An “Electronic Lung” in the Study of Pulmonary Function* , **

An "Electronic Lung" in the Study of Pulmonary Function*, ** M. LEWIS, Detroit, Michigan

BENJAMIN

W

M.D.

chambered model without a dead space, or a two-chambered model with separate dead spaces ignores important facts about ventilation of the lungs. We have therefore settled on a two-chambered model with a common dead space as the simplest concept that could be used in constructing a useful model. The next step is to reduce this concept to a mathematical fonnulation, usually a series of differential equations. In a lung containing alveoli ventilated thru a common dead space, the concentration of an insoluble gas, for example helium, in a given alveolus is by definition: F AI Hp =V AI Hp

ORKERS WITH COMPUTERS FRE-

quently construct a mathematical model of the system they are studying. I Mathematical models are popular for an obvious reason. All variablec;; which affect the behavior of a model are under the control of the investigator. He may use this control to predict the behavior of the system after any change in a variable, or knowing the behavior of the system, he may determine the combination of variables which produce this behavior. The attraction of a mathematical model for an investigator rises as the difficulty of isolating the factors which affect the behavior of a system increa~es. For example, the lungs are unevenly ventilated, even in nonnals. s Yet. this unevennes.'i is not a function of the usual anatomic subdivisions of the lung. It thus seemed to us that a mathematical model of the lung might be a useful tool in investigating uneven \'entilat!on of the lung and, more important. uneven diffusion and blood flow as well. For the nonmathematician, the construction of a mathematical model usually starts with a concept, frequently a mechanical concept of the workin~ of the system under study. This concept should be as simple as JX>ssible. but the model must be capable of duplicating the behavior of the system studied, to the extent that this is relevant. Possible models of the lung are shown in Fig. 1. It is obvious that a one-chambered model cannot be unevenly ventilated and is, therefore inadequate. It is also clear that a two-

VAl

Similarly the concentration space is FDHp=VDHp

10

the dead

VD

On inspiration the amount of helium in the first alveolus changes as dead space gas is inspired. \'.\I H •• =\lAIF D H •• The amount of helium in the dead space changes for two reasons: gas is inspired from outside and dead space gas pa~ses into the alveoli VDH .. =\lnFl u .. -F 1)H .. p:\l AI+V A2 etc) t On expiration the amount of helium in the first alveolus changes as gas containing it is expired: \'.\I u •. =\'.\IFAI H •• In the dead space, helium is expired to the outside and received from the alveoli ,', " Uu ..--y' D U .. F' D H .. -'''y' Al F .\I u .. +\'r A2 F· ,\2 u .. (It should be remembered that V Al etc. and VI> change sign on expiration.)

·From the Pulmonary Function Laboratory. Wayne State University and City of Detroit Receiving Hospital. ··Supported by a Public Health Service Research Career Award Program (5K6-HE-2182-02), a research grant from the National Heart Institute (HE 02379-07) and grants from the Michigan Heart Association and the Receiving Hospital Research Corporation. Presented at the 30th Annual M~eting, American College of Chest Physicians, San Francisco, June 18-22, 1964.

tStrictly, since V n is constant V n is meaningless. We have used it as a shortened way of expressing rate of flow from the outside to the dead space or vice vena. It is equal to l:V,\1 +~rA2 etc.

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BENJAMIN M. LEWIS

These equations can be used for any number of alveoli, for common or separate dead spaces and for washout (or wash-in) or rebreathing conditions (the rebreathing bag is treated as a single alveolus at the other end of the dead space. If the gas investigated is, for example, carbon monoxide, which diffuses from the alveoli into the blood, a term is added to express this. In the case of inspiration

\r AI('o=V AIF D('O -DAIP8~47F.\I('o

The symbols used above are standard. s V refers to gas volume, F to concentration, D to diffusing capacity and P to pressure. The first subscript refers to location, e.g., V ... I means volume of alveolus 1; the second subscript refers to molecular species, e.g., F AI H .. is the concentration of helium in alveolus 1. :\ dot above a symbol means the rate of change of that quantity, e.g., V Ai co means the rate of change of the quantity of CO in alveolus 1.

