J Appl Physiol 106: 520–530, 2009.
First published October 16, 2008; doi:10.1152/japplphysiol.90576.2008.
Assessment of heterogeneous airway constriction in dogs:
a structure-function analysis
David W. Kaczka,1,2 Robert H. Brown,1,3,4 and Wayne Mitzner1,2,3
Departments of 1Anesthesiology and Critical Care Medicine, 2Biomedical Engineering, 3Environmental Health Sciences,
and 4Radiology, The Johns Hopkins University, Baltimore, Maryland
Submitted 27 April 2008; accepted in final form 8 October 2008
resistance; elastance; parameter estimation; Akaike criterion; canine;
methacholine
THE MECHANICAL INPUT IMPEDANCE of the respiratory system (Zrs)
has been demonstrated to be quite sensitive to parallel time
constant heterogeneity in the lungs (19, 27, 36), specifically
with regard to alterations in the frequency dependence of
respiratory system resistance (Rrs) and elastance (Ers) (20, 25,
26). Often inverse modeling is applied to such Zrs spectra, in
which the parameters of a specified lumped-element topology
are estimated from the best-fit prediction to the actual data (2,
4). Ideally, the values of these parameters should correspond to
actual physical properties of the respiratory system, such as
airway resistance or tissue elastance. One particular inverse
model that has been widely used to characterize Zrs data,
regardless of pathology, has been the so-called “constantphase” model described by Hantos et al. (16): a single com-
Address for reprint requests and other correspondence: D. W. Kaczka, Dept.
of Anesthesiology and Critical Care Medicine, The Johns Hopkins Hospital,
600 North Wolfe St., Meyer 289, Baltimore, MD 21287 (e-mail: dkaczka1
@jhmi.edu).
520
partment, viscoelastic structure that allows for the partitioning
of airway and tissue resistances (20, 21). However, during
bronchoconstriction, a heterogeneous distribution of parallel
airway resistances may lead to biased model-based estimates of
such airway and tissue properties (21, 28). Recently, several
investigators have applied distributed inverse models to Zrs in
an effort to quantify and compensate for such heterogeneity,
reducing the estimation bias of airway and tissue properties
(18, 19, 23, 39, 47). However, in cases of induced or spontaneous bronchoconstriction, it is unclear how widely distributed
airway diameters should be before heterogeneity can adequately be assessed with such a distributed modeling approach.
Such information would be important to evaluate, since heterogeneity has implications both for the work of breathing as
well as the distribution of ventilation.
In addition, deep inspirations (DIs) have been shown to alter
the dynamic mechanical equilibrium between opposing airway
and tissue forces, leading to changes in the overall level of
airway resistance. Nonetheless, it is unclear whether a DI has
any sustained impact on the distribution of airway diameters
during bronchoconstriction.
The goal of this study was to determine the sensitivity of
detecting heterogeneous airway constriction in dogs using
inverse modeling applied to Zrs measured during different
infusion rates of a bronchonstricting agonist, and whether such
functional changes in lung mechanics could be linked to
specific structural alterations in airway diameter as assessed
with high-resolution computed tomography (HRCT). In addition, we assessed whether a deep inspiration (DI) had any
impact on changes in airway resistance or the heterogeneity of
bronchoconstriction. The specific aims of this study were: 1) to
measure Zrs in dogs at baseline and during the infusion of
intravenous methacholine (MCh), 2) to determine the sensitivity of detecting the heterogeneity of airway constriction from
Zrs using inverse modeling and HRCT, and 3) to determine the
impact of DI on airway and respiratory tissue mechanics during
induced bronchoconstriction.
METHODS
Animal preparation and protocol. The protocol was approved by
the Johns Hopkins Animal Care and Use Committee (Baltimore, MD)
to ensure humane treatment of animals. Measurements were made in
eight mongrel dogs weighing between 20 and 25 kg. Following
placement of a peripheral intravenous line, each dog was anesthetized
with intravenous thiopental (15 mg/kg induction dose followed by 10
mg 䡠 hr⫺1 䡠 kg⫺1 maintenance infusion) and paralyzed with 0.5 mg/kg
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.
8750-7587/09 $8.00 Copyright © 2009 the American Physiological Society
http://www. jap.org
Downloaded from http://jap.physiology.org/ by 10.220.33.3 on June 17, 2017
Kaczka DW, Brown RH, Mitzner W. Assessment of heterogeneous airway constriction in dogs: a structure-function analysis.
J Appl Physiol 106: 520 –530, 2009. First published October 16, 2008;
doi:10.1152/japplphysiol.90576.2008.—Obstructive lung diseases are
often characterized by heterogeneous patterns of bronchoconstriction,
although specific relationships between structural heterogeneity and
lung function have yet to be established. We measured respiratory
input impedance (Zrs) in eight anesthetized dogs using broadband
forced oscillations at baseline and during intravenous methacholine
(MCh) infusion. We also obtained high-resolution computed tomographic (HRCT) scans in 4 dogs and identified 20 –30 individual
airway segments in each animal. The Zrs spectra and HRCT images
were obtained before and 5 min following a deep inspiration (DI) to
35 cmH2O. Each Zrs spectrum was fitted with two different models of
the respiratory system: 1) a lumped airways model consisting of a
single airway compartment, and 2) a distributed airways model
incorporating a continuous distribution of airway resistances. For the
latter, we found that the mean level and spread of airway resistances
increased with MCh dose. Whereas a DI had no effect on average
airway resistance during MCh infusion, it did increase the level of
airway heterogeneity. At baseline and low-to-moderate doses of MCh,
the lumped airways model was statistically more appropriate to
describe Zrs in the majority of dogs. At the highest doses of MCh, the
distributed airways model provided a superior fit in half of the dogs.
There was a significant correlation between heterogeneity assessed
with inverse modeling and the standard deviation of airway diameters
obtained from HRCT. These data demonstrate that increases in airway
heterogeneity as assessed with forced oscillations and inverse modeling can be linked to specific structural alterations in airway diameters.
