JOURNAL
OF
APPLIED
Voi. 38, No. 3, March
PHYsXoLoGY
1975.
Printed
Resistance subjects
in U.S.A.
of intrathoracic during
periodic
airways
of healthy
flow
KEVIN E. FINUCANE, S. V. DAWSON, P. D. PHELAN, AND JERE MEAD Departments of Physiology, Harvard School of PublicHealth, Boston, Massachusetts 02115; and Pulmonary Physiulugy, Perth Medical Centre, West Australia
effect of periodic flow is illustrated in Fig. 1: the distribution of the velocity of air (relative to the mean velocity) across the section of a Z-cm diameter pipe during steady flow is compared with that at peak flow during forced oscillation at 9 Hz. In this example the resistance during periodic flow is approximately four times that during fully developed, steady laminar flow. The actual shape of the velocity profile during periodic flow depends upon the dimensionless parameter, a
FINUCANE, KEVIN E., S. V. LAWSON, P. II. PHELAN, AND JERE MEAD. Resistunce of intdwracic airways of healthy subjects during peridc J?OW. J. Appl. Physiol. 38(3) : 517-530. 1975.-The resistance and reactance of lower airways were measured as functions of the frequency and amplitude of periodic flow in three healthy subjects by relating flow, produced with a piston pump, to the difference between lateral tracheal and alveolar pressure, estimated Resistance consistently increased with plethysmographically. frequency; reactance was small never exceeding resistance. This result cannot be explained by distortion of velocity profiles by inertia because, in long pipes, resistance increases only when inertial forces are large and reactance exceeds resistance. Theoretical analyses of airway resistance suggested that the results reflected inhomogeneity. In lung models which considered airway wall distensibility and inertial reactance of airways, resistance increased with frequency and inertial reactance was small. These
a=r
results imply termined by the lung and airways. As
that in health, as in lung disease, resistance is dethe distribution of resistance and reactance within is not simply the total resistance of the individual flow amplitude increased at constant frequency, flow-pressure relationships became distorted and resistance increased, due probably to motion of airway walls and further distortion of velocity profiles. lower airway resistance; pendence; inhomogeneity; pliance; lung models
frequency dependence; amplitude deairway inertance; airway wall com-
THIS PAPER describes and analyzes the relationship between frequency and the resistance of the intrathoracic airways of healthy subjects measured during periodic flow. The study was undertaken to provide information on the nature of airway resistance. Airway resistance in healthy people is usually assumed to be independent of how rapidly flow is changing and, therefore, independent of respiratory frequency. This is not the case in long pipes during laminar periodic flow (3, 18, 31, 34); h ere resistance increases with frequency because 2:he inertia of the fluid alters the distribution of velocity across the pipe section, i.e., it alters the velocity profile. As frequency increases and the force required to accelerate and decelerate the fluid becomes appreciable, the velocity profile becomes more uniform in the center of the pipe and steeper near the wall. This increases the shear stress on the wall and hence the viscous resistance relative to that during steady flow when the velocity distribution is parabolic and the rate of shear is least. This
517
d/ WV
(4
where r is the radius of the pipe, ti the angular frequency (w = 2~ f, where f is frequency in Hz), and Y the kinematic viscosity of the fluid. The effect of frequency on resistance therefore depends on the size of the pipe and the kinematic viscosity of the gas. The parameter a expresses the ratio of inertial to viscous forces during periodic flow; theory predicts and empirical results confirm (3 1) that when inertial forces dominate, i.e., when the inertial reactance exceeds the resistance, the velocity profile is sufficiently different from the parabolic form that the Poiseuille expression for estimating resistance is no longer valid; this condition pertains when a 2 2.0. Calculations of the relationship between a and resistance based on Crandall’s solution for periodic flow through circular pipes of infinite length have been made by several authors (30, 3 1, 34) ; the general relationship is illustrated in Fig. 2. The a’s of the first 10 generations of airways at 1 and 10 Hz calculated from Weibel’s dimensions of airways (33) are shown in Table 1. These data suggest that if flow in airways behaved as it does in very long pipes then the airway resistance of a lung with these dimensions would increase with frequency during laminar periodic flow. The magnitude of this increase can be calculated from Poiseuille’s expression, Weibel’s data on the dimensions of airways, and the relationship between resistance and a given in Fig. 2; at IO-Hz resistance would be approximately 30 5% greater than during steady flow. The assumptions underlying these calculations are not strictly appropriate for the lung. First, flow in airways is not analogous to that in long pipes because velocity profiles in airways are nonparabolic even during steady flow (16, 23, 28). It is possible, however, that inertial forces associated with periodic flow could further distort velocity profiles in airways and cause resistance to increase with frequency. Second, in using Wiebel’s model we assume a
Downloaded from www.physiology.org/journal/jappl by ${individualUser.givenNames} ${individualUser.surname} (129.108.009.184) on November 2, 2018. Copyright © 1975 American Physiological Society. All rights reserved.
