Frequency Dependence of Flow Resistance

in Patients with Obstructive Lung Disease

GUNNARGnmmBy, TAMOTSUTAKSHIMA, WILLIAM GRAHAM,PETERMACKLEM,andJERE MEAD

From the Department of Physiology, School of Public Health, Harvard University, and theThoracic Services, Boston University Medical School,Boston, Massachusetts 02115

A B S T R A C T Total respiratory, pulmonary, andchest wall flow resistances were determined bymeans of forced pressure and flow oscillations(3-9 cps) superimposed upon spontaneous breath-ing in a group of patients with varying degrees ofobstructive lung disease. Increased total respira-tory and pulmonary resistances were found,whereas the chest wall resistance was normal orsubnormal. The total respiratory and pulmonaryresistances decreased with increasing frequencies.Static compliance of the lung was measured duringinterrupted slow expiration, and dynamic compli-ance was measured during quiet and rapid spon-taneous breathing. Compliance was found to befrequency-dependent. The frequency dependence ofresistance and compliance are interpreted as ef-fects of uneven distribution of the mechanical prop-erties in the lungs. The practical application ofthe oscillatory technique to the measurement offlow resistance in patients with lung disease isdiscussed. Measurements of total respiratory re-sistance by the forced oscillatory technique at fre-quencies less than 5 cps appear to be as useful forassessing abnormalities in airway resistance aseither the plethysmographic or esophageal pressuretechniques.

INTRODUCTION

DuBois, Brody, Lewis, and Burgess (1) were thefirst to study the response characteristics of the

Dr. Grimby's present address is Department of ClinicalPhysiology, Sahlgranska Sjukhuset, University of Gote-borg, Goteborg, Sweden.

Received for publication 1 November 1967 and in re-vised form 9 February 1968.

respiratory system. They applied sinusoidal pres-sures to subjects (who suspended their own ef-forts to breathe) and demonstrated that the humanrespiratory system has a resonant frequency atabout 6 cps. Since, at such a frequency, mechani-cal impedance is entirely flow-resistive, the ratioof pressure to flow amplitude could be used to mea-sure the flow resistance of the respiratory system.Mead (2) showed that this measurement could bemade during breathing by superimposing theforced oscillations on the breathing pattern. Sinceonly minimal cooperation is required, this approachis attractive for use in detecting abnormalities offlow resistance. But, does a measurement made ata frequency an order of magnitude higher applyto the conditions of ordinary breathing? In par-ticular, does it apply in abnormal lungs? Patientswith chronic obstructive disease show marked fre-quency dependence of pulmonary compliance (3),and, according to the theories advanced by Otis,McKerrow, Bartlett, Mead, McIlroy, Selverstone,and Radford (4), these patients should also be ex-pected to show frequency dependence of flow re-sistance.

To answer these questions, we measured thefrequency dependence of flow resistance in a groupof patients with different degrees of obstructivelung disease. We measured pulmonary flow re-

sistance during spontaneous breathing by means ofesophageal balloons, and we measured pulmonary,chest wall, and total respiratory flow resistanceduring forced oscillations at 3, 5, 7, and 9 cps. Inaddition, we made separate measurements of air-way resistance during voluntary panting at a fre-

The Journal of Clinical Investigation Volume 47 1968 1455

quency of about 2 cps by the plethysmographictechniques of DuBois, Botelho, and Comroe (5).

To make measurements at frequencies otherthan the resonant frequency of the respiratorysystem, we use the following general approach.Wedisplay the applied pressure and resulting flowon the x and y axes of an oscilloscope. Increasingflows in the inspiratory direction produce upwarddeflections (and vice versa) from a zero-flow mid-point. Increasing pressures relative to atmosphericpressures produce deflections to the right (andvice versa) from a zero-pressure midpoint. Whenpressures are applied at frequencies below theresonant frequency of the respiratory system, pres-sure-flow loops are formed which develop in theclockwise direction. When frequencies are abovethe resonant frequency, pressure-flow loops areformed in the anticlockwise direction. As onepasses from very low frequencies upward, theclockwise looping narrows and disappears, as theresonant frequency is approached, to be replacedby anticlockwise looping as the resonant frequencybecomes exceeded. The looping reflects phase dif-ferences between pressure and flow. For clockwiselooping, pressure lags behind flow. For anticlock-wise looping, pressure leads flow. These phase dif-ferences result from the combined influences of theelastic and inertial properties of the respiratorysystem. At low frequencies the elastic propertiesdominate. Elastic pressures rise during inspirationto maximally positive values at end inspiration; asa result, pressure lags flow, and clockwise loopingresults. At frequencies above resonance, inertialproperties dominate. Inertial pressures rise at themouth, relative to atmospheric pressures, to max-imum values at the end of expiration when the in-spiratory acceleration is greatest, and as a result,pressure leads flow. At the resonant frequency thelag of pressure due to elastic properties is exactlycounterbalanced by the lead as a result of inertialproperties; flow and pressure are in phase, and allpressure-flow looping disappears.