ASSESSMENT OF HETEROGENEOUS AIRWAY CONSTRICTION
៮ ⫺4 ⫽ 1
D
N
N
兺D
1
Signal processing and inverse model analysis. Zrs was computed
from the sampled oscillatory pressure and flow waveforms using a
Welch overlap-average periodogram technique with a 25.6-s rectangular window and 80% overlap (21). After neglecting the first 500
points in the data record (⬃12.5 s) to minimize the influence of
transient responses, between 12 and 20 overlapping windows were
used to calculate Zrs for each animal. Total respiratory system
resistance Rrs was determined from the real part of Zrs: Rrs ⫽
Re{Zrs}. The effective Ers was calculated from the imaginary part:
Ers ⫽ ⫺␻kIm{Ẑrs}, where ␻k is the angular frequency of oscillation.
The mechanical properties of the respiratory system were assessed
by fitting two different model topologies to each Zrs spectrum.
Topology A was the well-known constant-phase model which has
been used extensively to describe the oscillatory mechanics of the
lungs and total respiratory system (3, 4, 16, 20, 21, 30). This model
consists of a single, homogeneous, lumped airway compartment, with
parameters for airway resistance (R) and inertance (I), in series with
a tissue compartment with parameters for tissue damping (G) and
Downloaded from http://jap.physiology.org/ by 10.220.33.3 on June 17, 2017
succinylcholine with supplemental doses as required before measurements of respiratory impedance (see below). Each dog was orally
intubated with an endotracheal tube (8.0- to 10.0-mm ID), and
mechanically ventilated (Harvard Apparatus, Millis, MA) with a rate
of ⬃20 breaths/min and tidal volume of ⬃15 ml/kg, titrated to achieve
an end-tidal CO2 level of 30 – 40 Torr.
Forced oscillatory measurements of Zrs were obtained in each dog
at a mean airway pressure of 10 cmH2O under baseline conditions and
during continuous intravenous MCh infusion rates of 17, 67, and 200
␮g/min (Sigma Chemical, St. Louis, MO). For each condition, Zrs
was measured immediately before and 5 min following a DI to 35
cmH2O sustained for 5 s. The Zrs was obtained using a custom-built
servo-controlled pneumatic pressure oscillator (22) whose input driving signal consisted of nine sinusoids from 0.078 to 8.9 Hz arranged
in a nonsum nondifference pattern (38). This signal was periodic over
25.6 s, and it was repeated four to five times such that each Zrs
measurement lasted ⬃2 min. The amplitude of the driving signal was
adjusted to yield peak-to-peak pressures of 2–3 cmH2O. The resulting
tracheal pressure waveform was measured with a variable reluctance
transducer (LCVR 0 –50 cmH2O, Celesco, Canoga Park, CA) connected to a small polyethylene catheter inserted into the endotracheal
tube and allowed to extend ⬃2 cm into the trachea (35). Airway flow
was obtained with a screen pneumotachograph (model 4700A, Hans
Rudolph, Kansas City, MO) coupled to another pressure transducer
(LCVR 0 –2 cmH2O, Celesco). Both pressure and flow signals were
low-pass filtered at 10 Hz and sampled at 40 Hz by an analog-todigital converter (model DT-2811, Data Translations, Marlborough,
MA) for subsequent processing. Following the final dose of MCh, a
0.2 mg/kg intravenous atropine bolus was administered to block vagal
tone in each dog and maximally dilate the airways, and a final Zrs
measurement was obtained.
HRCT imaging of airways. In four dogs (including an additional
dog for which we did not have post-atropine Zrs measurements), we
also obtained HRCT scans using a Sensation-16 scanner (Siemens,
Iselin, NJ) immediately before each Zrs measurement. Images were
obtained using a spiral mode during an 8-s period of apnea at 137 kVp
and 165 mA. The computed tomography images were reconstructed
with 1 mm slice thickness and a 512 ⫻ 512 matrix using 175-mm field
at a window level of ⫺450 Hounsfield units (HU) and window width
of 1,350 HU. For each dog, we identified between 20 and 30
individual airway segments with 2– 4 separate airway diameter measurements per segment, for a total of 36 –124 diameters per dog. The
cross-sectional area and diameter (Dn) was determined using the
airway analysis model of the Volumetric Image and Display Analysis
software package (Department of Radiology, Division of Physiological Imaging, University of Iowa, Iowa City, IA). We made repeated
measurements of airway size in a given dog for each dose and
condition at approximately the same anatomic cross sections using
adjacent anatomic landmarks, such as airway and vascular branch
points. For each condition and MCh dose in the dog, we defined an
average diameter for all airways identified, but we expressed these in
terms of inverse diameters to the fourth power for the purposes of
correlating them with the mean resistance as determined from the
inverse modeling described below:
521
(1)
4
n
n⫽1
where N is the number of discrete airway diameters identified. In
addition, we also determined the standard deviation of airway diameters raised to the inverse fourth power
冑兺冉
N
S.D.共D ⫺4 兲 ⫽
n⫽1
1
៮ ⫺4
⫺D
D n4
冊
2
J Appl Physiol • VOL
(2)
Fig. 1. Flow chart illustrating process for parameter estimations and model
comparisons for Topologies A and B. Zrs, respiratory input impedance; R,
airway resistance parameter for Topology A; I, airway inertance; G, tissue
damping; H, tissue elastance; Rmin, Rmax, minimum and maximum airway
resistance parameters for Topology B, respectively; P(R), probability density
function; min(⌽), minimum model fitting performance index; AICc, corrected
Akaike Information Criterion; R, airway resistance; min(AICc), minimum
AICc; w(AICc), Akaike weight.