518
FINUCANE
I
-v9
z 0
RELATIVE 1. Comparison long pipe during steady mately 9 Hz. FIG.
Hz
1.0
VELOCITY of velocity flow and
profiles during
for larninar periodic flow
airflow in at approxi-
a
ET
AL.
has not been precisely assessed we measured airway resistance in three healthy subjects at several frequencies between 1 and 10 Hz. To detect small changes of airway resistance reliably we measured the resistance of airways between the upper trachea and the alveoli, i.e., lower airway resistance @law). This measurement is independent of two common sources of variability of measurements of total pulmonary resistance in an individual-that due to uncontrollable variation of upper airway resistance with time (7, 15, 27) and that due to variations of esophageal pressure with cardiovascular events. We found that Rlaw consistently increased with frequency but in contrast to the flow-resistive behavior of long pipes this increase was not associated with large inertial forces; indeed, these appeared small at all frequencies. Theoretical analysis of the relationships between frequency, inhomogeneity, and airway resistance in models of the lung showed that a model which considered the distensibility of airway walls and the inertial reactance of conducting airways exhibited frequency dependence of resistance similar to that observed in the empirical studies. We also examined the influence of the amplitude of periodic flow on the flow-pressure characteristics of airways and found that at a given frequency the slope of the flowpressure curve at zero flow decreased as flow amplitude was increased. In this, the airways mimicked behavior we had previously observed in simple mechanical systems with nonlinear steady-state flow-pressure characteristics. METHODS
FIG.
Rw/Ro steady
2. Relationship is the ratio flow.
Generation
between of resistance
Radius,
*cm
0
0.9
1 2
0.61 0.415
3 4 7
0.28
1Hz
dimensions
from
for
flow
A phat
(33).
10 Hz
8.2 5.5 4.5 3.5 2.8 2.3 1.8 1.5 1.3
0.5 0.4 Weibel
a long pipe, to that during
17.8 12.1
1.8 1 .4 1 .I 0.9 0.7 0.6
0.065
10
a
5.6 3.8 2.6
0.225 0.175 0*14 0.115 0.093 0.077
: 7 8 9
* Airway
resistance and during periodic
t Alpha
=
r m
symmetrically branching lung and therefore an homogeneous distribution of physical properties; however, the variable length of pathways from trachea to alveoli and the asymmetric branching pattern of airways necessarily implies inhomogeneity. Theoretically, the overall resistance of an inhomogeneous branched system can either decrease or increase as frequency increases (see APPENDIXES and DISCUSSION). For these reasons and because the influence of frequency on the airway resistance of healthy people
The measurements in this study employed two techniques introduced originally by DuBois et al. (5, 6) : a piston pump was used to modulate lung volume and airway resistance was estimated plethysmographically. The details of the technique are described separately (see accompanying for, and has, addipaper (9)) b ecause it was designed Here we recapitulate the principles tional applications. of the technique and describe the methodology specific to the present investigation. Pump and pwlysmugruph. An approximately sinusoidal oscillation of airflow was applied at the mouth of the subject with a variable-frequency piston pump situated outside the plethysmograph in which the subject sat. Volume change of the respiratory system was measured with. a pressure-corrected “flow” plethysmograph (see accompanying paper 9). Volume change measured with the plethysmograph (Npleth) was without phase or amplitude distortion over the range of frequencies O-10 Hz. ,4lueoZnr pressure. Alveolar pressure (PA~v) during flow was estimated from measurements of GVpleth, the volume change of the pump (GVpump) and mouth pressure (Pao): with each stroke of the pump gas moved into and out of the respiratory system and gas in the pump, airways, and alveoli was compressed and expanded by the pressure increments resulting from the impedances of the respiratory system. The gas in the pump and mouthpiece was maintained at body temperature; therefore the instantaneous difference between GVpump and Wpleth (obtained electrically) was the volume change due to compression
Downloaded from www.physiology.org/journal/jappl by ${individualUser.givenNames} ${individualUser.surname} (129.108.009.184) on November 2, 2018. Copyright © 1975 American Physiological Society. All rights reserved.
