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1 Vermont Lung Center, Department of Medicine, University of Vermont, Burlington, Vermont 05405; 2 Department of Clinical Physiology, Malmö University Hospital, Lund University, SE-205 02 Malmö, Sweden; and 3 Department of Biomedical Engineering, University of Sao Paulo, Sao Paulo, Brazil, CNPQ, Brazil
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ABSTRACT |
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 TOP
 ABSTRACT
 INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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Respiratory system
resistance (R) and elastance (E) are commonly estimated by fitting the
linear equation of motion P = EV + R
+ P0 (Eq. 1) to measurements of respiratory
pressure (P), lung volume (V), and flow (). However, the
respiratory system is unlikely to behave linearly under many
circumstances. We determined the importance of respiratory system
nonlinearities in two groups of mechanically ventilated Balb/c mice
[controls and mice with allergically inflamed airways (ova/ova)], by
assessing the impact of the addition of nonlinear terms
(E2V2 and
R2||) on the
goodness of model fit seen with Eq. 1. Significant improvement in fit (51.85 ± 4.19%) was only seen in the ova/ova mice during bronchoconstriction when the E2V2
alone was added. An improvement was also observed with addition of the
E2V2 term in mice with both low and high lung
volumes ventilated at baseline, suggesting a volume-dependent
nonlinearity of E. We speculate that airway closure in the constricted
ova/ova mice accentuated the volume-dependent nonlinearity by
decreasing lung volume and overdistending the remaining lung.
resistance; elastance; airway closure; hysteresis; asthma; pulmonary mechanics
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INTRODUCTION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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RESPIRATORY
SYSTEM RESISTANCE (R) and elastance (E) are commonly estimated by
fitting the linear equation of motion
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(1) |
), and volume (V),
where P0 is a constant the function of which is to absorb
any errors in estimating functional residual capacity (FRC)
(15). The single-compartment linear model corresponding to
this equation provides a reasonable description of respiratory system
mechanics under most circumstances. However, the lung can exhibit
nonlinear mechanical behavior under many circumstances, such as when
airflow in the airways becomes turbulent (R becomes nonlinear)
or when the lung parenchyma becomes overdistended (EV becomes
nonlinear). Under such circumstances, adding additional terms to
Eq. 1 to account for these nonlinear phenomena would be
expected to improve the description of the data, as has been previously
shown (2, 10, 18, 23).
Improving the goodness of fit with the addition of nonlinear terms is of more than purely mathematical interest. If one can ascribe to the additional terms a plausible physiological mechanism or explanation, our understanding of the link between lung structure and function will improve. For example, if the addition of nonlinear terms improves model fit in some circumstances, e.g., bronchoconstriction, but not in others, one can make inferences about the importance or unimportance that certain nonlinear phenomena such as turbulence or overdistention have in a given pathophysiological setting.
We conducted the current study to examine the utility of adding nonlinear terms to the standard equation of motion (Eq. 1). Assessments were made at baseline and during bronchoconstriction in untreated mice as well as mice with antigen-induced airway inflammation to determine utility of such an approach in detecting physiological and pathological alterations. We studied mice because of the obvious potential they provide for conducting mechanistic studies.
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METHODS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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Study animals. Female Balb/c mice (Jackson Laboratories) 6-8 wk of age free of known murine pathogens were acclimatized in an animal facility for 1 wk with the provision of adequate food and water. The protocol was approved by the institutional animal care and use committee of the University of Vermont.
Allergen sensitization and challenge. We studied two groups of animals: 1) a group in which allergic airway inflammation was produced by sensitization and challenge with chicken egg albumin (ovalbumin grade V, Sigma Chemical) and 2) a control group age matched by using techniques as previously described (22). Mice in the sensitized and challenged group (ova/ova) received an intraperitoneal injection of 400 µg of ovalbumin mixed with an equal volume of aluminum hydroxide solution on day 1 and day 14. On day 21, the mice were placed in a Plexiglas chamber and exposed to an aerosolized solution of ovalbumin mixed with Dulbecco's phosphate-balanced saline (PBS) to achieve a 1% concentration. Aerosol was delivered with a jet nebulizer (PARI LC PLUS, PARI Respiratory Equipment, Midlothian, VA) for 30 min a day for a total of 3 days. Forty-eight hours after the last exposure, a time point previously shown to coincide with maximal airway inflammation and responsiveness, the measurements described below were made. Inflammation was confirmed by counting cells by using a hemocytometer in fluid obtained by bronchoalveolar lavage with 0.8 ml of cold PBS.