106 • FEBRUARY 2009 •
www.jap.org
522
ASSESSMENT OF HETEROGENEOUS AIRWAY CONSTRICTION
elastance (H). The model has a predicted impedance (Ẑrs) as a
function of frequency (␻) given by:
Ẑ rs 共␻兲 ⫽ R ⫹ j␻I ⫹
G ⫺ jH
␻␣
(3)
Ẑ rs 共␻兲 ⫽
冢兰
Rmax
R min
冣
P共R兲
dR
G ⫺ jH
R ⫹ j␻I ⫹
␻␣
⫺1
(4)
In contrast to the homogeneous Topology A, this topology may
allow for a more accurate estimation of G and ␩ during heterogeneous
bronchoconstriction (39), albeit at the expense of an additional parameter (23). Given a specified distribution function P(R), an “effective” airway resistance can be determined from its mean value:
R␮ ⫽
兰
Rmax
RP共R兲dR
(5)
R min
while the heterogeneity of airway resistances can be determined from
the standard deviation of P(R):
R␴ ⫽
冑兰
Rmax
共R ⫺ R␮兲2 P共R兲dR
R min
(6)
K
⌽⫽
rs
共␻ k 兲 ⫺ Ẑ rs 共␻ k 兲兴 2
(7)
k⫽1
where K is the number of distinct frequencies used in the
excitation waveform (Step 1). For Topology B, we performed three
separate estimations of its five parameters using three different
forms of the airway distribution function P(R): hyperbolic, uniform, and linear (19, 23, 39). These particular forms of P(R) were
selected based on their mathematical simplicity as well as their
ability to yield a closed-form expression for the model predicted
impedance described by Eq. 4 (39). In the case of Topology B, if
the gradient search algorithm converged to a unique solution for
two or more airway distribution functions, the most appropriate
P(R) for a given Zrs spectrum was established based on the
minimum ⌽.
Next, the relative appropriateness of using either Topology A or
(the best form of) Topology B to describe the given Zrs spectrum was
compared using the corrected Akaike Information Criterion (AICc) (1,
33), as determined from the respective ⌽ values obtained for both
model fits (Step 2). The model with the lowest (i.e., most negative)
AICc score was assumed to be the most likely topology to have
generated the data (23). Finally, we computed the relative likelihood
that either Topology A or B generated the Zrs data by computing the
Akaike weight [w(AICc)] (23, 45), which can be interpreted as the
probability that the model in question generated the Zrs data (Step 3).
Thus for each Zrs spectrum fitted, the sum of the w(AICc) values from
Topologies A and B should be equal to 1.
To determine whether the use of a statistically less appropriate
model to describe a given Zrs spectrum would lead to biased estimates
of airway or tissue properties, we also inspected the correlations
between the individual parameter estimates from each topology for all
Fig. 2. Summary of respiratory resistance
(Rrs) and elastance (Ers) from 0.078 to 8.9
Hz at baseline (circles) and intravenous
MCh infusion rates of 17 (inverted triangles), 67 (squares), and 200 ␮g/min (diamonds) before (white) and 5 min following
DI (gray). Data are also shown following
intravenous atropine (black triangles). Error
bars, where shown, denote SDs. DI, deep
inspiration.
J Appl Physiol • VOL
兺 关Z
106 • FEBRUARY 2009 •
www.jap.org
Downloaded from http://jap.physiology.org/ by 10.220.33.3 on June 17, 2017
where j is the unit imaginary number and ␣ ⫽ (2/␲)tan⫺1(H/G).
Tissue hysteresivity, defined as the ratio of energy dissipation to
energy storage across the respiratory tissues (13), can be determined
as ␩ ⫽ G/H for this model. However, since this topology assumes that
the airway and tissue mechanical properties are homogeneously and
uniformly distributed throughout the lungs, it may yield in artifactually high values for G and ␩ when applied to Zrs during heterogeneous bronchoconstriction (20, 21, 28, 30).
Our second topology (B) was the distributed airways model originally described by Suki et al. (39) to provide a more accurate
partitioning of airway and lung tissue resistances in the presence of
heterogeneous bronchoconstriction. This model assumes that the respiratory system can be described by an arbitrary number of parallel
branches, each consisting of identical G and H tissue parameters but
unique airway resistance values. The values of these airway resistances vary from branch-to-branch in a probabilistic manner according to a predefined probability density function P(R) with upper and
lower bounds Rmax and Rmin, respectively. The for this model can thus
be expressed in terms of the five parameters Rmin, Rmax, I, G, and H:
Based on this mean (R␮) and standard deviation (R␴), we can
determine the coefficient of variation in the airway distribution function as Rcv ⫽ R␮/ R␴.
Inverse model comparison. A flow diagram illustrating the steps
used for comparing the relative appropriateness of either the
homogeneous airways model (Topology A) or distributed airways
model (Topology B) for describing each Zrs spectrum is shown in
Fig. 1. First, the parameters for both topologies were simultaneously estimated using a nonlinear gradient technique (Matlab
v7.0, The Mathworks, Natick, MA) that minimized the performance index ⌽:
ASSESSMENT OF HETEROGENEOUS AIRWAY CONSTRICTION
doses and conditions. For airway resistance comparisons, we correlated the R parameter from Topology A to the R␮ from Topology B.
Statistical analysis. For each MCh dose level, a one-way ANOVA
was used to compare the model parameters from both Topology A and
the best form of Topology B, as well as the derived parameters R␮, R␴,
and Rcv before and after DI (SAS v8.2, SAS Institute, Cary, NC). If
523
significance was obtained with ANOVA, post hoc analysis was
performed using the Tukey honestly significant difference criterion.
At each condition, pre- and post-DI comparisons of all variables were
made using two-tailed paired t-tests. Post-atropine values were compared with there corresponding pre- and post-DI values at baseline
using paired t-tests. P ⬍ 0.05 was considered statistically significant.
J Appl Physiol • VOL
106 • FEBRUARY 2009 •
www.jap.org
Downloaded from http://jap.physiology.org/ by 10.220.33.3 on June 17, 2017
Fig. 3. Summary of parameter values for
lumped airways model (Topology A) and
distributed airways model (Topology B) averaged across all 8 dogs. Error bars denote
SDs. ␩, Tissue hysteresivity. *Significantly
higher compared with baseline value, P ⬍
0.05 [using ANOVA and Tukey honestly
significant difference under same condition
(Pre-DI)]. †Significantly lower than pre- and
post-DI values at baseline, P ⬍0.05 (using
paired t-test). #Significantly higher than
pre-DI value, P ⬍ 0.05 (using paired t-test).
524
ASSESSMENT OF HETEROGENEOUS AIRWAY CONSTRICTION
RESULTS
Fig. 4. Summary of the airway resistance distributions obtained for Topology B for all 8 dogs at
baseline and 3 doses of methacholine before and
after DI. Data are also shown following intravenous administration of atropine.
