Journal of Clinical InvestigationVol. 43, No. 3, 1964

Total Respiratory Inertance and Its Gas and Tissue Com-ponents in Normal and Obese Men *

J. T. SHARP, J. P. HENRY, S. K. SWEANY,W. R. MEADOWS,ANDR. J. PIETRAS

(From the Cardiopulmonary Laboratory of the Veterans Administration Hospital, Hines, Ill.,and the Departments of Medicine of the University of Illinois College of

Medicine and the Stritch School of Medicine of Loyola University,Chicago, Ill.)

Total respiratory inertance may be defined asthat component of the total impedance to breathingthat relates to acceleration of respiratory gas andof all tissue elements (lungs, rib cage, diaphragm,and abdominal contents) that move during respi-ration. It is expressed in units of pressure re-quired to overcome this inertial component of thetotal impedance and produce air flow accelerationof 1 L per second per second. Thus its units arecentimeters H2Oper liter per second2. Intuitively,one would suspect that the inertance of the chestand the abdomen should be increased in severelyobese subjects. In investigations of total respira-tory mechanics in excessively obese persons, wemade measurements of total respiratory inertance.In addition, we attempted to separate the totalrespiratory inertance into its gas and tissue (in-cluding lung tissue, chest wall, and abdominal)components in three normal and three excessivelyobese subjects. These data form the substance ofthis report.

Inertance data on the normal human respiratorysystem were first published by DuBois, Brody,Lewis, and Burgess (1) in 1956. These authors,assuming that the respiratory system behavesmechanically as a simple or "lumped" physicalsystem, determined the total compliance and thenatural frequency of the respiratory system. Theythen calculated the total inertance of the respira-tory system by using the simple physical relation-ship by which the natural frequency of a systemmay be predicted if its elastic and inertial charac-teristics are known: fn = 1/274 1/jI *C, where fnis the natural frequency, I is the total inertance,

* Submitted for publication July 5, 1962; acceptedNovember 21, 1963.

Supported in part by National Institutes of Healthgrant H5124.

and C is the total compliance. Their estimatedvalue for total respiratory inertance was 0.0058cm H20 per L per second2, a value which, thoughmeasurable, is small enough to be neglected innormal subjects at ambient pressures and at theair flows and accelerations usually encountered.These authors pointed out that the respiratory sys-tem is more than critically damped, necessitatingthat the natural frequency be determined by ex-amining the phase relationship between sinusoidalwaves of driving pressure and the resulting oscil-lations of air flow. Estimates of natural frequencymade in this way, together with measurements ofthe total respiratory compliance, constitute thedata from which inertances were calculated in thepresent study.

Methods

Of the 22 subj ects studied, 8 were normal laboratorypersonnel of normal weight, and 14 were excessivelyobese persons varying in weight from 250 to 407 pounds.Of the obese subjects, 9 were otherwise normal exceptfor slight arterial hypoxemia in 2; their Pco%'s werenormal. The remaining 5 subjects had the obesity-hypo-ventilation syndrome, although Pco2 values were normalin 3 at the time these studies were performed.

The total respiratory compliance was measured by amodification of the method of Heaf and Prime (2), inwhich steady negative pressures are applied to the sur-face of the subject's thorax, which is enclosed in aplethysmograph. Volume changes in mid position areplotted against changes in applied pressure, and the totalrespiratory compliance is computed from the resultingstatic volume-pressure curve based upon 8 to 25 volume-pressure points. These measurements were made withsubjects in a supine position. The natural frequency ofthe respiratory system was determined by Mead's modi-fication of the oscillatory method of DuBois and associ-ates (1, 3) (Figure 1). Sine waves of pressure wereapplied to the surface of the body using an electronicsine wave generator, power amplifier, and high volumedisplacement high fidelity speaker as a variable frequency

503

SHARP, HENRY, SWEANY,MEADOWS,AND PIETRAS

FIG. 1. THE OSCILLATORY METHODUSED TO DETERMINETHE NATURAL FREQUENCYOF THE RESPIRATORY SYSTEM.P = applied pressure; NV = air flow; CRO= cathode rayoscilloscope. See text for discussion.

