Vol. 90, Issue 2, 571-578, February 2001
Airway resistance and tissue elastance from input or transfer
impedance in bronchoconstricted monkeys
Kristin R.
Black1,
Bela
Suki1,
Jeffrey B.
Madwed2, and
Andrew C.
Jackson1
1 Department of Biomedical Engineering, Boston
University, Boston, Massachusetts 02215 and 2 Department of
Pharmacology, Boehringer Ingelheim Pharmaceuticals, Ridgefield,
Connecticut 06877
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ABSTRACT |
Ascaris
suum (AS) challenge in nonhuman primates is used as an animal
model of human asthma. The primary goal of this study was to determine
whether the airways and respiratory tissues in monkeys that are
bronchoconstricted by AS inhalation behave similarly to those in
asthmatic humans. Airway resistance (Raw) and tissue elastance (Eti)
were estimated from respiratory system input (Zin) or transfer (Ztr)
impedance. Zin (0.4-20 Hz) and Ztr (2-128 Hz) were measured
in anesthetized cynomolgus monkeys (n = 10) under baseline (BL) and post-AS challenge conditions. Our results indicate that AS challenge in monkeys produces 1) predominately an
increase in Raw and not tissue resistance, 2) airway wall
shunting at higher AS doses, and 3) heterogeneous airway
constriction resulting in a decrease of lung parenchyma effective
compliance. We investigated whether the airway and tissue properties
estimated from Zin and Ztr were similar and found that Raw estimated
from Zin and Ztr were correlated [r2 = 0.76], not significantly different at BL (13.6 ± 1.4 and
13.1 ± 0.9 cmH2O · l
1 · s1,
respectively), but significantly different post-AS (20.5 ± 4.5 cmH2O · l1 · s1
and 18.5 ± 5.2 cmH2O · l1 · s1).
There was no correlation between Eti estimated from Zin and Ztr. The
changes in lung mechanical properties in AS-bronchoconstricted monkeys
are similar to those recently reported in human asthma, confirming that
this is a reasonable model of human asthma.
lung tissue resistance; lung tissue compliance; respiratory
mechanics
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INTRODUCTION |
ANIMAL MODELS OF HUMAN
ASTHMA are of considerable value in studying the mechanisms of
the disease and in developing therapies for its treatment. One such
model, Ascaris suum (AS) challenge in nonhuman primates, has
been used by numerous investigators (e.g., 10, 17, 18) and has been
shown to mimic several characteristics of human asthma, such as acute
reversible bronchoconstriction, pulmonary inflammation with significant
eosinophil infiltration, and airway hyperresponsiveness (4,
6). More recently, it has been shown that in this model several
well-known antiallergy and antiasthmatic compounds are consistent with
their effects in humans (22).
The most commonly used pulmonary function test in humans (spirometry)
requires subject cooperation and thus is not amenable for use in
laboratory animals. As a consequence, the pulmonary function tests of
choice in nonhuman primates are those based on forced oscillations
(4-6, 14, 22-24). Recent advances in methods
using forced oscillations have allowed for the noninvasive separation
of airway (Raw) and tissue (Rti) resistance, as well as measurements of
tissue compliance (8, 11, 13, 14). Kaczka and co-workers
(9) recently used low-frequency (0.1-8 Hz)
transpulmonary input impedance (Zin) to measure airway and tissue
mechanical properties in mild to moderate human asthmatic subjects
before and after bronchodilation. From their measurements they
concluded that bronchoconstriction induced by asthma results predominately and consistently in elevated Raw. However, the response of their tissue properties was inconsistent given that, in
approximately half of the subjects, lung tissue elastance (Eti) was
slightly elevated but lung tissue resistance (Rti) was normal whereas
in the remaining subjects Eti and Rti were both highly elevated
(9). The primary goal of the present study was to
determine whether the airways and respiratory tissues behave similarly
in monkeys that are bronchoconstricted by AS inhalation.
