INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

THE ASSESSMENT OF LUNG FUNCTION in mice is presently of great interest because of the prominent role played by these animals in translational research into the causes and mechanisms of respiratory and allergic diseases. Unrestrained plethysmography (UP) is widely used to assess bronchial responsiveness in mice. UP involves placing an animal inside a closed chamber, within which it is free to move about, while pressure changes induced by respiration are measured within the chamber. As such, UP is easy to use and largely noninterventional, so it is well suited to the screening of large numbers of animals. The fundamental operating assumption of UP is that changes in an animal's breathing pattern occur in a predictable way during bronchoconstriction and that these changes are correlated with alterations in airway physiology. In particular, this has allowed the calculation of a dimensionless quantity known as the enhanced pause (Penh), which affords a general characterization of the breathing pattern. Changes in Penh have been used widely as a measure of bronchial responsiveness (3, 4, 13, 14, 17).

Mitzner and Tankersley (25) recently questioned the utility of Penh and pointed out that the pressures generated inside the box by a breathing animal arise from two sources: gas compression and gas conditioning. The first source is a consequence of Boyle's law: gas compression and rarefaction of thoracic gas occur with changes in intrathoracic pressure, thereby producing inspiratory and expiratory flow. Gas conditioning, on the other hand, occurs with the humidification and heating of air as it moves between the box, where it is at ambient conditions, and the lungs, where the gas is saturated at body temperature. It is not possible to distinguish between these two contributions to box pressure merely from the changes in box pressure itself. Furthermore, the relative magnitudes of these two contributions are certain to change with bronchconstriction or indeed with any kind of mechanical lung abnormality. Thus one would predict that the box pressure variations would yield direct information only about the breathing pattern, breathing frequency, and, to some degree, tidal volume (VT), but not respiratory mechanics. This makes Penh highly suspect as a means of assessing bronchial responsiveness, despite its reported correlations to invasive measures of lung mechanics (17). Indeed, Petak et al. (29) have recently reported that Penh does not behave the same as lung impedance in mice with abnormal lung function.

In this paper, we examine the relative contributions of gas compression and gas conditioning to the box pressure variations measured during UP of mice. We also develop an extended form of UP in which we eliminate those contributions to chamber pressure variations due to gas conditioning. Finally, we derive a new quantity, based on those pressure variations due only to gas compression, which specifically reflects respiratory mechanics rather than simply the pattern of breathing.

Glossary

EL	Lung elastance
f	Frequency
FRC	Functional residual capacity
G	Tissue dissipation parameter
H	Tissue stiffness parameter
Iaw	Airway inertance
IPPI	Inspiratory plethysmographic pressure integral
P0	Estimate of end-expiratory pressure
Pao(t)	Airway opening pressure
Pb(t)	Pressure of gas in the box around the animal (relative to atmospheric)
Penh	Enhanced pause
PH2O	Water vapor pressure of air inside box (mmHg)
PL(t)	Pressure of gas in the thorax (relative to atmospheric)
Raw	Airway resistance
RL	Lung resistance
t	Time
Tb	Temperature (°C) inside box
UP	Unrestrained plethysmography
Va	Volume of animal, not including thoracic gas
Vb	Volume gas inside plethysmograph chamber
VL(t)	Thoracic gas volume
VN(t)	V(t) normalized to have a peak-peak excursion of 1.0
N(t)	(t) normalized to have a peak-peak excursion of 1.0
V(t)	Gas volume, referenced to FRC, inspired into lungs
V(t)	Change in lung volume
(t)	Flow into airway
VT	Tidal volume
Zin	Input impedance

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Theory of UP

We consider an animal breathing spontaneously inside a closed chamber of volume V_b. Suppose that a volume V(t) of gas is inspired into the lungs, starting from functional residual capacity (FRC). In the absence of both gas compression and gas conditioning effects, the new lung volume would be

(1)

where VL(t) is thoracic gas volume. The volume of gas in the chamber, but outside the animal, would then decrease by the same V(t). Thus the reduction in V_b would be perfectly offset by the increase in body volume of the animal, and there would be no change in chamber pressure (P_b). However, inspired gas becomes saturated with water vapor and is heated to body temperature, causing the inspired V(t) to increase in volume by an amount

(2)

where T_b and PH₂O are the temperature and water vapor pressure, respectively, inside the chamber, V is change in lung volume, and we assume that 310 K is body temperature for the mouse and 47 mmHg is the vapor pressure of water in saturated air at body temperature. Our expression for total lung volume thus becomes

(3)

The increase in lung volume [V(t) + V(t)] is now greater than the loss in chamber gas volume [V(t)], so the remaining chamber gas becomes compressed by an amount V(t), and its pressure rises accordingly.