pump. Pressure waves of 2 to 3 cm water amplitudewere produced, which were sensed by a Statham P23dtransducer and applied to the horizontal axis of an os-cilloscope. Air flow recorded at the mouth by a screenflow meter and a Sanborn gas differential pressuretransducer was applied to the vertical axis of the oscil-loscope (Figures 1 and 2). As shown in Figure 2, whenair flow and applied pressure are plotted one againstthe other in this fashion, loops are formed at frequen-cies above and below the natural frequency. The loopcloses and assumes the form of a diagonal line at thenatural f requency of the respiratory system when driv-ing pressure and resultant air flow are exactly in phase.In actual use, the frequency of oscillation was graduallyaltered while the oscilloscope was observed. Duringpreliminary observations the vertical and horizontal gainswere adjusted to give a large loop with an axis as closeas possible to 450 from horizontal. The determinationwas done with the subject relaxed with an open glottisat his mid position and moving no air on his own.These procedures were adopted because they allowedoptimal discrimination between closed and minimallyopened loops and increased the precision of naturalfrequency measurements. The frequency at which theloop closed was repeatedly determined while slowly de-creasing the frequency from an initial value of 8 to 10cps down to the range of the expected natural fre-quency (3 to 7 cps). The natural frequency then wasapproached repeatedly from lower frequencies, slowlyincreasing frequencies from 2 to 3 cycles, and the fre-quency at which the loop disappeared was again recordedfor several such determinations. Approaching fromhigh frequencies and from low frequencies, there was agap of from 0.7 to 1.8 cps between the frequencies atwhich the loop disappeared. The natural frequency wasassumed to lie midway between the upper and lowerlimiting frequencies. This method of determining thenatural frequency was found to be necessary because ofthe respiratory system's highly damped mechanical char-acteristics, which exclude sharp resonance. Once thenatural frequency and the total respiratory compliance

were known, the total respiratory inertance was calcu-lated using the simple physical relationship previouslycited, solved for -he total respiratory inertance:

0.0253(fn)2. C

In three normal subjects and three excessively obesesubjects, an attempt was made to measure separately thegas and the tissue components of total respiratoryinertance. The subjects breathed gas mixtures ofwidely differing densities, which altered the gas inertancein direct proportion to the change in gas density but lefttissue inertance unchanged. When two gas mixtures ofdiffering but known density are breathed and the naturalfrequency determined during the breathing of each, bothgas and tissue components of total inertance can be com-puted. The principle of this experiment and the cal-culation is shown in the two equations belo6w. Breathinggas mixture 1,

tiss + DgI0 -Ig=0.0253Itiss+ 91*I =(f.1) 2. C'

Breathing gas mixture 2,0.0253

Itiss + Dg2* Ig =_(____*C

Itiss = inertance of all tissue elements in the lung,thorax, and abdomen moved during respiration; Ig = in-ertance of gas in the respiratory system referred to thedensity of air; Dgi and D92=densities of the two gasmixtures breathed relative to that of air; f,u and fn2 =

natural frequencies determined during breathing of gasmixtures 1 and 2; and C= total respiratory compliance.

- el sEn.- 0.1 SEC. ,J\ \/\

BELOWfn AT fn ABOVEfn3 c.p.s. 6.5 c.ps. IOc.p.s.

VLEADSP PANDV P LEADSVBY 350 IN PHASE BY 400-

FIG. 2. TRACINGS AND OSCILLOSCOPIC PLOTS OF P ANDV. The left panel shows the situation below the naturalfrequency (f.) where flow leads pressure, and the rightpanel shows the situation above the natural frequencywhere pressure leads flow. At the natural frequency,shown in the center panel, flow and pressure are exactlyin phase.

504

TOTAL RESPIRATORYINERTANCE

The gas densities, the natural frequency during thebreathing of e;eh gas mixture,,qtid the total compliancemay be directly measured. Simultaneous linear algebraicequations result, each describing conditions during thebreathing of one of the gas mixtures. There are twounknowns, the gas inertance (I,) and the tissue inertance(It isa), and the equations may be simply solved.

