### Abstract

- Top of page
- Abstract
- Introduction
- Methods
- Results
- Discussion
- Acknowledgements
- References

*Please cite this paper as:* Larcombe *et al.* (2012) Factors influencing the assessment of lung function in mice with influenza-induced lung disease. Influenza and Other Respiratory Viruses DOI: 10.1111/irv.12034.

**Background ** The constant-phase model (CPM) is commonly fit to respiratory system input impedance (*Z*_{rs}) to estimate lung mechanics. Driving signal frequencies and the method of model fitting may influence the results, especially in cases of severe lung disease or under severe bronchoconstriction.

**Objective ** To illustrate the effects of different CPM fits to *Z*_{rs} data using a mouse model of influenza-induced lung disease.

**Methods ** BALB/c mice infected with influenza (or control) were challenged with methacholine. The CPM was fitted to *Z*_{rs}, measured between 0·25 and 19·625 Hz, using both unweighted and weighted fits. The effect of different lowest frequencies was assessed.

**Results and Conclusions ** For influenza-infected mice, the unweighted fit was poor, and airway resistance (*R*_{aw}) was often biologically impossible. The weighted fit provided more realistic estimates of *R*_{aw}. Different model fits and minimal frequencies had little effect on tissue mechanics.

### Introduction

- Top of page
- Abstract
- Introduction
- Methods
- Results
- Discussion
- Acknowledgements
- References

Measurement of lung function forms an important part of the use of animals to model human lung diseases. The effects of respiratory system insults are often obtained through fitting mathematical models, such as the constant-phase model (CPM), to respiratory system impedance (*Z*_{rs}). The CPM partitions low-frequency input *Z*_{rs} into components representing airway mechanics, that is, airway resistance (*R*_{aw}) and inertance (*I*_{aw}), and a strictly constant-phase tissue compartment characterized by the coefficients of tissue damping (*G*) and tissue elastance (*H*).^{1} The CPM has been validated in a variety of species,^{1,2} and its sensitivity has been assessed in mice.^{3} The relative contributions of the airway and tissue compartments to *Z*_{rs} within a given frequency range may change radically if any alterations occur predominantly in either compartment, such that the other compartment will be subjected to estimation bias. This may occur during acute bronchoconstriction where the contributions from the airway may increase markedly or in severe lung disease where the tissue component may dominate. It may be possible to alleviate the estimation bias by studying a more appropriate frequency range or by using different methods for fitting the CPM to *Z*_{rs}.^{3}

We investigated the influence of the frequency content of the driving signal and the method used to fit the CPM to *Z*_{rs} on estimates of *R*_{aw}, *G*, and *H* in mice with influenza-induced lung disease.

### Methods

- Top of page
- Abstract
- Introduction
- Methods
- Results
- Discussion
- Acknowledgements
- References

Eight-week-old female BALB/c mice, maintained under specific pathogen-free conditions and with food and water provided *ad libitum*, were intranasally inoculated with 10^{4·5} plaque-forming units of influenza A/Mem/1/71 diluted in 50 μl of virus production serum-free medium (VP-SFM; Gibco, Mulgrave, Victoria, Australia). Seven mice were infected (mass 17·6 ± 1·1 g), and seven control mice (mass 18·7 ± 0·5 g) received the same volume of the supernatant of uninfected Madin–Darby canine kidney cells diluted in VP-SFM. Influenza was grown and titrated as previously described.^{4} This strain replicates to high titres^{4} and causes significant disease in mice.^{5}

At the peak of infection,^{6} mice were surgically prepared as described previously.^{5} Anaesthetized, tracheostomized mice were ventilated using a *f*lexiVent small animal ventilator (SCIREQ, Montreal, Canada) at 450 breaths per min with a tidal volume of 8 ml/kg and a positive end-expiratory pressure of 2 cm H_{2}O. Lung volume history was standardized via three slow (16-s) deep inflations, spaced 1 min apart, to a pressure of 20 cm H_{2}O and *Z*_{rs} measured 1 min after increasing doses (0·1, 0·3, 1, 3, 10, and 30 mg/ml) of aerosolized methacholine (MCh; Sigma-Aldrich, St. Louis, MO, USA) generated by an ultrasonic nebulizer (DeVilbiss UltraNeb, Somerset, PA, USA).^{5,7} We report measurements at baseline (i.e., before any MCh) and after 30 mg/ml MCh.