J Appl Physiol • VOL
106 • FEBRUARY 2009 •
www.jap.org
Downloaded from http://jap.physiology.org/ by 10.220.33.3 on June 17, 2017
Figure 2 shows a summary of the Rrs and Ers spectra
averaged across all eight dogs at baseline and at each of the
three doses of MCh pre- and post-DI, as well as following
administration of intravenous atropine. Under pre- and post-DI
conditions, both Rrs and Ers increased at each frequency with
increases in MCh dose. At the lowest frequencies, Rrs increased ⬃50% during the highest dose of MCh compared with
baseline, while Ers increased by ⬃65%. There were no significant differences between the pre- and post-DI values of either
Rrs or Ers at any MCh dose or frequency. Following administration of intravenous atropine, both Rrs and Ers decreased
compared with their respective values at MCh dose of 200
␮g/min, and they demonstrated no significant difference compared with their baseline values at any frequency.
A summary of the estimated model parameters for both
Topologies A and B is shown in Fig. 3, with the most appropriate distribution functions P(R) used for Topology B in Fig. 4.
For Topology B, the hyperbolic distribution of airway resistances appeared to best describe Zrs for the majority of dogs
pre- and post-DI at most MCh doses. Following administration
of atropine, however, no airway distribution function outperformed the others. Both Topologies A and B detected significant increases in H with increased MCh dose pre-DI but not
post-DI. For Topology B, Rmax significantly increased with
increases in MCh dose. Topology A did demonstrate a trend of
increasing R with MCh dose, but this did not achieve statistical
significance pre- or post-DI. No significant change was observed for any model parameter between its pre- and post-DI
values using paired t-tests. Following administration of atropine, R from Topology A was significantly lower than its
pre-DI value at baseline. In addition, ␩ was significantly lower
than its pre-DI baseline value for both topologies.
Figure 5 shows the summary of the Topology B-derived
model parameters R␮, R␴, and Rcv at baseline and during MCh
infusion pre- and post-DI, as well as following administration
of atropine. While both R␮ and R␴ demonstrated an increasing
trend with MCh dose, ANOVA only detected a significant
dependence of the heterogeneity index R␴ on MCh dose preDI, with its value at 200 ␮g/min being significantly higher than
its values at baseline and 17 ␮g/min using Tukey honestly
significant difference. The pre-DI values of Rcv also demon-
strated a significant dependence on MCh dose, also with
significant pairwise differences between 200 ␮g/min compared
with baseline and 17 ␮g/min. There was a considerable increase in the intersubject variability for Rcv post-DI, and a
significant difference between its pre- and post-DI values at 17
␮g/min.
The correlations between the individual model parameter
estimates for Topologies A and B for the individual dogs under
all doses and conditions are shown in Fig. 6. In all cases, the
airway and tissue parameter estimates were nearly identical,
with regression lines indistinguishable from the lines of identity.
Figure 7 shows a summary of the values of ⌽, AICc, and
w(AICc) for Topologies A and B at each dose of MCh pre- and
post-DI, as well as following administration of atropine. In
addition, we also show the number of dogs for which either
Topology A or B best described their Zrs spectra under all
conditions and doses. Both topologies demonstrated trends of
increasing ⌽ and AICc with MCh dose, although this did not
achieve significance by ANOVA. Pre-DI values of w(AICc)
for both Topologies were significantly dependent on MCh dose
under pre-DI conditions but not post-DI. Pre-DI, nearly all
dogs were best characterized by homogeneous airways model
of Topology A under baseline conditions and at MCh doses of
17 and 67 ␮g/min. However, at the highest doses of MCh, half
of the dogs were better described by the distributed airways
model of Topology B. Under post-DI conditions, only two dogs
were better characterized by Topology B at baseline and during
MCh infusion rates of 67 and 200 ␮g/min. Following administration of atropine, all dogs were best described by Topology A.
Figure 8 shows the correlations between the mean and
standard deviations of the airway diameters measured by
HRCT with the R␮ and R␴ parameters from the distributed
airways model for both a representative dog as well as averaged across the four dogs for which scans were obtained.
While there was much intersubject variability, we found that
the relationship between the airway diameters and model
parameters was best described by the two-parameter regression
equation y ⫽ a(1 ⫺ e⫺bx). Using this relationship, we found
statistically significant (albeit nonlinear) correlations between
the airway diameters and inverse model parameters.
ASSESSMENT OF HETEROGENEOUS AIRWAY CONSTRICTION
DISCUSSION
This study has demonstrated that functional alterations in
lung mechanics assessed with forced oscillations, can be linked
to structural changes in the pattern of airway constriction
obtained from HRCT. Under induced bronchoconstriction,
heterogeneity in the distribution of airway diameters may arise
from differences in the pharmacological responsiveness of
smooth muscle among the various airway segments (7, 8), or
regional differences in perfusion-limited delivery of MCh due
to heterogeneous bronchial blood flow (32).1 Exclusive of any
1
Although variations in bronchial blood flow can affect the regional airway
constriction (46), this only occurs if the delivery of MCh is perfusion limited.
Given that our MCh was delivered as a constant infusion and its serum
concentration was stable for an extended period of time, it is more likely that
MCh delivery to the conducting airways was diffusion-limited in our experiments.
J Appl Physiol • VOL
increases in the effective airway resistance, heterogeneity in
and of itself can cause substantial elevations in the resistive and
elastic loads against which breathing occurs, which may exacerbate clinical symptoms in obstructive lung disease (29). Both
modeling and imaging studies have shown that such heterogeneity results in significant alterations in ventilation distribution
and gas exchange (15, 40, 41). In addition, ventilation heterogeneity has been strongly associated with airway hyperresponsiveness, raising questions as to its cause-and-effect relationship with reactive airway disease (44).
Using simple lumped-element models, both Otis et al. (36)
and later Mead (31) demonstrated how parallel and serial time
constant inhomogeneity can alter the frequency dependence of
Zrs and its components, Rrs and Ers. Subsequent studies using
more complicated anatomic computational models provided
direct evidence as to how specific patterns and distributions of
heterogeneous bronchoconstriction alter the frequency dependence of Rrs and Ers (11, 14, 25, 29, 43). More recent studies
combining positron emission tomography imaging with forced
oscillations in humans have elucidated a more definitive relationship between changes in Zrs and heterogeneous bronchoconstriction (40 – 42). The present study builds on this earlier
work in that it seeks to establish whether quantifiable information on airway heterogeneity can be extracted from Zrs measured during pharmacologically induced bronchoconstriction,
and whether such information is associated with anatomic
changes in airway diameters obtained from HRCT.
