Reliability of parameter estimates from models applied to respiratory impedance data

Many previous studies have fit lumped parameter models to respiratory input (Zin) and transfer (Ztr) impedance data. For frequency ranges higher than 4-32 Hz, a six-element model may be required in which an airway branch (with a resistance and inertance) is separated from a tissue branch (with a resistance, inertance, and compliance) by a shunt compliance. A sensitivity analysis is applied to predict the effects of frequency range on the accuracy of parameter estimates in this model obtained from Zin or Ztr data. Using a parameter set estimated from experimental data between 4 and 64 Hz in dogs, both Zin and Ztr were simulated from 4 to 200 Hz. Impedance sensitivity to each parameter was also calculated over this frequency range. The simulation predicted that for Zin a second resonance occurs near 80 Hz and that the impedance is considerably more sensitive to several of the parameters at frequencies surrounding this resonance than at any other frequencies. Also, unless data is obtained at very high frequencies (where the model is suspect), Zin data provides more accurate estimates than Ztr data. After adding random noise to the simulated Zin data, we attempted to extract the original parameters by using a nonlinear regression applied to three frequency ranges: 4-32, 4-64, and 4-110 Hz. Estimated parameters were substantially incorrect when using only 4- to 32-Hz or 4- to 64-Hz data, but nearly correct when fitting 4- to 110-Hz data. These results indicate that respiratory system parameters can be more accurately extracted from Zin than Ztr, and to make physiological inferences from parameter estimates based on Zin impedance data in dogs, the data must include frequencies surrounding the second resonance.     

Sensitivity analysis of respiratory parameter uncertainties: impact of criterion function form and constraints

A sensitivity analysis based on weighted least-squares regression is presented to evaluate alternative methods for fitting lumped-parameter models to respiratory impedance data. The goal is to maintain parameter accuracy simultaneously with practical experiment design. The analysis focuses on predicting parameter uncertainties using a linearized approximation for joint confidence regions. Applications are with four-element parallel and viscoelastic models for 0.125- to 4-Hz data and a six-element model with separate tissue and airway properties for input and transfer impedance data from 2-64 Hz. The criterion function form was evaluated by comparing parameter uncertainties when data are fit as magnitude and phase, dynamic resistance and compliance, or real and imaginary parts of input impedance. The proper choice of weighting can make all three criterion variables comparable. For the six-element model, parameter uncertainties were predicted when both input impedance and transfer impedance are acquired and fit simultaneously. A fit to both data sets from 4 to 64 Hz could reduce parameter estimate uncertainties considerably from those achievable by fitting either alone. For the four-element models, use of an independent, but noisy, measure of static compliance was assessed as a constraint on model parameters. This may allow acceptable parameter uncertainties for a minimum frequency of 0.275-0.375 Hz rather than 0.125 Hz. This reduces data acquisition requirements from a 16- to a 5.33- to 8-s breath holding period. These results are approximations, and the impact of using the linearized approximation for the confidence regions is discussed.     

Respiratory input impedance in anesthetized paralyzed patients

Respiratory impedance (Zrs) was measured between 0.25 and 32 Hz in seven anesthetized and paralyzed patients by applying forced oscillation of low amplitude at the inlet of the endotracheal tube. Effective respiratory resistance (Rrs; in cmH2O.l-1.s) fell sharply from 6.2 +/- 2.1 (SD) at 0.25 Hz to 2.3 +/- 0.6 at 2 Hz. From then on, Rrs decreased slightly with frequency down to 1.5 +/- 0.5 at 32 Hz. Respiratory reactance (Xrs; in cmH2O.l-1.s) was -22.2 +/- 5.9 at 0.25 Hz and reached zero at approximately 14 Hz and 2.3 +/- 0.8 at 32 Hz. Effective respiratory elastance (Ers = -2pi x frequency x Xrs; in cmH2O/1) was 34.8 +/- 9.2 at 0.25 Hz and increased markedly with frequency up to 44.2 +/- 8.6 at 2 Hz. We interpreted Zrs data in terms of a T network mechanical model. We represented the proximal branch by central airway resistance and inertance. The shunt pathway accounted for bronchial distensibility and alveolar gas compressibility. The distal branch included a Newtonian resistance component for tissues and peripheral airways and a viscoelastic component for tissues. When the viscoelastic component was represented by a Kelvin body as in the model of Bates et al. (J. Appl. Physiol. 61: 873-880, 1986), a good fit was obtained over the entire frequency range, and reasonable values of parameters were estimated. The strong frequency dependence of Rrs and Ers observed below 2 Hz in our anesthetized paralyzed patients could be mainly interpreted in terms of tissue viscoelasticity. Nevertheless, the high Ers we found with low volume excursions suggests that tissues also exhibit plasticlike properties.     