The second goal was to determine whether airway and tissue properties
estimated from higher frequency (2-128 Hz) transfer impedance
(Ztr) measurements were similar to those obtained from low-frequency
Zin data. Low-frequency measurements require that any respiratory
effort be voluntarily suspended for 60 to 90 s during the
measurement. Voluntary suspension of the respiratory effort could not
be done in anesthetized monkeys, but impedance measurements at higher
frequencies (f > 2 Hz) can be made while the
subject breathes normally. Finally, the third goal was to determine
whether additional information about lung properties could be obtained
by simultaneously fitting both Zin and Ztr data with a model that is
more complex than the models used to fit Zin and Ztr data separately.
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METHODS |
Animals
Ten AS-sensitive cynomolgus monkeys weighing between 4.4 and 9 kg (mean wt: 6.6 kg) were studied. These studies were conducted in a
facility accredited by the American Association for the Accreditation of Laboratory Animal Care. All animals received humane care in compliance with the Principles of Laboratory Animal Care
formulated by the Institute of Laboratory Animal Resources and the
Guide for the Care and Use of Laboratory Animals prepared by
the Institute of Laboratory Animal Resources and published by the
National Institutes of Health in 1996. The monkeys were housed in the
Animal Resource Center of Boehringer Ingelheim Pharmaceuticals, in
accordance with Animal Resources Standard Operating Procedures
addressing environmental control, husbandry, and sanitation standards,
psychological enrichment, and exercise. Animals were selected on the
basis of positive skin reaction to intradermal injections of AS extract (1 × 104 U) and airway responsiveness, requiring a
minimum of 150% increase in Raw above baseline (BL) levels within
1 h of AS challenge.
Monkeys were initially anesthetized with ketamine (20 mg/kg) and
xylazine (4 mg/kg) administered intramuscularly. They were then removed
from their cages and intubated with a 5.5-mm internal diameter cuffed
endotracheal tube. The monkeys were seated upright in a
head-out body plethysmograph. Anesthesia was maintained with ketamine
(5 mg/kg im) as needed, determined by eye reflexes. At the end of an
experiment, monkeys were returned to their cages and observed until upright.
Impedance Measurements
Zin measurements are made by applying forced oscillations at the
airway opening while measuring pressure (Pao) and flow (
ao) at
the airway opening (Zin = Pao/ao). The monkeys were seated upright in a head-out body plethysmograph with the doors open. A
pseudorandom noise (PRN) signal (forcing function) generated by the
computer was passed through a digital-to-analog converter (ComputerBoard, Mansfield, MA), amplified, high-pass filtered (f > 0.1 Hz) (Pulmetrics, Chestnut Hill, MA), and used
to drive a loudspeaker (Bose, series IV) connected to the endotracheal tube. The forcing function contained frequency components from 0.4 to
20.6 Hz (at 0.4, 1.0, 2.2, 3.8, 6.2, 11.8, and 20.6 Hz). The
frequencies selected are of a non-sum, non-difference design developed
by Suki and Lutchen (20). Using these frequencies significantly reduces the amount of harmonic distortion and harmonic cross-talk in the output pressure examined at the input frequencies and
hence allows estimation of smooth apparent impedance in the presence of
nonlinearities. Pao was measured with a transducer (Sensym) mounted at
the tip of the endotracheal tube. ao was measured at the
entrance of the endotracheal tube with a pressure transducer (Sensym)
mounted across a pneumotachometer (Fleisch No. 2). The measured
pressure and flow signals were band-pass filtered between 0.1 and 25 Hz. These signals were digitized by the analog-to-digital (A/D) board,
sampled at 205 Hz, and stored in the computer for later analysis.