It has been well established that changes in the frequency
dependence of Zrs and its resistive (Rrs) and elastic components (Ers) can be indicative of both the pattern and locus of
airway constriction (20). Morphometric modeling studies have
indicted that in the presence of severe homogeneous peripheral
airway constriction, Rrs will tend to increase uniformly at all
frequencies. The Ers will demonstrate minimal change below 1
Hz but pronounced elevations at higher frequencies as a result
of high-frequency oscillatory flow shunting into the central
airway walls (25, 31). In the presence of central airway
constriction, Rrs will demonstrate a mild uniform increases at
all frequencies, regardless of the distribution of airway diameters, whereas Ers will be minimally affected. However, if
central airway constriction includes mild peripheral airway
constriction and airway closure, Ers can be affected at all
frequencies (25). Thus our Zrs data in Fig.2 are most consistent
with a combination of predominately central airway constriction and mild peripheral involvement.
To assess the sensitivity of using Zrs to detect the heterogeneity of airway constriction, we compared the performances
of two different viscoelastic constant-phase models: 1) a
“lumped” airways model in which the resistive and inertial
properties of the airways is represented by individual R and I
parameters; and 2) a “distributed” airways model in which
airway resistance is assumed to be heterogeneously distributed
according to a predefined probability density function, P(R).
Both topologies were applied to the mechanical impedance
spectra of the total respiratory system. Thus the parameters
characterizing tissue mechanics are influenced by both the lung
parenchymal tissues and the chest wall. Thus, the parameters
characterizing airway resistance may in fact be biased due to
the purely Newtonian and volume-dependent component of
chest wall resistance. However, because our Zrs measurements
were made at a constant mean airway pressure and (presum-
106 • FEBRUARY 2009 •
www.jap.org
Downloaded from http://jap.physiology.org/ by 10.220.33.3 on June 17, 2017
Fig. 5. Summary of derived airway parameter values for distributed airways
model (Topology B) averaged across all 8 dogs. Error bars denote SDs. R␮,
mean airway resistance; R␴, SD of airway resistances; Rcv, coefficient of
variation for airway resistance. *Significantly higher than pre-DI value at
baseline, P ⬍ 0.05 (using ANOVA and Tukey honestly significant difference).
**Significantly higher than pre-DI value at methacholine dose of 17 ␮g/min,
P ⬍ 0.05 (using ANOVA and Tukey honestly significant difference). †Significantly higher than pre-DI value at baseline, P ⬍ 0.05 (using paired t-test).
#Significantly higher than pre-DI value at same methacholine dose, P ⬍ 0.05
(using paired t-test).
525
526
ASSESSMENT OF HETEROGENEOUS AIRWAY CONSTRICTION
Downloaded from http://jap.physiology.org/ by 10.220.33.3 on June 17, 2017
Fig. 6. Correlations between parameter estimates obtained from Topology A (lumped airways model) and Topology B (distributed airways model). Data are shown for all 8 dogs at
baseline (circles) and intravenous MCh infusion
rates of 17 (inverted triangles), 67 (squares), and
200 ␮g/min (diamonds) before (white) and 5
min following DI (gray). Data are also shown
following intravenous atropine (black triangles).
In all plots, actual regression lines demonstrated
no significant differences from the corresponding lines of identity.
ably) constant lung volume, we have assumed that the trends
observed in our data are due solely to changes in the distribution of airway diameters (5), because MCh should have minimal influence on chest wall resistance.
Both models were able to detect alterations in airway and
tissue mechanics with remarkable consistency, as we found no
significant difference between estimates of the parameter values from either the lumped airway model or the distributed
airways model (Fig. 5). This suggests that the R parameter of
the traditional single-compartment constant-phase model can
provide a reliable estimate of overall or average airway resistance, even during severe bronchoconstriction. Moreover, little-to-no estimation bias of the tissue properties was introduced
J Appl Physiol • VOL
when applying this model to data during intravenous MCh
infusion (Fig. 6). This is in contrast to the findings of Suki
et al. (39), who found a slight improvement in estimates of
tissue resistance when using the model of Topology B compared with Topology A during simulated heterogeneous bronchoconstriction in a canine lung (39). This may be due to
differences in the pattern of the heterogeneity of airway constriction in their theoretical model vs. our actual experimental
conditions. We note, too, that aerosolized deliveries of bronchoconstricting agonists may result in a different heterogeneous pattern of airway constriction (34).
Both inverse model topologies also detected significant
increases in tissue elastance H during MCh infusion (Fig. 3).
106 • FEBRUARY 2009 •
www.jap.org
ASSESSMENT OF HETEROGENEOUS AIRWAY CONSTRICTION
While the tissue damping parameter G did demonstrate a
tendency to increase with MCh dose (by ⬃50% at the highest
dose compared with baseline), this did not achieve statistical
significance. These increases may reflect a stiffening of the
parenchyma due to airway-tissue interdependence during bronchoconstriction, as suggested by the data of Mitzner et al. (32).
Alternatively, increases in H (and G) may also be the result of
a small number of closed airways randomly distributed
throughout the airway tree, which effectively reduces the
amount of lung tissue in communication with the airway
opening. The fact that ␩, or the ratio of G to H, did not show
any changes with MCh dose suggests that these dogs did
experience progressive airway closure and derecruitment. Such
derecruitment may alter the mean level and frequency dependence of Zrs, especially at low frequencies (25, 29). However,
J Appl Physiol • VOL
because we observed no significant pairwise differences in the
pre- and post-DI tissue parameter values, we conclude that any
benefits of DI were lost within the 5-min period between Zrs
measurements (see below).
In this study, both models yielded consistent estimates of
airway and tissue properties for all dogs under all conditions.
