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Preliminary study on the accuracy of respiratory input impedance measurement using the interrupter technique
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Preliminary study on the accuracy of respiratory input impedance measurement using the interrupter technique ∗ ´ Ireneusz Jabłonski , Adam G. Polak, Janusz Mroczka Chair of Electronic and Photonic Metrology, Wrocław University of Technology, ul. B. Prusa 53/55, 50-317 Wrocław, Poland
a r t i c l e
i n f o
a b s t r a c t
Article history:
Respiratory input impedance contains information about the state of pulmonary mechanics
Received 11 December 2009
in the frequency domain. In this paper the possibility of respiratory impedance measure-
Received in revised form
ment by interrupter technique as well as the accuracy of this approach are assessed.
22 October 2010
Transient states of flow and pressure recorded during expiratory flow interruption are sim-
Accepted 10 November 2010
ulated with a complex, linear model for the respiratory system and then used to calculate the impedance, including three states of respiratory mechanics and the influence of the
Keywords:
measurement noise. The results of computations are compared to the known, theoretical
Respiratory mechanics
impedance of the model. At 1 kHz sampling rate, the optimal time window lays between
Input impedance
100 and 200 ms and is centred around the pressure jump caused by the flow interruption.
Interrupter technique
The proposed algorithm yields satisfactory accuracy in the range from 10 to 400 Hz, particu-
Mathematical modelling
larly to 150 Hz. Depending on the simulated respiratory system state, the error of calculated
Measurement accuracy
impedance (relative Euclidean distance between the vectors of computed and theoretical values), for the window of 190 ms, varies between 5.0% and 7.1%. © 2010 Elsevier Ireland Ltd. All rights reserved.
1.
Introduction
Respiratory impedance represents the properties of pulmonary mechanics in the frequency domain. Depending on the position of flow and pressure transducers, input or transfer impedance is measured [1]. Resulting resistance and reactance spectra correspond to the state of the respiratory system and they are sensitive to pathological changes taking place in lungs. The level, location, and heterogeneity of airway constriction are well visible at low frequencies (around breathing rates) [2]. Spectra covering higher frequencies reveal one resonance and one or two antiresonance peaks whose character is correlated to the airway mechanics [3–5]. There are several techniques for respiratory input impedance measurement: the forced oscillation technique (FOT) assessing impedance typically in the range of 4–64 Hz [6]
∗
(and even up to 320 Hz [7]), the impulse oscillometry (IOS) with the range of 5–35 Hz [8], or the methods for determining the impedance spectrum around breathing frequencies (0.1–8 Hz) using specially designed and optimized ventilatory waveforms [9,10]. Frey et al. [11] have shown that input impedance can be measured between 32 and 800 Hz also by the interrupter technique. The interrupter technique (IT) proposed by von Neergaard and Wirtz [12] allows the determination of the so-called interrupter resistance Rint , encompassing mainly airway resistance. It is calculated from the pressure recorded at the airway opening after occlusion of a valve (for about 100 ms) divided by the flow measured during passive expiration just before interruption. Rint is the simplest and most popular representation of respiratory mechanics obtained by this technique [13,14]. The interest in enhancement of the diagnostic power of the interrupter technique results from its numerous advantages,
Corresponding author. Tel.: +48 71 3206329; fax: +48 71 3214277. ´ E-mail address: [email protected] (I. Jabłonski). 0169-2607/$ – see front matter © 2010 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.cmpb.2010.11.003
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as low hardware requirements, easy procedure, short time of measurement, and minimal requirements regarding patient co-operation. To date, it has been documented that the IT is well suited for patients suffering from chronic respiratory diseases, and especially for monitoring young patients – newborns and pre-school children [15,16]. A possible step in dissemination of such monitoring is related to eHealth and the implementation of the IT in telemedical systems [17]. Simplified assumptions (immediate compensation between alveolar and mouth pressures after interruption, constant airway resistance, lack of dynamic phenomena) explain why Rint overestimates airway resistance by about 30% [14,16,18,19]. This fact, together with limited repeatability, results in moderate interest and clinical use of the method [14,20]. Simultaneously, fast valves and good dynamics of contemporary medical transducers enable one to observe dumped oscillatory transients of the pressure signal. These transients measured for dogs and humans have been used to analyse the power spectra of pressure, and then to compare them to corresponding input impedances resulting from the FOT [4,11,21]. For both techniques, the characteristics with resonance and antiresonance peaks have been obtained. It is hypothesized that the first peak (around 50 ÷ 150 Hz) reflects the interaction between lung tissue and air volume, and the second one (from about 150 up to even 600 Hz), depending among others on airway walls compliance and respiratory gas properties, corresponds to a quarter-wave resonance in the airway duct [11,21,22]. Variations in frequency indices characterizing these peeks can be used to detect diagnostically relevant changes of respiratory impedance [4,22,23]. Although the published shapes of the power spectra from the IT and impedances from the FOT are in good agreement, the real respiratory properties could not be known in the reported investigations and the accuracy of retrieving complex respiratory mechanics from IT measurements is still in question. Additionally, one should be aware that these two techniques cannot be strictly compared to each other because an active excitation (oscillatory pressure generated by loudspeakers) together with a respiratory system response (oscillatory flow) are taken into account to calculate input impedance by FOT [24], whereas using the IT with the passively induced transient state only pressure oscillations are analysed when computing the power spectrum [11]. Moreover, it has been shown that the diagnostic relevance between the indexes of IT in the time domain and FOT is poor [25]. Broadening the IT by analyses in the frequency domain by Romero et al. [21] and Frey et al. [4,22] seems to be a promising direction, and currently is the area of investigations [23,26]. Despite pioneer experimental results of Frey et al. [5,11] on interrelations between the frequency indexes and the mechanical status of the lungs, there is still a lack of comparative analysis which would quantify this relationship. Imprecise physical–mathematical description of the respiratory system and its behaviour during a short-term airflow interruption is another question that conditions the accuracy and repeatability of the method. Typical one- or two-element representations, including airway resistance (Raw ) or resistive (Rrs ) and compliant (Crs ) properties of the whole system [12,13,27], are not suitable for the object responding with complex traces (i.e. damped transient oscillations of airway
