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.     

Frequency response of the chest: modeling and parameter estimation.

The frequency response of the respiratory system was studied in the range from 3 to 70 Hz in 15 normal subjects by applying sinusoidal pressure variations around the chest and measuring gas flow at the mouth. The observed input-output relationships were systematically compared to those predicted on the basis of linear differential equations of increasing order. From 3 to 20 Hz the behavior of the system was best described by a 3rd-order equation, and from 3 to 50 Hz by a 4th-order one. A mechanistic model of the 4th order, featuring tissue compliance (Ct), resistance (Rt) and inertance (It), alveolar gas compressibility (Cg) and airway resistance (Raw), and inertance (Iaw) was developed. Using that model, the following mean values were found: Ct = 2.08-10(-2)1-hPa-1 (1 hPa congruent to 1 cm of water); Rt = 1.10-hPa-1(-1)-s; It = 0.21-10(-2)hPa-1(-1)-s2; Raw = 1.35-hPa-1(-1)-s; Iaw = 2.55-10(-2)hPa-1(-1)-s2. Additional experiments devised to validate the model were reasonably successful, suggesting that the physical meaning attributed to the coefficients was correct. The validity of the assumptions and the physiological meaning of the coefficients are discussed.     

Flow and volume dependence of respiratory mechanical properties studied by forced oscillation

The influence of inspiratory and expiratory flow magnitude, lung volume, and lung volume history on respiratory system properties was studied by measuring transfer impedances (4-30 Hz) in seven normal subjects during various constant flow maneuvers. The measured impedances were analyzed with a six-coefficient model including airway resistance (Raw) and inertance (Iaw), tissue resistance (Rti), inertance (Iti), and compliance (Cti), and alveolar gas compressibility. Increasing respiratory flow from 0.1 to 0.4 1/s was found to increase inspiratory and expiratory Raw by 63% and 32%, respectively, and to decrease Iaw, but did not change tissue properties. Raw, Iti, and Cti were larger and Rti was lower during expiration than during inspiration. Decreasing lung volume from 70 to 30% of vital capacity increased Raw by 80%. Cti was larger at functional residual capacity than at the volume extremes. Preceding the measurement by a full expiration rather than by a full inspiration increased Iaw by 15%. The data suggest that the determinants of Raw and Iaw are not identical, that airway hysteresis is larger than lung hysteresis, and that respiratory muscle activity influences tissue properties.     

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.     

Density dependence of respiratory input and transfer impedances in humans

Total respiratory input (Zin) and transfer (Ztr) impedances were obtained from 4 to 30 Hz in 10 healthy subjects breathing air and He-O2. Zin was measured by applying pressure oscillations around the head to minimize the upper airway shunt and Ztr by applying pressure oscillations around the chest. Ztr was analyzed with a six-coefficient model featuring airways resistance (Raw) and inertance (Iaw), alveolar gas compressibility, and tissue resistance, inertance, and compliance. Breathing He-O2 significantly decreased Raw (1.35 +/- 0.32 vs. 1.74 +/- 0.49 cmH2O.l-1.s in air, P less than 0.01) and Iaw (0.59 +/- 0.33 vs. 1.90 +/- 0.44 x 10(-2) cmH2O.l-1.s2), but, as expected, it did not change the tissue coefficients significantly. Airways impedance was also separately computed by combining Zin and Ztr data. This approach demonstrated similar variations in Raw and Iaw with the lighter gas mixture. With both analyses, however, the changes in Iaw were more than what was expected from the change in density. This indicates that factors other than gas inertance are included in Iaw and reveals the short-comings of the six-coefficient model to interpret impedance data.     

Forced oscillatory impedance of the respiratory system at low frequencies

Respiratory mechanical impedances were determined during voluntary apnea in five healthy subjects, by means of 0.25- to 5-Hz pseudo/random oscillations applied at the mouth. The total respiratory impedance was partitioned into pulmonary (ZL) and chest wall components with the esophageal balloon technique; corrections were made for the upper airway shunt impedance and the compressibility of alveolar gas. Neglect of these shunt effects did not qualitatively alter the frequency dependence of impedances but led to underestimations in impedance, especially in the chest wall resistance (Rw), which decreased by 20-30% at higher frequencies. The total resistance (Rrs) was markedly frequency dependent, falling from 0.47 +/- 0.06 (SD) at 0.25 Hz to 0.17 +/- 0.01 at 1 Hz and 0.15 +/- 0.01 kPa X l-1 X s at 5 Hz. The changes in Rrs were caused by the frequency dependence of Rw almost exclusively between 0.25 and 2 Hz and in most part between 2 and 5 Hz. The effective total respiratory (Crs,e) and pulmonary compliance were computed with corrections for pulmonary inertance derived from three- and five-parameter model fittings of ZL. Crs,e decreased from the static value (1.03 +/- 0.18 l X kPa-1) to a level of approximately 0.35 l X kPa-1 at 2-3 Hz; this change was primarily caused by the frequency-dependent behavior of chest wall compliance.     