Finally, we must select computing equipment to solve these equations and "program" the computer. Computers may be roughly di\'ided into digital and analog tyPes. The relative merits of analog computers have been discussed elsewhere.· \Ve chose an analog computertt because of its relatively low cost, its simplicity of programming, it'\ modular construction, which allowed for expansion and modification of our model, and a precision consistent with that of the respiratory data to be used. :\s disc ussed abm'e. a mathematical model may be used in two ways. First. the known behavior of a sy~tem may be analyzed in terms of the factors that control it by varying these factors in the model until the behavior of the model duplicates that of the system. \Ve have used a computer in this way to analyze measurements of diffusing capacity of the lungs. ttApplied Dynamics. Inc .. Ann Arbor. Michigan.

WNG MODELS

FIGURE

1:

.....r"L. -..-. -.. '-...-/

(5

CONTINlOJS VENTlLATION

CYCLIC VENTILATION

CYCLIC VENTILATION

SINGLE CHAMBER

SINGLE CHAMBER

DOUBLE CHAMBER

CYCLIC VENTILATION

CYCLIC VENTILATION

DOUBLE CHAMBER SEPARATE DEAD SPACE

DOUBLE CHAMBER COMMON DEAD SPACE

Models of pulmonary ventilation of varying complexity. See text for discussion.

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We have elsewhere described a rebreathing method for measuring the diffusing capacity of the lungs. The subject rebreathes a low concentration of CO while continuous analysis of this gas is made. From the apparently exponential fall of concentration of CO, diffusing capacity of the lungs is calculated. However, when an insoluble gas like helium is mixed with the CO and analyzed continuously, its concentration also falls throughout the period of rebreathing (Fig. 2). The decline in CO concentration is not, then, solely a matter of diffusion; mixing of the CO with the residual volume is also occurrin~. \\'e have used our mathematical model of the lung to investigate what "diffusing capacity" means under these circumstances. This model consisted of two re~!ons, a common dead space and a rebreathing bag.' The volume of the subject's lungs before study wa~ measured independently by the helium closed circuit method. Then, during a 45 second period of rebreathing, the volume of each breath and the concentration of an insoluble gas (helium or neon) and CO were continuously measured and a curve like that of Fig. 2 was obtained. The known tidal volume and residual volume of the subject's lungs then were divided in various combinations between the two compartments of the model lung. After each setting of these values, a mixing curve was generated by the computer. The resulting curve was compared with the patient's curve and the values of tidal volume and residual volume of the two compartments of the mathematical model were adjusted until the mixing curve of the model matched the curve of the subject. The setting of the controls of the computer at this time gave a trial and error solution to the regional tidal volume and regional residual volume in the subject. The necessary connections for simulating a diffusing capacity in the two regions of the lung were then made and the process was repeated using various values for diffusing capacity of the regions until the subject's curve of carbon monoxide absorption was matched. This

constituted a trial and error solution to the regional diffusing capacities. In six patients with uneven ventilation due to emphysema, the model lung matched the behavior of the subject's lung when one region had a small residual volume, a large tidal volume and the other region a large residual volume and a small tidal volume. Further, the region with the high ventilation had a small diffusing capacity and the region of low ventilation had the larger part of the diffusing capacity. Finally, the sum of the diffusing capacities of the two regions was reasonably close to the "diffusing capacity" calculated in the conventional way using simply the overall decrease in Log concentration

1.0 .8

He mixing

.6 Helium mixing and carbon monoxide absorbtion

.4

Subject with airway Obstruction

.2

.1 .08

CO

absorbtion

.06

.04

.02

.01

o

10

20

30

40

Time in seconds FIGURE 2: Semi-logarithmic plot of the decrease of helium and carbon monoxide concentrations with time during a rebreathing experiment in a patient with emphysema. Note continued fall of helium concentration indicating continued mixing.