opening pressure) on quasi-step excitation by valve closure. Such reduction in applied description for the IT experiment resulted also directly in the amount of information obtained during its realizations. For this reason, including the postinterrupter transient states into protocol of data processing in the time and/or frequency domain could be thought of as a next step in the real system inspection. But such attempts have been mainly concentrated on the mathematical parameterisation of the measurement data set or on the generation of non-parametric spectral characteristics, and then searching for their interrelations with the mechanical status of the lungs [22,23]. Meanwhile, concluding on research findings, Frey and Kraemer suggested the need of more precise modelling of the respiratory system for the IT [4], to improve the quality of measurements and also the comprehension of processes during airflow cessation. In this context, complex – forward (used for simulations) and reduced – inverse (proper for parameter estimation) analogues proposed in [28,29] give more detailed insight into parametrical and structural characteristics of interruption and its explanations. The aim of this work is to analyse the possibility of accurate assessment of the respiratory input impedance, called from here the interrupter impedance Zint (by analogy to interrupter resistance), using the IT. A preliminary study with a six-element model proposed by DuBois [6] and more complex analogues have given satisfactory results [28,30]. In this work a complex model for the respiratory system, including a morphology-based bronchial tree structure, has been applied to simulate pressure and flow courses during spontaneous breathing and expiratory flow interruption. To calculate the impedance, both signals next to and during occlusion have been analysed. The model is linear, so the computed spectrum can be compared to the theoretical impedance values (i.e. the true input impedance of the model) and the accuracy of the method has been assessed. Simulations make it also possible to find an optimal range of the analysed samples and to investigate the impact of measurement noise on the determined impedance.
2.
Methods
2.1.
Computational model for flow interruption
A complex model for the respiratory system during flow interruption has been implemented in the Matlab-Simulink environment (The MathWorks, USA). It consists of six dynamic, lumped parameter submodels representing successive components of the system and a model of the interrupter (Fig. 1). The chest wall (W) is specified by chest wall compliance in series with tissue inertance and resistance (the R–I–C structure). An inherent (and invisible in Fig. 1) part of this subsystem is a pressure source, modelling inspiratory muscle. It generates exponentially rising and falling pressure with the inhalation to exhalation time ratio of 1/3 and the breathing rate of 0.25 Hz [31] (see Appendix A). The lung (L) is modelled as a viscoelastic structure of the second order [32] and the pressure between these two blocs is the pleural pressure (Ppl ). The acinar airways (AC), connected to the lung at the point of
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Fig. 1 – A Simulink model for the respiratory system during flow interruption, including the chest wall (W), the lung (L), the accinar airways (AC), the conductive airways (CN), the trachea (T), and the upper airways (UP).
P(g) = Ppl + Pc (g),
Fig. 2 – Electrical circuit modelling a single generation of conductive airways (see text for notation).
alveolar pressure (Pa ), are included similarly to the chest wall, as a single compartment with cumulative resistance, compliance and inertance representing airway generations from 16 to 23 (the so-called silent zone) [33]. The most complex part of the model is the structure of the intrathoracic conductive airways (CN, generations 1–15), being subject to pleural pressure and taking into account symmetrical bifurcations described by Weibel [34]. Each of 65,534 airways is represented again by the R–I–C structure, however, due to a parallel arrangement of the identical tubes in every generation, cumulative parameters and two differential equations are used to model such segment [35]. As an example, an electrical circuit representing the gth airway generation is shown in Fig. 2, together with the resulting model Eqs. (1)–(5) and their Simulink implementation (Fig. 3). dQ(g + 1) P (g) , = i dt Icn (g)
(1)
dPc (g) Qc (g) , = dt Ccn (g)
(2)
Pi (g) = P(g + 1) − Rcn (g)Q(g + 1) − Pc (g) − Ppl ,
(3)
Qc (g) = Q(g + 1) − Q(g),
(4)
(5)
where Q are flows, P are pressures, and the subscript cn labels cumulative parameters of the given generation of conductive airways. Each submodel cooperates with its neighbours connected in series, returning flow Q(g + 1) and pressure P(g) calculated from the input flow Q(g) and pressure P(g + 1), using common Ppl . The trachea (T) is no longer influenced by Ppl , so it is represented as a separate R–I–C block, likewise the upper airways (UP). The shutter valve closes for 100 ms after about a 10% decrease of the maximal expiratory flow. Its resistance both rises from 10−3 to 106 kPa/(L/s), and drops back, during 20 ms [21] (see Appendix A). The values of model parameters were collected from the literature and adjusted, when needed, to reproduce empirical IT results more precisely both in the time and frequency domains (see Appendix A for details). All the values are in accordance with physiological and clinical findings, and are a kind of consensus between numerous experimental and modelling reports, which provide some ranges for the parameters introduced in the model. Detailed protocol and discussion of the modelling methodology for the interrupter technique, and
Fig. 3 – A Simulink submodel of a single conductive airway generation (see text for notation).
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also its consequences for further analysis of this method, were given in [28,29]. Numerical simulations of spontaneous breathing with expiratory flow interruption were performed for the reference parameter values (Normal state), mild constriction of intrathoracic conductive airways (generations 1–15, Airway constriction), and cheeks supported externally by hands to reduce their compliance (Cheeks supported). Differential equations were solved with the Dormand–Prince algorithm and the relative tolerance of 10−6 . Two respiratory cycles (each of 4 s) were simulated and the second one, deprived of transient states resulting from inaccurate initial conditions, was chosen for further analyses. Flow interruption lasted 100 ms, from 1.85 s to 1.95 s during passive expiration. To avoid distortion artefacts resulting from a finite sampling frequency of A/D converters, analog antialiasing filters are used in real measurements. An antialiasing filter was implemented in the computational model as follows. Firstly, during simulations, the flow and pressure signals were oversampled at the frequency of 100 kHz. This reduced a highfrequency energy leakage (related to the fast dynamics of the interrupter valve) into the samples. Then the FIR (linear phase, Kaiser window) lowpass digital filter with a passband from 0 to 400 Hz and a stopband from 600 Hz (order of 1462 and attenuation of 50 dB) was applied to the simulated data [36,37]. In the end, the filtered samples were decimated with the factor of 100, yielding the final sampling frequency of 1 kHz, a typical value during IT measurements. This enabled calculation of the discrete impedance spectrum up to 500 Hz.