Ztr measurements are made by applying forced oscillations around the
chest wall while chest wall pressure and flow at the airway opening are
measured (Ztr = Pcw/ao). The monkeys were seated upright in
the same head-out body plethysmograph with the doors closed. A PRN
signal generated by the computer was passed through an A/D converter,
amplified, high-pass filtered (f >1.6 Hz), and used
to drive two loudspeakers (Focal, 5N411L) mounted on the front and back
of the plethysmograph. The forcing function contained frequency
components from 2 to 128 Hz in 2-Hz increments. Pressure was measured
at the chest wall (Pcw) using a transducer (Sensym) mounted on the wall
of the chamber. Flow (ao) was measured at the entrance of the
endotracheal tube with a pressure transducer (Sensym) mounted across
a pneumotachometer (Fleisch No. 2). The measured pressure and
flow signals were band-pass filtered between 1 and 160 Hz. These
signals were digitized by the A/D board (ComputerBoard, Mansfield, MA),
sampled at 512 Hz, and stored in the computer.
Experimental Protocol
Apnea must be induced during Zin measurements because they are
made at frequencies surrounding the natural breathing frequency of the
monkey. The monkeys were manually hyperventilated (HV) with an ambu
resuscitator (Mark III, Denmark) for 20 breaths to remove the effects
of breathing during the impedance measurements (17). BL
Ztr measurements were made by applying 5 PRN bursts for a 2.5-s
duration to the chest wall. The transducer measuring Pcw was then moved
to the tip of the endotracheal tube to measure Pao, and the doors on
the plethysmograph were opened. BL Zin measurements were made by
applying three PRN bursts for a 7.5-s duration to the airway opening.
AS, in a concentration ranging from 30 to 300 mg/ml, was administered
for 30 breaths (~2 min) as an aerosol by compressed air nebulization
and intermittent positive-pressure breathing with a respirator and
micronebulizer (Bird Mark 7A, model 8158). After 15 min, when the
monkeys reached a steady state as determined by the real component of
Ztr between 16 and 30 Hz, they were again subjected to manual HV for 20 breaths to induce apnea. Measurements of Ztr and Zin were repeated as
described above.
Data Analysis
For both Zin and Ztr, the time domain signals, Pao(t)
and Pcw(t) (for Zin and Ztr, respectively) and ao,
were converted to the frequency domain by discrete Fourier transforms.
The auto power spectrum, GPP, and the cross
power spectrum, GaoP, of P and ao
were estimated from overlapping blocks of data. Impedance (Z) was
computed using the technique of Michaelson et al. (16)
from
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(1)
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The coherence function (
2) was computed from
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(2)
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where Gaoao is the auto
power spectrum of ao.
Modeling.
Low-frequency Zin data were modeled with a four-element model in which
a homogeneous airway compartment containing Raw and airway inertance
(Iaw) leads to a viscoelastic compartment described by a
"constant-phase" impedance model containing two tissue properties, tissue damping (G) and tissue elastance (H) (Fig.
1A) (7). Tissue hysteresivity, 
(3), is characterized by the
ratio of G and H
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(3)
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Input tissue resistance (Rti-in) decreases
quasi-hyperbolically as
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(4)
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and input tissue elastance (Eti-in) increases slightly with
frequency as
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(5)
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By fitting this model to Zin data airway and tissue properties
can be estimated. A mathematical framework and molecular theory of the
constant-phase model have been offered by Suki et al.
(19).
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Fig. 1.
A: four-element model of homogeneous airway compartment
containing airway resistance (Raw) and airway inertance (Iaw) leading
to a viscoelastic constant-phase model compartment of tissues
containing tissue damping (G) and tissue elastance
(H) properties. B: six-element DuBois model of
the respiratory system. ao, flow at airway opening; Cg,
compliance of gas compression; Rti, lung tissue resistance; Iti, lung
tissue inertance; Cti, lung tissue compliance; Pcw, pressure at chest
wall; j, ( 1)1/2. C: nine-element
model of the respiratory system. The airway wall compliance (Caw)
separates Raw into a central (Rc) and peripheral (Rp) component while
keeping all of the inertance in the upper airways. The tissue
compartment contains both the Newtonian component of Rti as well as the
constant-phase model of the tissues.
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High-frequency Ztr data were modeled with the DuBois six-element model
of the respiratory system (Fig. 1A), consisting of three
branches: an airway impedance (Zaw), which is separated from the tissue
impedance (Zti) by a gas compression impedance (Zg) (2).