However, when gas flow () is nonzero, VL(t) is further changed as it is compressed and decompressed in response to changes in alveolar pressure according to Boyle's law. The alveolar pressure is

(4)

where PL(t) is gas pressure in the thorax and Raw is airway resistance, so the lung volume in Eq. 3 now becomes

(5)

The difference between the VL(t) in Eq. 5 and that which would have occurred if neither gas conditioning nor compression had taken place (Eq. 1) equals the amount by which the gas inside the box, but outside the animal, becomes compressed. This difference is

(6)

The V_b around the animal, before compression or decompression of thoracic gas, is V_b  V_a  FRC  V(t), where V_a is the volume of the animal's body, excluding the volume of gas in the lungs. This volume of gas becomes compressed by the amount given in Eq. 6, so, invoking Boyle's law and using Eqs. 2 and 6, the box pressure is

(7)

P_b(t) thus consists of two components: the first term in Eq. 7 is in phase with V(t) and describes changes in P_b(t) due to gas conditioning, whereas the second term is in phase with (t) and is the change in P_b(t) due to Boyle's law.

It is possible, in principle, to eliminate the effects due to gas conditioning by heating and humidifying the air in the box (25). Equation 7 then reduces to

(8)

If we make the additional simplifying assumptions that VT is small compared with FRC, that FRC is small compared with V_b, that PL is small compared with atmospheric pressure, and that V_a is small compared with V_b, then P_b(t) further reduces to

(9)

Now, the only quantity that pertains directly to lung mechanics in Eq. 9 is Raw. Measurements of P_b(t) would thus be expected to give a useful indication of changes in lung mechanics (i.e., Raw) during, say, a bronchial challenge test if the remaining quantities in Eq. 9 do not change significantly as the test proceeds. That this would happen is highly unlikely, because breathing pattern, and hence (t), will inevitably change as the airways become constricted. Indeed, it has been shown that the ventilatory response to bronchial irritants is variable among different strains of mice (31). However, if we integrate P_b(t) over the course of an inspiration, then

(10)

where TI is inspiratory time. We denote this quantity the inspiratory plethysmographic pressure integral (IPPI). In the experimental part of our study described below, we used IPPI to validate our theory of UP. Specifically, we determined IPPI from the lefthand side of Eq. 10 by measuring P_b(t) in spontaneously breathing mice. We then compared it to IPPI calculated from the righthand side of Eq. 10 using independent measurements of VT, Raw, and FRC.

Experimental

Initial Study

Experimental. We studied female mice (26.6-30.4 g) of the A/J strain (n = 4), which is known to be intrinsically hyperresponsive (6, 22, 23). The mice were anesthetized with an intraperitoneal injection of 70 mg/ml pentobarbital (Nembutal, Abbott, North Chicago, IL). After tracheostomy and tracheal cannulation with a 20-gauge Luer stub adaptor (Intramedic, Franklin Lakes, NJ), the mice were placed in a 300-ml body box (Buxco, Sharon, CT). P_b was measured (MP45, Validyne, Northridge, CA) with respect to a reference chamber ported to atmosphere. The box had a leak to atmosphere, giving it a time constant of 1.76 s. The frequency response of P_b to changes in V_b was assessed between 0.5 and 20 Hz with a piston pump (flexiVent, SCIREQ, Montreal, QC) and found to be flat to within 6% over this frequency range. was measured at the tracheal cannula using a custom-designed pneumotachograph similar to that described by Mortola and Noworaj (26). The pneumotachograph had a constant resistance of 0.060 ± 0.006 cmH₂O · s · ml¹ up to a flow of 4 ml/s. Esophageal pressure (Pes) was measured with a blood pressure transducer (Cobe, Lakewood, CO) connected to a 15-cm length of PE-50 saline-filled polyethylene tubing (Intramedic, Parsippany, NJ) positioned in the esophagus via the mouth so as to give maximum signal excursion during breathing. PH₂O was measured with a humidity sensor (Humidal, Colton, CA), and T_b was measured with a thermocouple (Omega, Stamford, CT).