2.2.
Calculation of input impedance
The structure of the linear model was taken into consideration when preparing a procedure for the computation of theoretical impedance Zth of the respiratory system for the three sets of parameter values, whereas the simulated and lowpass-filtered signals of flow and pressure were used to calculate interrupter impedance. Firstly, using the definitions of impedance for individual lumped resistive (ZR = R), inductive (ZI = jωI) and capacitive elements (ZC = 1/jωC), arranged in an appropriate net representing the scheme of electrical equivalent of the respiratory system, and the rules of their serial and parallel connections in the circuit, the theoretical input impedance of the model (Zth ) for a chosen range of frequencies (f = ω/2) was calculated. Secondly, the power spectral density of pressure GPP and the cross power spectral density of flow and pressure GQP were estimated using the Welch averaged periodogram method and the Hanning window, and finally the interrupter impedance Zint was calculated at every frequency as follows [38]: Zint (f ) =
GPP (f ) . GQP (f )
(6)
The accuracy of interrupter impedance assessment was determined by comparing its values with the theoretical ones in the range from 10 to 400 Hz: ıZint =
zint − zth × 100%, zth
(7)
where ıZint is the relative error of the measurement and zint and zth are vectors with interrupter and theoretical impedance values at this frequency range. It is obvious that the information content changes along the measured signals and the optimal time range of the pressure and flow samples used for impedance calculation can be searched. Ranges including 100, 125, 200, and 400 samples used to identify the impedance (i.e. 100–400 ms, regarding the sampling rate of 1 kHz) were investigated by shifting them sample-by-sample in the neighbourhood of flow interruption and calculating ıZint . Results of this part of study made it possible to propose the optimal range of samples as well as its location along the simulated data (see Section 3), and they were used in further analyses.
2.3. Analysis of noise impact on impedance measurement The accuracy of impedance measurement by interrupter technique depends not only on data processing algorithms but also on disturbances present in the recorded flow and pressure, such as measurement random noise or physiological artefacts. The effect of random noise disturbing the measured signals was analysed using the Monte Carlo method. An approach consisting in averaging impedances calculated from a few successive respiratory cycles had been reported [11], so in this study it was assumed that four sets of occlusion data would be used to compute one interrupter impedance spectrum. The Monte Carlo analysis covered 100 simulations of such measurement, each one consisting of four occlusions. Consecutive realizations of Gaussian noise characterized by a standard deviation equal to 0.5% of typical sensor ranges (±20 L/s for a pneumotachometer and ±2 kPa for a pressure transducer) were added to the simulated data, then low-pass filtered and used to compute Zint . Finally, mean values and standard deviations for the impedance spectrum were calculated at each analysed frequency.
3.
Results
Synthetic measurement data generated with the model are presented in Fig. 4. The valve occlusion begins after about a 10% decrease of the maximal expiratory flow and then the flow is stopped. At this time period, pressure rises to about 0.15 kPa indicating damped oscillations in the initial phase. Differences between signals representing different states of respiratory mechanics are well visible, particularly in the pressure transients. The observed trends are also in accordance with clinical and theoretical findings and well reproduce three zones which are typical for post-interrupter behaviour of the respiratory system in the time domain [22,39]. The first one, with a rapid change in mouth pressure (Pao ), is thought to be proportional to airway resistance. This period is followed by the oscillatory transient of Pao , reflecting the movement of gas down to the respiratory tract. The process arises from the kinetic to potential energy transfer, thus with interactions between inertial and compliant properties of the system and gas contained in it. The last section, a slow rise in pressure Pao , is ascribed to both the relax-
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Fig. 4 – Synthetic data of flow and pressure generated with the model for the respiratory system during flow interruption (flows for the normal state and cheeks supported are virtually undistinguishable). Vertical lines at the bottom zoomed panel indicate the optimal range of analysed samples.
ation of respiratory muscle and pendelluft in the airways [22,39,40]. As quite intuitive and relevant to clinical observations, the cheeks supporting is connected with modification of elastic properties in the upper airway segment, whereas asthmatic-like conditions of airway constrictions can manifest in increased airway resistance and decreased airway wall compliance and respiratory gas inertance in the bronchial tree. First condition influences mainly oscillatory profile of Pao just after occlusion, and this procedure is used for improving the reliability of the classical IT algorithm [41,42]. According to that, the twofold decrease of Cup produces higher frequency oscillations of the output Pao (Fig. 4). Furthermore, obstructive pathologies cause the decrease of airflow measured at the mouth (Qao ) and simultaneous increase in the pressure level (Pao ) [23,26], which also occurs during simulations with the complex model. On the other hand, changes of reactance properties (inertances, compliances) along the bronchial tree reshape the zone of postoclussional transient response (Fig. 4). The error of interrupter impedance assessment in the range from 10 to 400 Hz was dependent both on the width of the analysed range of samples and the location of the first sample. Minimal errors for the four ranges and three states of respiratory mechanics are shown in Table 1. These results suggest that the optimal range is situated between 100 and
Fig. 5 – Dependence of the error of interrupter impedance assessment on the position of the first sample for the case of 125 samples analysed.
