 5 2 5 0 , ' 7 ........ , ....... ySf/fe jr'/' j///" p jP:" p//J"

............. F I N A L U A L U E S

5 . . . . . . . . , ....... , . . . . . . ~ a C u ~ : ~ ....... ...... ...... p H = 7 . 4 2

....... , ....... d ....... H C 0 3 = 2 4 P U 0 2 = 1 7

~ L V , U E N T = 5 2 5 8

C~02 (UOLZ)

FIGURE 2. A graphic analysis of the Fick principle. Abscissa is arterial 02 content; ordinate is venous 02 content. The diagonal lines represent isof low condit ions. The diagram is constructed such that if 02 consumption (V02) is 300 ml/min the diagonal lines represent cardiac output (Q). If VO2 is not 300 ml/min, then the diagonal lines represent a f low ratio which equals OT/VO2. The circle indicates the initial condit ions, whereas the square represents the coordinate fo l lowing the intervention. This diagram indicates the changes that occur when the fraction of inspired 02 is reduced to 0 .12 from its normal value of 0.21. Note that the coordinate moves parallel to the f low lines since QT is assumed constant and that there are marked changes in arterial and venous 02 contents and tensions (inset).

20

. t5,

C U 0 2 18,

(UOLZ)

,

FR=201612 INITIAL VALUES Q= 643

~Hco3PaO2pac02== = 273997~142 ..................... , .......... ....... ............ b .....................

P O 0 2 = 3 ? A L O . U E N T = 5 2 5 0

....... F I N A L V A L U E S ........... Pa.02 = 76

............ Pa.C02= 39 S f

....... I; o3 f //j'//, Pf m

PU02 = 2 4 A L U . V E N T = 5 2 5 0

................................... .................................. ........................ ......................... ........................... '

CA02 (UOLZ)

FIGURE 3. A graphic of the Fick equation showing the effects of a decrease in the cardiac output f rom an initial value of 5.5 L/min (circle) to a final value of 3.0 L/min (square). Note that the move- ment is not parallel to the f low lines and that there is a decrease in arterial 02 content and tension caused by the marked drop in venous 02 content and tension. Symbols as in Fig. 2.

430 J. Boyle III

CO02 10,

(OOLZ)

2 0 . F R = 2 0 1 6 1 2 I N I T I A L U A L B E S q = 6 4 3

P a 0 2 = 9 5 ...... . ...... . ...... P a C 0 2 = 4 0 ....... . ..... . ...... p H = 7 , 4 2 ....... . ....... . .....

1 5 . R C 0 3 = 2 4 ........ . ....... . ....... P r O 2 = 3 ? ~ ....... . ......

ALV,VENT= 5 1 3 0 ~ .......... ......... /y//'J /Y/ y///'/'

............. ............ ............ F I N A L V A L t l E S ....... , ...... , ...... Pa02 = 56

5 . . . . . . . . , ...... , ...... P a C 0 2 = 4 0 ....... , ..... , ...... p H = 7 , 4 2

......... , ........ , ........ H C 0 3 = 2 4 PV02 = 3 3

A L V . V E N T = 5130

CA02 (VOLT.)

FIGURE 4. The effect of changes in 02 transport due to changes in the V/Q ratio distribution, The circle represents ABG for mean V/Q of O. 95 and standard deviation of 0.23. The square represents conditions when mean V/Q is 0 .95 and standard deviation has increased to 0.5. Note that the move- ment is parallel to the flow lines since cardiac output is unchanged in the two conditions. Other abbreviationas as in Fig. 2.

program as transparent as possible. The diffusion properties of the alveolar mem- brane depend on pulmonary blood volume and cardiac output, which determine the transit time of the red cells in the pulmonary capillaries, as well as the diffusion capacity of the lungs for 02 (DLO2). The pulmonary diffusion of 02 is modeled using an iteration of the blood 02 content during 50 intervals of the red cell transit through the pulmonary capillaries. The iteration integrates the 02 uptake in the pulmonary capillaries, and the interval of one fiftieth of the transit time was arbi- trarily selected to minimize the integration error and the delay necessitated by the repetitive calculations. The capillary transit time is determined by the ratio of pulmonary blood volume and the pulmonary blood flow.

