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1Department of Biomedical Engineering, Boston University, 02135; 4Pulmonary Division, Brigham and Women's Hospital, Boston, Massachussetts 02115; 2Dipartimento di Bioingegneria, Politecnico di Milano, and 3Centro di Bioingegneria, Fondazione Don Gnocchi Istituto di Ricovero e Cura a Carattere Scientifico and Politecnico di Milano, Milano, Italy
Submitted 4 December 2002 ; accepted in final form 5 April 2003
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ABSTRACT |
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 TOP ABSTRACT METHODSRESULTSDISCUSSIONDISCLOSURESREFERENCES |
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chest wall resistance; airway hypereactivity; asthma
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METHODS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONDISCLOSURESREFERENCES |
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2-agonist (albuterol), and two were on a combination of
albuterol and inhaled corticosteroids. Airway hyperreactivity was assessed
before the day of the study by interpolating the methacholine dose-response
curves to the concentration that causes a 20% decrease from the subjects'
baseline forced expiratory volume in 1 s (PC20)
(18). Subjects were instructed
not to take albuterol or any form of caffeine 8 h before the study. We also
asked each subject to refrain from taking other medications as directed by the
ATS guidelines for methacholine challenges
(6). Our institutional research
committees approved the study, with informed consent from each subject
required.
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Tracking airway caliber. At any given frequency, the lung can be
modeled as a single resistance and elastance in series (often called the
single-compartment model). This model has the governing equation
 | (1) |
ao is
flow at the airway opening, EL is lung elastance, and k is
the Ptp when flow and volume are zero. For Rrs, the same system is used,
except it is applied to airway opening pressure (Pao) rather than to Ptp,
i.e.,
 | (2) |
Now, Rrs = Raw + RTL + Rcw, where RTL is the
resistance of the parenchymal tissue of the lung. For an 8-Hz
ao the RTL is considered to be
essentially zero (12,
13,
15,
17). The application of
Eq. 2 presumes that we ignore all shunt impedances, including gas
compression and airway wall shunting, so that Rrs = Raw + Rcw. Here, Rcw is
not necessarily zero, and our study will quantify Rcw at FRC and during a DI
to TLC.
Experimental measurements. The experimental setup has been
previously described in detail elsewhere
(11). Briefly, we use a
computer-controlled pump to deliver 8-Hz oscillations with an amplitude of 0.9
l/s, which are superimposed on top of the subjects' normal breathing.
ao is measured by a pneumotachograph (Fleisch
no. 2) connected to a differential pressure transducer (±2
cmH2O, model LCVR, Celesco). Ptp is recorded with a differential
pressure transducer (±50 cmH2O, model LCVR, Celesco) with
one tap measuring esophageal pressure (Pes) via a 10-cm latex balloon catheter
inserted into the esophagus transnasally and the other tap measuring Pao. A
separate differential pressure transducer (±50 cmH2O, model
LCVR, Celesco) records transrespiratory pressure (Prs) with one tap measuring
Pao and the other measuring atmospheric pressure.
During 8-Hz DI maneuvers, there is a three-way valve that is opened that
allows the subject to breathe to atmosphere through a high-inertance tube. The
high-inertance tubing (
212 ml dead space) behaves as a low-pass filter,
allowing the patient to breathe to atmosphere while the energy from the
superimposed 8-Hz oscillations goes into the subject. The 8-Hz signal is
generated by a computer board (Data Translation, DT-2811
analog-to-digital/digital-to-analog board) at a sampling rate of 100 Hz. The
pressure and flow signals are stored digitally on the computer by the same
board at a sampling rate of 100 Hz.