200 samples included (i.e. between 0.1 and 0.2 s, since the signals are sampled at 1 kHz), whereas the largest errors have been obtained when using 400 samples. The error is sensitive not only to the width of the range but also to its position with respect to the occlusion. Fig. 5 demonstrates that only a specific location of the analysed samples assures minimal inaccuracy. What is interesting, for the first three cases the optimal location of samples is such that the centres of the ranges (around 1.865 s) are placed very close to the rapid jump of pressure (at 1.858 s). Additionally, when the right boundary of the range considerably goes beyond the rapid drop of pressure (as for 400 samples in Table 1), the accuracy decreases. Following these outcomes, the optimal range of the analysed samples has been proposed as centred around 1.865 s and almost not exceeding the time of the pressure drop, i.e. 190 samples between 1.77 and 1.96 s (see Fig. 4). To assure a 5 Hz resolution in the frequency domain, the flow and pressure vectors, after windowing, were additionally supplemented by zeros to reach exactly 200 samples (the zero-padding method). Impedances Zint calculated from the samples of flow (Qao ) and pressure (Pao ) belonging to the optimal range (1.77–1.96 s) have been compared to the theoretical values Zth for the three states of respiratory mechanics (Figs. 6–8). The interrupter and theoretical impedances are in very good agreement regarding both the real and imaginary parts, particularly in the region of antiresonance peaks. The impact of measurement noise on the accuracy of interrupter impedance determination, yielded by Monte Carlo
Table 1 – Minimal errors (ıZint ) of impedance assessment for different numbers of analysed samples (NS ), and related optimal time periods. NS
Normal state
100 125 200 400
7.4% 6.4% 7.9% 14.5%
Airway constriction 7.6% 5.6% 5.2% 11.8%
Cheeks supported 8.9% 7.4% 7.8% 15.1%
Optimal time period (s) 1.817 ÷ 1.916 1.806 ÷ 1.934 1.762 ÷ 1.961 1.568 ÷ 1.967
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Fig. 6 – Comparison of calculated interrupter impedance Zint to theoretical input impedance Zth for the normal state of respiratory mechanics.
Fig. 8 – Comparison of calculated interrupter impedance Zint to theoretical input impedance Zth for the cheeks externally supported.
model for the respiratory system during flow interruption was developed and implemented in the Matlab–Simulink environment. Performed simulations yielded synthetic flow and pressure signals related to the known states of respiratory mechanics and thus to the known impedances of the model. Finally, the calculated interrupter impedance could be compared with its theoretical values. Using both signals of flow and pressure recorded before and during occlusion seems to be superior to the approach when only pressure is analysed. Doing this, one provides real and imaginary parts of respiratory impedance, certainly containing more exhaustive information about respiratory mechanics than the pressure power spectrum alone. It is known that using the interrupter technique the values of acoustic antiresonance frequencies are influenced by geometrical dimensions
Fig. 7 – Comparison of calculated interrupter impedance Zint to theoretical input impedance Zth for the mild constriction of intrathoracic conductive airways.
analysis, is illustrated in Fig. 9. Both real and imaginary parts of impedance are assessed quite correctly at lower frequencies (to about 150 Hz), however a greater distortion of calculated impedance caused by the noise present in the measured signals should be expected at higher frequencies in real experiments.
4.
Discussion
In the present study the possibility of input impedance measurement using the interrupter technique, as well as the accuracy of such approach, were analysed. To be able to optimize the method and to assess its correctness, the complex
Fig. 9 – Effect of noise present in flow and pressure data on the accuracy of interrupter impedance assessment (mean ± one standard deviation, SD).
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of the shutter [22], and their amplitudes by the speed of shutter closure [21]. Nevertheless, relative changes during provocation tests (lung function tests causing airway narrowing by inhaled methacholine or histamine) should not be significantly influenced by these facts, because the shutter properties remain unchanged during examinations [4]. Most of real phenomena in the respiratory system are nonlinear. Among other things, the rapid drop of flow during occlusion modifies airway resistance (the primary component of the real part of respiratory impedance Zrs ), and the jump and fluctuations of pressure modify diameters of flexible airways, thus both their resistances and compliances (contributing to the real and imaginary parts of Zrs ). It has been also reported that flows higher than 0.1 L/s cause the decrease in the coherence function [11]. Despite this, a linear model was used, since this approach assures a proper calculation of theoretical impedance originally defined for linear systems. Nevertheless, one should be aware that this simplification could lead to overstated results, giving only a preliminary assessment of the measurement method. On the other hand, the inability to calculate Zint correctly from the data generated by a linear model would question the method itself, so this had to be done first. Having promising results, the next stage of investigations ought to take into account these nonlinear effects. One of the most interesting findings is that the minimal error of impedance calculation is obtained when the central sample from the analysed range lies near the jump of pressure and when the region of pressure drop accompanied by the highly damped flow oscillations is excluded from the analysis (see Table 1). In fact, the central sample is located at about 1.865 s. Comparing it with the time when the valve occlusion begins (1.85 s), a shift of 0.015 s is observed, equal exactly to the time resulting from the delay caused by the Kaiser filter used as the antialiasing filter (its order of 1462 at the sampling frequency of 100 kHz is equivalent to the shift of 0.01462 s). The symmetrical location of the analysed samples around the pressure jump and oscillations makes additionally that these data are least deformed by the Hanning window with the values close to 1 in this region. The rapid increase of the error when taking into calculations samples covering the end of occlusion demonstrates that the selected window should not contain the both pressure jumps simultaneously. This agrees also with the protocols of procedures applied by Romero et al. [21] and Frey at al. [22] or in the theoretical work by Bates at al. [39] who analysed the postinterrupter pressure and flow data in the frequency or time domain with only one of the slope’s directions (upward step – valve closing). Interrupter impedance was calculated in the frequency range from 10 to 400 Hz where, as reported by others, antiresonance peaks are expected. Simulations with undisturbed flow and pressure data (Figs. 6–8) have shown that the inaccuracy is virtually negligible. When random noise is present in the data, impedance at frequencies to about 150 Hz is still precisely assessed, however the accuracy of Zint reconstruction decreases for higher frequencies (Fig. 9). This effect can be explained by energy content in the frequency spectrum of the analysed signals. As depicted graphically by Frey et al. [11], the power spectra of pressure and flow decrease with frequency, and the first considerable drop is located at about 150 Hz, reducing the signal-to-noise ratio (SNR) at higher frequencies.
