## Abstract

An acoustic whole body plethysmograph was developed to estimate specific airway resistance (sRaw) in unrestrained mice. The plethysmograph uses acoustic principles to measure the thoracic breathing pattern and simultaneously measures the airflow entering and/or leaving the plethysmograph. Similarly to traditional methods utilizing a double-chamber plethysmograph, these measurements were combined to estimate sRaw. To evaluate the new system, we placed six conscious A/J mice individually in a whole body plethysmograph (Buxco System) for a 2-min exposure to aerosolized methacholine chloride dissolved in saline (0, 5, 10, and 20 mg/ml), which is known to increase sRaw in mice. Three minutes after exposure, the mice were transferred to the acoustic plethysmograph for 2 min for data collection. The mean baseline value of sRaw was 0.93 ± 0.10 cmH_{2}O·s. A dose-dependent increase in sRaw was shown, with an approximate tripling of sRaw at the highest dose. These results demonstrate the ability of the system to estimate sRaw based on plethysmograph airflow and acoustic amplitude.

- Helmholtz resonator
- unrestrained plethysmograph
- whole body plethysmograph

traditionally, the double-chamber plethysmograph has been used to estimate specific airway resistance (sRaw) (15) from the phase shift between flows measured at the thorax and at the nasal passage. In recent years, there has been a growing interest in measuring sRaw using the unrestrained (or single chamber) whole body plethysmograph (WBP). This type of plethysmograph is easy to use, allows repeated measurements in the same subject, and produces little stress in the animal. The disadvantage is that the single available pressure measurement is influenced by the mechanical properties of the airways and the shape of the breathing pattern. Isolating the component related to airway resistance is difficult, perhaps impossible, without a second measurement.

The most popular parameter derived using the single-chamber plethysmograph is an empirical index called Penh (9) that was said to reflect changes in airway reactivity. However, a number of articles have questioned the relationship between Penh and the mechanical properties of the lung (1, 3, 6, 14, 18, 22). Recently, other parameters have been developed that relate more closely to lung mechanics. Lundblad et al. (13) showed that the pressure measured in the unrestrained plethysmograph could be written as a function of airway resistance, functional residual capacity, and tidal volume when the chamber air is conditioned to body temperature and humidity. Lai-Fook and Lai (10) developed an estimate of airway resistance based on the area under the plethysmograph pressure curve, functional residual capacity, and tidal volume. As both these groups have pointed out, these methods may reflect changes in resistance, although it is necessary to either assume that the thoracic breathing pattern is not altered during or between measurements or obtain some measure of the thoracic breathing pattern. Such a system for obtaining this extra measure was recently reported by Bates et al. (2), who described an unrestrained video plethysmograph.

Similarly, we present a novel acoustic whole body plethysmograph (AWBP) capable of measuring sRaw. The plethysmograph not only acts as a traditional WBP but also uses acoustic principles to measure the thoracic breathing pattern (19). sRaw is then based on the phase shift between these two measurements, much like methods utilizing the double-chamber plethysmograph.

## MATERIALS AND METHODS

### System

This system is a modification of the previously described plethysmograph (19), which uses acoustics to measure the thoracic breathing pattern. Briefly, the plethysmograph operates as a resonating cavity. The amplitude of the acoustic pressure inside the cavity is determined by the cavity geometry. The volume of air surrounding a respiring mouse changes by the change in size of the mouse as it breathes. When the system is excited near the resonant frequency, the acoustic pressure amplitude in the plethysmograph is modulated in direct proportion to the change in volume of the mouse.

In the previously described system (19), a low-resistance nozzle was used to maximize the sensitivity of the system to changes in mouse volume. In that system, the nozzle resistance was too low to use as a pneumotachograph to measure the traditional WBP box flow. The current implementation is shown in Fig. 1. The speaker produces a constant-frequency (∼300 Hz) acoustic signal. The micrometer is used to adjust the volume surrounding the mouse so that the chamber is in a near resonant condition and changes in mouse volume produce linear changes in the acoustic pressure amplitude (see Ref. 19). A screen placed across the outside end of the plethysmograph nozzle acts as a pneumotachograph to enable measurement of box flow. The pressure drop across the screen was measured with a differential pressure transducer (Setra Systems, model 239). So the modified plethysmograph provides two measurements. A signal proportional to change in mouse volume is measured with a microphone from the high-frequency (relative to breathing frequency), low-amplitude (acoustic) pressure changes. The traditional WBP signal is measured from the low-frequency change in plethysmograph pressure, which is proportional to box flow. The restrainer keeps the mouse from occluding the nozzle, which would affect both measurements.