Protocol. All subjects first underwent baseline spirometry. A balloon catheter was then placed in the esophagus transnasally. The initial positioning of the balloon was verified with an occlusion test. After a brief training period (5–10 min) on the system, each subject was asked to make a tight seal around the mouthpiece with their mouth and firmly support their cheeks. Once set, they were asked to breathe tidally for 5–10 breaths, take a steady DI to TLC followed by a passive expiration to FRC, and then continue breathing tidally for another 5–10 breaths. This maneuver was done at baseline and after a methacholine challenge. The methacholine was administered by using a Rosenthal New Standard Dosimeter (Pulmonary Data Services) according to the fivebreath dosimeter protocol set forth by ATS. The methacholine dose sequence was 0.078, 0.156, 0.3125, 0.625, 1.25, 2.5, 5, 10, and 25 mg/ml. Healthy subjects were given a modified methacholine challenge. The modified challenge is a methacholine challenge in which DIs are prohibited. This type of challenge has been shown to amplify healthy subjects' airway hyperreactivity to a given dose of methacholine (16). In asthmatic subjects, however, the prohibition of DIs has only a minor impact on airway hyperreactivity (5). Thus asthmatic subjects performed a standard methacholine challenge in which basic spirometry was carried out after each dose, and the challenge continued until they reached their PC20 dose.
Data analysis. All recorded pressure and flow signals were
separately low- and high-pass filtered at a cutoff frequency of 4 Hz (4 Pole
Butterworth digital filter) to isolate the 8-Hz from the low-frequency tidal
volume changes. The 8-Hz pressure and flow data were sent through the
recursive least squares algorithm (RLS), and the resulting resistance vs. time
data was compensated for both the filter and the algorithm's phase response
(11). Lung volume changes were
calculated by integration of the low-frequency flow data. The overall result
was resistance vs. lung volume for all subjects, pre- and post-methacholine
challenge. Specifically, if we used Ptp and ao,
the RLS algorithm's output was Raw. If instead the input was Pao and
ao, then the resulting output was Rrs at 8 Hz.
Rcw at 8 Hz was estimated as the difference between Rrs at 8 Hz and Raw (Rcw =
Rrs - Raw). We examined three key features in the resistance vs. lung volume
data (Rrs and Raw): the minimum resistance achieved during a DI to TLC, the
mean pre-DI resistance, and the mean post-DI resistance.
Two separate transducers were used to measure Ptp and Prs, and each had
different connection tubing configurations. We evaluated the common mode
rejection ratio of each transducer at 8 Hz as a function of input pressure
amplitude and used these data to ensure that both transducers were matched
(9). For each transducer,
Ptrue = Pmeasured - PCm offset, where
Ptrue is the true pressure, PCM offset is the common
mode offset pressure, and Pmeasured is the pressure that would be
measured by the transducer in the single-ended transducer configuration. To
calculate Ptrue, the PCM offset must be expressed as a
function of the measured pressure amplitude. By linear regression, we found
that at 8 Hz
 | (3) |
The Raw or Rrs data were also converted to effective diameter variations as
used by Jensen et al. (11).
Here, we assume that resistance is related to airway diameter through the
fully developed Poiseuille flow
 | (4) |
 | (5) |
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RESULTS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONDISCLOSURESREFERENCES |
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Pooling the data for all subjects (Fig.
2), we see that, at FRC, Rrs is greater than Raw in all cases by
0.5–1.0 cmH2O · l-1 · s, which
is in agreement with the single subject data shown in
Fig. 1. The difference between
Rrs and Raw during tidal breathing (pre-DI) was significant (P <
0.0004) in healthy and asthmatic subject groups. However, at TLC, there was no
statistical difference between minimum Raw and minimum Rrs for healthy
subjects pre- or postmethacholine challenge conditions. Thus, in healthy
subjects, estimated Rcw at 8 Hz is essentially zero at TLC and minimum Rrs
reflects minimum Raw. Figure 3
isolates the estimate of Rcw at FRC and at TLC for all healthy and asthmatic
subjects, both at baseline and after a methacholine challenge. Likewise, in
asthmatic subjects, even though the difference between the minimum Rrs and the
minimum Raw was statistically significant at baseline (P = 0.034) and
postchallenge (P = 0.0007), the absolute value of the difference is
small. Again, the estimation of Rcw at 8 Hz is nearly zero, and Rrs reflects
primarily Raw.