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Fig. 10 – Effect of noise present in flow and pressure data on the accuracy of interrupter impedance assessment (mean ± one standard deviation, SD) by Monte Carlo procedure covering 1000 simulations: (A) oversampling at 100 kHz and (B) oversampling at 1 MHz.
Nevertheless, using the IT, the frequency zone including typical antiresonance peaks can be examined exactly enough, especially as the noise level used in the simulations was relatively high. The higher SNR in relation to the FOT is especially useful for increasing the frequency range for Zint enough to include the higher frequency antiresonances [5]. The obtained results could not be considerably improved by greater number of iterations in the Monte Carlo procedure. The example with 1000 repetitions of computer simulations gave the characteristics shown in Fig. 10A. On the other hand, the improved accuracy of Zint reconstruction was observed for the increased oversampling of Pao and Qao signals. Data acquisition at 1 MHz sampling rate narrowed the range of uncertainty of Zint assessment at higher frequencies (Fig. 10B). Characteristic glitches, observed also in the input impedance calculated from the FOT [7], are now reduced. They are the consequences of the filtration procedure and the accuracy of implementation of
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the analog antialiasing filter in the digital platform. This experiment reveals that it should be possible to reconstruct accurately the interrupter impedance also at higher frequencies when using an appropriate analog filter. Also the experimental finding that oscillatory pressure transients after flow interruption are sensitive to the change in lung volume ought to be taken into considerations when analysing the accuracy of respiratory input impedance measurement by interrupter technique [22]. The mechanical properties of the respiratory system are directly related to the lung volume, and this inevitably produces additional Zint variability, which can be evaluated during further model studies. Some existing analogies with the FOT should be helpful in this research [43]. At this stage of research it is difficult to address the problem of the impact of respiratory system nonlinearities on the accuracy of Zint measurement. According to the best knowledge of the authors, non-linear complex simulation models for the IT have not been analysed so far. This work proves, however, that input respiratory impedance can be precisely assessed by IT in case of the linear system, and this sets the direction of future studies – now it is justified to repeat the same analysis with a nonlinear model. Taking into account that the complex linear model presented here represents empirical signals very well, one can expect that the effects of nonlinearities will not be significant.
5.
Conclusions
The possibility of input impedance measurement using the interrupter technique instead of the FOT was analysed in this work. The advantage of this approach stems from its technical simplicity as well as from the fact that measurements can be performed breath by breath with minimal cooperation of a subject, which makes it particularly useful for the examination of children and infants, or in internet-based home monitoring systems. Both, real and imaginary parts of respiratory impedance can be measured in contrast to former analyses yielding only the power spectrum of the pressure
transients. Simultaneously, other authors have shown that the acoustic antiresonance phenomena are sensitive to airway mechanics and its change during the provocation tests. The results convince that the input respiratory impedance can be calculated using flow and pressure measured by IT, at least when the effects of nonlinear phenomena in the respiratory system can be neglected and the examination is focused on the antiresonance peak features. Although there are some interesting questions open, e.g. the cause of inability to Zint reconstruction from postocclusional data recorded in the time range of valve reopening, the main goal – the feasibility and precision assessment of the input interrupter impedance estimation – was achieved. These calculations were conducted for a case of the standard hardware configuration in the IT (shutter valve and pressure and flow transducer placed in the measurement path), in contrast to the wave-tube technique application postulated by Frey et al. [5,11]. Also the analysis in the frequency domain may be supplementary to the traditional measurement of the interrupter resistance performed in the time domain. Then it is enough to supplement the existing IT equipment with dedicated numerical algorithms appropriately processing flow and pressure data. This idea has influenced our activities when developing a telemedical system for the monitoring of patients suffering from pulmonary diseases. In this system, beside standard spirometry, also the IT is included, with the measurement results transmitted to a medical server via the Internet, phone or a GSM network. The IT analysis of respiratory impedance will broaden capabilities of the system without extending its electronic structure. Satisfactory results when retrieving impedance from the IT measurements have been achieved assuming that the respiratory system is linear. This implies necessity of further work and simultaneously encourages us to continue the investigations. A few succeeding steps can be anticipated, each of them motivated by successful completion of the previous one. First, the impact of respiratory nonlinearities on the impedance measurement should be assessed. Then the sensitivity and specificity of Zint to pathological changes ought to be examined. Finally, an effort to solve the inverse prob-
Table A1 – Values of conductive airway parameters at the Normal state of the respiratory system. Generation number g 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Rcn (kPa/(L/s)) −3
1.46 × 10 3.90 × 10−3 2.24 × 10−3 1.49 × 10−3 9.83 × 10−3 12.0 × 10−3 14.6 × 10−3 16.4 × 10−3 37.8 × 10−3 42.2 × 10−3 44.3 × 10−3 43.2 × 10−3 33.3 × 10−3 23.7 × 10−3 15.9 × 10−3 10.1 × 10−3
Icn (kPa/(L/s2 )) −6
416 × 10 414 × 10−6 140 × 10−6 51.0 × 10−6 189 × 10−6 136 × 10−6 97.5 × 10−6 67.0 × 10−6 56.6 × 10−6 32.1 × 10−6 21.3 × 10−6 13.7 × 10−6 7.80 × 10−6 4.29 × 10−6 2.26 × 10−6 1.17 × 10−6
Ccn (L/kPa) 28.5 × 10−4 3.12 × 10−4 5.10 × 10−4 3.48 × 10−4 1.75 × 10−4 2.10 × 10−4 2.40 × 10−4 2.70 × 10−4 2.92 × 10−4 3.22 × 10−4 3.57 × 10−4 4.00 × 10−4 4.99 × 10−4 6.65 × 10−4 8.64 × 10−4 11.8 × 10−4
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Table A2 – Values of upper (indexed up) and accinar (indexed ac) airway parameters at the Normal state of the respiratory system. Upper airways Rup (kPa/(L/s)) Iup (kPa/(L/s2 )) Cup (L/kPa)
Accinar airways 22.7 × 10 625 5 × 10−3
−3
Rac (kPa/(L/s)) Iac (kPa/(L/s2 )) Cac (L/kPa)
1.2 × 10−3 2.7 × 10−7 0.43
lem, i.e. to elaborate an identification algorithm for concluding quantitatively about respiratory mechanics from Zint , can be undertaken.