BEN J AMIN M. LEWIS

174

carbon monoxide concentration with time in three patients and exceeded moderately the diffusing capacity in three others. :\ second use of a mathematical model is to learn the way in which chan~es in one of the factors controlling the ~ystem affect itli overall behavior. We have used this approach to study the problem of seT quential ventilation. As the work of Fowler' ha~ made clear, the lungs are not only unevenly ventilated, but sequentially ventilated, so that the poorly ventilated parts empty lal;t. The sequence in which regions of the lun~ fill is unsettled. Various authors have found that the poorly ventilated region fills before,' at the same time.' or after lO the well ventilated reWon. Our mathematical model of the lung has heen used to explore the effects of each of

of the Chest

Di~as~s

the possible modes of sequential ventilation on the washout of nitrogen, a widely used technique for evaluating unevenness of pulmonary ventilation.' Preliminary studies showed the necessity for using the proper model. ..-\ model which does not have a dead space or a model in which the dead space of each region is separate will give the same curve of nitrogen washout regardless of the sequence in which the re~ions of the lung empty and fill. The effect of sequential ventilation on inert gas washout, then, is dependent on the presence of a common dead space. To investi~ate the effects of sequential ventilation on inert gas washout, our model lung had the parameters shown in Fig. 3. For the same values of tidal volume and residual volume it is apparent that the slow-

EFFECT OF SEQUENTIAL VENTILATION ON INERT GAS WASHOUT

POORLY

WELL

YENTILATED YENTILATED

~ Exp. ----- First Last -- - same Last

~~ Last First Some First

-

First

- - same Some sane sane

LOO%

2

Last

Last

First

INERT GAS

1+--.....- - . . - -.....---,--r--...,....-....,

o

10

20

30 40 BREATHS

50

60

70

3: Semi-logarithmic plot of mean expired per cent of inert gas during simulated washout of the lung model shown in upper right, with the regions filling and emptying in the sequences indicated.

FIGURE

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est washout occurs when the poorly ventilated region fills first, but empties last. Only slightly more rapid is the lung with simultaneous filling of both regions, but sequential emptying, the poorly ventilated region emptying last. Considerably more rapid is the nitrogen wa~hout of a model lung with simultaneous emptying and filling. Surprisingly, a model in which the poorly ventilated space fills last and empties la~t ha~ the most rapid washout. Since sequential ventilation clearly affects the evenness of pulmonary ventilation, the possibility that uneven ventilation of the lungs may be due solely to sequential ventilation was investigated. \Vhen our model lung was ventilated simultaneously and both regions had the same percentage increase in volume, the curve of nitrogen washout plotted semilogarithmically against time was a straight line. The same model

was then ventilated in a first in, first out sequence and the tidal volume and residual volume of the two regions were manipulated, maintaining equal percentage increase in volume in the two regions, to give the greatest pos.'\ible delay in inert gas washout. Only if the resulting plot were carried through three logarithmic cycles (that is, a fall of nitrogen concentration from 80 per cent to .08 per cent) was a difference between the simultaneously ventilated and the sequentially ventilated lung obvious. Sequential ventilation, alone, then can produce only a relatively minor degree of uneven ventilation. Finally, the fall of nitrogen concentrations in the individual alveoli was explored in our model lung (Fig. 4-). In the well ventilated region there is, at first, a rapid decrease. However, on each breath this region receives some gas from the dead space

ALVEOLAR CONCENTRATION OF INERT GAS DURING WASHOUT

1+--.....- .....---.,.....-....- ....- ....- - .

o

10

50

60

70

4: Semi-logarithmic plot of concentration of inert gas in the two lung regions during simulated washout of the lung model shown in the lower left. Poorly ventilated region fills tint, but empties lut.

FIGURE

Diseases of the Chest

BENJAMIN M. LEWIS

and the dead space contains gas of high nitrogen concentration from the poorly ventilated region. Thus, after a number of breaths, concentrations of inert gao;; in the two regions decrease in parallel fa"ihion. The reverse of this process is occurring in the poorly ventilated space, although it is les.~ obvious. Concentration of nitrogen at first falls slowly, and then more rapidly as ga"i containing little nitrogen is inspired from the dead space. The behavior of gas concentrations during the washout in the different regions hao;; practical implications in the use of nitrogen washout curves to calculate the alveolar ventilation and functional residual capacity of separate region"i of the lung. Because the common dead space serves as a mixing chamber ventilation of the poorly ventilated space is overestimated and ventilation of the well ventilated space is underestimated. The ma~itude of this error is related to the sequence of ventilation. It is smail if the poorly ventilated space fills first and empties last, since this sequence decreases mixing in the common dead space. It is large when the poorly ventilated space fills last and empties last since the well ventilated space now receives largely the gas of high nitrogen concentration last expired by the poorly ventilated space. SUMMARY