Three gas mixtures were used for these experiments,air, an 80%o helium-20% oxygen mixture, and an 80%sulphur hexafluoride-20% oxygen mixture. With thesemixtures, the data for the construction of three sets ofsimultaneous equations could be obtained, each set ofwhich would yield a value for tissue and gas compo-

nents of total respiratory inertance. Each gas mixturewas breathed deeply and rapidly in an open circuit forapproximately 2 minutes by the subject who was seatedin the plethysmograph so that the measurement could bemade immediately. A thin, supported 10-L neoprene bagwas attached to the distal end of the screen flow meterto contain the gas mixture and prevent its loss from thesystem. The natural frequency with each gas was de-termined between four and six times and the valuesaveraged. After each natural frequency determination,the subj ect expired maximally into an anesthesia bag,the contents of which were analyzed for nitrogen, oxygen,

and carbon dioxide. The remaining gas was assumed tobe the foreign gas, either helium or sulphur hexafluoride,and from the analyses, gas densities were calculated as-

suming full saturation with water vapor at 37° C.Analyses following repeated natural frequency deter-minations were generally similar during th- breathing ofa single mixture inasmuch as the prebreathing of themixture was repeated in the same manner. Hence theseveral gas analyses were averaged, and from this average

a single gas density value was calculated. Gas densitieswere expressed relative to air, averaging 0.6 during he-lium breathing experiments and 3.5 during sulphur hexa-fluoride breathing experiments.

In addition, the lung inertance (inertance of lung tis-sue plus contained gas), breathing air, was determinedin the three normal and the three excessively obese sub-jects in whom the differential gas density studies were

done. Lung inertance was measured by the techniquedescribed by Mead (4) using an esophageal ballooncatheter placed with its tip 40 cm from the nares. Theballoon was 10 cm in length, 1.5 cm in diameter, and was

used with an air volume of 0.4 ml. Movements of thehead and neck failed to produce significant alterations inesophageal pressure. A low resistance Krogh spirometer,a screen flow meter, and Sanborn differential transducerswere used, and measurements were made with the seatedsubj ect panting. Tracings of transpulmonary pressure,

air flow, and tidal volume were made at paper speedsof 200 mmper second and accelerations determined bydrawing tangents to the air flow curve at two pointsof zero flow at the ends of inspiration and expiration.The inertance pressures at these points were determinedby subtracting the calculated elastic change in trans-pulmonary pressure between end-inspiration and end-expiration from the observed differences in the esopha-

geal pressure tracings. The elastic pressure differencewas calculated by dividing the tidal volume by the lungcompliance previously determined during slow breathing.The resulting inertance pressure representing the sumof end-inspiratory and end-expiratory inertance pressureswas divided by the sum of end-inspiratory plus end-ex-piratory accelerations to yield lung inertance.

Results

Total inertance. Table I gives data on totalcompliance, natural frequency, total respiratoryinertance, and body weight in the 22 subjects.The mean inertance in the normal subjects was0.0098 + 0.0005 (SE) and in the obese subjectswas 0.0253 + 0.0022 (SE) cm H20 per L per sec-ond2. There were significant differences in totalrespiratory compliance (p < 0.01), natural fre-quency (p < 0.001), and total respiratory inert-ance (p < 0.001) between the normal and obesegroups. Total inertance was significantly corre-lated (r = + 0.86, p < 0.001) with body weightas shown in Figure 3. Total respiratory com-pliance also correlated significantly with bodyweight (r = - 0.74, p < 0.001), as did naturalfrequency (r = - 0.64, p < 0.01).