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The postchallenge Rcw at FRC is slightly higher both for the healthy and asthmatic subjects (Fig. 3). The slight increase was not significant for either group. After a methacholine challenge, Rcw at TLC increased for both the healthy subject group and the asthmatic subject group. The difference in Rcw at TLC from baseline to challenge was significant for asthmatic subjects but not for healthy subjects.
Using Eq. 5, we calculated the increase in an effective diameter associated with a DI as inferred by either Raw or by Rrs (Fig. 4). Using Raw, one would infer that healthy subjects could increase their effective airway diameters by 28.1% at baseline and 29.5% postchallenge when inhaling to TLC. In contrast, using Rrs, one would infer a 38.3% increase in the healthy subject group's effective diameter at baseline and a 32.4% increase postchallenge. Likewise, using Raw in asthmatic subjects, one would infer a 21.4% increase at baseline and a 21.4% increase postchallenge. When Rrs is used, these values become 25.0 and 21.3%, respectively. Generally, use of Rrs at 8 Hz overestimates the change in diameter during a DI, but the overestimation is less important as baseline Raw increases. This is because Rcw is essentially the same for all conditions, but in healthy subjects postchallenge or asthmatic subjects pre- or postchallenge, Raw increases and the ratio of Rcw to Rrs decreases. Thus Rcw is a smaller artifact on effective diameter reduction.
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DISCUSSION |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONDISCLOSURESREFERENCES |
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ao), decreases to nearly zero at
TLC. Jensen et al. (11) reported that minimum Raw in healthy subjects was nearly the same after a methacholine challenge as it was at baseline, i.e., healthy subjects retained the ability to maximally dilate their airways postchallenge. Our results show that Rrs displays this trend as well (Fig. 2). Jensen et al. also reported that asthmatic subjects have a decreased capacity to maximally dilate their airways at baseline and that this defect is further amplified after a methacholine challenge. This trend is still evident in minimum Rrs. At baseline, the minimum Rrs in asthmatic subjects is elevated above the level of healthy subjects, and it is even further elevated postchallenge.
One important consequence of using Rrs vs. Raw is the overestimation associated with the calculation of the increase in effective diameter with a DI. Our results show that because Rcw decreases from a finite value at FRC to zero at TLC, the Rrs would significantly overestimate the change in effective diameter during a DI for healthy subjects, both pre- and postmethacholine challenge. This difference is minimal in asthmatic subjects because they already have an elevated Raw, and so the constant Newtonian component due to Rcw is a smaller fraction of the measured Rrs.
Another goal of our study was to study the sensitivity of Rcw to changes in
lung volume. Barnas et al. (2)
proposed that total Rcw contains contributions from two major components:
1) a frequency-dependent plastic dissipation that is consistent with
measurements on both lung tissue and upper airways, and 2) a
frequency-independent Newtonian resistance. They showed that the Newtonian
component of the total Rcw (essentially the value of Rcw at 8 Hz) in four
healthy subjects at FRC varied between 0.5 and 1.25 cmH2O ·
l-1 · s (1).
At FRC, we found Rcw at 8 Hz to be between 0.5 and 1.0 cmH2O
· l-1 · s (Fig.
3). This range of values is also consistent with the data reported
by D'Angelo et al. (7) using
the interrupter technique. They found that the interrupter Rcw in
anesthetized, paralyzed humans ranged between 0.3 and 0.6 cmH2O
· l-1 · s. Although these values are slightly smaller
than those we report here, it may be argued that the resistance measured by
D'Angelo et al. does not include the resistive components associated with the
activated chest wall that are present during spontaneous tidal breathing.
Also, all methods, including ours, estimate Rcw as Rrs - RL. Thus
the assumption is that there is negligible gas compression and airway wall
shunting impacting the Ptp, Pao, and ao
data.