Low-frequency respiratory system resistance in the normal dog during mechanical ventilation

The low-frequency resistances of the respiratory system, lung, and chest wall were investigated in four anesthetized paralyzed dogs mechanically ventilated at various frequencies between 0.08 and 0.83 Hz. The resistances were calculated by three different methods: 1) as the real part of the complex impedance obtained from regular ventilation data, 2) as the effective resistance of a two-compartment model fitted to the same data, and 3) as the resistance of a single-compartment model fitted to data obtained during sinusoidal ventilation at various frequencies. Alveolar pressures were measured by a closed-chest alveolar capsule technique and afforded a direct measure of airways resistance. All three resistance estimates were very similar and decreased markedly with frequency between 0 and 1 Hz. The real part of lung impedance at the higher frequencies investigated (around 5 Hz) closely approximated airways resistance, as predicted by the eight-parameter viscoelastic model of respiratory mechanics proposed by Bates et al. (J. Appl. Physiol. 67:2276-2285, 1989).     

Physiological basis for resonant frequencies in respiratory system impedances in dogs

The lumped six-element model of the respiratory system proposed by DuBois et al. (J. Appl. Physiol. 8: 587-594, 1956) has often been used to analyze respiratory system impedance (Zrs) data. This model predicts a resonance (relative minimum in Zrs) at fr between 6 and 10 Hz and an antiresonance (relative maximum in Zrs) at far at higher frequencies (greater than 64 Hz). The far is due to the lumped tissue inertance (Iti) and the alveolar gas compression compliance (Cg). An fr and far have been recently reported in humans, but the far was shown to be not related to Iti and Cg, but instead it is the first acoustic antiresonance of the airways due to their axial dimensions). Zrs data to frequencies high enough to include the far have not been reported in dogs. In this study, we measured Zrs in dogs for frequencies between 5 and 320 Hz and found an fr at 7.5 +/- 1.6 Hz and two far at 97 +/- 13 and 231 +/- 27 Hz (far,1 and far,2, respectively). When breathing 80% He-20% O2, the fr shifted to 14 +/- 2 Hz, far,1 did not change (98 +/- 9 Hz), and far,2 increased to greater than 320 Hz. The behavior of fr and far,1 is consistent with the structure-function implied by the six-element model. However, the presence of an far,2 is not consistent with this model, because it is the airway acoustic antiresonance not represented in the model. These results indicate that, for frequencies that include the fr and far,1, the six-element model can be used to analyze Zrs data and reliable estimates of the model's parameters can be extracted by fitting the model to the data. However, more complex models must be used to analyze Zrs data that include far,2.     

Density dependence of respiratory system impedances between 5 and 320 Hz in humans