Separation of gas and tissue components of to-tal respiratory inertance. Table II gives the data

TABLE I

Inertance data in normal and obese subjects

TotalTotal Natural respiratory

Subject Weight compliance frequency inertance

kg L/cm H20 cps cm H20/L/sec2

Normal subjects1 62 0.101 4.8 0.01082 78 0.101 5.0 0.01003 78 0.156 4.8 0.00714 69 0.080 5.3 0.01125 94 0.091 5.0 0.01116 82 0.131 4.5 0.00957 80 0.117 5.0 0.00868 95 0.088 5.3 0.0103

Mean 79 0.108 5.0 0.0098SE 0.010 0.1 0.0005

Obese subjects1 167 0.038 4.1 0.03982 185 0.050 4.0 0.03163 146 0.091 3.5 0.02674 138 0.095 4.0 0.01665 149 0.033 5.0 0.03066 150 0.050 4.4 0.02647 134 0.080 4.3 0.01718 118 0.086 4.0 0.01859 128 0.063 4.6 0.0189

10 118 0.116 4.2 0.012411 148 0.056 4.2 0.025612 114 0.052 4.5 0.023913 146 0.051 4.5 0.024614 132 0.031 5.0 0.0328

Mean 141 0.064 4.3 0.0253SE 0.007 0.1 0.0022

505

SHARP, HENRY, SWEANY,MEADOWS,AND PIETRAS

TOTAL RESPIRATORY INERTANCE VS. BODY WEIGHT

0.040-

0.030 -

0.020-

0.010 -

o NORMALS* OBESESUBJECTS

0

00

0.

r -0.86ps 0.001

) o 10o

BODY WEIGHT-Kg.

150 200

FIG. 3. THE TOTAL RESPIRATORY INERTANCE PLOTTEDAGAINST BODY WEIGHT. The correlation is highly sig-nificant.

TABLE IIGas and tissue inertance data on

normal subject 3*

Mean gasdensity Meanrelative natural Total

Gas breathed to air as 1.0 frequency inertance

cps cm HsO/L/second2

Air 1.0 4.4 0.008480% He 0.43 6.6 0.003780%SF6 3.70 2.5 0.0260

Gas in-ertance

Paired (referred toequations density of Tissue Tissue

solved air as 1.0) inertance inertance

cm H20/L/second2 %of total

Air-SF6 0.0065 0.0019 23Air-He 0.0082 0.0002 2SF6-He 0.0068 0.0016 19Means 0.0072 0.0012 15

* Total compliance, 0.156 L per cm H20.

from a representative experiment in a single nor-

mal subject. The rather different values for gas

and tissue inertances obtained from solution ofthe three sets of equations are probably due to thedifficulty in determining precisely the natural fre-quency. In this subject the tissue inertance ap-

pears to constitute between 2% and 23% of thetotal respiratory inertance.

The first two columns of Table III give for thethree normal and three obese subjects the effectsof a unit change in gas density upon the naturalfrequency and upon the total inertance. Thevalues were calculated from helium and SF6 data

by dividing the differences in natural frequencyand in calculated total inertance encountered ineach subject by the difference in mean gas den-sity between the helium and SF0 experiments.For example, utilizing data from Table II (nor-mal subject 3), between helium and SF,0 experi-ments, the difference in natural frequency was

6.6 to 2.5 or 4.1 cps, and the difference in inert-ance, 0.0260 to 0.0037 or 0.0223 cm H20 per Lper second2. Dividing these values by the differ-ence in gas density, 3.70 to 0.43 or 3.27 yields thevalues 1.3 cps and 0.0068, the latter value being81% of the total inertance breathing air. A unit

TABLE III

Total respiratory inertance and its components in 3 normal and 3 obese subjects

Change inChange in total in-

natural ertance per Ufrequency change in

per U gas density ex-change in pressed as %of Total

gas total inertance respiratory Gas (air) LungSubject density (breathing air) inertance inertance inertance Tissue inertance

cps cm H20/L/second 2 %oftotal

Normal1 1.3 71% 0.0092 0.0085 0.0055 0.0007 82 1.3 85% 0.0105 0.0079 0.0070 0.0026 253 1.2 81% 0.0084 0.0072 0.0094 0.0012 14

Obese1 (167) 0.3 9% 0.0396 0.0082 0.0057 0.0314 792 (185) 0.5 21% 0.0316 0.0117 0.0099 0.0199 593 (146) 0.3 19% 0.0267 0.0091 0.0074 0.0176 66

506

e4

0

-i

0Lx

EU)

a:

0

TOTAL RESPIRATORYINERTANCE

change in gas density produced a much smallerchange in natural frequency and in inertance inthe obese subjects than in the normals. Thesedata imply that the major component in the ex-cessively obese subject is tissue inertance.