But the phase differences as reflected by thelooping of the pressure-flow pattern can also bechanged without altering frequency. For example,if one subtracts from the pressure signal anothersignal which varies with volume, at frequenciesbelow resonance the clockwise looping will be di-minished. Indeed, at some fixed frequency belowresonance, if just the right amount of volume sig-

nal is subtracted from the pressure signal, the loopcan be caused to disappear. Alternatively, if onesubtracts from the pressure signal one proportionalto volume acceleration, at frequencies above reso-nance the looping will be diminished. Again, if, ata fixed frequency above resonance, just the rightamount of this signal is subtracted, the loopingcan be made to disappear.

The explanation of this behavior is that by sub-tracting these signals from the pressure signal,one in effect simulates changes in the properties ofthe respiratory system: the elastic component ofpressure developed by the respiratory system isdirectly proportional to volume change, whereasthe inertial component is directly proportional tovolume acceleration. Subtracting from the appliedpressure a signal proportional to volume is likesubtracting elasticity from the respiratory system,whereas subtracting signals proportional to vol-ume acceleration is like subtracting inertia fromthe system. An important feature from the presentstandpoint is that neither subtraction in any wayinfluences the flow resistance of the system. Toestablish the inphase, pressure-flow relationship,which defines the flow resistance of the respiratorysystem at frequencies other than resonant fre-quency, we achieve resonant behavior by simu-lating changes in the elastic or inertial propertiesof the respiratory system which reduce pressure-flow looping to a minimum and thereby achieve asimulated resonance.

Details of this approach are presented in thenext section. At this point it should be mentionedthat whereas in normal subjects resonant frequen-cies are usually found in the range of 5-7 cps, inpatients with chronic obstructive disease com-monly no resonant frequencies are demonstrable,at least up to frequencies of 10 cps. This is notsurprising, since the elastic behavior of the lungsof such patients tends itself to be frequency-de-pendent (4). Reductions in dynamic compliancewith increasing frequency imply increases in reso-nant frequency as well. Apparently, as the fre-quency is increased in these patients, resonant fre-quency remains above applied frequencies. In orderto measure flow resistance by the method of forcedoscillations in these patients, it was necessary touse our method for simulating resonance at all ofthe frequencies used.

14i56 G. Grimby, T. Takishima, W. Graham, P. Macklem, and J. Mead

TABLE IPhysical Characteristics and Clinical Diagnosis of the Patients

Patient Sex Age Height Weight Diagnosis

yr cm kgCl M 20 186 75 Bronchial asthmaJo M 21 173 77 Bronchial asthmaBac F 16 173 64 Postpneumonia, cystsCr M 58 180 77 Chronic obstructive lung diseaseWa M 52 178 100 Bronchial asthmaGi M 41 185 62 Chronic obstructive lung disease,

pneumonectomy, left

Bar M 58 173 87 Chronic obstructive lung diseaseMc M 42 170 60 Chronic obstructive lung diseaseCon M 48 186 76 Chronic obstructive lung diseaseSan M 74 173 52 Chronic obstructive lung diseaseHug M 58 168 66 Chronic obstructive lung diseaseHun M 61 173 87 Chronic obstructive lung diseaseFa M 63 180 76 Chronic obstructive lung diseaseCol M 77 168 66 Chronic obstructive lung disease,

lobectomy, right upper

Du M 49 170 73 Chronic obstructive lung disease

METHODS

15 patients with obstructive lung disease, of whom onewas a female, were studied. The diagnosis, age, bodyweight, and body height are given in Table I. The patientsare ranked according to the degree of abnormality oftheir maximum expiratory flow-volume curve, as judgedby the eye, starting with those with the most normalcurves.

All measurements, except airway resistance, were madewith the patients seated in a volume-displacement plethys-mograph (J. H. Emerson Co., Cambridge, Mass.) whichdiffered in two respects from the one described by Mead(6). (a) The temperature within the box was regulatedwith an air-cooling system. Heat exchange between air inthe box and the coolant from a 0.25 horsepower compres-sor was accomplished within a 6.5 cm, diameter, 120 cmlong copper pipe attached to the outside wall of the box.Air from the box was moved through the pipe and backinto the box by means of a motor-driven blower, whilecoolant moved in the opposite direction through a centralcoaxial copper tube, feathered to increase the surface forheat exchanges. (b) The response characteristics of theplethysmograph were improved by mixing a signal pro-portional to box pressure with the spirometer output.Such a pressure-volume plethysmograph combines use-ful features of pressure plethysmography (speed of re-sponse) with those of volume plethysmography (rela-tively small size and light weight construction, plus ex-tended range of measurement). In practice proper mixingof the signals was accomplished by comparing flow intothe box, as measured with the Fleisch flowmeter, with thederivative of the mixed signal. The relative gains wereadjusted so as to minimize phase and amplitude differ-

ences. Over the range from 0 to 9 cps, the phase differ-ence and relative amplitude could be rendered negligible.