For respiratory system impedance (Zrs), the six-element model of DuBois et al. (J. Appl. Physiol. 8: 587-594, 1956) suggests three resonant frequencies (f1,f2,f3), where f1 is the result of the sum of tissue and airway inertances and tissue compliance and f2 is the result of alveolar gas compression compliance (Cg) and tissue inertance (Iti). Three such resonant frequencies have been reported in humans. However, the parameter estimates resulting from fitting this model to the data suggested that f2 and f3 were not associated with Cg and Iti but with airway acoustic properties. In the present study, we measured Zrs between 5 and 320 Hz in 10 healthy adult humans breathing room air or 80% He-20% O2 (HeO2) to gain insight as to whether airway or tissue properties are responsible for the f2 and f3. When the subjects breathed room air, f2 occurred at 170 +/- 16 (SD) Hz, and when they breathed HeO2 it occurred at 240 +/- 24 Hz. If this resonance were due to Cg and Iti it should not have been affected to this extent by the breathing of HeO2. We thus conclude that f2 is not due to tissue elements but that it is an airway acoustic resonance. Furthermore, application of the six-element model to analyze Zrs data at these frequencies is inappropriate, and models incorporating the airway acoustic properties should be used. One such model is based on the concept of equivalent length, which is defined as the length of an open-ended, cylindrical tube that has the same fundamental acoustic resonant frequency.(ABSTRACT TRUNCATED AT 250 WORDS)     

Inverse modeling of dog airway and respiratory system impedances

Mechanical parameters of the respiratory system are often estimated from respiratory impedances using lumped-element inverse models. One such six-element model is composed of an airway branch [with a resistance (Raw) and inertance (Iaw)] separated from a tissue branch [with a resistance (Rt), inertance (It), and compliance (Ct)] by a shunt compliance representing alveolar gas compression (Cg). Even though the airways are known to have frequency-dependent resistance and inertance, these inverse models have been composed of linear frequency-independent elements. In this study we investigated the use of inverse models where the airway branch was represented by a frequency-independent Raw and Iaw, a Raw that is linearly related to frequency and an Iaw that is independent of frequency, and a system of identical parallel tubes the impedance of which was computed from the tube radius and length. These inverse models were used to analyze airway and respiratory impedances between 2 and 1,024 Hz that were predicted from an anatomically detailed forward model. The forward model represented the airways by an asymmetrically branched network with a terminal impedance representative of known Cg, Rt, It, and Ct. For respiratory impedances between 2 and 128 Hz, all models fit the data reasonably well, and reasonably accurate estimates of Cg, Rt, It, and Ct were extracted from these data. For data above 200 Hz, however, only the multiple-tube model accurately fitted respiratory impedances (Zrs). This model fitted the Zrs data best when composed of 27 tubes, each having a radius of 0.148 cm and a length of 16.5 cm.     

Effects of tidal volume and methacholine on low-frequency total respiratory impedance in dogs

The frequency dependence of respiratory impedance (Zrs) from 0.125 to 4 Hz (Hantos et al., J. Appl. Physiol. 60: 123-132, 1986) may reflect inhomogeneous parallel time constants or the inherent viscoelastic properties of the respiratory tissues. However, studies on the lung alone or chest wall alone indicate that their impedance features are also dependent on the tidal volumes (VT) of the forced oscillations. The goals of this study were 1) to identify how total Zrs at lower frequencies measured with random noise (RN) compared with that measure with larger VT, 2) to identify how Zrs measured with RN is affected by bronchoconstriction, and 3) to identify the impact of using linear models for analyzing such data. We measured Zrs in six healthy dogs by use of a RN technique from 0.125 to 4 Hz or with a ventilator from 0.125 to 0.75 Hz with VT from 50 to 250 ml. Then methacholine was administered and the RN was repeated. Two linear models were fit to each separate set of data. Both models assume uniform airways leading to viscoelastic tissues. For healthy dogs, the respiratory resistance (Rrs) decreased with frequency, with most of the decrease occurring from 0.125 to 0.375 Hz. Significant VT dependence of Rrs was seen only at these lower frequencies, with Rrs higher as VT decreased. The respiratory compliance (Crs) was dependent on VT in a similar fashion at all frequencies, with Crs decreasing as VT decreased. Both linear models fit the data well at all VT, but the viscoelastic parameters of each model were very sensitive to VT. After methacholine, the minimum Rrs increased as did the total drop with frequency. Nevertheless the same models fit the data well, and both the airways and tissue parameters were altered after methacholine. We conclude that inferences based only on low-frequency Zrs data are problematic because of the effects of VT on such data (and subsequent linear modeling of it) and the apparent inability of such data to differentiate parallel inhomogeneities from normal viscoelastic properties of the respiratory tissues.     