FREQUENCY
DEPENDENCE
OF
LOWER
AIRWAY
and expansion of gas in the pump, airways, and alveoli (GVgc(aw+Alv))* A signal approximately proportional to the volume change due to gas compression in the pump and airways (GVgc(aw))l was subtracted from GVgc(aw+Alv) to obtain a signal proportional to the volume change due to gas compression in the alveoli (8Vgc(dv)). This signal and a signal proportional to lung volume (VL), obtained plethysmographically, were used to estimate P~lv according to Boyle’s law PAlV
=
&6VgC(Ah)/VL
(2)
In practice Wgc(Alv) and VL were measured continuously and fed to the numerator and denominator of an analog divider. The proportionality constant, K, was atmospheric pressure minus the water vapor pressure of saturated gas it was established by adjusting the at body temperature; gain of the output from the divider until it equaled Pao when the subject made respiratory efforts against the staUnder these circumstances Pao = P~lv tionary pump. (Pascal’s law). Derivahn of resz’slance and reactance. The pressure drop across the lower airways (APlaw) was obtained by electrically subtracting estimated alveolar pressure from the lateral pressure in the upper trachea. During periodic flow APlaw has two components: one is proportional to flow and is defined as the resistive pressure (Pres), the other is proportional to acceleration and is defined as the inertial reactive pressure (Pi). Pres was obtained by displaying APlaw and flow at the mouth (vao) on the abscissa and ordinate, respectively, of a storage oscilloscope; any phase lag between J?ao and APlaw was assumed to be due to the inertial reactance of the gas in the airways and a signal proportional to volume acceleration at the mouth (Tao), obtained by differentiating vao, was added, in the appropriate sign, to APlaw until there was no phase lag between the summed signal and vao. Rlaw was calculated as the reciprocal of the slope, at zero flow, of the relationship between vao and the summed signal, Pres; the relationship between the added signal, Pi, and vao permitted calculation of the inertance and inertia1 reactance of the lower airways (Ilaw and wIIaw, respectively). Measuremants. The details of measuring Wpump, Wpleth, Pao, VL, J?ao, and vao are given in the accompanying paper w The lateral pressure in the trachea was measured with a polyethylene catheter (PE-240) and differential pressure transducer (Sanborn, model 268B). The catheter was 35-39 cm long; its tip was sealed and three to four spirally arranged holes were cut in the wall of the distal 2 cm. Angulation of the catheter relative to the axis of flow did not detectably influence measurements of lateral pressure when this was examined in a model. The model consisted of a pipe 2.8 cm internal diameter, 15 cm long, covered at one end with a cloth with a resistance to flow of approximately 2.5 cmHzO/l per s at a flow of 0.5 l/s, and having at the 1 AVgc(aw) was taken as the volume in the pump and an attached pipe which anatomic dead space and impedance accompanying manuscript (9)).