Thus a relevant question may be which topology is most
appropriate to describe Zrs data during induced bronchoconstriction. Topology A appears to be the statistically superior
model for low-to-moderate doses of MCh based on Akaike
criteria, an index derived from information theory to determine
which model, in a maximum likelihood sense, is most appropriate to describe a given data set (1). However, statistical tests
of model appropriateness, whether based on hypothesis testing
paradigms (such as F tests) (20, 21) or maximum likelihood
theory (1, 45), do not always indicate the utility of a particular
model or the relevant physiological information it may provide
(23). For example, Topology B has the advantage of providing
information on the distribution of airway resistances, which is
strongly correlated with the distribution of diameters obtained
from randomly selected central airway segments measured
with HRCT (Fig. 8). The fact that this relationship was nonlinear may indicate that Zrs is actually more sensitive to
changes in airway resistance due to peripheral airway constriction, which HRCT will not detect (4, 41). Such information
cannot be extracted from Zrs using Topology A, despite its
apparent statistical superiority over Topology B.
This is not to suggest that formal statistical tests of model
comparison are entirely without merit, because they may provide some insight into how strongly a physical mechanism
influences a specified data set: in our case, the degree to which
parallel airway heterogeneity influences Zrs. We used the
technique of Akaike weights to determine the relative likelihood that the topology in question generated the Zrs data (45).
Our results demonstrate that w(AICc) for the distributed airways model increases with increasing MCh dose under pre-DI
conditions, suggesting that it becomes more appropriate (in a
maximum likelihood sense) to characterize Zrs data during
higher levels of bronchoconstriction compared with Topology
A. Indeed, the relative likelihood that Topology B generated the
data as assessed with w(AICc) progressively increased with
MCh dose (Fig. 7). Moreover, the Zrs spectra for half of the
dogs were best described by Topology B at the highest dose of
MCh. This indicates that the spectral features of Zrs is not only
influenced by heterogeneous bronchoconstriction, but the sensitivity of detecting airway heterogeneity from Zrs using inverse modeling is enhanced at higher MCh doses.
For the Topology B model fits, we limited our description of
the parallel airway resistance distributions with only three
different probability density functions: hyperbolic, uniform, or
linear, with the most appropriate distribution for a given Zrs
spectrum selected according to AICc comparisons (19, 23).
These functions were used based on their mathematical simplicity and their ability to yield closed-form expressions for the
predicted impedance of Eq. 4. Similar to the study of Suki et al.
(39), we found that the hyperbolic distribution function was
most appropriate to describe Zrs under the majority of conditions (Fig. 5). In reality, very little data exist as to how airway
diameters are actually distributed in dogs at baseline or during
induced bronchoconstriction (39), with diameters as measured
by HRCT representing a gross undersampling of the actual
106 • FEBRUARY 2009 •
www.jap.org
Downloaded from http://jap.physiology.org/ by 10.220.33.3 on June 17, 2017
Fig. 7. Summary of ⌽, AICc, and w(AICc) for Topologies A (black) and B
(gray) before and after DI at each methacholine dose as well as following
administration of intravenous atropine. Error bars, where shown, denote SDs.
*Significantly lower that pre-DI value at same MCh dose, P ⬍ 0.05 (using
paired t-test). †Significantly lower than corresponding values at baseline and
MCh dose of 17 ␮g/min, P ⬍ 0.05 (using ANOVA and Tukey honestly
significant difference). #Significantly higher than corresponding values at
baseline and methacholine dose of 17 ␮g/min, P ⬍ 0.05 (using ANOVA and
Tukey honestly significant difference).
527
528
ASSESSMENT OF HETEROGENEOUS AIRWAY CONSTRICTION
population of airway segments (6, 7, 9). An additional limitation of Topology B is its assumption that all airway heterogeneity can be characterized by a parallel arrangement of conduits. In reality, the canine airway tree is a complex, asymmetric branching structure (17), and both serial (31) and
parallel (36) heterogeneity can exist simultaneously during
bronchoconstriction.
The distributed airways model was able to track significant
increases in the heterogeneity of bronchoconstriction with
MCh as quantified by either R␴ or Rcv. However, we observed
no apparent changes in either Zrs or in the individual model
parameters 5 min following a DI, similar to the findings of
Kaminsky et al. (24). Given the very low frequency content of
our driving signal (lowest frequency 0.078125 Hz), combined
with our desire to maintain system stationarity during the
forced oscillatory measurements, we waited several minutes
following lung inflation before making post-DI measurements.
This would ensure that any immediate transient effects of the
DI would minimally influence our Fourier-based estimates of
Zrs. Nonetheless, we did detect significant increases in our
derived heterogeneity index Rcv 5 min following a DI. Such a
sustained effect of a DI on airway heterogeneity may reflect
local or regional differences in the mechanical equilibrium that
is achieved between the opposing airway and tissue forces
following inflation. For example the immediate effects of a DI
may be to simultaneously dilate many airways, resulting in a
transient lowering of airway resistance and a reduction in the
J Appl Physiol • VOL
heterogeneity of airway diameters. However, during the continuous infusion of a bronchoconstricting agonist, airway
smooth muscle will reconstrict against the opposing parenchymal tethering forces. Any relative differences in the post-DI
airway-parenchymal stress-relaxation responses may result in a
new equilibrium of airway-parenchymal interdependence. This
new mechanical equilibrium across many intraparenchymal
airway segments may be sufficient to cause a widened distribution of diameters, although the net effect on global measures
of effective airway resistance will be minimal.
Such an effect may be one of the reasons for the variable
response of a DI during spontaneous and induced bronchoconstriction (10). Traditionally, it has been assumed that individuals with asthma have a diminished capacity to dilate their
airways in response to a DI compared with healthy subjects
(29, 37). This behavior has been speculated to be the result of
diminished airway-parenchymal interdependence due to longstanding inflammation, or alterations in the length-tension
properties of airway smooth muscle (12). During MCh-induced
bronchoconstriction, a heterogeneous pharmacological response of airway smooth muscle, as suggested by increases in
airway resistance heterogeneity, may also lead to heterogeneous alterations in parenchymal distortions and smooth muscle properties. If one assumes that a DI would alter airwayparenchymal interactions in a heterogeneous manner, a post-DI
increase in Rcv would be expected.