Respiratory impedance to ambient pressure changes at low frequencies

Respiratory impedance may be studied by measuring airway flow (Vaw) when pressure is varied at the mouth (input impedance) or around the chest (transfer impedance). A third possibility, which had not been investigated so far, is to apply pressure variations simultaneously at the two places, that is to vary ambient pressure (Pam). This provides respiratory impedance to ambient pressure changes (Zapc = Vaw/Pam). In that situation airway impedance (Zaw) and tissue impedance (Zt) are mechanically in parallel, and both are in series with alveolar gas impedance (Zg): Zapc = Zaw + Zg + Zaw.Zg/Zt. We assessed the frequency dependence of Zapc from 0.05 to 2 Hz in nine normal subjects submitted to sinusoidal Pam changes of 2-4 kPa peak to peak. The real part of Zapc (Rapc) was of 6.2 kPa.1(-1).s at 0.05 Hz and decreased to 1.9 kPa.1(-1).s at 2 Hz. Similarly the effective compliance (Capc), computed from the imaginary part of Zapc, decreased from 0.045 1.kPa-1 at 0.05 Hz to 0.027 1.kPa-1 at 2 Hz. Breathing against an added resistance of 0.46 kPa.1(-1).s exaggerated the negative frequency dependence of both Rapc and Capc. When values of airway resistance and inertance derived from transfer impedance data were introduced, Zapc was used to compute effective tissue resistance (Rt) and compliance (Ct). Rt was found to decrease from 0.32 to 0.15 kPa.1(-1).s and Ct from 1.11 to 0.64 1.kPa-1 between 0.25 and 2 Hz. Ct was slightly lower with the added resistance. These results are in good agreement with the data obtained by other approaches.     

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.     

Mechanically induced pendelluft flow in a model airway bifurcation during high frequency oscillation

A single bifurcation with adjustable branch compliances, resistances and inertances was used to study the generation of pendelluft flows during ventilation at tidal volumes of 5-15 ml and frequencies of 6-26 Hz, corresponding to parent branch Reynolds numbers of 400-8000 and Womersley parameter values of 12-25. Pendelluft was quantified by the ratio of tidal volume sum in sibling branches to tidal volume in the parent branch. This tidal volume fraction being greater than one in all experiments where an asymmetry in branch mechanics was imposed, indicated that some degree of pendelluft was always present. Asymmetries in compliance and in inertance produced much greater pendelluft than an asymmetry in resistance. The largest tidal volume fraction, equal to 2.75, was recorded when inertance in both sibling branches was high, resistance was low, and compliances differed by a factor of five. Tidal volume fraction always peaked at an optimal frequency between 12-24 Hz, similar to the frequencies at which physiologic transport optima have previously been observed.     

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)     

One-dimensional computer analysis of oscillatory flow in rigid tubes.

The dynamic characteristics of catheter-transducer systems using rigid tubes with compliance lumped in the transducer and oscillatory flow of fluid in rigid tubes were analyzed. A digital computer model based on one dimensional laminar oscillatory flow was developed and verified by exact solution of the Navier-Stokes Equation. Experimental results indicated that the damping ratio and resistance is much higher at higher frequencies of oscillation than predicted by the one dimensional model. An empirical correction factor was developed and incorporated into the computer model to correct the model to the experimental data. Amplitude of oscillation was found to have no effect on damping ratio so it was concluded that the increased damping ratio and resistance at higher frequencies was not due to turbulence but to two dimensional flow effects. Graphs and equations were developed to calculate damping ratio and undamped natural frequency of a catheter-transducer system from system parameters. Graphs and equations were also developed to calculate resistance and inertance for oscillatory flow in rigid tubes from system parameters and frequency of oscillation.     

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.     

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.     

Rib cage versus abdominal displacement in rabbits during forced oscillations to 30 Hz

We measured relative displacement of the rib cage (RC) and abdomen (ABD) in 12 anesthetized rabbits during forced oscillations. Sinusoidal volume changes were delivered through a tracheostomy at frequencies from 0.5 to 30 Hz and measured by body plethysmography. Displacements of the RC and ABD were measured by inductive plethysmography. During oscillation at fixed tidal volume (VT = 1.3 ml/kg) the ratio ABD/RC, normalized to unity at 0.5 Hz, was 0.88 +/- 0.06 at 2 Hz and increased to 1.28 +/- 0.13 at 6 Hz (P less than 0.01). As frequency increased further ABD/RC fell sharply but between 20 and 30 Hz reached a plateau of 0.17 +/- 0.02 (P less than 0.001). Displacements of RC and ABD were nearly synchronous from 0.5 to 2 Hz, but as frequency increased ABD lagged RC progressively, reaching a phase difference of 90 degrees between 6 and 8 Hz and 180 degrees between 16 and 20 Hz. In six additional rabbits we measured chest wall displacements while varying VT from 0.5 to 3.7 ml/kg. ABD/RC was independent of VT at low frequencies (less than or equal to 6 Hz) but fell sharply with increasing VT at the higher frequencies. We interpreted these findings using a chest wall model having an RC compartment whose displacements are governed primarily by a nonlinear compliance, in parallel with an ABD compartment whose displacements are governed by a series resistance, inertance, and in addition a nonlinear compliance. The experimental findings are in large measure accounted for by such a model if the degree of nonlinearity of ABD and RC compliances are comparable.(ABSTRACT TRUNCATED AT 250 WORDS)     

Inspiratory flow in the nose: a model coupling flow and vasoerectile tissue distensibility.