The Tissue 02 subroutine requires the input of four parameters for the particu- lar organ being studied: 02 consumption per 100 grams of tissue; blood flow per 100 grams of tissue; the number of capillaries per mm 3 of tissue; and the percent of blood flow which is shunted between arteriole and vein. Figure 5 is a listing from the program of normal values for these parameters (19). An outline of the three- dimensional capillary segment is drawn, and the calculated tissue PO2 profiles are plotted for 10 segments of the capillary (Fig. 6). Tissue 02 tension is calculated in steps since the intercapillary distance decreases as the intracapillary PO2 decreases. If the capillary PO2 is insufficient to drive 02 diffusion to the center of the tissue segment, then additional capillaries are recruited, up to the maximum, and intercapillary distance decreases. If 02 diffusion is less than the O2 required, then tissue PO2 is zero and in the body lactate production would occur. The capillary 02 content is assumed to decrease linearly down the capillary, whereas the PO2 appears to fall exponentially because of the shape of the hemoglobin equilibrium curve. Figure 7


ENTER 02 C~SBMPTION PER 100 GM TISSBE PER MINBTE, 10 ENTER BLOOD FLOW PER IN GM TISSflE PER NINgTE, 50 ENTER Z BLOOD FLOW SHUNTED BETWEEN ARTERY AND VEIN, 0 ENTER CnP, DENSITY (lg^6/CC TISSflE), 4

NORMAL OALUES

TISSUE gO2 BLOOD FLOH CAPILL, DENSITY CClI09GNININ CClI06GNININ #1CC TISSOE ~ 19^6

BRAIN HEART LIVER KIDNEY MUSCLE

3,3 8 2,0 6,0 0,2

54 70 54 436 2,?

l ,! 5,3 4,2 4,5 2,0

FIGURE 5. A table of normal values and the statements which require data input in order to run the Tissue PO2 Subroutine are shown.

is a table which is generated by the program to summarize the tissue gas exchange data.

DISCUSSION

The coefficient of oxygen delivery (COD = Qr * CaO2/VO2) was proposed by Mithoeffer et al. (10) to evaluate the O2 delivery system. However, it has been shown that the COD can increase, decrease or remain constant under various conditions when O2 transport is limited (20). The factors which determine the O2 delivery can be better evaluated b y graphing the Fick equation (2), which is done in this program. If CaO2 is plotted on the abscissa and CVO2 on the ordinate, as in Figs. 2-4, then decreases in cardiac output cause the coordinate to move downward and to the left; i.e. to lower arterial and venous O2 contents (Fig. 3). In contrast, if 02 delivery is reduced because of a decrease in hemoglobin concentration or 02 tension, then the coordinate moves diagonally, parallel to the flow lines (Figs. 2 and 4). Thus the factors affecting the 02 delivery, either changes in 02 content or the bulk flow of blood, can be evaluated by this type of graphic analysis, and the effects of various interventions can be followed. By studying the Fick graphic (Figs. 2-4) and the printed data within the insets the user can evaluate blood gas tensions and the 02 delivery system.

The arterial O2 content is a function of the diffusion properties of the lungs, the hemoglobin concentration, the alveolar ventilation, the Ps0 of hemoglobin, the cardiac output, the amount of true shunt (V/Q -- 0 or blood flow not exposed to alveoli), the V/Q ratio and the venous 02 content. All of these factors are incorpo- rated into this model so that it should be possible to simulate virtually any condition and observe its effect on gas exchange. The first seven of these factors are well understood and will not be discussed further. The last factor has been shown to be

432 J. Boyle III

CAP. ( '

97 '

P02

0

21 CAP.

DI SIANCE (HI CRA)

FIGURE 6. A three-dimensional plot showing capillary length, intercapillary distance and tissue P02. Note that intercapillary distance varies from the arterial to the venous end of the capillary, which shortens the diffusion distance and helps to maintain the tissue PO2 toward the venous end of the capillary, By altering various parameters the user can observe the effect of the intervention on the tissue P02,

extremely important in determining the arterial 0 2 content (25) and is frequently overlooked as a cause of arterial hypoxia. The effect of venous O2 levels on arterial O2 content is best described by rearranging the shunt equation

Qs/Qr = ( C I O 2 - C a O 2 ) / ( C I O 2 - C V O 2 ) , (3)

where Qs is the shunt flow, and CIO2 is the pulmonary capillary 02 content. Thus CaO2 = CIO2 - Qs/QT * (CIO2 - - C V O 2 ) -

UENOtlS 02 CONTENT I S 7.9

UPNO[IS P 0 2 IS 21

OXYGENATED T I S S U E = 1 0 1 Z

V. CAPS. USED= 23

IqEAN T I S S U E P 0 2 (KROGH MODEL)= 28

MINIIqAL P 0 2 ( P I I P E R H O D E L ) - 17 IqRXIHAL T I S S U E P 0 2 ( P I I P E R MODEL)" 2 0

DIFFIISION/PERFIISION RATIO VARIES FROIq 2.93 TO 4.78

FIGURE 7. A printout of the screen showing the summary of gas exchange parameters at the tissue level, These data are calculated using normal parameters for the coronary vascular bed.