106 • FEBRUARY 2009 •
www.jap.org
Downloaded from http://jap.physiology.org/ by 10.220.33.3 on June 17, 2017
Fig. 8. Correlations between the airway diameters measured with high-resolution computed tomography (Eqs. 1
and 2) and derived airway resistance parameters from Topology B (Eqs. 5 and 6) for a representative dog (left) and
averaged across four dogs (right). Data were obtained at
baseline (circles) and intravenous MCh infusion rates of 17
(inverted triangles), 67 (squares), and 200 ␮g/min (diamonds) before (white) and 5 min following DI (gray).
Dashed line represents rising exponential regression equation y ⫽ a(1 ⫺ e⫺bx). Data for representative dog is
not included in Figs. 2–7 due to lack of atropine data.
៮ (D⫺4): mean of HRCT airway diameters to the inverse
D
fourth power; S.D. (D⫺4), standard deviation of HRCT
airway diameters to the inverse fourth power; R␮, average
airway resistance parameter from Topology B; R␴, standard
deviation of airway resistances from Topology B.
ASSESSMENT OF HETEROGENEOUS AIRWAY CONSTRICTION
CONCLUSION
In summary, these data demonstrate that changes in Zrs as
assessed with forced oscillations and inverse modeling can be
linked to specific structural alterations in the lung using HRCT.
When inverse modeling is applied to Zrs data obtained in dogs
during MCh-induced bronchoconstriction, either lumped or
distributed airways models can accurately partition average
airway and tissue properties. Distributed airways models, however, appear to be most appropriate during severe bronchoconstriction.
ACKNOWLEDGMENTS
The authors thank Beatrice Mudge and Richard Rabold for technical
assistance in this study. The authors also thank Dr. Monica Hawley for her
assistance with statistical analysis of the data and Dr. Brett Simon for his many
helpful suggestions during the preparation of the manuscript.
GRANTS
REFERENCES
1. Akaike H. A new look at the statistical model identification. IEEE Trans
Automat Contr 19: 716 –723, 1974.
2. Bates JHT. Lung mechanics-the inverse problem. Austral Phys Eng Sci
Med 14: 197–203, 1991.
3. Bates JHT, Allen G. The estimation of lung mechanics parameters in the
presence of pathology: a theoretical analysis. Ann Biomed Eng 34: 384 –
392, 2006.
4. Bates JHT, Lutchen KR. The interface between measurement and
modeling of peripheral lung mechanics. Respir Physiol Neurobiol 148:
153–164, 2005.
5. Black LD, Dellaca R, Jung K, Atileh H, Israel E, Ingenito EP, Lutchen
KR. Tracking variations in airway caliber by using total respiratory vs.
airway resistance in healthy and asthmatic subjects. J Appl Physiol 95:
511–518, 2003.
6. Brown RH, Mitzner W. Functional imaging of airway narrowing. Respir
Physiol Neurobiol 137: 327–337, 2003.
7. Brown RH, Herold CJ, Hirshman CA, Zerhouni EA, Mitzner W.
Individual airway constrictor response heterogeneity to histamine assessed
by high-resolution computed tomography. J Appl Physiol 74: 2615–2620,
1993.
8. Brown RH, Kaczka DW, Fallano K, Chen S, Mitzner W. Temporal
variability in the responses of individual canine airways to methacholine.
J Appl Physiol 104: 1381–1386, 2008.
9. Brown RH, Mitzner W. Understanding airway pathophysiology with
computed tomography. J Appl Physiol 95: 854 – 862, 2003.
10. Fredberg JJ. Airway obstruction in asthma: does the response to a deep
inspiration matter? Respir Res 2: 273–275, 2001.
11. Fredberg JJ, Hoenig A. Mechanical response of the lungs at high
frequencies. J Biomech Eng 100: 57– 66, 1978.
12. Fredberg JJ, Inouye D, Miller B, Nathan M, Jafari S, Raboudi SH,
Butler JP, Shore SA. Airway smooth muscle, tidal stretches, and dynamically determined contractile states. Am J Respir Crit Care Med 156:
1752–1759, 1997.
13. Fredberg JJ, Stamenovic D. On the imperfect elasticity of lung tissue.
J Appl Physiol 67: 2048 –2419, 1989.
14. Gillis HL, Lutchen KR. Airway remodeling in asthma amplifies heterogeneities in smooth muscle shortening causing hyperresponsiveness.
J Appl Physiol 86: 2001–2012, 1999.
15. Gillis HL, Lutchen KR. How heterogeneous bronchoconstriction affects
ventilation distribution in human lungs: a morphometric model. Ann
Biomed Eng 27: 14 –22, 1999.
16. Hantos Z, Daroczy B, Suki B, Nagy S, Fredberg JJ. Input impedance
and peripheral inhomogeneity of dog lungs. J Appl Physiol 72: 168 –178,
1992.
17. Horsfield K, Kemp W, Phillips S. An asymmetrical model of the airways
of the dog lung. J Appl Physiol 52: 21–26, 1982.
J Appl Physiol • VOL
18. Ito S, Ingenito EP, Arold SP, Parameswaran H, Tgavalekos NT,
Lutchen KR, Suki B. Tissue heterogeneity in the mouse lung: effects of
elastase treatment. J Appl Physiol 97: 204 –212, 2004.
19. Kaczka DW, Hager DN, Hawley ML, Simon BA. Quantifying mechanical heterogeneity in canine acute lung injury: impact of mean airway
pressure. Anesthesiology 103: 306 –317, 2005.
20. Kaczka DW, Ingenito EP, Israel E, Lutchen KR. Airway and lung
tissue mechanics in asthma: effects of albuterol. Am J Respir Crit Care
Med 159: 169 –178, 1999.
21. Kaczka DW, Ingenito EP, Suki B, Lutchen KR. Partitioning airway and
lung tissue resistances in humans: effects of bronchoconstriction. J Appl
Physiol 82: 1531–1541, 1997.
22. Kaczka DW, Lutchen KR. Servo-controlled pneumatic pressure oscillator for respiratory impedance measurements and high frequency ventilation. Ann Biomed Eng 32: 596 – 608, 2004.