The remainder of Table III summarizes the dataon the gas and tissue components of the total in-ertance and also includes the lung inertances meas-ured separately by the esophageal pressure methodof Mead (4). The different values for total inert-ances given in Tables I and III in normal sub-jects 1, 2, and 3 are explained by the fact thatdata given in Table I were obtained in a separatedetermination a few days before the data in TableIII were obtained. To this extent they representthe reproducibility of the total inertance measure-ment on separate days. Mead's data indicatingthat lung tissue inertance is virtually zero implythat lung and gas inertances should be very simi-lar. Considering the many possibilities for inac-curacy of measurement in both lung and totalinertance methods, the correspondence betweenlung and gas inertance in both obese and normalsubjects may be considered reasonably good.The lung and gas inertance values in the obesesubjects are in the same range as the normals,and their increased total inertance results solelyfrom an increase in tissue inertance.

Discussion

Validity of the method. The meaning of theinertance measurements presented herein restsupon the validity of three assumptions that re-quire examination. The first is that the respira-tory system behaves essentially as a simple physi-cal system. The second is that change in the den-sity of the gas breathed produces no change inthe effective compliance. The third is that the ef-fective total compliance at the natural frequencyis the same as that during slow breathing.

The assumption that the respiratory system be-haves as a simple or "lumped" physical systemmeans that its many elastic, inertial, and resistiveelements may be faithfully represented by an ap-propriate arrangement of a single elastic, a singleinertial, and a single resistive element. DuBoisand associates (1) and Brody, DuBois, Nisell, andEngelberg (5) found that the response of the ab-domen and lower chest to forced sinusoidal pres-

sure waves at the mouth lags somewhat behindthat of the upper thorax particularly at higher fre-quencies. They also describe in man and the catpropagated surface waves over the abdomen, whichin the cat are unaffected by evisceration. Inaddition, Coermann, Ziegenruecker, Wittwer, andvon Gierke (6) have compared in whole body os-cillation ("shake table") experiments data ob-tained on intact supine man with calculations basedupon a hypothetical model in which the lungs,thorax, and abdomen are assumed to be a simpleor "lumped" system. The close correspondencebetween predicted and experimental data led theauthors to conclude that the thoracicoabdominalsystem is a simple one with lumped physical pa-rameters. These data indicate then that the as-sumption of a lumped system is clearly a simpli-fication, although close enough to the truth to beuseful.

The question of whether a change in gas densityproduces a change in compliance is also one forwhich there is no satisfactory answer. Anychange in total compliance produced by alteringthe properties of the gas breathed would have to bein the lung compliance component. In the courseof the present experiments, lung compliance meas-urements at slow breathing rates were made innormal subjects 1, 2, and 3 breathing air and thehelium and sulphur hexafluoride mixtures.Breathing the heavy and light mixtures producedno significant differences in compliance. There isno available datum, however, nor methods forobtaining it, on whether breathing heavy gas mix-tures alters effective compliance at oscillation fre-quencies near the respiratory system's naturalfrequency. One would predict, however, that ifthere were some inequality of time constants ofterminal lung units tending to diminish effectivecompliance at higher frequencies, the presence ofa heavy or a viscous gas in the respiratory sys-tem might accentuate this tendency by dispropor-tionately increasing the resistance of the narrowerairways. The likelihood of the gases used in thestudy causing a major change in effective lungcompliance is slight because gas flow in the lowerairways is almost wholly laminar (7), implyingthat flow resistance ought to be little affected bydifferences in gas density. Nor would the vis-cous airway resistances of terminal lung units bemuch affected by either of the foreign gases used

507

SHARP, HENRY, SWEANY,MEADOWS,AND PIETRAS

in this study because their viscosities are close tothat of air.