It can be seen that increases in Qs or decreases in Qr and CVO2 will reduce the arterial 02 content. Therefore, any reduction in Qr has a powerful effect on 02 transport since the O2 transport is reduced by the decreased cardiac output, and CaO2 is further reduced by the lowering of the CVO2, which accompanies any decrease in the cardiac output. This effect can be weII documented by the use of this program (Fig. 3).

Measurements of PVOz or CVO2 can provide evidence regarding the overall effi- ciency of the Oz delivery system. However, each organ has its own unique ratio of Oz consumption and blood flow which generates a unique value for the respective venous 02 tension and content. Therefore, it is possible that the overall Oz delivery system is adequate so that mixed venous PO2 is normal while blood flow is inadequate to a specific organ.

The actual tissue PO2 depends not only on the ratio of O2 consumption and blood flow but is also dependent on the microvascular geometry, the degree of a-v shunting, the counter-current mechanism between the arterioles and venules and especially on the number of perfused microvessels, which is the primary determinant of the intercapillary distance. None of these parameters can be measured clinically but examination of their effects by means of this mathematical model provides insight into their interaction. The PO 2 decreases in an exponential function as O2 diffuses from the capillary into the tissues (Fig. 6), even though 02 content decreases linearly down the capillary (24). The PO2 approaches zero in the mitochondria, where O2 is consumed, even when O2 is adequately supplied.

The capillary PO2 determines the driving force for diffusion into the tissues. The PCAPO2 is determined by the hemoglobin concentration, the Ps0; the amount of blood flow, the distance along the capillary which the blood has traversed and the rate of 02 utilization by the tissues. It is obvious that predicting the PO 2 in any tissue is a complex problem given the number of variables that are involved. Most of the difficulty arises because of the complex and unknown geometry in the microvas- culature. The most common model used for predicting the tissue PO2 and the pres- ence of tissue hypoxia is the Krogh-Erlang equation. This equation utilizes 15 assumptions in its derivation all of which are probably untrue in most tissues (6). The most serious errors appear to arise from the assumptions dealing with the microvascular geometry. The Krogh model (7) assumes that all capillaries are parallel, of equal length and receive equal blood flow. Additionally, it is assumed that blood flow is concurrent, i.e. in the same direction, in adjacent capillaries and that there is no exchange between adjacent vessels (shunting). Thus in the Krogh model the lowest POz in the capillaries occurs at the venous end, and obviously then venous POz would be a good measure of the minimal vascular PO2. However, recent studies indicate that the PVO2 may not reflect changes in the tissue PO2 under many different conditions (6,9) and other techniques are being investigated to better evaluate the adequacy of O2 delivery (8,11,18).

The modified Krogh model, which has been developed, incorporates variations in the intercapillary distance along the length of the capillary. The variable intercapillary distance is based on anatomic evidence, and results in a microvascular unit which has been called the Krogh cone rather than the Krogh cylinder by Weibel (24). The model also includes the effects of both diffusion and perfusion shunts on capillary and tissue PO2, thus eliminating the assumptions of concurrent flow and no diffu- sional shunts. Results from this model indicate that mean tissue POz and venous

434 J. Boyle I I I

PO2 can be dissociated whenever there is a-v shunting, if the number of perfused capillaries is reduced and if counter-current flow exists in adjacent capillaries. Accu- rate evaluation of the 02 delivery system is obviously an important factor in treat- ing many clinical conditions. While PVO2 has been used in the past as an indication of tissue anoxia, it is now recognized as having marked limitations as noted above and as emphasized recently by Miller (9).

This program has been developed to provide an educational tool to demonstrate the effects of various factors on the overall 02 delivery to the tissues. Even though several simplifying assumptions are used, the results of both the pulmonary and tissue gas exchange sections can provide students and residents the opportunity to investi- gate the interaction of a large number of factors on the gas concentrations in the body. The program is available from the author by sending a blank IBM-compatible diskette and self-addressed envelope to the following address: Joseph Boyle, MD, Department of Physiology, NJ Medical School, 100 Bergen St., Newark, NJ 07103.

REFERENCES

1. Altman, P.L. and D.S. Dittmer, Respiration and Circulation. Bethesda, MD: FASEB, 1971. 2. Boyle III, J. Graphic analysis of the Fick equation to evaluate oxygen transport. Respiration

45:353-359, 1984. 3. Haab, P. A model for the study of diffusion and perfusion limitation. Fed. Proc. 41:2119-22, 1982. 4. Hill, A.V. The possible effects of the aggegation of the molecules of haemoglobin on its dissocia-

tion curves. J. Physiol. (London) 142:iv, 1910. 5. Kelman, G.R. Digital computer subroutine for the conversion of oxygen tension into saturation. J.