Rapid oscillations of flow at the mouth were producedwith a loudspeaker system driven by a low frequencysine-wave generator and power amplifier. Measurementswere made during quiet breathing at frequencies of 3, 5,7, and 9 cps. The pressure generator is schematicallyshown in Fig. la together with the equivalent electricalcircuit of the system. Fig. 1 b shows a photograph of theequipment.

The design of the pressure generator was directed to-ward these ends: (a) to apply at a given setting of thesine-wave generator a pressure variation at the airwayopening which is, as nearly as possible, independent ofchanges in mechanical impedance offered by the subject.(b) to offer as little impedance to breathing as possible.(c) to avoid rebreathing of expired air. The last is ac-complished by withdrawing air at a constant rate of 0.4liter/sec through a side tap at the mouthpiece. The re-sulting shift in the flowmeter signal is suppressed elec-trically. The impedance to breathing is minimized by usinga low-resistance flow meter (Fleisch Model No. 4, 1 mmof H20 at 1.49 liters/sec) and a low-resistance exit fromthe box (the 170 cm long, 5 cm, I.D., tube connecting theinside of the box to the atmosphere). The pressure varia-tion at the mouth associated with spontaneous breathingis less than 6 mmof H20. The first point is a conveniencerather than a necessity. To the extent that the appliedpressure can be held constant, the flow amplitude variesinversely with flow resistance (at the resonant fre-quency). This simplifies measurement. For the mea-surements reported in this study, this feature is not used.It is achieved (to a close approximation) by using aflowmeter of the lowest practical resistance so as to re-

Frequency Dependence of Flow Resistance 145o7

Bias flow

FIGURE 1 a Schematic drawing of the loudspeaker system and the equivalent elec-trical circuit. 1, Two Acoustic Research (Cambridge, Mass.) Model No. 1 loud-speakers are arranged mechanically in series, as shown. The polarity of applied vol-tage is such that the speaker displacement is in the same direction; 2, tubing fromthe atmosphere to the box. It gives high inertial impedence at high frequencies(for the oscillations) and low inertial impedance at low frequencies (quiet breath-ing) ; 3, volume of gas in the box; 4, bias flow to reduce the dead space.

FIGURE 1 b Photograph of the loudspeaker box, thetemperature regulated body plethysmograph, and the bias-flow system.

duce pressure losses between the generator and the sub-ject, and by rendering the loading of the loudspeakersnearly constant. This load consists of the impedance ofthe tube, of the compressible gas within the box, and ofthe experimental subject, all three operating together.The impedance of a parallel network is relatively insen-

sitive to changes of impedance in one of its branches solong as the impedance of that branch is high compared tothat of the others. The 130 liters of gas within the box isa low impedance compared to that of the respiratory sys-tem and, accordingly, the loading of the loudspeaker isquite insensitive to changes in impedance of the respira-tory system.

The electrical equivalent of the respiratory system isshown in Fig. 2 together with the equations for calcu-lating the resistance of the different compartments. Theair flow at the mouth (Vao) was measured with theFleisch flowmeter and a Sanborn transducer (No. P270)and used for calculating the total respiratory (Rrs) andpulmonary resistance (R1). To calculate the chest wallresistance (Rw), the volume recording from the plethys-mograph was differentiated (Ve).

Esophageal pressure, as an index of pleural pressure(Pp.), was measured with a 10 cm rubber balloon con-taining 0.2-0.5 ml of air (8). The transpulmonary pres-sure (mouth pressure minus esophageal pressure) and thetransrespiratory pressure (mouth pressure minus pres-sure in the plethysmograph) were measured with induc-tance manometers (Sanborn Co., Waltham, Mass., No.268-B). All volumes, flows, and pressures were recordedon a 6-channel tape recorder (Precision Instrument Co.,Palo Alto, Calif.).