The third assumption, that the effective com-pliance at the natural frequency is the same asthat determined at slow breathing rates, also de-fies verification by present methods. Mead (4)has, however, cited indirect evidence suggestingthat the effective compliance of the respiratorysystem diminishes at frequencies approaching itsnatural frequency. He called attention to the ob-servations of Dubois and co-workers (1) that thelower chest and abdomen oscillate in phase withthe upper chest at frequencies below 2 cps but in-creasingly lag behind the upper chest at higherfrequencies. This implies slight differences intime constants between different areas of the chestwall or underlying lung that are too small to bedetectable at frequencies below 2 cps. That sucha condition may prevail in the normal human lungis not unreasonable from anatomical considera-tions. The lungs of excessively obese personsprobably contain regions of compressed lung, asevidenced by the mild arterial hypoxemia recti-fied by a deep breath seen in many of them (8).Seven of the obese subjects in this study had evi-dence of this. In such subjects time constant in-equality of terminal lung units is very likely,which would make the differences between theeffective compliance at slow and rapid cyclinggreater than in normals. Mead (4) points outthat assuming the effective total compliance to begreater than it actually is results in an under-estimation of total respiratory inertance. Hencethe total inertance values may represent an un-derestimation in normals and a somewhat greaterunderestimation of the true value in the obesesubjects.

An empirical validification of the method sug-gesting that the values for gas and tissue inertanceare approximately correct is the reasonably closecorrespondence between lung and gas inertances inboth normal and obese subjects. If Mead's dataindicating that lung tissue inertance is virtuallyzero are correct, lung and gas inertances should bepractically identical.

Precision of the method. The accuracy of inert-ance values obviously depends upon the accuracywith which the total compliance and the naturalfrequency may be measured. The accuracy andvalidity of total compliance measurements have

been dealt with elsewhere (9, 10). Inspection ofthe expression used to calculate inertance, I =.O253/(fn)22 C, reveals that, inasmuch as thenatural frequency is squared in the denominator,an error in its determination will produce a muchgreater error in inertance than an error in meas-uring the total compliance. Moreover, the per-centage of error resulting from a given error inmeasuring natural frequency will vary with fre-quency. A reasonable estimate of the averageerror of the natural frequency measurement is+ 0.5 cps based on the reproducibility of mieasure-ments in single individuals and a consideration ofthe gap of 0.7 to 1.8 cps, over which frequencyrange the flow-pressure loop is closed. At 3 cpsan underestimate of 0.5 cps would give a 40%ooverestimation of inertance, and an overestimateof 0.5 cps would result in a 30% underestimationof inertance. At 5 cps, underestimating the nat-ural frequency by 0.5 cps would cause a 24%overestimate in inertance, and a 0.5 cps overesti-mation would give a 17% underestimate of inert-ance. Assuming the highly unlikely situation thatinertances in all the normals have been under-estimated by 20% and inertances in all the obeseoverestimated by 30%o, the differences remainsignificant (p < 0.05) between the two groups,and tissue inertances are still impressively in-creased.

Implications of the data. In normal subjectsbreathing quietly, accelerations of from 2 to 10 Lper second2 are encountered. These accelerationswould require pressures of 0.02 to 0.10 cm H2Oin the normal subject and 0.08 to 0.40 cm H,O inour obese subject with the greatest total inertance.During maximal ventilation maneuvers, we havemeasured accelerations between 200 and 500 Lper second2, which would require pressures of 2to 5 cm H2O in the normal and 8 to 20 cm H2Oin obese subjects with the highest total inertances.During cough, although reliable measurementsare not available, accelerations as great as 1,000L per second2 probably occur, requiring inertancepressures of 10 cm H20 in the normal and up to40 cm H20 in the excessively obese. Thus, whileincreased inertance may possibly have a limitinginfluence upon cough velocities and maximal ven-tilatory velocities in the excessively obese, it isprobably of little importance in limiting ventilatoryperformance under less extreme circumstances.