We have developed a discrete multisegmental model describing the coupling between inspiratory flow and nasal wall distensibility. This model is composed of 14 individualized compliant elements, each with its own relationship between cross-sectional area and transmural pressure. Conceptually, this model is based on flow limitation induced by the narrowing of duct due to collapsing pressure. For a given inspiratory pressure and for a given compliance distribution, this model predicts the area profile and inspiratory flow. Acoustic rhinometry and posterior rhinomanometry were used to determine the initial geometric area and mechanical characteristics of each element. The proposed model, used under steady-state conditions, is able to simulate the pressure-flow relationship observed in vivo under normal conditions (4 subjects) and under pathological conditions (4 vasomotor rhinitis and 3 valve syndrome subjects). Our results suggest that nasal wall compliance is an essential parameter to understand the nasal inspiratory flow limitation phenomenon and the associated increase of resistance that is well known to physiologists. By predicting the functional pressure-flow relationship, this model could be a useful tool for the clinician to evaluate the potential effects of treatments.     

Airway pressure-volume curve estimated by flow interruption during forced expiration

We attempted to estimate the pressure-volume characteristics of airways downstream from the choke point when the airflow was abruptly interrupted during forced expiration. The change of gas volume of the downstream segment after interruption could be estimated by multiplying the maximum flow (Vmax) immediately before interruption by the interruption time because the Vmax is maintained for a short period after airflow interruption at the mouth, as described in our previous report (J. Appl. Physiol. 66: 509-517, 1989). For the pressure of the downstream segment, we used the mouth pressure itself. Airway compliance, a slope of the pressure-volume curve, was measured in an airway model in eight normal subjects, in six patients with chronic obstructive pulmonary disease (COPD), and in one patient with tracheobronchopathia osteochondroplastica. Airway compliance was 0.96 ml/cmH2O in normal subjects and 2.49 ml/cmH2O in COPD patients. This difference of airway compliance was believed to be caused by the longitudinal expansion of the downstream segment and changes in the properties of the airway wall.     

A new method to measure nasal impedance in spontaneously breathing adults

As an alternative to standard rhinomanometric methods, we applied forced oscillations at the mouth in five normal subjects and determined their nasal impedance with a novel method involving flow subtraction. Pressure oscillations of constant amplitude were applied at the mouth of a subject both when the nostrils were open and when they were closed with a noseclip. The airflows measured under the two conditions were subtracted to yield the oscillating nasal airflow at the imposed pressure. The resultant pressure-flow relation defined the nasal impedance of the subject. For frequencies between 3 and 15 Hz, the transnasal pressure-flow relation was well described by a linear lumped parameter model consisting of a resistive and inertial element. Nasal resistance obtained with flow subtraction did not differ significantly from control measurements obtained while the subjects performed the Valsalva maneuver. In contrast, nasal inertance obtained with flow subtraction was approximately twice that obtained with the Valsalva method. The difference between inertances may reflect structural changes in nasopharyngeal dimensions that occur with the Valsalva maneuver. We conclude that the mechanical impedance of the nasal passage may be determined during spontaneous breathing from the response to imposed forced oscillations at the mouth. The noninvasive nature of this method suggests that it may be simpler to implement than traditional rhinomanometric methods.     

Partitioning of airway and respiratory tissue mechanical impedances by body plethysmography

Peslin, R., and C. Duvivier. Partitioning of airway andrespiratory tissue mechanical impedances by body plethysmography. J. Appl. Physiol. 84(2): 553-561, 1998.We have tested the feasibility of separating the airway (Zaw)and tissue (Zti) components of total respiratory input impedance(Zrs,in) in healthy subjects by measuring alveolar gas compression bybody plethysmography (Vpl) during pressure oscillations at the airwayopening. The forced oscillation setup was placed inside a bodyplethysmograph, and the subjects rebreathedBTPS gas. Zrs,in and the relationship between Vpl and airway flow (Hpl) were measured from 4 to 29 Hz. Zawand Zti were computed from Zrs,in and Hpl by using the monoalveolar T-network model and alveolar gas compliance derived from thoracic gasvolume. The data were in good agreement with previous observations: airway and tissue resistance exhibited some positive and negative frequency dependences, respectively; airway reactance was consistent with an inertance of 0.015 ± 0.003 hPa · s² · l¹and tissue reactance with an elastance of 36 ± 8 hPa/l. The changes seen with varying lung volume, during elastic loading of the chest andduring bronchoconstriction, were mostly in agreement with the expectedeffects. The data, as well as computer simulation, suggest that thepartitioning is unaffected by mechanical inhomogeneity and onlymoderately affected by airway wall shunting.

     

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.