Data analysis. The theory outlined above predicts that, when a mouse breathes spontaneously inside a box at room temperature, there will be two contributions to the resulting P_b(t): one due to gas conditioning and one due to gas compression. Equation 7 shows that the first contribution will be in phase with V(t), whereas the second will be in phase with (t). Because we measured (t) directly at the tracheal opening, and by numerical integration obtained V(t), we were able to determine these phase relationships. We made this determination in a 10-s epoch of regular breathing data at each methacholine dose, as follows. We scaled the and V signals from each epoch so that each signal had a peak-peak amplitude of unity, yielding the normalized signals _N and V_N, respectively. We then determined the parameters A, B, and C of the regression equation

(11)

Equation 11 is an empirical description of P_b(t) in terms of a component proportional to V_N and a component proportional to _N. The parameters A and B in Eq. 11 thus represent the fractions of the respiratory variations in P_b(t) that can be attributed to _N and V_N, respectively. The parameter C takes into account the mean value of P_b(t). Consequently, the quantity A/(A + B), which we call the flow phase fraction of P_b(t), is a measure of the fractional contribution of _N to the variations in P_b(t). If _N and V_N were perfect sine waves, the flow phase fraction would be an exact estimate of the fraction of P_b in phase with _N. This was not the case because the spontaneous breathing wave forms of _N and V_N were not sinusoidal. In some cases, the maximum in the _N power spectrum was at the fundamental, whereas in others the first or second harmonics were maximal (particularly when the breathing rate was slow). Therefore, the quantity A/(A + B) only gives an approximation to the fraction of the respiratory variations in P_b attributable to _N.

(12)

Validation Study

Experimental. We studied BALB/c female mice (17-20 g, n = 4) obtained from Charles River. The animals were acclimatized in our animal facility for at least 1 wk before the experiments. The mice were anesthetized with intraperitoneal pentobarbital sodium (90 mg/kg), and the trachea was dissected free of surrounding tissue and cannulated with a 18-gauge cannula. The mouse was then installed in a custom-designed chamber (Fig. 1), and the tracheal cannula was connected to a port through one of the chamber walls.

View larger version (33K): [in this window] [in a new window]   Fig. 1.   The plethysmographic chamber used to measure input impedance, functional residual capacity, and unrestrained plethysmography. The chamber itself was essentially leak free (time constant >500 s). Chamber pressure was measured with a differential pressure transducer that was referenced to a second chamber with a volume of 1 liter and a slow leak (time constant ~6 s) to atmosphere.

1

1

1

Data analysis. We determined Raw from the data collected when the flexiVent was used to apply volume oscillations to the lungs, as follows. Lung input impedance (Zin) was calculated as described previously (15, 19). This included employing a dynamic calibration procedure to account for the physical properties of the flexiVent itself (15, 19). We interpreted our measurements of Zin in terms of the following model (18)

(13)

where Raw is a frequency-independent Newtonian resistance reflecting that of the conducting airways, Iaw is airway gas inertance, G characterizes tissue damping, H characterizes tissue stiffness, i is the imaginary unit,  links G and H, and f is frequency. We have previously demonstrated that Raw obtained from the above model is a good approximation to Raw in the normal closed chest rat (19) and the open chest mouse (32). We made two to four separate determinations of Raw in each mouse and took the average for use in the calculation of IPPI.

(14)

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Initial Study

View larger version (11K): [in this window] [in a new window]   Fig. 2.   Flow phase fraction vs. lung resistance (RL) for the 4 mice (indicated by the different symbols) from the initial study. The range of RL values was achieved by subjecting the mice to various concentrations of aerosolized methacholine.