Appl. Physiol. 12:1375-1376, 1966. 6. Kreuzer, F. Oxygen supply to tissues: the Krogh model and its assumptions. Experientia 38:1415-1426,

1984. 7. Krogh, A. The number and distribution of capillaries in muscle with calculation of the oxygen pres-

sure head necessary for supplying the tissue. J. Physiol. (London) 52:409-415, 1918/19. 8. Mahutte, C.K., T.M. Michiels, K.T. Hassel and D.M. Trueblood. Evaluation of a single transcutane-

ous PO 2 and PCO 2 sensor in adult patients. Critical Care Med. 12:1063-1066, 1984. 9. Miller, M.J. Tissue oxygenation in clinical medicine: an historical review. Anesth. Analges. 61:527-535,

1982. 10. Mithoeffer, J.C., F.D. Holford and J.F.H. Keighley. The effect of oxygen administration on mixed

venous oxygenation in chronic obstructive pulmonary disease. Chest 66:11-132, 1974. 11. Nelimarkka, O., L. Halkola and J. Niinikoski. Renal hypoxia and lactate metabolism in hemorrhagic

shock in dogs. Critical Care Med. 12:656-660, 1984. 12. Piiper, J., M. Meyer and P. Scheid. Dual role of diffusion in tissue gas exchange: blood:tissue equil-

ibration and diffusion shunt. Respir. Physiol. 56:131-144, 1984. 13. Severinghaus, J.B. Blood gas calculator. J. Appl. Physiol. 12:1108-1116, 1966. 14. Riley, R.L. and A. Cournand. "Ideal" alveolar air and the analysis of ventilation-perfusion ratios

in the lungs. J. Appl. Physiol. 1:825-847, 1949. 15. Riley, R.L. and A. Cournand. Analysis of factors affecting partial pressures of oxygen and carbon

dioxide in gas and blood of lungs: Theory. J. Appl. Physiol. 4:102-120, 1951. 16. Riley, R.L., A. Cournand and K.W. Donald. Analysis of factors affecting partial pressures of oxy-

gen and carbon dioxide in gas and blood of lungs: Methods. J. Appl. Physiol. 4:102-120, 1951. 17. Spain. J.D. BASIC Microcomputer Models in Biology. Reading, MA: Addison-Wesley, 1982. 18. Sugimoto, H., N. Ohashi, Y. Sawada, T. Yoshioka and T. Sugimoto. Effects of positive end-

expiratory pressure on tissue gas tensions and oxygen transport. Critical Care Med. 12:661-663, 1984. 19. Tenney, S.M. and T.W. Lamb. Physiological consequences of hyperventilation and hypoventilation.

In: Handbook of Physiology. Section 3. Respiration Physiology, 1Iol. 2., edited by W.O. Fenn and H. Rahn. Washington, D.C.: American Physiological Society, 1965.

20. Tenney, S.M. and J.C. Mithoeffer. The relationship of mixed venous oxygenation to oxygen transport: with special reference to adaptation to high altitude and pulmonary disease. Am. Rev. Resp. Dis. 125:474-479, 1982.


21. Vincent,, J.L. et aL Serial lactate determinations during circulatory shock. Critical Care Med. 11:449-451, 1983.

22. Wagner, P.D. and J.W. Evans, Conditions of equivalence for gas exchange in series and parallel models of the lung. Resp. PhysioL 31:117-138, 1977.

23. Wagner, P.D., H.A. Saltzman and J.B. West. Measurement of continuous distributions of ventilation- perfusion ratios: theory. J. Appl. Physiol. 36:588-599, 1974.

24. Weibel, E.R. The Oxygen Pathway. Cambridge, MA: Harvard University Press, 1984. 25. West, J.B. Ventilation-Perfusion Relationships. Am. Rev. Resp. Dis. 116:919-943, 1977.

V / Q = ABG =

QT = CaO2 = P A L V O 2 = P A C O 2 =

Pso = V02 =

CVO2 =

PVO2 = C I 0 2 = DLO2 = P C A P O 2 = C C A P 1 (L % ) =

R T ( L % ) =

Os = COD =

N O M E N C L A T U R E

ven t i l a t i on /pe r fus ion rat io arterial b lood gases cardiac ou tput

arterial oxygen con ten t alveolar oxygen tens ion alveolar and arterial ca rbon dioxide tens ion oxygen tens ion at 50% hemog lob in sa tu ra t ion oxygen consumpt ion venous oxygen conten t venous oxygen tens ion oxygen content o f p u l m o n a r y capi l lary b lood p u l m o n a r y di f fus ing capacity

capillary oxygen tens ion oxygen content of capi l lary b lood at each segment ( L % )

intercapi l lary distance for each segment of capi l lary shunt flow through the lungs coefficient of oxygen delivery

a microcomputer program of pulmonary and tissue gas exchange

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