Although the acoustic plethysmograph is designed to be a second-order system having a resonant frequency near 300 Hz, Sinnett et al. (21) have shown that these types of flow plethysmographs act as first-order systems at low frequencies. Furthermore, they have shown that a flow plethysmograph with a first-order time constant of 1.5 ms or less has a fast enough response for accurate measurement of forced vital capacity maneuvers in mice. Given the AWBP volume (∼75 ml) and screen resistance (0.00224 cmH_{2}O·s·ml^{−1}), the first-order time constant is ∼0.168 ms in isothermal conditions and 0.120 ms in adiabatic conditions. Since we are inferring flow from pressure at low frequencies (mouse breathing frequencies, <10 Hz), whether the system operates in either an adiabatic or isothermal mode (or changes between the two) has little effect on the box flow measurement.

### Model

sRaw is derived from a model (15) of the respiratory system as shown in Fig. 2*A*. The current source, *I*_{t}, represents the thoracic flow produced by the animal. *Z*_{t} represents the impedance of the lung tissues, *I*_{a} represents flow in the airways, *R*_{a} represents the flow resistance of the airways, and *C*_{g} represents the compressibility of the gas in the lung and airways. P_{t} and P_{ao} represent the pressures (relative to atmospheric pressure) produced at the thorax and airway opening, respectively. P_{alv} is alveolar pressure, and P_{atm} is atmospheric pressure. Note that the direction of the currents indicated in Fig. 2 are for expiration and are reversed during inspiration.

When an animal respires air at room conditions, the gas is warmed and humidified on inspiration, and the reverse (approximately) takes place on expiration. Therefore, there is an effective change in volume flow due to this thermohygrometric effect. This thermohygrometric “flow” (*I*_{th}) is in phase with *I*_{a} and can be modeled as (1) where *G* (5) is given as (2) where the subscripts c and a denote conditions of chamber and alveolar gas, respectively, and *T* and P are absolute temperature and pressure, respectively. Incorporating this effect results in the model shown in Fig. 2*B*.

It has been suggested that differences between inspiratory and expiratory conditions would necessitate separate calculations of *G* (7, 12, 14). Consider an animal placed inside a WBP. During inspiration, the gas is warmed from chamber temperature to body temperature and humidified from chamber humidity to saturation. In humans, expiratory gas exits at nasal conditions of ∼32°C and saturated with water vapor (7). Whereas the human respiratory tract is not a very efficient heat exchanger, that of the small rodent is much more efficient. Schmid (20) studied the exit temperature of respired air for many small mammals, including several species of mouse, and found the exit temperature to be ∼1°C above ambient.

Consider a mouse inspiring air at 50% relative humidity and 22°C, with expiratory conditions of 100% relative humidity and 23°C. For this case, the inspiratory value of *G* is 0.0956 and the expiratory value is 0.0816, a difference of ∼17%. For an animal placed in a chamber with an open nozzle, the relative humidity in the chamber will increase with each breath until the moisture added per breath is equal to the moisture leaving the chamber via diffusion. Therefore, the inspiratory *G* will move toward the expiratory *G* the longer the animal stays in the chamber, so there is a slight variation in *G* from inspiration to expiration during tidal breathing. Also, small baseline changes in *G* might occur if the efficiency of heating and cooling is affected by changes in respiratory rate, depth of breathing, and core temperature, among others. The model used in this research considers a fixed *G* estimated as the average of the inspiratory *G* calculated at room conditions and the expiratory *G* calculated at 100% relative humidity and 1°C above room temperature. Room temperature and relative humidity during this research were 22.7°C and 47%, respectively. Using an assumed body temperature of 37°C resulted in an average *G* of 0.084.