These separate impedances can be represented as
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(6)
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(7)
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(8)
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where Raw, Iaw, Rti, and Iti are resistance and inertance of the
airways and tissues, respectively. Cti-tr and Cg are compliance of the
tissues and gas compression, respectively; 
is
2
f with f as the frequency in Hertz, and
j is (1)1/2. Ztr from this model is then given by
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(9)
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A third model, which includes airway wall compliance (Caw), was
used to simultaneously fit the low-frequency Zin and high-frequency Ztr
data (Fig. 1C). This model is a modification of the
six-element DuBois model to include Caw (15) and the
constant-phase model of the tissues. Zin and Ztr from this model are
given by
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(10)
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(11)
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where
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(12)
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(13)
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(14)
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(15)
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(16)
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Parameter estimates.
Parameters for these models were estimated using a global optimization
technique (1) that minimized the performance index (PI) where
![PI<IT>=</IT><LIM><OP>∑</OP><LL><IT>i=1</IT></LL><UL><IT>n</IT></UL></LIM> ({Re<SUB><IT>d</IT></SUB>[Z(<IT>i</IT>)]Re<SUB><IT>m</IT></SUB>[Z(<IT>i</IT>)]}<SUP><IT>2</IT></SUP><IT>+</IT>{Im<SUB><IT>d</IT></SUB>[Z(<IT>i</IT>)]Im<SUB><IT>m</IT></SUB>[Z(<IT>i</IT>)]}<SUP><IT>2</IT></SUP>)](/content/vol90/issue2/fulltext/571/img018.gif)
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(17)
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where d and m represent experimental data
and model data, respectively, i is the frequency index, and
n is the number of data points. This technique minimizes the
difference between measured and model impedance data values. Parameter
estimates from Ztr were obtained in the range of frequencies at which
the coherence function2 > 0.9. At the lower
frequencies at which Zin was measured, the respiratory system has very
nonlinear behavior. As a consequence, estimates of Zin may be poor
without noticeably influencing 2 (20).
Therefore, poor data points were removed manually from the Zin spectra
before model fitting.
For Ztr data, one of the parameters in the six-element model must be
determined by an independent technique because only five of the
parameters can be uniquely estimated. The Cg was estimated from the
animals' weight on the basis of a regression obtained from Pare et al.
(17) relating functional residual capacity (FRC) and body
weight. By assuming isothermal conditions, Cg can then be calculated
from
|
(18)
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where FRC is in liters, Patm is atmospheric pressure (1,033 cmH2O) and PH2O is the partial
pressure of water vapor at 100% saturation and 37°C (64 cmH2O). Cg was assumed to be the same during BL and post-AS
because Pare et al. (17) reported that AS challenge in
monkeys does not alter their FRC.
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RESULTS |
Zin Spectra
The low-frequency Zin data for each monkey pre- and post-AS are
shown as the effective respiratory system resistance (Rrs), (the real
part of Zin) and elastance (Ers = 2 · · Xin,
where Xin is the imaginary part of Zin) (Fig.
2). In BL as well as postchallenge conditions, Rrs was positive, decreasing hyperbolically with frequency for f < 6 Hz then in most monkeys it increased
slightly for f > 6 Hz. In BL conditions, Ers,
increased slightly at low frequencies, reached a maximum at 4 Hz, then
decreased with increasing frequency. The resonant frequency,
f0 (point of zero crossing), occurred at
7.8 ± 2.2 Hz. After AS challenge, there was a consistent increase in Rrs, i.e., the real part increased on average by 53 ± 17%
(P < 0.05) over the entire frequency range in all 10 monkeys. In one monkey, the real part increased substantially. After AS
challenge, the changes in Ers were less consistent than the changes in
Rrs. The responses appeared to be of three types: type 1 (n = 5), in which Ers was negligibly increased at low
frequencies and slightly increased at high frequencies; type
2 (n = 2), in which Ers was increased more for
higher frequencies (f > 4 Hz); and type
3 (n = 3), in which Ers post-AS was elevated more
at low frequencies, reaching a maximum at ~6 Hz, then decreased with
increasing frequency. It is possible that the type 3 response is simply a more significant type 1 response
because the shapes of the Ers-frequency curves are similar. Our
type 1 and type 2 responses are analogous to the
Type A and Type B response reported in bronchoconstricted human
asthmatic subjects (9).