A mathematical model of the lung, consisting of two regions and a common dead space, is described. An analog computer is used to solve the equationo;; of this model. Two examples of the use of this computer are given. In the first, curves of the mixing of an inert gas and the absorption of carbon monoxide obtained in emphysema patients were analyzed. Such curves were the result in tenns of our model, of a small, well-ventilated region with a low diffusing capacity and a large poorly ventilated region having most of the diffusing capacity of the lung. The computer wa~ used to predict the effects on inert gas washout of ventilating the lung in various sequences. The slowest washout was obtained when

the poorly ventilated region filled first and emptied last, the most rapid when this region filled last and emptied last. Sequential ventilation alone can produce relatively minor delays in inert gas wa"ihout. Error in estimating regional ventilation from inert gao;; washout is ~mall when the poorly ventilated region fills first and empties last, but appreciable when this region fills last and empties last. ACK:-:OWLEOOMENT: The invaluable assistance of Professor Robert M. Howe in fonnulating the equations for the lung model and in selecting and programming the computing equipment is gratefully acknowledged. ZUSAMMENFASSUNG

Beschreibung eines mathematil'chen Lungenmodelll', dal' aus zwei Bereichen und einem gemeinsamen Totraum hel'teht. Ein entsprechendes Rechengerat wird benutzt, urn die Gleichungen diesel' Modells ZlI losen. Es werden zwei Beil'piele fiir den Einsatz diesel' Rechengerates gegeben. Bei dem ersten wurdt'n die KurTen der Mil'chung eines Edelgases und der Absorption von Kohlenmonoxyd analYl'iert, wie sie bei emphysematol't'n Patienten gewonnen wurden. Solche Kurven waren dal' Ergebnis-in Ausdriickt'n unseres Modellel' --{'ines kleinen gut ventilierten Bereiches mit geringer Diffusionskapazitat und eines grol3en schlecht ventilierten Bereiches, das iiber den grofleren Teil der Diffusionskapazitat der Lunge verfiigt. Das Rechengerat wurde eingesetzt zur Voraussage der Wirkungen der Vf"ntilation der Lungs in verschiedener Stufenfolge auf den Austausch eines Edelgases. Der schwachste Austausch wurde erzielt, wenn l'ich die schlecht ventilierte Region zuerst fiillte und zuletzt entleerte. Der schnellste, wenn diese Region sich zuletzt fiillte und zuletzt entleerte. Stufenweise Ventilation allein vermag relativ geringere Verzogenmgen bei dem Austausch des Edelgases zu bewirken. Ein Jrrtum bei der Beurteilung der regionalen Ventilation aufgrund eines Edelgas-Austaul'ches ist gering, sofern sich die schlecht ventilierte Region zuerst fiillt und zuletzt entleert, aber betrachtlich, wenn sich diese Region zuletzt fiillt und zuletzt entleert. REFERENCES RAND, C.: "Center of a New World," Neu.' Yorker, 40:57, 1964. 2 FOWLER, W. S., CORNISH, E. R., JR. AND KETY, S. S.: "Lung Function Studies VIII. Analysis of Alveolar Ventilation by Pulmonary N2 Clearance Curves," ]. elin. Invest., 3: 40, 1952. 3 PAPPENHEIMER. J. R.: "Standardization of Definitions and Symbols in Respiratory Physiology," Fed. Proc., 9: 602, 1950.

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AUJ:u\t 19M

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ELECTRONIC LUNG IN PULMONARY FUNCTION

.J KORS, G. A. ASD KORN, T. M.: Electronic

Analog Computers, McGraw Hill Book Co.. !':t"w York, 1952. .l LEWIS, B. M., LIN, T. H., NOE, F. E. A:"OD HAYFORI>-WELSING, E. J.: "The Measurement of Pulmonary Diffusing Capacity for Carbon Monoxide by a Rebreathing Method," ]. Clin. Inl'est .. 38: 2073, 1959. 6 LEWIS. B. M., ADHIKAllJ, P. K., BoUSHY, S. F. A:"OD SAKAMOTO, A.: "Analog Computer Analysis of Diffusing Capacity Measurements." Fed. Proc .. 21 :444, 1962. 7 LEWIS, B. M. ASD BoUSH\'. S. F.: "Sequential Ventilation: What Difference Does It Makt"?," Fed. Proc .. 23:364. 1964.