Now consider an animal placed in a double-chamber plethysmograph (DCP), which is the traditional system used to estimate sRaw. This system uses a neck seal to enable simultaneous measurement of nasal flow and thoracic flow. Figure 2*C* shows the electric circuit analog corresponding to the DCP. *Z*_{bc} represents the impedance of the body chamber, and *Z*_{hc} represents the impedance of the head chamber. This system restrains the animal but allows independent measurements of two flows (or pressures) from which sRaw can be estimated.

When an animal is placed in an unrestrained WBP, there is an interaction between the thorax and nasal flows (i.e., no neck seal). Figure 2*D* shows the electric circuit analog corresponding to the WBP. In this case, *Z*_{b} represents the box impedance. Without modification, this circuit can be redrawn as shown in Fig. 3. This represents the low-frequency bulk flow model of the WBP.

#### Mathematical description.

An expression for sRaw can be derived based on the model shown in Fig. 3. Summing the currents in the lung, (3) where *I*_{c}(*t*) is the current into the capacitor, *C*_{g}, such that (4) Alveolar pressure is (5) Since the box pressure, P_{b}, is extremely small compared with alveolar pressure, the box pressure term can be neglected. Substituting into the preceding equation gives (6) Now substituting this expression into *Eq. 3* and solving for thoracic flow gives (7) Summing the currents at the airway opening, (8) Solving for airway flow gives (9) Substituting into *Eq. 7* and rearranging gives (10) Taking the Laplace transform, (11) (12) The transfer function from thoracic flow to box flow, *I*_{b}, is (13) The transfer function from thoracic volume, V_{t}, to box volume, V_{b}, is then equal to the transfer function from thoracic flow to box flow: (14) Since the derivative is inherently noisy, it is more convenient to integrate box flow and use volume signals than to take the derivative of thoracic volume and use flow signals. Substituting *s* = *j*ω: (15) (16) (17) so the phase angle, θ, between thoracic volume and box volume is given as (18) Rearranging gives (19) Solving for *R*_{a}*C*_{g}, (20) Only the smaller root of the *Eq. 20* yields physiologically relevant values (see Appendix): (21) Alternately, dropping the higher order term of *Eq. 19* provides reasonable accuracy. This results in the following solution: (22) Where frequency, *f*, is *f* = ω/(2π). Results presented in this research were calculated using *Eq. 21*.

#### Specific airway resistance.

Specific airway resistance is defined as (23) where TGV is thoracic gas volume. Gas compliance in the lung (assuming isothermal conditions) can be written as (24) By substitution of *Eq. 24* into *Eq. 23*, it is seen that sRaw is the time constant *R*_{a}*C*_{g} multiplied by pressure P_{atm} − P: (25)

In this research, the measurements were made over a relatively short span of time. Therefore, the pressure term can be considered a constant, and *R*_{a}*C*_{g} is then a direct measure of sRaw. In this study, estimates of *R*_{a}*C*_{g} have units given in milliseconds. However, if sRaw is estimated based on P_{atm} − P≈ 1,000 cmH_{2}O, then from *Eq. 25*, (26) (27) (28) Under these conditions, sRaw in units of cmH_{2}O·s will have the same numerical value as *R*_{a}*C*_{g} in units of milliseconds.

#### Experimental design.

Six 21.0 (SD 1.7)-g, specific pathogen-free female A/J mice (Jackson Laboratory) were housed in an American Association for Accreditation of Laboratory Animal Care-accredited animal facility at 23°C and 50% humidity with a 12:12-h light-dark cycle and were provided standard laboratory mouse chow and tap water ad libitum. Each mouse was placed in a chamber for a 2-min exposure to aerosolized methacholine chloride dissolved in saline (0, 5, 10, and 20 mg/ml). Three minutes after exposure, the mice were transferred to the acoustic plethysmograph for 2 min, where box flow and thoracic volume were measured at a sampling rate of 2,000 Hz. Since all six mice were tested at each concentration before increase to the next concentration of methacholine, the time between doses for each mouse was ∼45 min. All animal procedures were performed following an animal protocol approved by the National Institute for Occupational Safety and Health Institutional Animal Care and Use Committee.