519
RESISTANCE
change due to gas compression roughly modelled the human of the respiratory system (see
other end an orifice with a diameter of 1.3 cm. The catheter was inserted through the orifice into the pipe so that its tip lay between the orifice and the cloth resistor with the side holes 3 cm from the orifice and at the same level as a side hole in the wall of the pipe. Over the range of frequencies and flows used in the present measurements the amplitude of pressure measured with the catheter was the same as that measured with the side hole even when the catheter was angled to the axis of flow in positions it might have adopted in the trachea.2 At high frequencies there was a small phase difference (approximately loo at 10 Hz) between catheter pressure and true lateral pressure. The phase distortion was the same when the downstream impedance was that of the respiratory system and was not affected by the changes of respiratory impedance that accompany change cf lung volume. The phase distortion was corrected at all frequencies up to 10 Hz by adding to the pressure signal a signal proportional to ?ao. The tracheal catheter was introduced through the nose and pharynx; 2 % lidocaine was used for topical anesthesia. The anesthetic was sprayed into the laryngopharynx over the back of the tongue while the subject inhaled deeply. This was somewhat unpleasant because of coughing and retching and was not always successful in adequately anesthetizing the larynx; in two potential subjects we were unable to get the catheter into the trachea mainly because of inadequate topical anesthesia. The catheter was most readily introduced when the subject panted through his open mouth while holding his head erect and tongue forward. Immediately the catheter was introduced lidocaine was injected through it into the trachea; thereafter anesthesia was maintained, at a level sufficient to prevent coughing, throughout the period of measurement by introducing l- to 2-ml aliquots of lidocaine as necessary. The amount of lidocaine used over a 3-h period did not exceed 250 mg. Because the freqeuncy response of the catheter-manometer system was mainly a function of the diameter of the catheter, care was taken to keep the catheter free of mucus; between successive measurements of resistance (see below) the catheter was disconnected from the transducer and mucus was removed by having the subject draw air through the catheter by making an inspiratory efiort while keeping his glottis closed. Subjects. The subjects were three healthy men; their ages, physical characteristics, and total lung capacities (TLC) are shown in Table 2. Procadure. Lower airway resistance was measured at six frequencies between 1 and 10 Hz, each at approximately 80, 55, and 40-45% of the subject’s TLC; the peak flow rate at each frequency was 0.5 l/s. Maw was also measured at peak flow rates of 0.5, 1.0, 1.5, and 2.0 l/s at the constant frequency of 5 Hz and at approximately 80, 55, and 4550 % of the subject’s TLC. In these measurements the lowest lung volume used was 400-600 ml higher than in the studies at different frequencies because 2 l/s was similar to the maximum expiratory flow rate at 4-O-45 % TLC and we wished to minimize the effect of airway compression. The 2 Independence to the axis of flow near the orifice.
of catheter presumably
pressure relates
on catheter to the disturbed
position nature
relative of flow
Downloaded from www.physiology.org/journal/jappl by ${individualUser.givenNames} ${individualUser.surname} (129.108.009.184) on November 2, 2018. Copyright © 1975 American Physiological Society. All rights reserved.
520
FINUCANE
TABLE Subj
JM KF DL
2. Subjects, anthropometric
data, and lung volumes
Age, yr
Ht, cm
VC, liters
49
187 180 185
6.9 5.8 6.1
35 36
TLC,
liters
9.0 7.5 7.32
stroke volume of the pump varied according to the frequency and peak flow rate required, it varied between 130 and 16 ml. The order in which the measurements were performed was selected randomly before each experiment. Each measurement was preceded by the following preliminary maneuvers designed to standardize the volume and temporal histories of the lung: the subject took three deep breaths, then inhaled maximally, and at TLC placed his mouth around the mouthpiece which was immediately switched, with a solenoid valve, to a high-impedance suction pump which maintained a constant flow rate of 0.5 l/s. The subject exhaled at this flow and the change of lung volume was monitored by displaying AVpleth on an oscilloscope. At the lung volume chosen for measurement the suction was turned off and the subject maintained this lung volume throughout the period of measurement. To calibrate alveolar pressure the subject now made respiratory efforts against the stationary pump; tracheal pressure (Pt), or mouth pressure, and the output from the analog divider, 6vgC(Ah)/vL, were displayed on another oscilloscope and the gain of the latter signal was adjusted until it was equal to Pt. The pump was then turned on and vao, on the Y axis, and APlaw, on the X axis, were displayed on the oscilloscope. During these measurements the subject braced his cheeks with the palms of his hands in order to minimize motion of the soft tissues of the upper airway. The signals GVpump, Pt, qao, and pressure in the plethysmograph were recorded on a six-channel tape recorder (Precision Instrument Co., Palo Alto,.. Calif.) and, together with the derived signals GVpleth, Vao, and APlaw, on an eight-channel direct-writing recorder (Sanborn, model 350). Because the primary signals were recorded from the time the subject went on the mouthpiece at TLC all derived signals could be reconstituted and the measurements were analyzed subsequently. To minimize the influence of low-frequency vibrations of the tape and improve the signal-to-noise ratio on replay all measurements made at frequencies
OF
APPLIED
Voi. 38, No. 3, March
PHYsXoLoGY
1975.