177

8 FOWLER, W. S.: "Lung Function Studies III. Uneven Pulmonary Ventilation in Nonnal Subjects and in Patients with Pulmonary Disease," ]. Appl. Physiol., 2: 283, 1949. 9 MCGRATH, M. W. AND HUGH-JONES, P.: "Some Observations on the Distribution of Gas Flow in the Human Bronchial Tree," Clin. Sci., 24: 209. 1963. 10 MILlC-EMILI. J. A:"OD HENDERSON, J. A. M.: "Studies of Regional Pulmonary Ventilation Using Xe 1U ," Fed. Proc.. 23: 117. 1964. For reprints, please write Dr. Lewis, Receiving Hospital Research Corporation. 1326 St. Antoine Street. Detroit.

ACUTE MASSIVE PULMONARY EMBOLISM Recent experience has demonstrated feasibility of pulmonary embolectomy using total cardlopulm~ nary bypass for acute massive pulmonary embolism. However. many patients with this condltlon die during preparations for embolectomy or are unable to tolerate stresses of Inducing anesthesia and standard cannulation for total cardiopulmonary bypass. In order to evaluate usefulness of partial cardiopulmonary bypass for resuscitation of patients with acute massive pulmonary embolism while preparations for embolectom~' are completed. mongrel dogs were anesthetized and acute obstruction of the pulmonary artery was produced by almost complete occlusion with a tourniquet. In alternate animals. partial cardiopulmonary bypass was Instituted from

the femoral vein to the femoral artery using disposable plastic oxygenators primed with 5 per cent dextrose In distilled water. This technique of partial bypass adequately supported these animals for periods of one hour. after which pulmonary arte~' tourniquets were removed with long-term survival in all Instances. Control animals all survived less than 20 minutes. These findings suggest that similar techniques of partial bypass may be helpful In resuscitation of patients with acute massive pulmona~' embolism. BI',uL, A. C. JR.. AL·ATTAR, A. S.• MANI, P. AND TUTTLE, \.. l. D .• JR.: "R~suscitation Aft~r Acut~ Massiv~ Pulmonary Embolism." J. Tho, lI"d CII,diorIlJ. S.,/( .. 49:419. 196'1.

ELECTRO-OSCILLOGRAPHIC STUDIES OF PERIPHERAL ARTERIES IN MYOCARDIAL INFARCTION The author resorted to electro-osclliography In the study of the peripheral circulation in 50 patients affected with myocardial Infarction complicated by collapse. On the basis of the clinical picture. nature of the reaction to the Introduction of pressor amlnes and the form of the electro-osclllogram. the author established three types of peripheral artery tone; reduction of the tone. normal or slightly elevated

tone and a sharply augmented tone of peripheral arteries. The author is of the opinion that mild forms of collapse In myocardial Infarction are attended by a reduction of the vascular tone. whereas severe forms. by an Increased tone.

KAKHNOVSKY, I. M.: "EI~ctro.osciliographic Studies of Pe· ripheral Art~ries in Myocardial Infarction Complicakd by Collapse." 501'. M~d., 38:20. 19M.

CYSTIC FIBROSIS A procedure Is described for the analysis of s~ dium and potassium In fingernail and toenail clippings. The results. expressed In terms of mEq. of sodium or potassium per kg. of nails. are based on an empiric standardized method used in sample preparation. Elevated sodium values were found In 147 of 149 patients with cystic fibrosis. There was a significant separation and little overlap in the s~ dlum levels of the control group and of the patients with cystic fibrosis. thus providing a supplementar~' means for diagnosing this disease In conjunction with the "sweat test" and clinical evaluation. The measurement of nail sodium might facilitate

preliminary diagnosis when a patient resides In a remote area or when the "sweat test" Is dlmcult to administer or unreliable. Nalls. because of their ease In collection and storage. may be forwarded by mall. thus providing access to specimens of diagnosis either from members of affected families not readily accessible to clinical testing. or from racial groups known to have different rates of Incidence of cystic fibrosis. KOP1TO, L.. MAHWOOD1AN. A.. TOWNLEY. R. R. W .•

KHAW, K. T. AND ScHWACHWAN. H.: "Studies in Cystic Fibrosis: Analysis of Nail Clippings for Sodium and Potassium." Ntu' Engl. J. Mtd.. 272:504. 1965.