Confidence intervals of respiratory mechanical properties derived from transfer impedance

Short-term intraindividual variability of the parameters derived from respiratory transfer impedance (Ztr) measured from 4 to 32 Hz was studied in 10 healthy subjects. The corresponding 95% confidence intervals (CIo) were compared with those computed from a single set of data (CIL) according to Lutchen and Jackson (J. Appl. Physiol. 62: 403-413, 1987). Ztr was analyzed with the six-coefficient model of DuBois et al. (J. Appl. Physiol. 8: 587-594, 1956), which includes airway resistance (Raw) and inertance (Iaw), tissue resistance (Rti), inertance (Iti), and compliance (Cti), and alveolar gas compressibility (Cg). The lowest variability was seen for Iaw (CIo = 11.1%), closely followed by Raw (14.3%) and Cti (14.8%), and the largest for Rti and Iti (24.6 and 93.6%, respectively). Using a simpler model, where Iti was excluded, significantly decreased the variability of Iaw (P less than 0.01) and Rti (P less than 0.05) but was responsible for a systematic decrease of Raw and Iaw and increase of Rti. Except for Raw with both models and Iaw with the simpler model, CIL was greater than CIo. Whatever the model, a high correlation between both sets of confidence intervals was found for Rti and Iaw, whereas no correlation was seen for Raw. This suggests that the variability of the former coefficients mainly reflects experimental noise, whereas that of the latter is largely due to biological variability.     

Effects of heterogeneities on the partitioning of airway and tissue properties in normal mice.

We measured the mechanical properties of the respiratory system of C57BL/6 mice using the optimal ventilation waveform method in closed- and open-chest conditions at different positive end-expiratory pressures. The tissue damping (G), tissue elastance (H), airway resistance (Raw), and hysteresivity were obtained by fitting the impedance data to three different models: a constant-phase model by Hantos et al. (Hantos Z, Daroczy B, Suki B, Nagy S, Fredberg JJ. J Appl Physiol 72: 168-178, 1992), a heterogeneous Raw model by Suki et al. (Suki B, Yuan H, Zhang Q, Lutchen KR. J Appl Physiol 82: 1349-1359, 1997), and a heterogeneous H model by Ito et al. (Ito S, Ingenito EP, Arold SP, Parameswaran H, Tgavalekos NT, Lutchen KR, Suki B. J Appl Physiol 97: 204-212, 2004). Both in the closed- and open-chest conditions, G and hysteresivity were the lowest and Raw the highest in the heterogeneous Raw model, and G and H were the largest in the heterogeneous H model. Values of G, Raw, and hysteresivity were significantly higher in the closed-chest than in the open-chest condition. However, H was not affected by the conditions. When the tidal volume of the optimal ventilation waveform was decreased from 8 to 4 ml/kg in the closed-chest condition, G and hysteresivity significantly increased, but there were smaller changes in H or Raw. In summary, values of the obtained mechanical properties varied among these models, primarily due to heterogeneity. Moreover, the mechanical parameters were significantly affected by the chest wall and tidal volume in mice. Contribution of the chest wall and heterogeneity to the mechanical properties should be carefully considered in physiological studies in which partitioning of airway and tissue properties are attempted.     

Lung impedance in healthy humans measured by forced oscillations from 0.01 to 0.1 Hz