Flow and pressure signals from the tape recorder werecombined after the experiments on an X-Y cathode-raystorage oscilloscope (Tektronix Model 564, with twotype 3A72 plug-in amplifiers, Portland, Oreg.), andcorrections were made to obtain flow-resistive pres-

1458 G. Grimby, T. Takishima, W, Graham, P. Macklem, and I. Mead

Lung

PpI

At resonant frequency or with electrical correctionfor reactance:

R =.ao Pbsrs 0bs

VaoIPao - PpI

VaoR =p I s

_ %wsure by adding or subtracting signals proportional tovolume and (or) volume acceleration in the mannerdescribed in the Introduction. An example of an uncor-rected and a corrected recording is shown in Fig. 3.Since, in general, the corrections were different for thelungs, chest wall, and total respiratory system, the taperecording facility was essential. Corrections made at thetime would have required intolerably long experiments.Photographs of flow versus pressure were measured toyield the flow resistance for the total respiratory system(Rrs), for the airways plus the lung tissue (R1), and forthe chest wall (Rw). Simultaneous recordings on a di-rect-writing Sanborn Recorder were also obtained. Theresistance was measured as the inverse of the slope offlow-pressure tracing at about 0.5 liter/sec of inspira-tory air flow, which usually approximated the maximalinspiratory flow rate. It was not possible to estimateslopes at lower flows because the flow rate on which theoscillations were superimposed changed too rapidly be-tween the respiratory phases (see Figs. 3 and 4).

Pulmonary resistance (resistance of airways plus lungtissue) was also measured during quiet and rapid breath-ing, with the electrical subtraction of a signal proportionalto volume in order to correct for lung elastic pressure.The proportionality constant was set on the X-Y oscillo-scope and the line, usually S-shaped with or without aloop in the expiratory phase, was photographed. The re-sistance was calculated as the pressure-flow ratio from0.5 liter/sec inspiratory flow to zero flow. The nonlinearpressure-flow relationship was also used for calculatingthe constants in Rohrer's expression (P = K1\ + K2V2,in which P is pressure in cm of H20, and V is flow inliters/sec) in a similar way to that used by Mead and

FIGURE 2 Equivalent electrical circuitfor the respiratory system. For sym-bols see Mead and Milic-Emili (7).

Whittenberger (9). These constants were then used tocalculate the slope of the pressure-flow relationship at aflow of 0.5 liter/sec in order to obtain a value duringquiet breathing which could be compared with the oneobtained during forced oscillations.'

The total lung capacity was measured plethysmographi-cally by the method of DuBois, Botelho, Bedell, Marshall,and Comroe (10). Dynamic compliance was estimatedfrom the end-inspiratory and expiratory pressures atzero-flow points and the volume change. About 1-2 hrbefore the oscillatory measurements were made, airwayresistance was measured in a pressure plethysmographby the method of DuBois et al. (5) at a panting fre-quency of approximately 2 cps. At this time the forcedexpiratory volume in 1 sec (FEVy.o) was determined witha Collins spirometer, and the maximum voluntary ven-tilation (MVV) with a spontaneous frequency was mea-

sured with a Douglas bag in an open system. The normalvalues for total lung capacity and vital capacity were

predicted according to Baldwin, Cournand, and Richards(11), and for FEV,.o and MVV according to Kory,Callahan, Boren, and Syner (12).

RESULTS

The results of the spirometric studies are givenin Table II.

1 The slope of the pressure-flow relationship, dP/dV,at a flow of 0.5 liter/sec was calculated from Rohrer'sexpression as follows : P = KV+ K2VW; dP/dV = K1 +2K2V; at V = 0.5 liter/sec dP/dV = K1+ 2K2 (0.5) =K, + K2.

Frequency Dependence of Flow Resistance 1459

FIGURE 3 Pressure-flow relationship during oscillations at 9 cps of the total respiratory system. Horizontal axis,mouth pressure minus pressure in the body plethysmograph, 1 subdivision = 1 cm of H20; vertical axis; mouth flow1 subdivision = 0.25 liter/sec. Zero flow is indicated on the horizontal line in the middle with inspiratory direction to-wards the top of the figure. The left part of the figure shows recording before correction for the reactance; the rightpart shows the same pressure-flow relationship after electrical correction.

TABLE I ISpirometric Data

Patient Total lung capacity Vital capacity RV/TLC FEVIDo MVV

liters %pre- liters %Pre- % liters %c pre- liters/ %pre-dicted dicted dicted min dicted

Cl 6.70 113 5.20 110 22 3.70 79 112 56Jo 6.50 119 5.20 119 20 3.60 85 158 85Bac 4.70 108 2.80 80 40 2.40 75 95Cr 7.10 129 3.70 97 48 2.25 66 92 64Wa 6.60 118 2.90 75 56 1.47 41Gi 5.50 100 2.60 61 53 1.35 37 32 19Bar 6.70 127 2.70 74 60 1.20 36 35 26Mc 6.00 118 3.00 77 50 1.95 56 63 41Con 8.10 150 2.50 60 69 1.70 44 46 28San 10.00 207 3.20 96 68 1.50 56 29 25Hug 6.90 135 3.30 93 52 1.45 49 32 25Hun 6.90 133 2.70 75 61 1.30 36 28 21Fa 10.70 200 3.70 100 65 1.15 35 32 23Col 5.90 128 2.50 78 58 1.65 67 49 47Du 8.15 166 3.10 82 62 1.95 59 18 13

RV/TLC, quotient between residual volume (RV) and total lung capacity (TLC); FEV1.o, forced expiratory volume in 1sec; MVV, maximum voluntary ventilation.