Printed
Resistance subjects
in U.S.A.
of intrathoracic during
periodic
airways
of healthy
flow
KEVIN E. FINUCANE, S. V. DAWSON, P. D. PHELAN, AND JERE MEAD Departments of Physiology, Harvard School of PublicHealth, Boston, Massachusetts 02115; and Pulmonary Physiulugy, Perth Medical Centre, West Australia
effect of periodic flow is illustrated in Fig. 1: the distribution of the velocity of air (relative to the mean velocity) across the section of a Z-cm diameter pipe during steady flow is compared with that at peak flow during forced oscillation at 9 Hz. In this example the resistance during periodic flow is approximately four times that during fully developed, steady laminar flow. The actual shape of the velocity profile during periodic flow depends upon the dimensionless parameter, a
FINUCANE, KEVIN E., S. V. LAWSON, P. II. PHELAN, AND JERE MEAD. Resistunce of intdwracic airways of healthy subjects during peridc J?OW. J. Appl. Physiol. 38(3) : 517-530. 1975.-The resistance and reactance of lower airways were measured as functions of the frequency and amplitude of periodic flow in three healthy subjects by relating flow, produced with a piston pump, to the difference between lateral tracheal and alveolar pressure, estimated Resistance consistently increased with plethysmographically. frequency; reactance was small never exceeding resistance. This result cannot be explained by distortion of velocity profiles by inertia because, in long pipes, resistance increases only when inertial forces are large and reactance exceeds resistance. Theoretical analyses of airway resistance suggested that the results reflected inhomogeneity. In lung models which considered airway wall distensibility and inertial reactance of airways, resistance increased with frequency and inertial reactance was small. These
a=r
results imply termined by the lung and airways. As
that in health, as in lung disease, resistance is dethe distribution of resistance and reactance within is not simply the total resistance of the individual flow amplitude increased at constant frequency, flow-pressure relationships became distorted and resistance increased, due probably to motion of airway walls and further distortion of velocity profiles. lower airway resistance; pendence; inhomogeneity; pliance; lung models
frequency dependence; amplitude deairway inertance; airway wall com-
THIS PAPER describes and analyzes the relationship between frequency and the resistance of the intrathoracic airways of healthy subjects measured during periodic flow. The study was undertaken to provide information on the nature of airway resistance. Airway resistance in healthy people is usually assumed to be independent of how rapidly flow is changing and, therefore, independent of respiratory frequency. This is not the case in long pipes during laminar periodic flow (3, 18, 31, 34); h ere resistance increases with frequency because 2:he inertia of the fluid alters the distribution of velocity across the pipe section, i.e., it alters the velocity profile. As frequency increases and the force required to accelerate and decelerate the fluid becomes appreciable, the velocity profile becomes more uniform in the center of the pipe and steeper near the wall. This increases the shear stress on the wall and hence the viscous resistance relative to that during steady flow when the velocity distribution is parabolic and the rate of shear is least. This
517
d/ WV
(4
where r is the radius of the pipe, ti the angular frequency (w = 2~ f, where f is frequency in Hz), and Y the kinematic viscosity of the fluid. The effect of frequency on resistance therefore depends on the size of the pipe and the kinematic viscosity of the gas. The parameter a expresses the ratio of inertial to viscous forces during periodic flow; theory predicts and empirical results confirm (3 1) that when inertial forces dominate, i.e., when the inertial reactance exceeds the resistance, the velocity profile is sufficiently different from the parabolic form that the Poiseuille expression for estimating resistance is no longer valid; this condition pertains when a 2 2.0. Calculations of the relationship between a and resistance based on Crandall’s solution for periodic flow through circular pipes of infinite length have been made by several authors (30, 3 1, 34) ; the general relationship is illustrated in Fig. 2. The a’s of the first 10 generations of airways at 1 and 10 Hz calculated from Weibel’s dimensions of airways (33) are shown in Table 1. These data suggest that if flow in airways behaved as it does in very long pipes then the airway resistance of a lung with these dimensions would increase with frequency during laminar periodic flow. The magnitude of this increase can be calculated from Poiseuille’s expression, Weibel’s data on the dimensions of airways, and the relationship between resistance and a given in Fig. 2; at IO-Hz resistance would be approximately 30 5% greater than during steady flow. The assumptions underlying these calculations are not strictly appropriate for the lung. First, flow in airways is not analogous to that in long pipes because velocity profiles in airways are nonparabolic even during steady flow (16, 23, 28). It is possible, however, that inertial forces associated with periodic flow could further distort velocity profiles in airways and cause resistance to increase with frequency. Second, in using Wiebel’s model we assume a
Downloaded from www.physiology.org/journal/jappl by ${individualUser.givenNames} ${individualUser.surname} (129.108.009.184) on November 2, 2018. Copyright © 1975 American Physiological Society. All rights reserved.