Lung impedance was measured from 0.01 to 0.1 Hz in six healthy adults by superimposing small-amplitude forced oscillations on spontaneous breathing. Measurements were made with an almost constant-volume input (160-180 ml) or with an almost constant-flow input (20-30 ml.s-1). No significant difference was found between the two conditions. Lung resistance (RL) sharply decreased from 0.97 kPa.l-1.s at 0.01 Hz to 0.27 kPa.l-1.s at 0.03 Hz and then mildly to 0.23 kPa.l-1.s at 0.1 Hz. Lung effective compliance (CL) decreased slightly and regularly from 0.01 Hz (2.38 l.kPa-1) to 0.1 Hz (1.93 l.kPa-1). The data were analyzed using a linear viscoelastic model adapted from Hildebrandt (J. Appl. Physiol. 28:365-372, 1970) and complemented by a Newtonian resistance (R): RL = R + B/(9.2f); CL = 1/(A + 0.25B + B.log2 pi f), where f is the frequency and B/A is an index of lung tissue viscoelasticity. A good fit was generally obtained, with an average difference of 10% between the observed and predicted values. The ratio B/A was not affected by the breathing and was 10.6 and 13.6% in the constant-volume and constant-flow conditions, respectively, which agrees with Hildebrandt's observations in isolated cat lungs. R was systematically larger than the plethysmographic airway resistance, suggesting that lung tissue resistance might also include a Newtonian component.     

Determination of airway and tissue resistances after antigen and methacholine in nonhuman primates

Madwed, Jeffrey B., and Andrew C. Jackson.Determination of airway and tissue resistances after antigen andmethacholine in nonhuman primates. J. Appl.Physiol. 83(5): 1690-1696, 1997.Antigen challenge of Ascaris suum-sensitiveanimals has been used as a model of asthma in humans. However, noreports have separated total respiratory resistance into airway (Raw)and tissue (Rti) components. We compared input impedance (Zin) andtransfer impedance (Ztr) to determine Raw and Rti in anesthetizedcynomolgus monkeys under control and bronchoconstricted conditions. Zindata between 1 and 64 Hz are frequency dependent during baselineconditions, and this frequency dependence shifts in response toA. suum or methacholine. Thus itcannot be modeled with the DuBois model, and estimates of Raw and Rticannot be determined. With Ztr, baseline data were much less variablethan Zin in all monkeys. After bronchial challenge withA. suum or methacholine, the absoluteamplitude of the resistive component of Ztr increased and its zerocrossing shifted to higher frequencies. These data can estimate Raw and Rti with the six-element DuBois model. Therefore, in monkeys, Ztr hasadvantages over other measures of lung function, since it provides amethodology to separate estimates of Raw and Rti. In conclusion, Ztrshows spectral features similar to those reported in healthy andasthmatic humans.

     

Respiratory transfer impedances with pressure input at the mouth and chest

Two methods of measuring respiratory transfer impedance (Ztr) were compared in 14 normal subjects, from 4 to 30 Hz, 1) studying the relationship between transrespiratory pressure (Prs) and flow at the chest when varying pressure at the mouth (Ztrm) and 2) studying the relationship between Prs and flow at the mouth when varying pressure around the chest wall (Ztrw). The similarity of the two relationships was expected on the basis of a T-network model. Almost identical phase responses were obtained from the two methods. Pressure-flow ratios were slightly larger for Ztrw than for Ztrm, but differences did not exceed 2% on average in 11 of 14 subjects. When the data were analyzed with the six-coefficient model proposed by DuBois et al. (J. Appl. Physiol. 8: 587-594, 1956), similar values were found for tissue compliance and tissue inertance but slightly different values for gaseous inertance in the airways (1.97 +/- 0.35 X 10(-2) cmH2O X l-1 X s2 for Ztrw vs. 1.73 +/- 0.26 for Ztrm; P less than 0.01). Similar results were also found for total respiratory resistance but with a slightly larger contribution of airway resistance for Ztrw (64 +/- 14 vs. 57 +/- 10%; P less than 0.05). As a practical conclusion it is recommended to measure Ztrw, which is technically much easier.     