Acknowledgment This work was financed from the Resources for Polish Science in 2007–2010 as the research and development project (No.: R01 028 03).
Appendix A. Values of parameters used in the complex model for the Normal state of the respiratory system are brought together in Tables A1–A3. They describe the lumped properties of the conductive airways including the trachea as generation 0 (Table A1), upper and accinar airways (Table A2), and lung and chest wall tissues (Table A3). Structure and parameter values of the upper airway model were deduced according to [44–47]. The main basis for the parameters of conductive and accinar airways was the paper by Lambert [48]. Originally, it presented the parameters of the airway area – transmural pressure characteristics for the bronchial tree generations together with airway lengths. From these characteristics airway areas and elementary compliances were calculated at 0.5 kPa transmural pressure (being equivalent to the Functional Residual Capacity, FRC), and then, using appropriate formulas [35,48], airway resistances, compliances and inertances of separate airways were computed. These data were aggregated for each generation (0–23), taking into account the parallel arrangement of identical airways in every segment [35], yielding Rcn (g), Ccn (g), and Icn (g) for the conductive region (g: 0–15), whereas the parameters of generations 16–23 (accinar airways) were further combined into cumulative Rac , Cac , and Iac , having in mind their serial distribution. The properties of lung and chest wall tissues were taken from [49]. After the basal values of the parameters had been implemented in the model, preliminary simulations of flow
interruptions were analysed both in the time and frequency domain. The pressure oscillations were in good accordance with empirical data published (e.g. [22,23,26]), however, to reproduce better the respiratory impedance spectrum (central frequencies and widths of resonance and antiresonance peeks), values of some parameters were manually modified. Lambert has extrapolated his data from measurements of big airways to higher generations and this is why they are less reliable. It has been found for example, that they give too small resistances of peripheral airways [49]. Thus, the resistances and inertances of conductive airways were iteratively increased and compliances decreased (according to their distinct dependences on cross-section area [35] and changes during airway constriction [50]) to mimic the published respiratory impedances or power spectra [4,21–23]. The final values used in the model are summarized in Tables A1–A3. Conditions of Airway constriction were simulated by twofold increase of Rcn and 1.5-times decrease of Icn and Ccn (generations 1–15) in relation to the Normal state [50]. The state of Cheeks supported uses only modified Cup , equal half of the normal value. The respiratory drive was implemented as the changes of pressure (Pm ) generated by respiratory muscle, similarly to the work by Lutchen et al. [31]. Its time trace, consisting of two exponential slopes with various time constants ( 1 = 0.11 s and 2 = 0.22 s), was imitated for every respiratory cycle of duration time equal to 4 s. Depending on the actual time (t) within the following respiratory cycle, this pressure is given as:
−t for 0 < t ≤ 1.3 s, 1 t − 1.3 = Apm exp − for 1.3 < t ≤ 4 s, −2 Pm = Apm 1 − exp
Pm
(A1)
where the amplitude of muscle pressure Apm = 0.4 kPa. The interrupter valve was simulated with a timevarying resistance Rv , switched within 0.02 s between its minimal (Rmin = 0.001 kPa/(L/s) – fully open) and maximal (Rmax = 1 × 10−6 kPa/(L/s) – fully closed) values, according to the formulas:
Rv =Rmin +
Ar 1 + sin 225 (t − tint ) − 2 2
Rv =Rmin +
Ar 1 + sin 225 (t − tint ) + 2 2
when closing,
when opening, (A2)
where Ar = Rmax − Rmin and tint denotes the time within a respiratory cycle when the interrupter manoeuvre starts.
references Table A3 – Values of lung (indexed l) and chest wall (indexed w) parameters at the Normal state of the respiratory system, including viscoelastic properties (indexed ve). Chest wall Rw (kPa/(L/s)) Cw (L/kPa) Iw (kPa/(L/s2 ))
Lungs −3
41 × 10 2.0 2.6 × 10−4
Rl (kPa/(L/s)) Cl (L/kPa) Rlve (kPa/(L/s)) Clve (L/kPa)
8.0 × 10−3 2.4 0.34 3.1
[1] R. Peslin, C. Duvivier, C. Gallina, Total respiratory input and transfer impedances in humans, J. Appl. Physiol. 59 (1985) 492–501. [2] K.R. Lutchen, H. Gillis, Relationship between heterogeneous changes in airway morphometry and lung resistance and elastance, J. Appl. Physiol. 83 (1997) 1192–1201. [3] A.C. Jackson, K.R. Lutchen, Physiological basis for resonant frequencies in respiratory system impedances in dogs, J. Appl. Physiol. 70 (1991) 1051–1058.