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Fig. 2.
Respiratory system resistance (Rrs) and elastance (Ers)
vs. frequency obtained by low-frequency Zin in 10 monkeys at BL and
post-AS challenge.  , Mean BL results of all animals;
 ,  , and  , type
1, type 2, and type 3 post-AS challenge
results, respectively.
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Zin and Ztr Spectra
For sake of comparison, the Ztr as well as the Zin data for two
representative monkeys are plotted in Fig.
3 as their real and imaginary parts vs.
frequency. For all monkeys, the real part of Ztr decreased with
frequency for all frequencies under BL and post-AS conditions. The real
part was positive for low frequencies, with a zero crossing at an
average of 55 ± 5 Hz under BL conditions and 60 ± 8 Hz
post-AS. AS challenge resulted in an elevation of the real part at
frequencies below ~72 Hz. The imaginary part of Ztr was negative for
frequencies below f0, which occurred at 7.3 ± 1.3 Hz and 8.4 ± 1.5 Hz in BL and post-AS conditions,
respectively. The imaginary part of the spectra became increasingly
positive up to 80 Hz and then decreased. The imaginary part of Ztr
after challenge was slightly higher than BL at frequencies >32 Hz.
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Fig. 3.
Real and imaginary (Imag) parts of impedance vs. frequency in 2 representative monkeys, showing a moderate (type 1;
A) and a more severe response (type 3;
B). Low-frequency input impedance (Zin) data (triangles) fit
with constant-phase model (solid lines) and high-frequency transfer
impedance (Ztr; circles) fit with 6-element model (dotted lines
obscured by circles) during baseline (BL; open symbols) conditions and
15 min after Ascaris suum challenge (post-AS; solid
symbols).
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Modeling Results
Zin and Ztr data during BL and post-AS conditions were fit well
with the models (Fig. 3). Under BL and challenge conditions, the
spectra and model fits of the real part of Zin and Ztr data overlap for
6 Hz < f < 12 Hz and 10 Hz < f < 12 Hz, respectively. However, the imaginary parts
of Zin and Ztr data as well as their corresponding model fits do not
overlap, and this discontinuity was more pronounced in those monkeys
whose response was greater.
BL values of Raw from Zin and Ztr were not significantly
different, 13.6 ± 1.4 and 13.2 ± 0.9 cmH2O · l1 · s1,
respectively. After challenge, Raw from Zin and Ztr increased substantially by 50% and 41% to 20.5 ± 4.5 and 18.5 ± 5.2 cmH2O · l1 · s1,
respectively. The postchallenge value of Raw from the Zin (Raw-in) was
10% higher than that from the Ztr (Raw-tr), and this difference was
statistically significant (P < 0.05). After challenge,
Iaw and Rti from Ztr did not change significantly from BL values. The
G and H from Zin and Iti from Ztr increased
significantly from 34 ± 15 cmH2O · l1 · s1,
125 ± 38 cmH2O/l, and 0.0065 ± 0.0017 cmH2O · l1 · s2
under BL conditions to 43 ± 18 cmH2O · l1 · s1,
176 ± 100 cmH2O/l, and 0.0071 ± 0.0019 cmH2O · l1 · s2
after AS challenge, respectively. Cti-tr showed a significant decrease
of 59% from a BL value of 0.0058 ± 0.0050 to 0.0024 ± 0.0011 l/cmH20 after challenge. Raw-in and Raw-tr estimated
during BL and post-AS conditions were correlated
(r2 = 0.76) with the equation Raw-in = 0.91 Raw-tr + 2.7. There was no significant correlation among any
other parameters.