Comparison of plethysmographic methods for obtaining thoracic gas volume in anesthetized dogs

In dogs, respiratory system resistance (Rrs) is frequency independent, and during high-frequency oscillatory ventilation (HFO) the relationship between CO2 elimination (VCO2) and frequency is linear. In contrast, we found in rabbits a large frequency-dependent decrease in Rrs with increasing frequency along with a nonlinear relationship between frequency and VCO2 (J. Appl. Physiol. 57: 354-359, 1984). We proposed that frequency dependent mechanical properties of the lung account for inter-species differences in the frequency dependence of gas exchange during HFO. In the current study we tested this hypothesis further by measuring VCO2 and Rrs as a function of frequency in a species of monkey (Macaca radiata). In these monkeys, Rrs decreased minimally between 4 and 8 Hz and in general increased at higher frequencies, whereas VCO2 was linearly related to frequency. This is further evidence supporting the hypothesis that nonlinear frequency-VCO2 behavior during HFO is related to frequency-dependent behavior in Rrs.     

Measurement of total respiratory impedance in infants by the forced oscillation technique

The forced oscillation technique according to Làndsér et al. (J. Appl. Physiol. 41:101-106, 1976) was modified for use in infants. Adaptations, including a flexible tube to connect the infant to the measuring system and a bias flow to avoid rebreathing, did not influence impedance values. The linearity of the respiratory system was assessed and confirmed by 1) applying pseudo-random noise oscillations at three different amplitudes to 7 infants and 2) comparing in 12 infants impedance values obtained with pseudo-random noise and with sinusoidal oscillations at 12 and 32 Hz. Intersubject variability, averaged for all frequencies, was 6%. In 17 infants the relative error (+/- SD) between two series of five measurements within a time interval of 15 min was 0.5 +/- 5.7%. No statistically significant difference was found between impedance values before and after repositioning of the infant's head, whereas rotation resulted in a decrease in resistance and no effect on reactance. Our results indicate that the infant-adapted forced pseudo-random noise oscillation technique has the potential to give valuable information about ventilatory lung function in infants.     

Inability to separate airway from tissue properties by use of human respiratory input impedance

Respiratory input impedance (Zrs) from 2.5 to 320 Hz displays a high-frequency resonance, the location of which depends on the density of the resident gas in the lungs (J. Appl. Physiol. 67: 2323-2330, 1989). A previously used six-element model has suggested that the resonance is due to alveolar gas compression (Cg) resonating with tissue inertance (Iti). However, the density dependence of the resonance indicates that is associated with the first airway acoustic resonance. The goal of this study was to determine whether unique properties for tissues and airways can be extracted from Zrs data by use of models that incorporate airway acoustic phenomena. We applied several models incorporating airway acoustics to the 2.5- to 320-Hz data from nine healthy adult humans during room air (RA) and 20% He-80% O2 (HeO2) breathing. A model consisting of a single open-ended rigid tube produced a resonance far sharper than that seen in the data. To dampen the resonance features, we used a model of multiple open-ended rigid tubes in parallel. This model fit the data very well for both RA and HeO2 but required fewer and longer tubes with HeO2. Another way to dampen the resonance was to use a single rigid tube terminated with an alveolar-tissue unit. This model also fit the data well, but the alveolar Cg estimates were far smaller than those expected based on the subject's thoracic gas volume. If Cg was fixed based on the thoracic gas volume, a large number of tubes were again required. These results along with additional simulations show that from input Zrs alone one cannot uniquely identify features indigenous to alveolar Cg or to the respiratory tissues.     

Effect of variable parenchymal expansion on gas mixing

Using implanted radiopaque markers, Hubmayr et al. (J. Appl. Physiol. 54: 1048-1056, 1983) and Olson et al. (J. Appl. Physiol. 57: 1710-1714, 1984) detected a variability in the volume changes of regions defined by the markers in intact and excised dog lungs, respectively. In dogs lying prone and in excised lobes, there is virtually no large-scale spatial organization of the variability. We interpret these data as evidence of an intrinsic heterogeneity of parenchymal expansion. The effect of variability of parenchymal expansion on gas mixing is calculated. From a statistical model, we infer that the variability of volume changes observed by Olson et al. is a result of an underlying variability with a larger magnitude at a smaller scale and that the variability at the smaller scale is large enough to explain the inefficiency of mixing observed in single-breath oxygen tests on excised dog lobes.     