#### Statistics.

All experimental data (means ± SE) were analyzed using one-way ANOVA followed by post hoc analysis using Fisher's protected least significant difference. Log transformation was applied to equalize variance between doses. Dose-response trends were determined using regression analysis. Differences were considered significant at *P* < 0.05.

### Signal Processing

The electromechanical delay between the pressure transducer and the microphone was assessed by lightly tapping the nozzle opening with no animal in the chamber. This produced a pressure drop across the screen while simultaneously interrupting the acoustic signal measured by the microphone. These data were used to calculate the phase shift produced by the electromechanical properties of the transducers, which was subsequently subtracted from the phase shift measured with the animal present in the plethysmograph.

The animal data were processed as follows. A 15-Hz low-pass filter was applied to the data for noise reduction. Box flow was integrated to obtain box volume. The data were broken into 6-s segments with a 50% overlap; that is, the first segment is from *t* = 0 s to *t* = 6 s, the second segment from *t* = 3 s to *t* = 9 s, and so on. An estimate of the transfer function was computed using Welch's averaged periodogram method (Matlab “tfe” function) with a 4,000-point transform size, a 4,000-point window, and an overlap of 2,000 samples. By using these same parameters, an estimate of the coherence was determined for each segment.

For each segment, the angle of the transfer function was determined at the breathing frequency by linear interpolation from the estimate above. This angle and breathing frequency were used with *Eq. 21* to calculate an estimate of *R*_{a}*C*_{g} for each segment. Similarly, coherence for each segment was determined at the breathing frequency. The mean *R*_{a}*C*_{g} value was found by averaging the estimates for all the segments whose coherence was ≥0.9.

## RESULT

The results of the methacholine aerosol exposure are shown in Fig. 4. At doses of 5 and 10 mg/ml, five of the six mice had elevated *R*_{a}*C*_{g} compared with baseline (Fig. 4*A*). At the highest methacholine dose (20 mg/ml), each mouse had an increased *R*_{a}*C*_{g} compared with saline. The mean *R*_{a}*C*_{g} dose-response curve is shown in Fig. 4*B*. The mean increase from baseline for doses of 5 and 10 mg/ml was 57 and 61%, respectively. At the 20 mg/ml dose, the mean increase was >227%, or a little more than a tripling of *R*_{a}*C*_{g}.

The airway resistance-compliance values were calculated based on the phase shift and the breathing frequency. The results for these two component measurements are shown in Fig. 4, *C–F*. In general, there was a dose-dependent increase in phase shift accompanied by a decrease in breathing frequency at the highest dose.

## DISCUSSION

The signal measured from a spontaneously respiring animal in the traditional WBP is generated from the thoracic flow of the animal, filtered by the mechanical properties of the airways. Therefore, changes in this signal can result from either changes in the thoracic flow pattern or changes in the respiratory “filter.” The drawback of past methods utilizing the unrestrained plethysmograph is that to relate changes in the filter (i.e., sRaw) based solely on changes in the WBP signal, it must be assumed that the thoracic flow pattern is unchanged. The plethysmograph presented in this research overcame this issue by allowing measurement of the thoracic flow signal in addition to the WBP signal. This allows assessment of *R*_{a}*C*_{g} even in cases where the breathing pattern of the animal is significantly affected.

The baseline sRaw value of 0.93 ± 0.10 cmH_{2}O·s obtained in this research is consistent with previously reported baseline values in A/J mice. Lofgren et al. (11) found a baseline sRaw value of 0.676 ± 0.027 cmH_{2}O·s in A/J mice using a restrained WBP. However, in a direct comparison of systems using BALB/c mice, they found that sRaw determined in their restrained WBP was about one-third the value they measured using a DCP. Delorme and Moss (4) measured sRaw in A/J mice using a DCP. In two trials performed a minimum of 2 days apart, they found values of 1.68 ± 0.06 and 1.49 ± 0.14 cmH_{2}O·s. In addition, our baseline results are nearly identical to those of Flandre et al. (8) for BALB/c and C57BL/6 mice, measured using a DCP.

Direct comparison of dose-response curves is inexact, since the actual delivered dose is affected by the specific nebulizer, airflow, tubing arrangement, and such. However, there is general agreement in our results and those of Lofgren et al. (11), particularly at the highest dose used, where sRaw was elevated and the breathing frequency was depressed.

