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INNOVATIVE METHODOLOGY

Unrestrained acoustic plethysmograph for measuring specific airway resistance in mice

¹Pathology and Physiology Research Branch and ²Toxicology and Molecular Biology Research Branch, Health Effects Laboratory Division, National Institute for Occupational Safety and Health, Morgantown, West Virginia

Submitted 6 September 2007 ; accepted in final form 25 April 2008

	ABSTRACT

TOP ABSTRACT MATERIALS AND METHODS RESULT DISCUSSION APPENDIX DISCLOSURES REFERENCES

 
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 cmH₂O·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

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

TOP ABSTRACT MATERIALS AND METHODS RESULT DISCUSSION APPENDIX DISCLOSURES REFERENCES

 
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.

View larger version (14K): [in this window] [in a new window]   Fig. 1. Schematic of the modified acoustic plethysmograph. The speaker generates a constant frequency (300 Hz) that resonates the air in the chamber. The micrometer is used to adjust the chamber volume. Movement of the animal chest wall modulates the sound amplitude, which is measured by the microphone. The pressure transducer measures the pressure drop across the screen, which is proportional to flow into and out of the chamber. The restrainer inhibits the animal from occluding the nozzle.

Model

sRaw is derived from a model (15) of the respiratory system as shown in Fig. 2A. 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.

View larger version (11K): [in this window] [in a new window]   Fig. 2. Development of the whole body plethysmograph electric circuit analog model. A: simple model of the respiratory system (15). It represents flow produced by the thorax, Zt represents tissue impedance, Ra is airway resistance, and Cg represents compliance of alveolar gas. Pt represents pressure produced at the thorax, and Pao is pressure at the airway opening. Palv and Patm represent alveolar and atmospheric pressure, respectively. B: the term GIa represents the flow "lost" on expiration ("gained" on inspiration) due to changes in temperature and humidity. C: model of the animal placed in a restrained, or double-chamber, plethysmograph. Zbc and Zhc represent the flow impedances of the body chamber and head chamber, respectively. Pbc and Phc are the pressures measured in the body chamber and head chamber, respectively. D: model of the animal placed in an unrestrained, or whole body plethysmograph. Zb represents the box flow impedance, and Pb represents the box pressure.

(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. 2B.

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 2C 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 2D 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.

View larger version (6K): [in this window] [in a new window]   Fig. 3. Model of animal in the unrestrained plethysmograph. This model is exactly the same circuit as in Fig. 2D. It has been redrawn in a more concise manner.

(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:

(15)

(16)

(17)

so the phase angle, , between thoracic volume and box volume is given as

(18)

Rearranging gives

(19)

Solving for R_aC_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 = /(2). 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_aC_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_aC_g is then a direct measure of sRaw. In this study, estimates of R_aC_g have units given in milliseconds. However, if sRaw is estimated based on P_atm – P 1,000 cmH₂O, then from Eq. 25,

(26)

(27)

(28)

Under these conditions, sRaw in units of cmH₂O·s will have the same numerical value as R_aC_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_aC_g for each segment. Similarly, coherence for each segment was determined at the breathing frequency. The mean R_aC_g value was found by averaging the estimates for all the segments whose coherence was 0.9.

	RESULT

TOP ABSTRACT MATERIALS AND METHODS RESULT DISCUSSION APPENDIX DISCLOSURES REFERENCES

 
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_aC_g compared with baseline (Fig. 4A). At the highest methacholine dose (20 mg/ml), each mouse had an increased R_aC_g compared with saline. The mean R_aC_g dose-response curve is shown in Fig. 4B. 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_aC_g.

View larger version (21K): [in this window] [in a new window]   Fig. 4. Results (means ± SE) of the methacholine aerosol exposure. A: individual RaCg dose responses. B: average RaCg dose response. C: individual phase-shift dose responses. D: average phase-shift dose response. E: individual breathing frequency dose responses. F: average breathing frequency dose response. a,b,cLowercase letters denote statistically significant differences.

	DISCUSSION

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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_aC_g even in cases where the breathing pattern of the animal is significantly affected.

The baseline sRaw value of 0.93 ± 0.10 cmH₂O·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 cmH₂O·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 cmH₂O·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_aC_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_aC_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_aC_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_aC_g has been provided. This system provides an efficient and accurate method of assessing specific airway resistance of mice in an unrestrained plethysmograph.

	APPENDIX

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To infer sRaw from the phase shift of the transfer function given in Eq. 17, Eq. 19 must be solved for R_aC_g. Since Eq. 19 is quadratic in R_aC_g, the phase angle, , initially increases with an increase in R_aC_g but eventually reaches a peak and then decreases as R_aC_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).

View larger version (9K): [in this window] [in a new window]   Fig. 5. Curves represent the theoretical phase response, as a function of RaCg, of the model for 2 different frequencies.

View larger version (13K): [in this window] [in a new window]   Fig. 6. For any given frequency, the model phase shift increases monotonically with RaCg up to a maximum phase (denoted by the line), after which the phase angle decreases.

View larger version (9K): [in this window] [in a new window]   Fig. 7. RaCg as predicted from the model phase shift at a frequency of 5 Hz. The solid line represents the exact solution (Eq. 21). The dashed line represents the solution to the simplified expression (Eq. 22).

	DISCLOSURES

TOP ABSTRACT MATERIALS AND METHODS RESULT DISCUSSION APPENDIX DISCLOSURES REFERENCES

	FOOTNOTES

 

Address for reprint requests and other correspondence: J. S. Reynolds, Pathology and Physiology Research Branch, Health Effects Laboratory Division, National Institute for Occupational Safety and Health, 1095 Willowdale Rd., ms L2101, Morgantown, WV 26505 (e-mail: jsr0{at}cdc.gov)

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.

	REFERENCES

TOP ABSTRACT MATERIALS AND METHODS RESULT DISCUSSION APPENDIX DISCLOSURES REFERENCES

 

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This Article Abstract Full Text (PDF) Free All Versions of this Article: 105/2/711    most recent 00949.2007v1 Submit a response Alert me when this article is cited Alert me when eLetters are posted Alert me if a correction is posted Citation Map Services Email this article to a friend Similar articles in this journal Similar articles in Web of Science Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by Reynolds, J. S. Articles by Frazer, D. G. Search for Related Content PubMed PubMed Citation Articles by Reynolds, J. S. Articles by Frazer, D. G.