Human respiratory input impedance from 4 to 200 Hz: physiological and modeling considerations

Recent studies on respiratory impedance (Zrs) have predicted that at frequencies greater than 64 Hz a second resonance will occur. Furthermore, if one intends to fit a model more complicated than the simple series combination of a resistance, inertance, and compliance to Zrs data, the only way to ensure statistically reliable parameter estimates is to include data surrounding this second resonance. An additional question, however, is whether the resulting parameters are physiologically meaningful. We obtained input impedance data from eight healthy adult humans using discrete frequency forced oscillations from 4 to 200 Hz. Three resonant frequencies were seen: 8 +/- 2, 151 +/- 10, and 182 +/- 16 Hz. A seven-parameter lumped element model provided an excellent fit to the data in all subjects. This model consists of an airway resistance (Raw), which is linearly dependent on frequency, and airway inertance separated from a tissue resistance, inertance, and compliance by a shunt compliance (Cg) thought to represent gas compressibility. Model estimates of Raw and Cg were compared with those suggested by measurement of Raw and thoracic gas volume using a plethysmograph. In all subjects the model Raw and Cg were significantly lower than and not correlated with the corresponding plethysmographic measurement. We hypothesize that the statistically reliable but physiologically inconsistent parameters are a consequence of the distorting influence of airway wall compliance and/or airway quarter-wave resonance. Such factors are not inherent to the seven-parameter model.     

Chest wall and respiratory system mechanics in cats: effects of flow and volume

The effects of inspiratory flow rate and inflation volume on the resistive properties of the chest wall were investigated in six anesthetized paralyzed cats by use of the technique of rapid airway occlusion during constant flow inflation. This allowed measurement of the intrinsic resistance (Rw,min) and overall dynamic inspiratory impedance (Rw,max), which includes the additional pressure losses due to time constant inequalities within the chest wall tissues and/or stress adaptation. These results, together with our previous data pertaining to the lung (Kochi et al., J. Appl. Physiol. 64: 441-450, 1988), allowed us to determine Rmin and Rmax of the total respiratory system (rs). We observed that 1) Rw,max and Rrs,max exhibited marked frequency dependence; 2) Rw,min was independent of flow (V) and inspired volume (delta V), whereas Rrs,min increased linearly with V and decreased with increasing delta V; 3) Rw,max decreased with increasing V, whereas Rrs,max exhibited a minimum value at a flow rate substantially higher than the resting range of V; 4) both Rw,max and Rrs,max increased with increasing delta V. We conclude that during resting breathing, flow resistance of the chest wall and total respiratory system, as conventionally measured, includes a significant component reflecting time constant inequalities and/or stress adaptation phenomena.     

Contribution of electrogenic ion transport to impedance of the algae Valonia utricularis and artificial membranes.

The cell membrane of Valonia utricularis contains an electrogenic carrier system for chloride (Wang et al., Biophys J. 59:235-248 (1991)). The electrical impedance of V. utricularis was measured in the frequency range between 1 Hz and 50 kHz. The analysis of the impedance spectra from V. utricularis and its comparison with equivalent circuit models showed that the transport system created a characteristic contribution to the impedance in the frequency range between 10 Hz and 5 kHz. The fit of the impedance spectra with the formalism derived from the theory of carrier-mediated transport allowed the determination of the kinetic parameters of chloride transport through the cell membrane of V. utricularis, and its passive electrical properties. Simultaneous measurements of the kinetic parameters with the charge pulse method demonstrated the equivalence of both experimental approaches with respect to the evaluation of the translocation rate constants of the free and the charged carriers and the total density of carriers within the membrane. Moreover, the impedance spectra of the protonophor-mediated proton transport by FCCP (carbonylcyanide p-trifluoromethoxyphenyl-hydrazone) were measured in model membranes. The carrier system made a substantial contribution to the impedance of the artificial membranes. The analysis of the spectra in terms of a simple carrier system (Benz and McLaughlin, 1983, Biophys. J. 41:381-398) allowed the evaluation of the kinetic and equilibrium parameters of the FCCP-mediated proton transport. The possible application of the measurement of impedance spectra for the study of biological transport systems is discussed.