Unlike Zin, we were able to measure Ztr both prior to and after HV.
Post-AS Ztr data as well as the estimated post-AS values of Raw were
significantly different (P < 0.01) before and after HV
(24.3 ± 4.9 cmH2O · l1 · s1
vs. 18.5 ± 5.2 cmH2O · l1 · s1,
respectively). Therefore, the hyperventilation used to produce apnea
required for low-frequency measurements resulted in a significant decrease in the bronchoconstrictive response. There was no significant change in any other Ztr parameters before and after HV.
The nine-element model (Fig. 1C) was used to estimate
parameters for Zin and Ztr data simultaneously. In comparing BL and Post-AS values from the nine-element model, Iaw, Rti, Iti, and G after challenge did not change significantly from BL
values. After challenge, average values of central and peripheral
airway resistance increased significantly by 42% and 164%,
respectively, implying that peripheral Raw increased considerably more
than central Raw. The H showed a statistically significant
increase of 20% (P < 0.05) whereas Caw decreased
significantly by 52% (P < 0.01) with challenge. There
was no difference among analogous parameter values obtained by model
fitting with the four- and six-element models separately to those
obtained from the simultaneous fitting of the nine-element model to Zin
and Ztr data.
| |
DISCUSSION |
Animal Model of Human Asthma
In all monkeys, Rrs at low frequencies was increased with
AS-induced bronchoconstriction (Fig. 2), and this is consistent with a
significant increase in Raw but not in Rti. The changes that occurred
in the frequency-dependent behavior of Ers were qualitatively similar
to those reported by Kaczka et al. (9) in humans. In
bronchoconstricted asthmatic humans, either there is a small increase
in Ers or Ers is increased considerably, becoming positive with a
positive slope for all frequencies. These two different responses were
called Type A and Type B asthmatic subjects, respectively. Five of our
monkeys had a response to bronchoconstriction that was similar to their
Type A asthmatic subjects, i.e., slight increase in Rrs and little
change in Ers. Kaczka et al. reasoned that the Type A response
indicates mild airway constriction and little change in the actual or
apparent tissue properties. Our findings are consistent with this; that
is, in those monkeys in which the increase in Raw (from analysis of Zin
or Ztr) was minimal, there were little or no changes in Ers or Rti.
Kaczka et al. (9) reasoned that the mechanisms that could
cause the Type B response (i.e., a positive frequency dependence in
Ers) are increased tissue viscoelasticity, parallel time constant heterogeneities, and/or airway wall shunting. To determine which of
these mechanisms might be responsible, we thoroughly investigated these
possibilities below.
To investigate the effects of airway wall shunting, we fit a
nine-element model, which includes Caw, to both Zin and Ztr data simultaneously. In general, the model was able to fit both Zin and Ztr
during bronchoconstriction. Although, in cases of severe obstruction,
it could produce a discontinuity in the real part as seen in the data,
it was not able to produce a discontinuity in the imaginary part. Zin
and Ztr data were also simulated by using the nine-element model. These
data were then fit with the four- and six-element models over the same
frequency range as measured data. Under BL conditions, Raw and Eti were
estimated with an error of 9.9% and 9.2%, respectively, from the
four-element model and 1.7% and 2.7%, respectively, from the
six-element model. After challenge, Raw and Eti were estimated with
errors of 3.1% and 11.5% from the four-element model and 1.1% and
11.6% from the six-element model, respectively. These results prove
that, although the six-element model is more precise in estimating Raw and Eti, both models can be used to accurately extract these parameters.
This nine-element model may not be an appropriate way of modeling
nonrigid airways because this pathway should lead to pleural pressure,
not ground or atmospheric pressure as in this model. A more
appropriate method of modeling the airway walls would necessitate a
separation of the lung tissue and chest wall properties, which would
make the model exceedingly complex. Nevertheless, one important result
of the simultaneous fitting is that G was not sensitive to
bronchoconstriction. Thus, when airway wall shunting is allowed in the
simultaneous fitting, the model did not need to increase G
to account for the increased real part of Zin at low frequencies. This
is certainly due to the extra pathway for the input flow, which
represents a certain kind of heterogeneity.