Validation Study

The thin lines in Fig. 3 show typical records of five consecutive breaths of P_b(t) and (t) obtained from one of the mice during spontaneous rebreathing from within the chamber. The temperature of the air in the box was 23°C, and its relative humidity was 29%. Both respiratory and cardiogenic variations are clearly visible in both signals. The thick lines in Fig. 3 show five breaths from the same mouse when the gas in the box was heated to 37°C and humidified to a relative humidity of 85%. The breathing pattern, as evidenced by (t), is about the same as before, but the excursions in P_b(t) are markedly diminished.

View larger version (26K): [in this window] [in a new window]   Fig. 3.   Records of gas flow (top) and gas box pressure (Pb; bottom) made with a mouse breathing spontaneously while enclosed in the chamber, with the gas inside the chamber at 23°C and relative humidity 29% (thin lines), and after the chamber gas was heated to 37°C and humidified to 85% (thick lines). Inspiratory flow is positive.

Figure 4 shows the ensemble average of P_b(t) plotted against the ensemble average of (t) for each of the four mice when they breathed spontaneously through the low-resistance conduit with the gas in the chamber at a temperature of 23-25°C and a relative humidity of 27-34%. The signals are almost completely out of phase in this situation, so P_b(t) is in phase with V(t), which is consistent with the phenomenon of gas conditioning. When the gas in the box was conditioned to a temperature of 35-39°C and a relative humidity of 85-93%, the excursions in P_b(t) were greatly reduced and much more in phase with flow (Fig. 4). When the animals breathed conditioned gas through the medium-resistance and high-resistance conduits, the swings in P_b(t) became appreciable again and were clearly in phase with (t) (Fig. 5), consistent with compression and decompression of thoracic gas.

View larger version (16K): [in this window] [in a new window]   Fig. 4.   Ensemble average of Pb(t) (where t is time) vs. ensemble average of flow into airway [(t)] for each of the 4 mice in the validation study. The mice breathed spontaneously through the low-resistance conduit with the gas in the chamber at a temperature of 23-25°C and a relative humidity of 27-34% (thin lines) and with the gas in the box conditioned to a temperature of 35-39°C and a relative humidity of 85-93% (thick lines). Inspiratory flow is positive.

View larger version (13K): [in this window] [in a new window]   Fig. 5.   Ensemble average of Pb(t) vs. ensemble average of (t) for each of the 4 mice in the validation study. The mice breathed spontaneously through the medium-resistance conduit (thick lines) and the high-resistance conduit (thin lines) with the gas in the chamber conditioned to a temperature of 35-39°C and a relative humidity of 85-93%.

Finally, we used the measured values of Raw, VT, and FRC to calculate IPPI, according to Eq. 10, and compared the results to IPPI determined from the integrated ensemble-averaged P_b(t) signal. This calculation was performed in each mouse by using four to six different 6-s data segments obtained with each of the three resistive conduits, when the gas in the box was heated to body temperature and humidified. Figure 6 shows an identity plot of the corresponding estimates of IPPI.

View larger version (10K): [in this window] [in a new window]   Fig. 6.   Inspiratory plethysmographic pressure integral (IPPI) determined by integrating the ensemble-averaged Pb(t) signal (horizontal axis) vs. its determination by the formula given in Eq. 10 (vertical axis). The different symbols represent the 4 mice in the validation study. Raw, airway resistance; VL, lung volume; VT, tidal volume; Vb, gas volume inside box.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

UP was first investigated in 1868 by Bert (2) and then further developed in 1955 by Drorbaugh and Fenn (10) as a method for assessing lung function in infants. It was pursued further in a small number of subsequent studies (11, 12, 21, 28, 30) but never gained much of a following until recently. Now the quantity Penh, derived from UP, is being widely used as a means for studying bronchial responsiveness in various animals models of lung disease (1, 5, 7, 13, 14, 16, 17, 27). Although some studies have shown a good correlation between Penh and other measures of lung function (8, 13, 17), others have shown that Penh does not correlate well with morphometric changes in mice (24). Some degree of correlation between Penh and bronchoconstriction is expected, because anything that affects lung mechanics is likely to also affect the breathing pattern; VT is probably just as good an index to follow as Penh in this regard (25). However, just because two quantities are correlated does not mean that one can be used as a surrogate for the other. Also, Petak et al. (29) have just shown that, under some circumstances, Penh may behave very differently from more direct measures of lung mechanics. Thus, as Drazen et al. (9) point out, changes in Penh need to be confirmed with an independent method of assessing airway obstruction based on appropriate physical principles.