23. Kaczka DW, Massa CB, Simon BA. Reliability of estimating stochastic
lung tissue heterogeneity from pulmonary impedance spectra: a forwardinverse modeling study. Ann Biomed Eng 35: 1722–1738, 2007.
24. Kaminsky DA, Irvin CG, Lundblad LKA, Thompson-Figueroa J,
Klein J, Sullivan MJ, Flynn F, Lang S, Bourassa L, Burns S, Bates
JHT. Heterogeneity of bronchoconstriction does not distiguish mild asthmatic subjects from healthy controls when supine. J Appl Physiol 104:
10 –19, 2008.
25. Lutchen KR, Gillis H. Relationship between heterogeneous changes in
airway morphometry and lung resistance and elastance. J Appl Physiol 83:
1192–1201, 1997.
26. Lutchen KR, Greenstein JL, Suki B. How inhomogeneities and airway
walls affect frequency dependence and separation of airway and tissue
properties. J Appl Physiol 80: 1696 –1707, 1996.
27. Lutchen KR, Hantos Z, Jackson AC. Importance of low-frequency
impedance data for reliably quantifying parallel inhomogeneities of respiratory mechanics. IEEE Trans Biomed Eng 35: 472– 481, 1988.
28. Lutchen KR, Hantos Z, Petak F, Adamicza A, Suki B. Airway inhomogeneities contribute to apparent lung tissue mechanics during constriction. J Appl Physiol 80: 1841–1849, 1996.
29. Lutchen KR, Jensen A, Atileh H, Kaczka DW, Israel E, Suki B,
Ingenito EP. Airway constriction pattern is a central component of asthma
severity: the role of deep inspirations. Am J Respir Crit Care Med 164:
207–215, 2001.
30. Lutchen KR, Suki B, Zhang Q, Petak F, Daroczy B, Hantos Z. Airway
and tissue mechanics during physiological breathing and bronchoconstriction in dogs. J Appl Physiol 77: 373–385, 1994.
31. Mead J. Contribution of compliance of airways to frequency-dependent
behavior of lungs. J Appl Physiol 26: 670 – 673, 1969.
32. Mitzner W, Blosser S, Yager D, Wagner E. Effect of bronchial smooth
muscle contraction on lung compliance. J Appl Physiol 72: 158 –167,
1992.
33. Motulsky H, Christopoulos A. Fitting Models to Biological Data using
Linear and Nonlinear Regression. A Practical Guide to Curve Fitting.
New York: Oxford University Press, 2004.
34. Nagase T, Moretto A, Ludwig MS. Airway and tissue behavior during
induced constriction in rats: intravenous vs. aerosol administration. J Appl
Physiol 76: 830 – 838, 1994.
35. Navalesi P, Hernandez P, Laporta D, Landry JS, Maltais F, Navajas
D, Gottfried SB. Influence of site of tracheal pressure measurement on in
situ estimation of endotracheal tube resistance. J Appl Physiol 77: 2899 –
2906, 1994.
36. Otis AB, McKerrow CB, Bartlett RA, Mead J, McIlroy MB, Selverstone NJ, Radford EP Jr. Mechanical factors in the distribution of
pulmonary ventilation. J Appl Physiol 8: 427– 443, 1956.
37. Skloot G, Permutt S, Togias A. Airway hyperresponsiveness in asthma:
a problem of limited smooth muscle relaxation with inspiration. J Clin
Invest 96: 2393–2403, 1995.
38. Suki B, Lutchen KR. Pseudorandom signals to estimate apparent transfer
and coherence functions of nonlinear systems: applications to respiratory
mechanics. IEEE Trans Biomed Eng 39: 1142–1151, 1992.
39. Suki B, Yuan H, Zhang Q, Lutchen KR. Partitioning of lung tissue
response and inhomogeneous airway constriction at the airway opening.
J Appl Physiol 82: 1349 –1359, 1997.
40. Tgavalekos NT, Musch G, Harris RS, Vidal Melo MF, Winkler T,
Schroeder T, Callahan R. Relationship between airway narrowing,
patchy ventilation and lung mechanics in asthmatics. Eur Respir J 29:
1174 –1181, 2007.
106 • FEBRUARY 2009 •
www.jap.org
Downloaded from http://jap.physiology.org/ by 10.220.33.3 on June 17, 2017
This work was supported by National Heart, Lung, and Blood Insitute
Grants P01 HL-010342 and K08 HL-089227, as well as by a Research Starter
Grant from the Foundation for Anesthesia Education and Research.
529
530
ASSESSMENT OF HETEROGENEOUS AIRWAY CONSTRICTION
41. Tgavalekos NT, Tawhai M, Harris RS, Musch G, Vidal-Melo MF,
Venegas JG, Lutchen KR. Identifying airways responsible for heterogeneous ventilation and mechanical dysfunction in asthma: an image functional modeling approach. J Appl Physiol 99: 2388 –2397, 2005.
42. Tgavalekos NT, Venegas JG, Suki B, Lutchen KR. Relation between
structure, function, and imaging in a three-dimensional model of the lung.
Ann Biomed Eng 31: 363–373, 2003.
43. Thorpe CW, Bates JHT. Effect of stochastic heterogeneity on lung
impedance during acute bronchoconstriction: a model analysis. J Appl
Physiol 82: 1616 –1625, 1997.
44. Venegas JG, Schroeder T, Harris S, Winkler RT, Vidal Melo MF. The
distribution of ventilation during bronchoconstriction is patchy and bimodel: A PET imaging study. Respir Physiol Neurobiol 148: 57– 64, 2005.
45. Wagenmakers EJ, Farrell S. AIC model selection using Akaike weights.
Psychon Bull Rev 11: 192–196, 2004.
46. Wagner EM, Mitzner W. Contribution of pulmonary versus systemic
perfusion of airway smooth muscle. J Appl Physiol 78: 403– 409, 1995.
47. Yuan H, Suki B, Lutchen KR. Sensitivity analysis for evaluating
nonlinear models of lung mechanics. Ann Biomed Eng 26: 230 –241,
1998.
Downloaded from http://jap.physiology.org/ by 10.220.33.3 on June 17, 2017
J Appl Physiol • VOL
106 • FEBRUARY 2009 •
www.jap.org