Barnas et al. (3) reported
that when measurements of Rcw were made with oscillations of a volume of
1.1 liters greater than a subject's FRC, there was a decrease in total
Rcw between 0.5 and 4 Hz. Although these results imply an inverse dependence
of Rcw on lung volume, we could not find a previous study that reported on the
change in Rcw with lung volume during a DI from FRC to TLC. In this study, we
found that the estimated Rcw changed significantly with an increase in lung
volume from FRC to TLC (Fig. 3)
for both healthy and asthmatic subjects, pre- and postmethacholine challenge.
Our results show that the estimated Rcw decreases to around zero at TLC in the
healthy subject both pre- and postmethacholine challenge
(Fig. 3) and close to zero in
the asthmatic subject, especially at baseline conditions.
Rcw vs. lung volume. Why would our estimation of the Newtonian
component of Rcw decrease from a finite value to nearly zero at TLC? We first
address methodological issues. Initially, we considered potential artifacts
from the esophageal balloon method. For example, although the balloon position
relative to the nasal passage could not have changed (it was taped in place),
with increasing lung volume its position relative to the contents of the
thoracic cage could be different. If the pleural pressure variations are not
uniform around the lung, then the balloon could be picking up a different form
of the fluctuations in pleural pressure for FRC vs. TLC, depending on its
position relative to the lungs. Although we did not perform the occlusion test
at different lung volumes in all subjects (only to check the initial position
of the balloon at FRC), we did perform it in one subject. In that subject, we
found that the ratio of change in Pes to change in Pao (
Pes/Pao)
during the test was essentially unity even up to 3 liters above FRC. Also,
Baydur et al. (4) showed that
even at 80% of vital capacity, the change in Pes was only slightly larger than
the change in Pao during occlusion tests. Moreover, an overestimation of Pes
would lead to an increase in Rcw, not to a decrease. Peslin et al.
(14) also showed that the
amplitude ratio of Pes to Ppl was <10% from unity for oscillations from 2
to 32 Hz. It is also possible that the esophageal wall does not transmit the
pressure identically at FRC vs. TLC. There is some evidence in the literature
that the greater the tone in the esophageal wall the smaller the pressure
difference picked up by the balloon because some of the pressure is not
transmitted across the esophageal wall
(8). But it is unlikely that
the pressure variations transmitted to the balloon would decease to
essentially zero, such that the estimation of Rcw becomes zero.
A far more likely methodological candidate for why our estimate of Rcw
decreases during a DI derives from our assumption that
ao equals the flow (rate of change in volume)
of the chest wall (cw). This is true so long as
there are no shunt flow pathways between the mouth and chest wall. But, in
concept, there could be shunting into the airway walls and into alveolar gas
compression. In fact, Hantos et al.
(10) showed that when they
neglected shunt pathway impedances in the model used to fit their forced
oscillatory impedance data of the respiratory system there was an
underestimation of Rcw of 20–30% at higher frequencies. We created
a simple lumped model to estimate the potential impact of shunting into gas
compression. The model topology is shown in
Fig. 5. Here, an airway
resistance compartment leads to a gas compression compliance, Cg, in parallel
with the lung and chest wall tissues. The tissue compartment has separate
properties for the lung and chest wall tissues. Specifically, RLT
and CLT are the resistance and compliance of the lung tissue,
respectively, and Ccw is the compliance of the chest wall. We simulated a DI
and calculated the ratio of Rcw that would be estimated on the basis of airway
opening data only (i.e., applying the assumption that
ao = cw) vs. the
true Rcw that was assigned at FRC (Fig.