The modified acoustic plethysmograph does present some technical difficulties that can be addressed in future revisions. The addition of a screen to the plethysmograph nozzle adds significant acoustic resistance to the system. This in turn reduces volume sensitivity. This reduction in sensitivity complicates calibration of the volume signal and allows significant noise degradation of the volume measurement. On the other hand, a higher screen resistance increases the sensitivity and noise immunity of box pressure measurements. The ideal solution (and future improvement) would be a device for measuring nozzle flow that has little flow resistance.

Although a low-resistance flowmeter would be ideal, the method presented in this research allows us to overcome the shortcomings of measuring flow with a screen pneumotach. We have presented a method of estimating *R*_{a}*C*_{g} that is dependent only on the phase of the transfer function. As described in the Appendix, using only phase does limit the range of measurable *R*_{a}*C*_{g}. The ability to use magnitude and phase information over a range of frequencies is desirable and would likely remove these limitations. However, the limits of *R*_{a}*C*_{g} using phase are high enough that they are likely irrelevant for assessing the pulmonary response of the mouse in most cases. Because we are only using phase, it is not necessary to calibrate the thoracic volume or the box volume signal, since the magnitude is unimportant. Furthermore, even in the presence of significant noise on the thoracic volume signal, we are able to measure the increase in sRaw due to methacholine exposure using only the phase information.

Although the results are preliminary in nature, we have described a modified acoustic plethysmograph that allows measurement of both the traditional unrestrained plethysmograph flow signal and the thoracic volume signal in mice. Furthermore, a method of using the phase shift between these signals to evaluate *R*_{a}*C*_{g} has been provided. This system provides an efficient and accurate method of assessing specific airway resistance of mice in an unrestrained plethysmograph.

## APPENDIX

To infer sRaw from the phase shift of the transfer function given in *Eq. 17*, *Eq. 19* must be solved for *R*_{a}*C*_{g}. Since *Eq. 19* is quadratic in *R*_{a}*C*_{g}, the phase angle, θ, initially increases with an increase in *R*_{a}*C*_{g} but eventually reaches a peak and then decreases as *R*_{a}*C*_{g} continues to increase. As a result, there are two solutions for any given phase shift. Figure 5 displays the phase angle vs. airway resistance-compliance for the model at two frequencies and *G* = 0.1. A reasonable approach is to use only the portion of the curve that is monotonically increasing (that is, the smaller of the 2 solutions).

It can be shown that the value of the peak angle is constant for a constant *G*. However, the phase angle reaches a peak at a lower *R*_{a}*C*_{g} as frequency increases. The curve denoting the peak angle (which is constant for constant *G*) as a function of frequency and *R*_{a}*C*_{g} is shown in Fig. 6. Given the breathing frequency *f*, this curve defines the maximum *R*_{a}*C*_{g} that can be inferred from the phase angle. As an example, consider a mouse breathing at 5 Hz. As the animal's airways constrict, the phase angle would increase until *R*_{a}*C*_{g} reaches ∼10 ms. As the airways continue to narrow, the phase would begin to drop, appearing as though *R*_{a}*C*_{g} were actually decreasing. However, since the *R*_{a}*C*_{g} for normal mice is ∼1 ms, it would appear to be an extreme case for *R*_{a}*C*_{g} to cross the limit shown in Fig. 6. Even for a mouse breathing at the unusually high frequency of 10 Hz, airway resistance-compliance could quintuple before the limit would be reached.

Finally, for *f* = 5 Hz, Fig. 7 displays *R*_{a}*C*_{g} as a function of the phase angle for *Eqs. 21* and *22*. The simplified expression of *Eq. 22* produces a slight underestimation of *R*_{a}*C*_{g}. For assessing mice whose *R*_{a}*C*_{g} is in the range of normal to 300% of normal, *Eq. 22* provides reasonable accuracy.

## DISCLOSURES

The findings and conclusions of this report are those of the authors and do not necessarily represent the views of the National Institute for Occupational Safety and Health.

## Footnotes

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- Copyright © 2008 the American Physiological Society