508

TOTAL RESPIRATORYINERTANCE

Another situation in which increased respira-tory inertance may be detrimental is during ab-normal body acceleration such as in low altitudeoperations in high performance aircraft and incertain phases of escape and re-entry during space

flight. Magid, Coermann, and Ziegenruecker (11)have investigated the effects of whole bodyvibration over a frequency range of 1 to 20cps. Because acceleration was of primary in-terest to these investigators, their experimentswere done at uniform accelerations, with theresult that displacements were very much greaterat lower than at higher frequencies. At fre-quencies below 3 cps, dyspnea and air hungerwere experienced, and at frequencies between 4and 8 cps, dyspnea was replaced by a sensationof difficulty in making and controlling respiratorymovements. The dyspnea experienced below 3cps was thought to be related to the effects of thelarge displacements upon the pulmonary circula-tion as well as the thorax, whereas the somewhatdifferent sensations experienced between 4 and8 cps were thought to be due solely to directmechanical interference with the motions of thelungs and thorax. Their values for the naturalfrequency of the thorax and abdomen, using a

shake table on supine subjects, were between 3.0and 3.5 cps, somewhat below our normal mean

of 5 cps. Differences in the method of applyingthe forced vibration and in the subjects' body posi-tion probably account for their lower natural fre-quencies. With their method the thorax and ab-domen appeared to be underdamped rather thancritically damped as found by DuBois and col-leagues (1, 5).

Summary

1. Total respiratory compliance, respiratorysystem natural frequency, and total respiratoryinertance were measured in 8 normal and 14 ex-

cessively obese subjects. The mean total inertancein the normals was 0.0098 cm H20 per L per sec-

ond2, and that in the obese subjects, 0.0253 cm

H2O per L per second2. This difference was

highly significant (p < 0.001).2. There were significant inverse correlations

between total respiratory compliance and bodyweight (r = - 0.74) and between natural fre-quency and body weight (r = - 0.64). Therewas a significant positive correlation between total

respiratory inertance and body weight (r = +0.86).

3. A method for estimating separately the gasand tissue components of total respiratory inert-ance is described and applied to three normal andthree obese subjects.

4. In three normal subjects, tissue inertanceaveraged 16%o of the total inertance. In threeexcessively obese subjects, tissue inertance aver-aged 68% of the total inertance.

AcknowledgmentsThe authors are grateful to Dr. Jere Mead for his

valuable advice and criticism during the progress of thiswork and for his review of the manuscript. The tech-nical assistance of Mr. Frank King, Mr. Andrew Mis-kowsky, and Miss Karin Ekstrand is also gratefullyacknowledged.

References1. DuBois, A. B., A. W. Brody, D. H. Lewis, and

B. F. Burgess, Jr. Oscillation mechanics of lungsand chest in man. J. appl. Physiol. 1955, 8, 587.

2. Heaf, P. J. D., and F. J. Prime. The compliance ofthe thorax in normal human subj ects. Clin. Sci.1956, 15, 319.

3. Mead, J. Control of respiratory frequency. J. appl.Physiol. 1960, 15, 325.

4. Mead, J. Measurement of inertia of the lungs atincreased ambient pressure. J. appl. Physiol. 1956,9, 208.

5. Brody, A. W., A. B. DuBois, 0. I. Nisell, and J.Engelberg. Natural frequency, damping factorand inertance of the chest-lung system in cats.Amer. J. Physiol. 1956, 186, 142.

6. Coermann, R. R., G. H. Ziegenruecker, A. L. Wittwer,and H. E. von Gierke. The passive dynamicmechanical properties of the human thorax-ab-domen system and of the whole body system.Aerospace Med. 1960, 31, 443.

7. Ferris, B. G., Jr., L. Opie, and J. Mead. Partition-ing of respiratory resistance in man. Fed. Proc.1960, 19, 377.

8. Said, S. I. Abnormalities of pulmonary gas ex-change in obesity. Ann. intern. Med. 1960, 53,1121.

9. Sharp, J. T., J. P. Henry, S. K. Sweany, W. R.Meadows, and R. J. Pietras. The effects of massloading the respiratory system in man. Submittedfor publication.

10. Sharp, J. T., J. P. Henry, S. K. Sweany, W. R.Meadows, and R. J. Pietras. The total work ofbreathing in normal and obese men. Submittedfor publication.

11. Magid, E. B., R. R. Coermann, and G. H. Ziegen-ruecker. Human tolerance to whole body sinus-oidal vibration. Aerospace Med. 1960, 31, 915.

509