Determination of respiratory mechanics. Anesthesia was achieved with 90 mg/kg of pentobarbital sodium injected intraperitoneally and confirmed by the absence of response to paw pinch. Mice were then tracheostomized, and an 18-gauge metal IV adaptor, the tip of which had been beveled and ground smooth, was inserted into the trachea and firmly tied in place. Mice were then connected to a computer-controlled small animal ventilator (flexiVent, SCIREQ, Montreal, PQ, Canada), which allowed the application of specifically tailored volume perturbations to the lungs (8, 9, 21). Positive end-expiratory pressure (PEEP) of 3 cmH2O was generated by submerging the expiratory line 3 cm into a water trap.
P and V data were generated by applying a 2-s sine wave volume perturbation (SW) with an amplitude of 0.2 ml and a frequency of 2.5 Hz (simulating typical mechanical ventilation with the flexiVent piston) (18). V (i.e., volume delivered to the animal) was determined by correcting the volume displacement of the ventilator piston for gas compression in the ventilator cylinder as previously described (2, 9). P (i.e., pressure at the tracheal opening) was obtained by subtracting the resistive pressure across the flexiVent tubing from the pressure in the flexiVent cylinder. The E of gas in the cylinder and the R of the tubing were determined in separate calibration experiments. was determined by numerically differentiating volume. After 5 min of regular mechanical ventilation, the SW perturbation was applied three times and the average was taken
to generate a baseline measurement.
The standard linear equation of motion (Eq. 1) was extended
in two ways, by the addition of a nonlinear E term
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(2) |
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(3) |
data.
Goodness of model fit of each model was quantified in terms of the estimated noise variance (ENV)
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(4) |
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(5) |
ENV of 30% or greater as signifying a
statistically significant improvement in model fit in going from the
linear model (Eq. 1) to the nonlinear model (Eq. 2 or 3, as the case may be).
Methacholine challenge. Bronchospasm was induced with methacholine in PBS at a concentration of 10 mg/ml aerosolized by an ultrasonic nebulizer (DeVilbuss AeroSonic 5000D, Somerset, PA). The aerosol was delivered to the airway opening by diverting the inspiratory ventilator flow through the aerosol chamber of the nebulizer for a total of 20 breaths at a tidal volume of ~0.4 ml (allowing for gas compression in the nebulizer chamber) at a rate of 30 breaths/min. After the methacholine, the SW perturbation was applied every 30 s for a period of 10 min.
PEEP challenge.
PEEP was randomly changed from 0 to 9 cmH2O in 3-cm
increments in each mouse. Three successive SW perturbations were
applied at each PEEP level, and the average ENV was determined.
Static P-V curve measurements. Starting at FRC, the flexiVent was programmed to deliver seven inspiratory volume steps for a total volume of 1 ml followed by seven expiratory steps, pausing at each step for at least 1 s. Plateau P at each step was recorded and related to the total V delivered. For each mouse, two successive P-V curves were measured before the methacholine challenge, and the values were averaged.
The shape factor (k) of the expiratory limb of each P-V curve was determined by fitting the Salazar-Knowles equation
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(6) |
Statistics. The values of k and the P-V loop areas were compared by use of paired two-tailed t-tests.
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RESULTS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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Cell counts confirmed that the ova/ova mice were inflamed compared with the controls (cell numbers: 37.12 ± 10.10 × 106/ml vs. 7.0 ± 0.655 × 106/ml, P < 0.05).
We first compared linear and nonlinear model fits in all mice at 3 cmH2O PEEP. When the model with the
R2|| term (Eq. 3) was compared with the linear model (Eq. 1) at
baseline and during bronchoconstriction in both ova/ova and control
mice, ENV did not exceed the 30% significance level
(max = 16.06 ± 2.60% SE) (Fig.
1). The 30% significance level was also
not exceeded with addition of the E2V2 term
(Eq. 2) in the control mice; at baseline ENV was
9.56 ± 1.87% (n = 8), whereas 2 min after
methacholine delivery the ENV was 9.23 ± 2.8%. In contrast,
in the ova/ova mice (n = 8), after methacholine the
ENV rose significantly to 51.85 ± 4.19% from a baseline value
of 4.28 ± 2.27% (Fig. 2). Thus a
significant improvement in the goodness of model fit was observed only
in the inflamed mice during bronchoconstriction when a nonlinear E term
was added to the linear model. Table 1
gives the parameter values of all the models in the control and ova/ova
mice both at baseline and after bronchoconstriction.