6). Specifically, we set Raw to 2.0 cmH2O ·
l-1 · s, RLT to zero (i.e., no Newtonian
component to parenchymal tissues), and Rcw to 1.0 cmH2O ·
l-1 · s. Assuming an FRC of 3.0 liters, we set Cg
to 0.003 l/cmH2O. Likewise, at FRC, we set CLT = Ccw =
0.2 l/cmH2O. To simulate a DI, we let lung volume vary from an FRC
of 3.0 liters to a TLC of 7.0 liters by increasing Cg. As volume
increased, Raw decreased linearly from 2.0 to 1.0 cmH2O ·
l-1 · s (as would occur for a healthy subject). Also,
CLT and Ccw were either held constant or allowed to decrease. The
decrease in compliances during the DI occurred either linearly by a designated
percentage or according to the slope of a sigmoidal curve fit to the
quasistatic pressure-volume curve from a typical healthy subject at baseline.
The key point is that as volume approaches TLC, lung and chest wall tissues
become very stiff while the increase in alveolar gas provides for an increased
shunt compliance.
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Figure 6 shows that the
estimate of Rcw based on ao will be within 10%
of the true value at FRC, but then decreases during a DI. The underestimation
in Rcw is substantial for when the tissue compliances at TLC experience a 95%
decrease from their values at FRC. Finally, although not shown, we also
expanded the simulation study to include a shunt compliance for the airway
walls, and the effect was small but in the direction of further
underestimation of the true Rcw.
These simulation results largely implicate that the reported decrease in
Rcw at TLC from the value at FRC (Fig.
3) derives from a breakdown in the assumption that
ao and cw are
identical at all lung volumes. In fact,
Fig. 2 showed that Rcw is
elevated postchallenge and/or does not decrease at TLC from FRC as much in
asthmatic subjects. This may reflect that such subjects simply cannot reach a
point on the pressure-volume curve for which large decreases in tissue
compliances occur (i.e., they stay to the left of
Fig. 6 even at TLC). The net
effect is a false apparent increase in the Rcw at TLC from its value
preconstriction.
With regard to biological issues, it is possible that the activation of the
chest wall muscles, particularly on inspiration to TLC, contribute to an
increase in Rcw postchallenge. As the pressure needed to generate an increase
in lung volume to TLC becomes larger postchallenge, the subject would need a
corresponding increase in chest wall muscle activation to overcome this. Such
activation could further decrease Ccw, which would reduce the true
cw and therefore increase Rcw. Consequently,
the increase in Ccw would also amplify the bias due to shunting as lung volume
increased above FRC as per our simulations
(Fig. 6).
Also, constriction can lead to some hyperinflation, and, according to our data, increases in lung volume result in a corresponding decrease in our estimation of Rcw. Unfortunately, we did not look at absolute volumes before and after the methacholine challenge in this study. Measurements of absolute lung volume may have given us more insight into the effects of hyperinflation on the Rcw at FRC and TLC.
In conclusion, measured with this approach, Rcw appears volume dependent,
having a magnitude of 0.5–1.0 cmH2O · l-1
· s during tidal breathing and decreasing to zero at TLC. The decrease
in apparent Rcw during a DI is likely a consequence of
ao underestimating
cw at increased lung volume. Hence, although
this technique would overestimate the net decrease in Raw and net increase in
effective diameter during a DI, the general trends in the DI response shown by
Jensen et al. (11) with Raw
tracking are still present in Rrs tracking. Therefore, we conclude that Rrs
can be used as an effective index to quantify maximum airway caliber
achievable. That is, estimates of Raw at TLC obtained by using Rrs would be
nearly identical to the estimate obtained with RL.
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DISCLOSURES |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONDISCLOSURESREFERENCES |
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FOOTNOTES |
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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.
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, Constant Ccw and CLT of 0.2 l/cmH2O throughout
the full DI; 
, a 50% linear decrease from 0.2 l/cmH2O over
the range of FRC to TLC; 
, a 95% linear decrease from 0.2
l/cmH2O; 
, Ccw and CLT as calculated from the
local slope of a sigmoidal curve fit to the quasistatic pressure-volume curve
of a healthy subject at baseline. Here RcwM is Rcw measured in the
manner described in this study, and Rcwtrue is the true Rcw in the
model with a value of 1 cmH2O · l-1 ·
s.