518
FINUCANE
I
-v9
z 0
RELATIVE 1. Comparison long pipe during steady mately 9 Hz. FIG.
Hz
1.0
VELOCITY of velocity flow and
profiles during
for larninar periodic flow
airflow in at approxi-
a
ET
AL.
has not been precisely assessed we measured airway resistance in three healthy subjects at several frequencies between 1 and 10 Hz. To detect small changes of airway resistance reliably we measured the resistance of airways between the upper trachea and the alveoli, i.e., lower airway resistance @law). This measurement is independent of two common sources of variability of measurements of total pulmonary resistance in an individual-that due to uncontrollable variation of upper airway resistance with time (7, 15, 27) and that due to variations of esophageal pressure with cardiovascular events. We found that Rlaw consistently increased with frequency but in contrast to the flow-resistive behavior of long pipes this increase was not associated with large inertial forces; indeed, these appeared small at all frequencies. Theoretical analysis of the relationships between frequency, inhomogeneity, and airway resistance in models of the lung showed that a model which considered the distensibility of airway walls and the inertial reactance of conducting airways exhibited frequency dependence of resistance similar to that observed in the empirical studies. We also examined the influence of the amplitude of periodic flow on the flow-pressure characteristics of airways and found that at a given frequency the slope of the flowpressure curve at zero flow decreased as flow amplitude was increased. In this, the airways mimicked behavior we had previously observed in simple mechanical systems with nonlinear steady-state flow-pressure characteristics. METHODS
FIG.
Rw/Ro steady
2. Relationship is the ratio flow.
Generation
between of resistance
Radius,
*cm
0
0.9
1 2
0.61 0.415
3 4 7
0.28
1Hz
dimensions
from
for
flow
A phat
(33).
10 Hz
8.2 5.5 4.5 3.5 2.8 2.3 1.8 1.5 1.3
0.5 0.4 Weibel
a long pipe, to that during
17.8 12.1
1.8 1 .4 1 .I 0.9 0.7 0.6
0.065
10
a
5.6 3.8 2.6
0.225 0.175 0*14 0.115 0.093 0.077
: 7 8 9
* Airway
resistance and during periodic
t Alpha
=
r m
symmetrically branching lung and therefore an homogeneous distribution of physical properties; however, the variable length of pathways from trachea to alveoli and the asymmetric branching pattern of airways necessarily implies inhomogeneity. Theoretically, the overall resistance of an inhomogeneous branched system can either decrease or increase as frequency increases (see APPENDIXES and DISCUSSION). For these reasons and because the influence of frequency on the airway resistance of healthy people
The measurements in this study employed two techniques introduced originally by DuBois et al. (5, 6) : a piston pump was used to modulate lung volume and airway resistance was estimated plethysmographically. The details of the technique are described separately (see accompanying for, and has, addipaper (9)) b ecause it was designed Here we recapitulate the principles tional applications. of the technique and describe the methodology specific to the present investigation. Pump and pwlysmugruph. An approximately sinusoidal oscillation of airflow was applied at the mouth of the subject with a variable-frequency piston pump situated outside the plethysmograph in which the subject sat. Volume change of the respiratory system was measured with. a pressure-corrected “flow” plethysmograph (see accompanying paper 9). Volume change measured with the plethysmograph (Npleth) was without phase or amplitude distortion over the range of frequencies O-10 Hz. ,4lueoZnr pressure. Alveolar pressure (PA~v) during flow was estimated from measurements of GVpleth, the volume change of the pump (GVpump) and mouth pressure (Pao): with each stroke of the pump gas moved into and out of the respiratory system and gas in the pump, airways, and alveoli was compressed and expanded by the pressure increments resulting from the impedances of the respiratory system. The gas in the pump and mouthpiece was maintained at body temperature; therefore the instantaneous difference between GVpump and Wpleth (obtained electrically) was the volume change due to compression
Downloaded from www.physiology.org/journal/jappl by ${individualUser.givenNames} ${individualUser.surname} (129.108.009.184) on November 2, 2018. Copyright © 1975 American Physiological Society. All rights reserved.