1460 G. Grimby, T. Takishima, W. Graham, P. Macklem, and J. Mead

TABLE IIIPulmonary Resistance, K1 and K2 in Rohrer's Expression, and Dynamic Compliance

during Quiet Breathing, Static Compliance, and Airway Resistance

Quiet breathing

Patient f Ri K1 K2 Cdyn(l) Cat Raw

cps cm HgO/ liters/cm liters/cm cm H20/litersliters H20 H2O per sec

per secC1 0.40 4.7 2.2 3.2 0.13 0.17 4.2Jo 0.25 5.0 2.9 4.2 0.16 0.26 4.7Bac 0.40 2.0 2.0 0.8 0.07 0.15 3.8Cr 0.34 2.4 2.3 0.7 0.32 0.55 2.3Wa 0.30 8.5 7.8 4.8 0.11 0.25Gi 0.17 8.5 5.0 2.4 0.07 0.25 7.2Bar 0.47 5.6 5.4 2.7 0.11 0.35 5.2MC 0.38 6.5 6.4 2.2 0.12 0.25 4.5Con 0.35 8.3 5.0 5.2 0.05 4.6San 0.44 6.7 5.0 2.0 0.12 0.39 4.0Hug 0.30 14.0 7.4 10.8 0.13 0.42 5.6Hun 0.41 8.0 3.7 8.0 0.10 0.28 4.0Fa 0.36 6.0 5.6 3.6 0.11 0.48 4.3Col 0.40 8.4 7.4 2.2 0.04 0.19 4.9Du 0.40 - - 0.08 0.23 4.5

f, respiratory frequency; R1, pulmonary resistance; Cdn,, dynamic compliance;sistance.

Table III gives pulmonary resistance (calcu-lated as the slope between zero flow and 0.5liter/sec inspiratory flow), K1-K, of Rohrer'sexpression, and dynamic compliance, all duringquiet breathing, as well as static compliance andairway resistance, determined according to DuBoiset al. (5).

An example of the oscillographic recordings for

Rrs 9.2 6.6

Ct, static compliance; Raw, airway re-

measurements of total respiratory resistance at dif-ferent frequencies is given in Fig. 4. Patient Mchad a definite increase in resistance compared withthe normal range and a moderate frequency de-pendence of the resistance.

Fig. 5 presents the results of the measurementsof the total respiratory resistance in all patients.The resistance was lower in all patients at 9 cps

cmH206.7 6.3 fiters/sec

3 5 7 9 cpsFIGURE 4 Relationship between resistive pressure and flow for the total respiratory system atoscillations of 3, 5, 7, and 9 cps in patient Mc. Horizontal axis, resistive pressure, 1 subdivision= 1 cm of H20; vertical axis; mouth flow, 1 subdivision = 0.25 liter/sec. The total respiratoryresistance for each frequency is given.

Frequency Dependence of Flow Resistance

I %, I j I j %., .,

1461

R cm H20rs liters/sec

16 1

14 f

12 +

10 t8 t

6-

4-

2-

3 5 7 9cps

FIGURE 5 Total respiratory resistance at different fre-quencies. 0, chronic obstructive disease; X, bronchialasthma; 0, postpneumonia. The shaded area indicates therange for a group of five normal subj ects (Wohl et al.,unpublished observations). The line in the middle con-nects the mean values for the normal subject.

than at 3 cps. There was individual variation inthe frequency dependence of the resistance; thosewith the highest resistance at 3 cps showed themost pronounced fall in resistance with increasingfrequencies. The mean values and range from agroup of five normal subjects in the age 22-45 yr,who recently have been studied in this laboratorywith similar techniques (Wohl, M. E., P. Gross,and J. Mead, unpublished observations), are alsoshown in the figure. All values from the patientsat 3 cps fell above the normal range, and a five- toeightfold increase in the resistance was observed.

Fig. 6 demonstrates the pulmonary (airway pluslung tissue) resistance at different oscillatory fre-quencies. In addition to this, the resistance duringquiet breathing, calculated as the tangent to thepressure-flow relationship at 0.5 liter/sec, is given.As in the previous figure, a fall in resistance withincreasing frequency was found. It occurred inmost patients over the whole frequency range, butusually with a less marked fall between the highestfrequencies. The range for a normal group (Wohlet al., unpublished observations) are also given.All values from the patients at 3 cps fell above thenormal range. At higher frequencies patient Bachad values within the normal range.