Given the present interest in using Penh to assess lung function in mice, we felt that a detailed study of the physics and physiology behind UP and its relation to lung mechanics was warranted. We began our investigations with an initial study aimed at determining how P_b relates to and V in a relevant experimental situation. We chose to examine the hyperresponsive A/J strain of mouse challenged with methacholine because of the substantial changes in lung mechanics induced. Each mouse produced a strong, positive correlation between the flow phase fraction and RL (Fig. 1), showing that the proportions of P_b in phase with changed substantially as the animals became bronchoconstricted. By the theory encapsulated in Eq. 7, this means that the relative contributions to P_b of gas conditioning and gas compression also changed. This is not surprising for the following reasons. Under baseline conditions, we would expect most of the respiratory fluctuations in P_b to be due to gas conditioning, because only small changes in alveolar pressure are necessary to generate flow along unconstricted airways. However, when the airways become constricted, greater changes in alveolar pressure, and hence greater degrees of gas compression and decompression, are required to generate respiratory flows. This causes the proportional contribution from gas compression to increase progressively as an animal becomes constricted, as illustrated by the results in Fig. 2. An increase in breathing frequency would also increase the flow phase fraction. However, in the mice we studied, breathing frequency did not increase with methacholine challenge and by the highest doses had even decreased considerably. Thus the increases in flow phase fraction with RL that we see in Fig. 2 likely underestimate the increased contributions to P_b from gas compression.

The results of our initial study lead us to follow up with a validation study in order to gain a deeper understanding of the physics underlying UP and to test our theory outlined above in METHODS. As in the initial study, the follow-up study showed that, when a normal mouse breathes air at room temperature and humidity, the respiratory fluctuations in P_b(t) are dominated by warming and humidification of the gas as it enters the lungs (Fig. 3). About two-thirds of these fluctuations in P_b(t) disappeared when the gas in the chamber was preconditioned to be at body temperature and humidity (Figs. 3 and 4). The validation study also confirmed that the fluctuations that remain after preconditioning are due to gas compression and decompression in the lung, because they were amplified by having the animal breathe through an increased external resistor (Fig. 5).

The quantitative validation of our theory of UP is demonstrated by the assessment of IPPI. When IPPI was calculated by integrating P_b(t) over inspiration and compared with its theoretical equivalent given in Eq. 10, a tight relationship was obtained (Fig. 6). Of course, equating IPPI to the righthand side of Eq. 10 assumes that the values of Raw and FRC, measured through independent maneuvers, still pertained during the period of spontaneous breathing from which VT and IPPI were calculated. We have no reason to suspect that Raw should have changed throughout the course of the experiment, because the values of Raw used in Eq. 10 were dominated by the added conduit resistances, which were fixed. Furthermore, FRC was determined several times in each mouse used in the validation study, both with and without the additional conduit resistances, and the variations found were neither systematic nor large (±10%). We, therefore, conclude that IPPI accurately embodies the physical processes responsible for the respiratory fluctuations in P_b(t) when an animal breaths spontaneously inside a closed chamber.

Only those changes in P_b due to gas compression have direct relevance to the mechanical properties of the lungs. As Raw increases, these changes are combined in an indeterminate and variable way with the changes in P_b(t) due to gas conditioning, which are not relevant to lung mechanics. Such findings have major significance for the use of UP, as it is presently practiced in mice, by delineating the problems of assuming that Penh is a valid measure of lung function. Not only is Penh limited to be a reflection of the pattern of breathing, but also the signal on which it is based is a variable composite of two phenomena, only one of which is relevant to respiratory mechanics. Whereas an animal may change its breathing pattern as it becomes bronchoconstricted, it seems unreasonable to expect that the nature and extent of these changes should precisely mirror the alterations in lung mechanics. Therefore, whereas a change in Penh may be useful as a general indicator that some reaction has taken place in an animal, it seems unlikely to be a meaningful measure of changes in the mechanical properties of the lung.