FREQUENCY
DEPENDENCE
OF
LOWER
AIRWAY
and expansion of gas in the pump, airways, and alveoli (GVgc(aw+Alv))* A signal approximately proportional to the volume change due to gas compression in the pump and airways (GVgc(aw))l was subtracted from GVgc(aw+Alv) to obtain a signal proportional to the volume change due to gas compression in the alveoli (8Vgc(dv)). This signal and a signal proportional to lung volume (VL), obtained plethysmographically, were used to estimate P~lv according to Boyle’s law PAlV
=
&6VgC(Ah)/VL
(2)
In practice Wgc(Alv) and VL were measured continuously and fed to the numerator and denominator of an analog divider. The proportionality constant, K, was atmospheric pressure minus the water vapor pressure of saturated gas it was established by adjusting the at body temperature; gain of the output from the divider until it equaled Pao when the subject made respiratory efforts against the staUnder these circumstances Pao = P~lv tionary pump. (Pascal’s law). Derivahn of resz’slance and reactance. The pressure drop across the lower airways (APlaw) was obtained by electrically subtracting estimated alveolar pressure from the lateral pressure in the upper trachea. During periodic flow APlaw has two components: one is proportional to flow and is defined as the resistive pressure (Pres), the other is proportional to acceleration and is defined as the inertial reactive pressure (Pi). Pres was obtained by displaying APlaw and flow at the mouth (vao) on the abscissa and ordinate, respectively, of a storage oscilloscope; any phase lag between J?ao and APlaw was assumed to be due to the inertial reactance of the gas in the airways and a signal proportional to volume acceleration at the mouth (Tao), obtained by differentiating vao, was added, in the appropriate sign, to APlaw until there was no phase lag between the summed signal and vao. Rlaw was calculated as the reciprocal of the slope, at zero flow, of the relationship between vao and the summed signal, Pres; the relationship between the added signal, Pi, and vao permitted calculation of the inertance and inertia1 reactance of the lower airways (Ilaw and wIIaw, respectively). Measuremants. The details of measuring Wpump, Wpleth, Pao, VL, J?ao, and vao are given in the accompanying paper w The lateral pressure in the trachea was measured with a polyethylene catheter (PE-240) and differential pressure transducer (Sanborn, model 268B). The catheter was 35-39 cm long; its tip was sealed and three to four spirally arranged holes were cut in the wall of the distal 2 cm. Angulation of the catheter relative to the axis of flow did not detectably influence measurements of lateral pressure when this was examined in a model. The model consisted of a pipe 2.8 cm internal diameter, 15 cm long, covered at one end with a cloth with a resistance to flow of approximately 2.5 cmHzO/l per s at a flow of 0.5 l/s, and having at the 1 AVgc(aw) was taken as the volume in the pump and an attached pipe which anatomic dead space and impedance accompanying manuscript (9)).