Another type of heterogeneity is parallel time constant inequalities.
We investigated this possibility by fitting the low-frequency Zin data
with a model that includes a distribution of parallel pathways as
described by Suki et al. (21). The model contains a
continuous distribution of resistance pathways each terminated in the
same constant-phase tissue model. This model has only one additional
parameter compared with the four-element (Raw, Iaw, G,
H) model. The Raw parameter is replaced by two resistance
values Ra and Rb, which define the upper and lower limits of resistance that are included in the distributed model. Thus the model can account
for the increased low-frequency real part of Zin by tissue changes or
by increasing the impact of parallel inhomogeneities (increasing the
range of resistance defined by Ra and Rb). Raw can be obtained from the
model as the expected value (Rmean) of the estimated resistance
distribution. On the basis of previous experience (21), we
chose the distribution function for the resistance to be hyperbolically
decreasing between Ra and Rb and to be zero otherwise. Compared with
the single-compartment constant-phase model, the error of fitting PI
(given by Eq. 17) was reduced by adding parallel
inhomogeneities from 1.23 ± 0.98 to 1.15 ± 1.05 cmH2O · l1 · s1
in control (P < 0.02) and from 3.83 ± 4.53 to
3.54 ± 4.2 cmH2O · l1 · s1
after AS challenge. The values of G were not statistically
different in control, but the multicompartment model gave a
significantly smaller G after AS challenge than the
single-compartment model (36 ± 19 vs. 43 ± 18 cmH2O · l1 · s1,
P < 0.05). The values of H were almost
identical in both models. At the same time, Rmean is significantly
higher than Raw from the single-compartment model both in control and
after challenge. Thus, in agreement with the nine-parameter model
exercise, the increase in the real part of Zin after AS challenge was
partly attributed to increased heterogeneities. This finding is similar to that obtained by Kaczka et al. (9), who found very
minor increases in G in asthmatic subjects. Additionally,
using gases of different viscosity, Lutchen et al. (12)
directly showed that in rats the increase in G after
methacholine challenge was a pure artifact of increased parallel time
constant inequalities.
Comparison Between Zin- and
Ztr-Derived Parameters
After AS challenge in a primate model of asthma, the most
significant changes occur in Raw from both low-frequency Zin and high-frequency Ztr measurements. During BL and bronchoconstricted conditions, Raw-in and Raw-tr were correlated
(r2 = 0.76) with a nonzero Raw-in
intercept. The value of this intercept (2.7 cmH2O · l1 · s1)
is interesting because in the four-element constant-phase model any
flow-independent, Newtonian component of tissue resistance (e.g., chest
wall resistance) is included in the Raw parameter. However, this
Newtonian component of tissue resistance is correctly assigned to Rti
in the six-element model, and it was estimated to be 2.7 ± 0.6 cmH2O · l1 · s1
from the Ztr data. The nonunity slope of 0.91 suggests that Raw-in may
underestimate Raw-tr. This underestimation of Raw becomes more evident
during bronchoconstriction, in which the slope decreases further to
0.73 for post-AS values only. Tissue properties (G and
H as well as Rti and Cti) estimated from both frequency
ranges also changed after challenge, but these changes appear less
important. There was no correlation between Eti from Zin [i.e.,
Eti-in = H(/
)] from Zin evaluated
at 10 Hz and Eti from Ztr (i.e., 1/Cti-tr), but both significantly
increased (P < 0.01) with AS challenge (Eti-in
increased from 247 ± 72 to 337 ± 141, and Eti-tr increased from 273 ± 151 to 513 ± 220 cmH2O/l,
respectively). The measured apparent tissue properties appear to be
influenced by the other mechanisms critically evaluated above as well
as alveolar gas compression.