Fig. 7 shows the results of the measurementsof chest wall flow resistance. The trans-chest wall

cm H20liters /sec20

16

2

1 3 5 7 9cps

FIGURE 6 Pulmonary resistance at different frequencies.*, chronic obstructive disease; X, bronchial asthma; 0,postpneumonia. The tangent to the pressure-flow curveduring quiet breathing at a flow of 0.5 liter/sec is givenin the left part of the figure. For explanation see Results.The shaded area indicates the range for a group of fivenormal subjects (Wohl et al., unpublished observations).Values from the report of Channin and Tyler ([16] seeDiscussion) are shown by open squares.

pressure oscillations were in most patients only aminor fraction of the forced oscillations at themouth. The relatively small pressure variations de-creased the accuracy of the measurement, and thevalue for the resistance could in some patients notbe distinguished from zero. No significant decrease

R cm H20W liters/sec

8

6

4

2

1 3 5 7 9cps

FIGURE 7 Chest wall resistance at different frequencies.0, chronic obstructive disease; X, bronchial asthma; 0,postpneumonia. The shaded area indicates the range for agroup of five normal subjects (Wohl et al., unpublishedobservations).

1462 G. Grimby, T. Takishima, W. Graham, P. Macklem, and J. Mead

with increasing frequency was found. Most valuesfell in or even below the normal range (Wohl etal., unpublished observations). The mean valuesfor all patients were 0.6 (range 0-2.5), 0.5 (range0-2.3), 0.5 range 0-1.9), and 0.4 (range 0-1.5)cm of H2O per liters per sec for 3, 5, 7, and 9cps, respectively.

The chest wall resistance comprised only aminor fraction of the total respiratory resistancein most of the patients. The values for pulmonaryand total respiratory resistance were thereforefairly close at all frequencies, as can be seen inFig. 8.

Airway resistances, measured separately in apressure plethysmograph, were based on the bestlinear approximation made by the eye to the flow-pressure relationship during inspiration in theneighborhood of zero flow. For comparison weused values of K1, which defines flow resistance atzero flow, as estimated graphically for spontaneousbreathing and as calculated for forced oscillations.The calculation was based on the assumption thatthe ratio of Rohrer's constants, K1/K2, is the sameduring forced oscillations as during spontaneousbreathing. The comparison is presented in Fig. 9.The airway resistance was measured at fre-

Rrs cm H20liters/sec16 r

14 1

12 -[

10 -t

8-

6-

4-

2-

o x

0 0

0

0

* eS00

dA A

, 0

x

dx

o x

2 4 6 8 10 12 14

R cm H20liters/sec

FIGURE 8 The relationship between total respiratory andpulmonary resistance, measured with the oscillatory tech-nique in the patients. 0, 3 cps; 0, 5 cps; A, 7 cps; X,9 cps.

Rat V.0

cm H20liters /sec10 1

8

6

2

1 3 5 7 9

cps

FIGURE 9 Pulmonary resistance at zero flow calculatedfrom the oscillatory measurements. 0, chronic obstructivedisease; X, bronchial asthma; 0, postpneumonia. For ex-planation see Results. Similar values for quiet breathingare given to the left. The shaded area describes the rangefor the airway resistance measured according to DuBoiset al. (5), with the individual values indicated.

quencies estimated to range from 1.5 to 2.5 cps.The range and individual values for airway re-sistance are indicated within the shaded area.Although the individual variation is strikingly less,the general level of resistance interpolates reasona-bly well between the values for pulmonary resist-ance at lower and higher frequencies.

DISCUSSION

The results are interesting both practically andtheoretically. From a practical viewpoint themethod of forced oscillations, even applied only tomeasure total respiratory resistance, appears to beas good a method as either the plethysmographicor esophageal pressure techniques for estimatingresistance to breathing. This is true because theresistance of the chest wall, if anything, tends tobe reduced in chronic obstructive lung disease andis small compared to pulmonary flow resistance,and because the frequency dependence of resist-ance, although demonstrable in many instances, isgenerally small in the range from spontaneousbreathing through 5 cps (see Figs. 6 and 9).

An essential feature of the method of forcedoscillations as applied to patients in contrast tonormal subjects is the requirement of electricaltuning to establish resonance at the lowest fre-quency practical, thereby minimizing reductions inresistance from frequency sensitivity. Measure-ments below about 3 cps are impractical becauseof mounting difficulty in distinguishing forced

Frequency Dependence of Flow Resdstance

x&

1463

oscillations in flow from the spontaneous flow pat-tern on which they are superimposed. Tuning inthe neighborhood of 3-5 cps appears to offer thebest compromise between this unfavorable signal-to-noise ratio at low frequencies and the drop inresistance at high frequencies.