We have shown that UP can provide accurate reflections of mechanical lung function, provided gas conditioning effects are eliminated and both VT and FRC are known. Only if these conditions prevail does a change in IPPI reflect a change solely in Raw (Eq. 10). Preconditioning the chamber air, as we have done, is a practical solution to eliminating the effects of heating and humidification on P_b(t), even if animals have difficulty maintaining thermal equilibrium in a heated and humidified box for long periods of time. However, monitoring VT and FRC was only possible in our experiments because the animals were anesthetized and tracheostomized. Unfortunately, this does not make this version of UP practical, because the major virtue of UP is that it can be undertaken on conscious, unrestrained animals. Following changes in VT and FRC accurately under such conditions is problematic yet is required because both quantities are subject to change as the airways constrict. In the validation experiments, we found that altering the conduit resistance that the mice breathed through had very little effect on FRC. However, using the same technique as described above for the validation study, we also measured FRC in the mice in the initial study that was challenged with methacholine. FRC in these animals increased progressively with methacholine dose, reaching >50% above baseline by the time the methacholine aerosol had reached a concentration of 12.5 mg/ml. This indicates that the lungs of these animals experienced a substantial amount of gas trapping. We might expect changes in FRC to be even more marked in intact, conscious animals because they breathe significantly more quickly than anesthetized animals (33) and so would be expected to experience a greater degree of dynamic hyperinflation. Also, conscious animals have the potential for glottic regulation of end-expiratory lung volume. Equation 7 shows that a change in FRC produces a proportional change in P_b(t). This leads to a proportional change in Penh, independent of any changes in Raw, which further argues against any usefulness of Penh as a meaningful standalone measure of bronchial responsiveness.

The animals examined in the follow-up study also changed their VT a great deal as external resistance was added to their breathing circuit. With the low-resistance conduit, mean VT for all determinations in all animals was 0.064 ml, with a standard deviation of 0.024 ml. With the medium-resistance conduit, VT increased substantially to 0.164 ml, perhaps due to the respiratory stimulation of the added resistance. The effect was quite reproducible, with the standard deviation of VT being still small at 0.032 ml. When the high-resistance conduit was used, VT decreased somewhat to 0.147 ml, but the standard deviation was markedly increased at 0.80 ml, possible reflecting the difficulty that the animals experienced in breathing through such a severe constriction. These results thus show that constriction in spontaneously breathing mice may cause marked changes in the breathing pattern. Furthermore, our animals were anesthetized, so their changes in VT may have been less marked than those that would occur in conscious animals. Interestingly, the changes in breathing pattern that can occur with increased respiratory rate have also been applied to the diagnosis of lung disease in humans (20). In any case, it is clear that much of the change in P_b(t), and hence in Penh, that occurs during bronchoconstriction may be due to a change in VT. This has nothing to do with any changes in lung mechanics. It must also be noted that the values of VT obtained with the medium- and high-resistance conduits were not particularly small compared with FRC (Table 1), which is one of the conditions on which Eq. 10 is based. Equation 8 shows that a large VT should increase P_b(t), and hence increase IPPI, over that calculated through Eq. 10. We do not see such an effect in Fig. 6, which suggests that either it was small or else it was canceled out by some other systematic effect.

In conclusion, we have shown that P_b(t) obtained during UP is determined in large part by gas conditioning when normal mice breathe spontaneously inside a closed chamber in which the air is at room temperature and humidity. When the air in the chamber is preconditioned to body temperature and humidity, the changes in P_b(t) are greatly reduced. The remaining changes are due to gas compression and decompression within the lung and can be amplified by having the animals breathe through increased resistances. The gas compression and decompression effect is also increased when mice are bronchoconstricted with methacholine. When the chamber gas is appropriately conditioned, we have shown that IPPI, the time integral of P_b(t) over inspiration, is accurately predicted by a term containing Raw, FRC, and VT as factors. This validates our quantitative theory of UP and shows that we have identified the important parameters and variables that determine P_b(t). Our study also shows that, unless these various quantities can be either controlled or measured, UP is not likely to be of practical use as a means of obtaining accurate measures of mechanical lung function. This applies in particular to Penh, which we conclude should not be used as a means of assessing bronchial responsiveness.