124
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 1 ( 2 0 1 1 ) 115–125
[4] U. Frey, R. Kraemer, Oscillatory pressure transients after flow interruption during bronchial challenge test in children, Eur. Respir. J. 10 (1997) 75–81. [5] U. Frey, M. Silverman, R. Kraemer, A.C. Jackson, High-frequency respiratory input impedance measurements in infants assessed by the high speed interrupter technique, Eur. Respir. J. 12 (1998) 148–158. [6] A.B. DuBois, A.W. Brody, D.H. Lewis, B.F. Burgess Jr., Oscillation mechanics of lungs and chest in man, J. Appl. Physiol. 8 (1956) 587–594. [7] A.C. Jackson, C.A. Giurdanella, H.L. Dorkin, Density dependence of respiratory system impedances between 5 and 320 Hz in humans, J. Appl. Physiol. 67 (1989) 2323–2330. [8] H. Bisgaard, B. Klug, Lung function measurement in awake young children, Eur. Respir. J. 8 (1995) 2067–2075. [9] K.R. Lutchen, K. Yang, D.W. Kaczka, B. Suki, Optimal ventilatory waveform for estimating low frequency mechanical impedance, J. Appl. Physiol. 75 (1993) 478–488. [10] D.W. Kaczka, E.P. Ingenito, K.R. Lutchen, Technique to determinate inspiratory impedance during mechanical ventilation: implications for flow limited patients, Ann. Biomed. Eng. 27 (1999) 340–355. [11] U. Frey, B. Suki, R. Kraemer, A.C. Jackson, Human respiratory input impedance between 32 and 800 Hz, measured by interrupter technique and forced oscillations, J. Appl. Physiol. 82 (1997) 1018–1023. [12] J. von Neergaard, K. Wirz, Die Messung der Strömungswiderstände in den Atemwegen des Menschen, insbesondere bei Asthma und Emphysem, Z. Klin. Med. 105 (1927) 51–82. [13] M. Gappa, A.A. Colin, I. Goetz, J. Stocks, Passive respiratory mechanics: the occlusion techniques, Eur. Respir. J. 17 (2001) 141–148. [14] A.M. Adams, C. Olden, D. Wertheim, A. Ives, P.D. Bridge, J. Lenton, P. Seddon, Measurement and repeatability of interrupter resistance in unsedated newborn infants, Pediatr. Pulmunol. 44 (2009) 1168–1173. [15] J. Stocks, Pulmonary function testing in infants, in: Encyclopaedia of Respiratory Medicine, Acad. Press, Amsterdam, 2006, pp. 564–577. [16] M. Oswald-Mammosser, A. Charloux, L. Donato, C. Albrech, J.P. Speich, E. Lampert, J. Lonsdorfer, Interrupter technique versus plethysmography for measurement of respiratory resistance in children with asthma or cystic fibrosis, Pediatr. Pulmunol. 29 (2000) 213–220. ´ [17] A.G. Polak, G. Głomb, T. Guszkowski, I. Jabłonski, B. ´ ˛ ˛ ´ Z. Swierczy ´ Kasprzak, J. Pekala, A.F. Stepie n, nski, J. Mroczka, Development of a telemedical system for monitoring patients with chronic respiratory diseases, IFMBE Proc. (Berlin) 25 (2009) 51–54. [18] J. Mead, J.L. Whittenberger, Evaluation of airway interruption technique as a method for measuring pulmonary air-flow resistance, J. Appl. Physiol. 6 (1954) 408–416. [19] A.C. Jackson, H.T. Milhorn Jr., J.R. Norman, A reevelauation of the interrupter technique for airway resistance measurement, J. Appl. Physiol. 36 (1974) 264–268. [20] B. Klug, H. Bisgaard, Measurement of lung function in awake 2–4-year-old asthmatic children during methacholine challenge and acute asthma: a comparison of the impulse oscilation technique the interrupter technique, and transcutaneous measurement of oxygen versus whole-body plethysmography, Pediatr. Pulmonol. 21 (1996) 290–300. [21] P.V. Romero, J. Sato, F. Shardonofsky, J.H.T. Bates, High-frequency characteristics of respiratory mechanics determined by flow interruption, J. Appl. Physiol. 69 (1990) 1682–1688.
[22] U. Frey, A. Schibler, R. Kraemer, Pressure oscillations after flow interruption in relation to lung mechanics, Respir. Physiol. 102 (1995) 225–237. [23] P.D. Bridge, D. Wertheim, A. Jackson, S.A. McKenzie, Pressure oscillation amplitude after interruption of tidal breathing as an index of change in airway mechanics in preschool children, Pediatr. Pulmonol. 40 (2005) 420–425. [24] D. MacLeod, M. Birch, Respiratory input impedance measurement: forced oscillation methods, Med. Biol. Eng. Comput. 39 (2001) 505–516. [25] C. Delacourt, H. Lorino, C. Fuhrman, M. Herve-Guillot, P. Reinert, A. Harf, B. Housset, Comparison of the forced oscillation technique and the interrupter technique for assessing airway obstruction and its reversibility in children, Am. J. Respir. Crit. Care Med. 164 (2001) 965–972. [26] J. Kivastik, J. Talts, R.A. Primhak, Interrupter technique and pressure oscillation analysis during bronchoconstriction in children, Clin. Physiol. Funct. Imaging 29 (2009) 45–52. [27] I. Goetz, A.F. Hoo, S. Loom, J. Stocks, Assessment of passive respiratory mechanics in infants: double versus single occlusion, Eur. Respir. J. 17 (2001) 449–455. ´ [28] I. Jabłonski, J. Mroczka, A forward model of the respiratory system during airflow interruption, Metrol. Meas. Syst. 16 (2009) 219–232. ´ [29] I. Jabłonski, J. Mroczka, Reduction of a linear complex model for respiratory system during airflow interruption, in: Proc. 32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Buenos Aires, Sept., 2010, pp. 2172–2175. ´ [30] I. Jabłonski, A.G. Polak, J. Mroczka, Methods for identification of a model of the respiratory system during airflow interruption, Meas. Automat. Control 8 (2000) 18–22 (in Polish). [31] K.R. Lutchen, F.P. Primiano Jr., G.M. Saidel, Nonlinear model combining pulmonary mechanics and gas concentration dynamics, IEEE Trans. Biomed. Eng. 29 (1982) 629–641. [32] J.H.T. Bates, M. Decramer, W.A. Zin, A. Harf, J. Milic-Emili, H.K. Chang, Respiratory resistance with histamine challenge by single-breath and forced oscillation methods, J. Appl. Physiol. 