Z_{rs} was measured using the “Primewave” signal of the *f*lexiVent small animal ventilator, which is comprised of 19 mutually prime sinusoidal frequencies (0·25, 0·625, 1·375, 2·125, 2·875, 3·875, 5·125, 5·875, 7·375, 8·375, 9·125, 10·375, 12·125, 12·875, 13·625, 15·875, 17·125, 18·625, and 19·625 Hz). The CPM^{1} was used to calculate Newtonian resistance (*R*_{n}), *I*_{aw}, *G*, and *H*. Hysteresivity (η) was calculated as *G*/*H*. We assumed that the contribution of the lung parenchyma and the chest wall to *R*_{n} was insignificantly small^{8} and hence *R*_{n }= *R*_{aw}. *I*_{aw} values were negligible and are not reported. *Z*_{rs} data were imported into custom-made analysis software (University of Szeged, Hungary) for analysis, which uses a global optimization algorithm^{9} to fit the CPM to *Z*_{rs}. Data were initially analyzed using the complete set of 19 frequencies using an unweighted fitting criterion:

where Φ is the fitting error, and *Z*_{d}(*f*_{i}) and *Z*_{m}(*f*_{i}) correspond to the measured and model-predicted impedance value at the *i*th frequency, respectively.^{3} The CPM was then fitted to the measured data using a weighted fitting criterion, where non-negative weights were incorporated into the fitting criterion:

The weighted fitting criterion scales the contribution of each frequency by the magnitude of the impedance at that frequency, such that model fit is not dominated by frequency points where *Z*_{rs} is larger compared to other frequencies. *Z*_{rs} data were then adjusted to alter the lowest frequency, and the model was refit using the weighted fitting criterion, such that we had one set of data which was analyzed in six ways;

- 1
Fu_{0·25}: unweighted fit/0·25–19·625 Hz,

- 2
Fw_{0·25}: weighted fit/0·25–19·625 Hz,

- 3
Fw_{1·375}: weighted fit/1·375–19·625 Hz,

- 4
Fw_{2·875}: weighted fit/2·875–19·625 Hz,

- 5
Fw_{3·875}: weighted fit/3·875–19·625 Hz, and

- 6
Fw_{5·125}: weighted fit/5·125–19·625 Hz.

### Discussion

- Top of page
- Abstract
- Introduction
- Methods
- Results
- Discussion
- Acknowledgements
- References

This study illustrates the importance of selecting appropriate settings for the measurement of lung mechanics when applying the CPM to *Z*_{rs} spectra. The greatest differences were found when comparing an unweighted (Fu_{0·25}) fit of the CPM to *Z*_{rs} spectra with any of the weighted fitting criteria. Applying a weighted fit of the CPM to *Z*_{rs} spectra can improve measures of lung mechanics under acutely bronchoconstricted conditions by preventing undue contributions from the lower frequencies, which have intrinsically larger magnitudes. In severe lung disease, such as that caused by influenza infection, *Z*_{rs} may increase even further at low frequencies, and the negative frequency dependence of the real part of *Z*_{rs} may strengthen^{10–12} leading to misestimation of *R*_{aw}. We have also shown that selecting different lowest frequencies of the forced oscillation signal can have considerable impacts on the estimation of CPM parameters. Generally, we identified slight differences in the model fit with increasing lowest frequency, up to a point where the potential benefits of the removal of additional low frequencies were outweighed by the loss of degrees of freedom of the model.

Our data show that the frequencies of a forced oscillation technique signal should be carefully selected so that the measured *Z*_{rs} as a result of the tissues and airways has an equal “opportunity” to contribute to parameters specified in the model. Selection of an appropriate frequency range is dependent on multiple factors including species and disease state. Under the particular set of circumstances employed in the current study (i.e., mice with influenza), an unweighted fit and frequency range of 1·375–19·625 Hz provided the most realistic measurements. When undertaking studies that apply the CPM to *Z*_{rs} spectra, researchers need to be aware that fitting criteria and frequency selection are important. Without previous knowledge of what frequencies are appropriate, a useful starting point may be the selection of the lowest frequency based on the resting respiratory rate of the study species. For example, the laboratory mouse has a resting breathing rate (ƒ_{R}) ∼80 to 200 breaths per minute.^{13} Thus, the lower end of the forced oscillatory signal, for an animal this size, should be ∼1·3 to 3·3 Hz. This relationship holds for larger species, such as humans with a resting ƒ_{R} of 15 breaths per min (0·25 Hz); indeed, many studies on low-frequency respiratory mechanics in humans select similar frequencies.^{14,15} In saying this, some researchers employ much lower minimum frequencies (e.g., 0·078 Hz) in studies of broncho-constriction and acute lung injury.^{16,17} The selection of the highest frequency is perhaps not as vital, although they are usually within the medium frequency range (4–40 Hz)^{18,19}, which means that resonance and anti-resonance phenomena^{19,20} are not examined in low-frequency studies.