The DuBois model assumes that the airways can be modeled by a single
resistance and inertance in series, i.e., that the airway walls are
rigid and parallel pathways are homogeneous. Mead (15) suggested the possibility that with significant peripheral airway constriction the impedance of the peripheral airways and tissues could
increase such that they are of the same order of magnitude as the shunt
impedance of the upper and/or central airway walls. In this case with
Zin, the airway wall impedance would be in parallel with Zti whereas
with Ztr the airway wall impedance would be in parallel with the
impedance of the upper airways (Zuaw) and any equipment impedance
(Zeq). Because Zti > Zuaw + Zeq, airway wall impedance
(Zaww) would have a greater influence on Zin than it would on Ztr. A
forward model with seven elements that incorporates all features of the
DuBois and constant-phase models [i.e., the DuBois model with Cti-tr
replaced by (G jH)/]
was used to examine Zin and Ztr for 0.4 < f < 100 Hz (Fig. 4).
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Fig. 4.
Computer simulation of Zin (solid lines) and Ztr (dotted
lines) from 7-element model. A: at BL, Raw = 13.0 cmH2O · l1 · s1,
Iaw = 0.18 cmH2O · l1 · s2,
Rti = 1.9 cmH2O · l1 · s1,
Iti = 0.0056 cmH2O · l1 · s2,
G = 51 cmH2O · l1 · s1,
H = 186 cmH2O/l. B: post-AS,
Raw = 30.7 cmH2O · l1 · s1,
Iaw = 0.16 cmH2O · l1 · s2,
Rti = 2.8 cmH2O · l1 · s1,
Iti = 0.0057 cmH2O · l1 · s2,
G = 88 cmH2O · l1 · s1,
H = 215 cmH2O/l. (Cg = 0.0003 l/cmH2O for both BL and post-AS.)
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|
In this seven-element model, the basic difference between Zin and Ztr
is that Cg is in parallel with Zti in Zin whereas it is in parallel
with Zaww in Ztr. Under BL conditions, the low-frequency asymptotes of
the predicted Zin and Ztr are different, and this difference increases
with bronchoconstriction. Evidence that the differences in Zin and Ztr
in this model are due to Cg is that when Cg approaches 0, Zin and Ztr
are identical for all frequencies in the seven-element model. Our
measured Zin and Ztr data are consistent with these computer
predictions. The real part of the Ztr data is greater than the real
part of the Zin data at low frequencies. Furthermore, under BL
conditions, the values of the extracted Raw were not significantly
different because Raw is accurately estimated from both Zin and Ztr.
In comparison, Zin and Ztr are two methods of estimating respiratory
mechanics each having advantages as well as disadvantages over the
other. Although low-frequency Zin provides information about
the frequency dependence of tissue resistance and elastance and can be
measured at normal breathing frequencies, it takes ~2.5 s to acquire
a single spectrum and thus requires apnea. Also, the hyperventilation
used to induce apnea results in a significant reduction in the
bronchoconstrictive response. High-frequency Ztr measurements may give
a less reliable estimate of the tissue properties but can be measured
during normal breathing, take only 0.5 s/spectrum to measure, and
provide a more robust estimate of Raw during bronchoconstriction.
With regards to the physiological implications, our results indicate
that AS challenge in monkeys produces 1) predominately an
increase in Raw and not Rti [as shown previously by Madwed and Jackson
(14)], 2) airway wall shunting at
higher AS doses, and 3) heterogeneous airway constriction
resulting in a decrease of dynamic lung compliance. Because these
changes in lung mechanical properties are similar to those recently
reported in human asthma (9), our results confirm that AS
challenge in monkeys is a reasonable model of this human disease.
| |
ACKNOWLEDGEMENTS |
This research was funded by National Heart, Lung, and Blood
Institute Grant HL-53449 and Boehringer Ingelheim Pharmaceuticals.
| |
FOOTNOTES |
Address for reprint requests and other correspondence: A. C. Jackson, Dept. of Biomedical Engineering, Boston Univ., 44 Cummington St., Boston, MA 02215 (E-mail: ajax{at}bu.edu).
The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
"advertisement"
in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 2 February 2000; accepted in final form 12 September 2000.
| |
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