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Next, we assessed whether the improvement in the goodness of model fit
was affected by increases in mean lung volume. ENV was assessed in
both control and ova/ova mice under baseline conditions at various lung
volumes achieved by varying PEEP. At PEEP levels of 0, 6, and 9 cmH2O, ENV was 36.47 ± 5.11, 72.9 ± 2.34, and 81.44 ± 0.74, respectively (Fig.
3). Table
2 gives the parameter values of all
the models at the various PEEP levels in the control and ova/ova mice.
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Static P-V curves of control and ova/ova mice were similar during
expiration (Fig. 4), confirmed by a lack
of significant difference between values of k from the two
groups (Table 3). (The difference between
the mean k values was 0.005; at a power level of 70% with
our sample size of 6, we would be able to detect a difference in
k between the two groups of 0.028, whereas at a power level
of 80% we could detect a difference of 0.031.) However, the area of
the static P-V curves was significantly increased in the ova/ova mice
compared with the control animals (Table 3). This matches the
observation of a difference in the inspiratory limbs of the P-V curves
from the two groups (Fig. 4).
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DISCUSSION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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We have shown that the respiratory mechanics of bronchoconstricted
mice with airway inflammation are significantly better described by a
model including a E2V2 term than by the
conventional linear equation of motion (Fig. 2). This phenomenon has
also been demonstrated in adult humans (3), neonates and
dogs (11), infants (20), and neonatal lambs
(25). The EV term, as used in the conventional equation of
motion (Eq. 1), assumes that the dynamic pressure-volume
relationship of the respiratory system is linear. Addition of a
E2V2 herein enables the model to significantly
better describe nonlinear pressure-volume behavior. Therefore, the
improvement we observed with the addition of the
E2V2 term indicates that during
bronchoconstriction the dynamic pressure-volume curve of
the inflamed ova/ova mouse lung becomes significantly curvilinear (or
nonlinear). In contrast, addition of a
R2|| term did not
result in a significant improvement in fit in either control or
inflamed mice (Fig. 1), suggesting that turbulent gas flow in the
airways was not occurring to a significant degree.
Bronchoconstriction resulted in an increase in all model parameters over their baseline values in both the control and ova/ova mice, but the increases were substantially greater in the ova/ova mice (Table 1), which is consistent with previously published data (13).
The necessity for a nonlinear volume-dependent E term in the constricted inflamed mice can potentially be explained by three mechanisms. First, the intrinsic properties of the lung parenchyma may have changed. Changes in the intrinsic properties of the parenchyma as seen in pulmonary fibrosis have been correlated with changes in the shape of the expiratory limb of the static P-V curve quantified by the shape factor (6). We did not find a difference in the values of the shape factor obtained from the expiratory limbs of the static P-V curves of the ova/ova mice compared with controls (Table 3). Therefore, we conclude that at baseline the intrinsic properties of the ova/ova mouse lung are not much different from untreated controls. We did see differences in the inspiratory limbs of the P-V curves from the two groups (Fig. 4) and in the areas circumscribed by the inspiratory and expiratory limbs (Table 3). This area is significantly increased in the ova/ova mice, yet the expiratory limbs in the two groups are virtually congruent (Fig. 4). This suggests that there was increased airway recruitment during inspiration in the ova/ova mice, not surprisingly because the inflamed epithelium of these animals would likely have encroached more than normal on the airway lumen and so predisposed them to experiencing closure at the end of the preceding expiration. An alteration in the amount or effectiveness of surfactant could also lead to enhancement of airway closure.
Second, the lung parenchyma could have stiffened during bronchoconstriction. Lung parenchyma has been shown to respond to exogenous constrictors (5, 16, 17). This response, which leads to increased tissue R, has been attributed to either contraction of parenchymal contractile elements or airway-parenchymal interdependence (1, 19). It has also been speculated that contractile elements are present in the alveoli and the alveolar ducts (12, 14) and in parenchymal blood vessels (4), although it is difficult to separate these elements experimentally from those of the airway. The difficulty of separating these two components functionally is exemplified by the fact that, in most studies, the increase in tissue resistance has been linked with increases in airway R (16, 17). It has also been suggested (2, 7) that this apparent increase in tissue resistance is the result of the emergence of heterogeneity of lung ventilation, thereby leading to overdistention of some units that is being observed as increased tissue resistance, which suggests the third explanation of our findings.