The equipment required for such a measure-ment could be far simpler than that used in ourstudy. The electrical tuning can be accomplishedat the time of the measurement, and thus no taperecorder is necessary. The source of oscillatingpressure need not require a large chamber or twoloudspeakers. We designed our pressure sourcefor additional uses which tequired these features.A single loudspeaker connected directly to theflowmeter parallel with a long tube (such astube 2 in Fig. 1 a) and incorporating a bias-flowsystem (tube 4, Fig. 1 a ) produces adequate pres-sure oscillations. The body plethysmograph, al-though a convenient device for measuring an im-portant adjunct to the measurement, namely lunggas volume, is not needed for measurements ofeither total respiratory resistance or pulmonaryresistance per se.

Brody, O'Halloran, Wander, Connolly, Roley,Kohold, and Swertley (13, 14) have given normalvalues for total respiratory resistance obtainedduring forced oscillations at 10 cps. Our resultssuggest that values obtained in patients at such afrequency would not differ from normal valuesin some instances

We chose to calculate the resistances duringinspiration, in which the pressure-flow relation-ship is fairly consistent. During expiration largeand sudden variations in resistance occur. Theseare found commonly even in normal subjects, andappear to be due to changes in the cross-sectionalarea in the upper airway, presumably in thelarynx (15). In patients with chronic obstructivedisease, changes in resistance during expirationinvariably occur and reflect dynamic compressionof intrathoracic airways. There is, however, in thepresent study, a high degree of nonlinearity asdemonstrated by the large values of K2 in Rohrer'sexpression (see Table III). This makes the resist-ance measurements very sensitive to the flow rangeover which they are measured, e.g., compare Figs.6 and 9. In normal lungs K9 for intrathoracic air-ways is probably not more than 0.1 (see reference15). If K2 in the upper airways of patients is

assumed to be normal, i.e. about 0.3, this meansthat K2 of intrathoracic airways is increased atleast 10 times.

From a theoretical point of view, our results areof interest since they confirm a prediction madeby Otis et al. (4), namely, that patients who ex-hibit frequency dependence of compliance shouldalso exhibit frequency dependence of resistance.These authors consider the implications of non-uniform distribution of mechanical properties oflungs to their over-all mechanical behavior. Thefinding in patients with chronic obstructive pul-monary disease that compliance drops as frequencyincreases, according to their theories, reflects dis-crepancies in time constants between differentparts of the lung. (The time constant of a regionis the product of the flow resistance of all airwayssupplying the region and the compliance of theregion.) They show that inequality of time con-stants would also lead to frequency dependence offlow resistance.

In apparent contradiction to the prediction ofOtis et al. (4), Channin and Tyler (16) foundthat total pulmonary resistance fell substantiallyin only two of six patients each of whom haddemonstrated a marked fall in dynamic compliancewith frequency. Fig. 6 presents their results alongwith our own, and demonstrates that the frequencyrange encompassed by their experiments (thelargest range practical during spontaneous breath-ing without shifting lung volume) was too smallto detect frequency sensitivity of the order ob-served by us.

Although both compliance and resistance de-crease with increasing frequency in chronic ob-structive lung disease, it is not possible to comparethese decreases because of the widely differingranges of frequencies over which the reductionshave been observed. The most striking reductionin compliance occurs between static values andspontaneous breathing, a range in which no resist-ance measurements are available and, indeed, inwhich measurements would be difficult to make.On the other hand, measurements of dynamic com-pliance at frequencies above approximately 2 cpsare difficult to interpret due to the mounting andunknown contribution of inertial pressures. Thefrequency range over which both resistance andcompliance can be measured is probably not muchgreater than that observed by Channin and Tyler

1464 C. Grimby, T. Takishima,, W. Graham, P. Macklem, and J.' Mead

(Fig. 6) and is too restricted to permit adequatedefinition of their relative frequency sensitivity.

The total respiratory and the pulmonary resist-ance at low frequencies was in all patients in-creased compared with normal values. At most,the total respiratory resistance was increased 6-7-fold. At higher frequencies the differences wereless, and in some patients, they were almost abol-ished. The frequency dependence of resistance innormal subjects (Wohl et al., unpublished obser-vations) is of much smaller magnitude than thatin most of the patients.