519
RESISTANCE
change due to gas compression roughly modelled the human of the respiratory system (see
other end an orifice with a diameter of 1.3 cm. The catheter was inserted through the orifice into the pipe so that its tip lay between the orifice and the cloth resistor with the side holes 3 cm from the orifice and at the same level as a side hole in the wall of the pipe. Over the range of frequencies and flows used in the present measurements the amplitude of pressure measured with the catheter was the same as that measured with the side hole even when the catheter was angled to the axis of flow in positions it might have adopted in the trachea.2 At high frequencies there was a small phase difference (approximately loo at 10 Hz) between catheter pressure and true lateral pressure. The phase distortion was the same when the downstream impedance was that of the respiratory system and was not affected by the changes of respiratory impedance that accompany change cf lung volume. The phase distortion was corrected at all frequencies up to 10 Hz by adding to the pressure signal a signal proportional to ?ao. The tracheal catheter was introduced through the nose and pharynx; 2 % lidocaine was used for topical anesthesia. The anesthetic was sprayed into the laryngopharynx over the back of the tongue while the subject inhaled deeply. This was somewhat unpleasant because of coughing and retching and was not always successful in adequately anesthetizing the larynx; in two potential subjects we were unable to get the catheter into the trachea mainly because of inadequate topical anesthesia. The catheter was most readily introduced when the subject panted through his open mouth while holding his head erect and tongue forward. Immediately the catheter was introduced lidocaine was injected through it into the trachea; thereafter anesthesia was maintained, at a level sufficient to prevent coughing, throughout the period of measurement by introducing l- to 2-ml aliquots of lidocaine as necessary. The amount of lidocaine used over a 3-h period did not exceed 250 mg. Because the freqeuncy response of the catheter-manometer system was mainly a function of the diameter of the catheter, care was taken to keep the catheter free of mucus; between successive measurements of resistance (see below) the catheter was disconnected from the transducer and mucus was removed by having the subject draw air through the catheter by making an inspiratory efiort while keeping his glottis closed. Subjects. The subjects were three healthy men; their ages, physical characteristics, and total lung capacities (TLC) are shown in Table 2. Procadure. Lower airway resistance was measured at six frequencies between 1 and 10 Hz, each at approximately 80, 55, and 40-45% of the subject’s TLC; the peak flow rate at each frequency was 0.5 l/s. Maw was also measured at peak flow rates of 0.5, 1.0, 1.5, and 2.0 l/s at the constant frequency of 5 Hz and at approximately 80, 55, and 4550 % of the subject’s TLC. In these measurements the lowest lung volume used was 400-600 ml higher than in the studies at different frequencies because 2 l/s was similar to the maximum expiratory flow rate at 4-O-45 % TLC and we wished to minimize the effect of airway compression. The 2 Independence to the axis of flow near the orifice.
of catheter presumably
pressure relates
on catheter to the disturbed
position nature
relative of flow
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520
FINUCANE
TABLE Subj
JM KF DL
2. Subjects, anthropometric
data, and lung volumes
Age, yr
Ht, cm
VC, liters
49
187 180 185
6.9 5.8 6.1
35 36
TLC,
liters
9.0 7.5 7.32
stroke volume of the pump varied according to the frequency and peak flow rate required, it varied between 130 and 16 ml. The order in which the measurements were performed was selected randomly before each experiment. Each measurement was preceded by the following preliminary maneuvers designed to standardize the volume and temporal histories of the lung: the subject took three deep breaths, then inhaled maximally, and at TLC placed his mouth around the mouthpiece which was immediately switched, with a solenoid valve, to a high-impedance suction pump which maintained a constant flow rate of 0.5 l/s. The subject exhaled at this flow and the change of lung volume was monitored by displaying AVpleth on an oscilloscope. At the lung volume chosen for measurement the suction was turned off and the subject maintained this lung volume throughout the period of measurement. To calibrate alveolar pressure the subject now made respiratory efforts against the stationary pump; tracheal pressure (Pt), or mouth pressure, and the output from the analog divider, 6vgC(Ah)/vL, were displayed on another oscilloscope and the gain of the latter signal was adjusted until it was equal to Pt. The pump was then turned on and vao, on the Y axis, and APlaw, on the X axis, were displayed on the oscilloscope. During these measurements the subject braced his cheeks with the palms of his hands in order to minimize motion of the soft tissues of the upper airway. The signals GVpump, Pt, qao, and pressure in the plethysmograph were recorded on a six-channel tape recorder (Precision Instrument Co., Palo Alto,.. Calif.) and, together with the derived signals GVpleth, Vao, and APlaw, on an eight-channel direct-writing recorder (Sanborn, model 350). Because the primary signals were recorded from the time the subject went on the mouthpiece at TLC all derived signals could be reconstituted and the measurements were analyzed subsequently. To minimize the influence of low-frequency vibrations of the tape and improve the signal-to-noise ratio on replay all measurements made at frequencies