We were able to increase ENV in both control and ova/ova animals by
changing lung volume through an increase or decrease in PEEP from its
initial value of 3 cmH2O. These new values of PEEP would
have likely placed the lung on curvilinear portions of its P-V curve,
as opposed to the relatively linear portion around 3 cmH2O
(Fig. 5). P-V curves have accentuated
curvilinearity (concave upward) at low lung volumes, at which air space
closure tends to occur close to FRC (Fig. 5, PEEP = 0). At high
lung volumes, the elastic limit of the lung parenchyma is approached
(Fig. 5, PEEP = 9). Lung parenchyma contains both extensible
(elastin) and very stiff (collagen) fibers (24) and is
structured so that at low volumes the extensible elements bear most of
the stress whereas at high volumes the relatively stiff elements take
over. This results in a progressive increase in lung stiffness with increasing volume. These conclusions are supported by the values on the
nonlinear model parameters (Table 2). Specifically at PEEP 3, E2 is close to zero, corresponding to the straight
portion of the P-V curve (Fig. 5). At PEEP 0, E2 is
negative, matching the upward concavity of the lower portion of the PV
curve. At PEEP 6 and 9, E2 becomes progressively more
positive, corresponding to the downward concavity of the upper end of
the PV curve.
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The increases in ENV we observed in the bronchoconstricted ova/ova
mice were similar to those we saw under baseline conditions at
increased PEEP levels. One explanation is that the combination of
airway inflammation and bronchoconstriction changed lung volume, thereby placing the lung on a curvilinear portion of its static P-V
curve. There are two mechanisms that could be responsible. One
possibility is that lung volume could have increased as the result of
dynamic hyperinflation, as occurs when lung emptying is diminished
because of airflow limitation (23). This would have had
the effect of pushing the lung toward the curvilinear upper portion of
its P-V curve (Fig. 5). Alternatively, airway closure could have
decreased the amount of lung parenchyma available to receive the
imposed tidal volume. When mechanically ventilated, mice receive a
constant volume, so partial closure of the lung pushes the remaining
lung parenchyma closer to its elastic limit, accentuating the
curvilinearity of the dynamic P-V curve. We cannot distinguish between
these two possibilities from our present data. However, we have
evidence, as discussed (Fig. 4) above, for greater airway closure in
the ova/ova mice. Consequently, we speculate that partial closure of
the lung in the constricted ova/ova mice was the primary mechanism
accounting for the dynamic P-V nonlinearity indicated by the large
values of ENV that were obtained.
Improving our ability to measure features of the pathophysiology of asthma is crucial to the continuing investigation of the mechanisms of physiological alterations in this disease. We have shown that, by assessing the impact of adding terms to the equation of motion of the single-compartment linear model, one can infer the significance or insignificance of the physiological process described by the additional terms, in this case, airway closure leading to overdistention of the remaining patent parenchyma.
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ACKNOWLEDGEMENTS |
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This work was supported by National Institutes of Health Grants HL-56638, HL-60793, and COBRE 1 P20 RR-15557-01.
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FOOTNOTES |
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Address for reprint requests and other correspondence: S. Wagers, HSRF, Rm. 226B, 149 Beaumont Ave., Burlington, VT 05405-0075 (E-mail: ssw6609739{at}cs.com).
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.
10.1152/japplphysiol.00883.2001
Received 27 August 2001; accepted in final form 13 December 2001.
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
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C. Edibam, A. J. Rutten, D. V. Collins, and A. D. Bersten Effect of Inspiratory Flow Pattern and Inspiratory to Expiratory Ratio on Nonlinear Elastic Behavior in Patients with Acute Lung Injury Am. J. Respir. Crit. Care Med., March 1, 2003; 167(5): 702 - 707. [Abstract] [Full Text] [PDF]
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K. L. J. Evans, R. A. Bond, D. B. Corry, and F. R. Shardonofsky Frequency dependence of respiratory system mechanics during induced constriction in a murine model of asthma J Appl Physiol, January 1, 2003; 94(1): 245 - 252. [Abstract] [Full Text] [PDF]
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J. H. T. Bates and C. G. Irvin Time dependence of recruitment and derecruitment in the lung: a theoretical model J Appl Physiol, August 1, 2002; 93(2): 705 - 713. [Abstract] [Full Text] [PDF]
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