The chest wall resistance was, with two excep-tions, either in the low-normal range or below thenormal range. The subnormal values could, hypo-thetically, be explained as an effect of increasedlung volumes. For example, it is reasonable toassume that pressure losses associated with tissueviscous resistances are proportional to linear ve-locities of tissues. Accordingly, since a given rateof volume change would be associated with a de-crease in linear movements of tissues as the volumeat which the volume change is produced is in-creased, the chest wall resistance in patients whobreathe at increased lung volumes should be lessthan in normal individuals. For a doubling of lungvolume, not an unreasonable value, one wouldanticipate a reduction in tissue resistance on thisbasis alone of approximately 37 %O (This followsfrom our assumption that tissue resistance is pro-portional to tissue velocity and the further as-sumption of spherical geometry, such that thelinear differential, dr = 1/4r2 X dV, varies in-versely with r2 and hence inversely with V2/3).The reductions in chest wall resistance appear tobe consistent with this interpretation.

ACKNOWLEDGMENTSWeare indebted to Drs. E. A. Gaensler and H. Constan-tine for valuable assistance and cooperation in the selec-tion of the patients and the determination of airwayresistance.

This work was supported by U. S. Public Health Re-search Grant No. AP 00229 (Mechanical Factors in theControl of Breathing) and No. 6M 12564 (Studies inRespiratory Mechanics).

REFERENCES1. DuBois, A. B., A. W. Brody, D. H. Lewis, and B. F.

Burgess, Jr. 1956. Oscillation mechanics of lungs andchest in man. J. Appl. Physiol. 8: 587.

2. Mead, J. 1960. Control of respiratory frequency. J.Appl. Physiol. 15: 325.

3. Mead, J., I. Lindgren, and E. A. Gaensler. 1955. Themechanical properties of the lungs in emphysema.J. Clin. Invest. 34: 1005.

4. Otis, A. B., C. B. McKerrow, R. A. Bartlett, J. Mead,M. B. McIlroy, N. J. Selverstone, and E. P. Radford,Jr. 1956. Mechanical factors in distribution of pul-monary ventilation. J. Apip. Physiol. 8: 427.

5. DuBois, A. B., S. Y. Botelho, and J. H. Comroe, Jr.1956. A new method for measuring airway resistancein man using a body plethysmograph: values in nor-mal subjects and in patients with respiratory disease.J. Clin. Invest. 35: 327.

6. Mead, J. 1960. Volume displacement body plethysmo-graph for respiratory measurements in human sub-jects. J. Appl. Physiol. 15: 736.

7. Mead, J., and J. Milic-Emili. 1964. Theory andmethodology in respiratory mechanics with glossaryof symbols. In Handbook of Physiology. AmericanPhysiology Society, Washington, D. C. 1: 363.

8. Milic-Emili, J., J. Mead, J. M. Turner, and E. M.Glauser. 1964. Improved technique for estimatingpleural pressure from esophageal balloons. J. Appl.Physiol. 19: 207.

9. Mead, J., and J. L. Whittenberger. 1953. Physicalproperties of human lungs measured during spon-taneous respiration. J. Appl. Physiol. 5: 779.

10. DuBois, A. B., S. Y. Botelho, G. N. Bedell, R. Mar-shall, and J. H. Comroe, Jr. 1956. A rapid plethysmo-graphic method for measuring thoracic gas volume:a comparison with a nitrogen washout method formeasuring functional residual capacity in normal sub-jects. J. Clin. Invest. 35: 322.

11. Baldwin, E. de F., A. Cournand, and D. W. Richards,Jr. 1948. Pulmonary insufficiency. I. Physiologicalclassification, clinical methods of analysis, standardvalues in normal subjects. Medicine. 27: 243.

12. Kory, R. C., R. Callahan, H. G. Boren, and J. C.Syner. 1961. The Veterans Administration-Armycooperative study of pulmonary function. I. Clinicalspirometry in normal men. Am. J. Med. 30: 243.

13. Brody, A. W., P. S. O'Halloran, H. J. Wander, J. J.Connolly, Jr., E. E. Roley, and E. Kobold. 1960.Ventilatory mechanics and strength: long-term re-examinations and position change.. J. Appl. Physiol.15: 561.

14. Brody, A. W., H. J. Wander, P. O'Halloran, J. J.Connolly, Jr., and F. W. Schwertley. 1964. Correla-tions, normal standards and interdependence in testsof ventilatory strength and mechanics. Am. Rev.Respirat. Diseases. 89: 214.

15. Ferris, B. G., Jr., J. Mead, and L. H. Opie. 1964.Partitioning of respiratory flow resistance in man.J. AppL. Physiol. 19: 653.

16. Channin, E., and J. Tyler. 1962. Effect of increasedbreathing frequency on inspiratory resistance in em-physema. J. Appl. Physiol. 17: 605.

Frequency Dependence of Flow Resistance 1465