61 (1986) 873–880. [33] G. Nucci, S. Tessarin, C. Cobelli, A morphometric model of lung mechanics for time-domain analysis of alveolar pressures during mechanical ventilation, Ann. Biomed. Eng. 30 (2002) 537–545. [34] E.R. Weibel, Morphometry of the Human Lung, Springer, Berlin, 1963. [35] I. Ginzburg, D. Elad, Dynamic model of the bronchial tree, J. Biomed. Eng. 15 (1993) 283–288. [36] J.F. Kaiser, Nonrecursive digital filter design using the I0-sinh window function, in: Proc. IEEE Int. Symp. Circuits and Systems, San Francisco, April, 1974, pp. 20–23. [37] A.D. Poularikas, Signals and Systems Primer with Matlab, CRC Press, Boca Raton, 2007. [38] H. Franken, J. Cl(ment, K.P. van de Woestijne, Systematic and random errors in the determination of respiratory impedance by means of the forced oscillation technique: a theoretical study, IEEE Trans. Biomed. Eng. 30 (1983) 642–651. [39] J.H.T. Bates, P. Baconnier, J. Milic-Emili, A theoretical analysis of interrupter technique for measuring respiratory mechanics, J. Appl. Physiol. 64 (1988) 2204–2214. [40] P.D. Sly, J.H.T. Bates, Computer analysis of physical factors affecting the use of interrupter technique in infants, Pediatr. Pulmunol. 4 (1988) 219–224. [41] J.H.T. Bates, P.D. Sly, T. Kochi, J.G. Martin, The effect of a proximal compliance on interrupter measurements of resistance, Respir. Physiol. 70 (1987) 301–312. [42] F. Child, S. Clayton, S. Davies, A.A. Fryer, P.W. Jones, W. Lenney, How should airways resistance be measured in
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 1 ( 2 0 1 1 ) 115–125
[43]
[44] [45]
[46]
young children: mask or mouthpiece? Eur. Respir. J. 7 (2001) 1244–1249. C. Thamrin, K.E. Finucane, B. Singh, Z. Hantos, P. Sly, Volume dependence of high-frequency respiratory mechanics in healthy adults, Ann. Biomed. Eng. 36 (2008) 162–170. M.J. Jaeger, H. Matthys, The pattern of flow in the upper human airways, Respir. Physiol. 6 (1968–1969) 113–127. M.J. Jaeger, Effect of the cheeks and the compliance of alveolar gas on the measurement of respiratory variables, Respir. Physiol. 47 (1982) 325–340. R. Peslin, C. Duvivier, P. Jardin, Upper airway walls impedance measured with head plethysmograph, J. Appl. Physiol. 57 (1984) 596–600.
125
[47] A.G. Polak, A forward model for maximum expiration, Comput. Biol. Med. 28 (1998) 613–625. [48] R.K. Lambert, Sensitivity and specificity of the computational model for maximal expiratory flow, J. Appl. Physiol. 57 (1984) 958–970. [49] A.G. Polak, J. Mroczka, Nonlinear model for mechanical ventilation of human lungs, Comput. Biol. Med. 36 (2006) 41–58. [50] B. Morlion, A.G. Polak, Simulation of lung function evolution after heart–lung transplantation using a numerical model, IEEE Trans. Biomed. Eng. 52 (2005) 1180–1187.
journal homepage: www.intl.elsevierhealth.com/journals/cmpb
Preliminary study on the accuracy of respiratory input impedance measurement using the interrupter technique ∗ ´ Ireneusz Jabłonski , Adam G. Polak, Janusz Mroczka Chair of Electronic and Photonic Metrology, Wrocław University of Technology, ul. B. Prusa 53/55, 50-317 Wrocław, Poland
a r t i c l e
i n f o
a b s t r a c t
Article history:
Respiratory input impedance contains information about the state of pulmonary mechanics
Received 11 December 2009
in the frequency domain. In this paper the possibility of respiratory impedance measure-
Received in revised form
ment by interrupter technique as well as the accuracy of this approach are assessed.
22 October 2010
Transient states of flow and pressure recorded during expiratory flow interruption are sim-
Accepted 10 November 2010
ulated with a complex, linear model for the respiratory system and then used to calculate the impedance, including three states of respiratory mechanics and the influence of the
Keywords:
measurement noise. The results of computations are compared to the known, theoretical
Respiratory mechanics
impedance of the model. At 1 kHz sampling rate, the optimal time window lays between
Input impedance
100 and 200 ms and is centred around the pressure jump caused by the flow interruption.
Interrupter technique
The proposed algorithm yields satisfactory accuracy in the range from 10 to 400 Hz, particu-
Mathematical modelling
larly to 150 Hz. Depending on the simulated respiratory system state, the error of calculated
Measurement accuracy
impedance (relative Euclidean distance between the vectors of computed and theoretical values), for the window of 190 ms, varies between 5.0% and 7.1%. © 2010 Elsevier Ireland Ltd. All rights reserved.
1.
Introduction
Respiratory impedance represents the properties of pulmonary mechanics in the frequency domain. Depending on the position of flow and pressure transducers, input or transfer impedance is measured [1]. Resulting resistance and reactance spectra correspond to the state of the respiratory system and they are sensitive to pathological changes taking place in lungs. The level, location, and heterogeneity of airway constriction are well visible at low frequencies (around breathing rates) [2]. Spectra covering higher frequencies reveal one resonance and one or two antiresonance peaks whose character is correlated to the airway mechanics [3–5]. There are several techniques for respiratory input impedance measurement: the forced oscillation technique (FOT) assessing impedance typically in the range of 4–64 Hz [6]
∗
(and even up to 320 Hz [7]), the impulse oscillometry (IOS) with the range of 5–35 Hz [8], or the methods for determining the impedance spectrum around breathing frequencies (0.1–8 Hz) using specially designed and optimized ventilatory waveforms [9,10]. Frey et al. [11] have shown that input impedance can be measured between 32 and 800 Hz also by the interrupter technique. The interrupter technique (IT) proposed by von Neergaard and Wirtz [12] allows the determination of the so-called interrupter resistance Rint , encompassing mainly airway resistance. It is calculated from the pressure recorded at the airway opening after occlusion of a valve (for about 100 ms) divided by the flow measured during passive expiration just before interruption. Rint is the simplest and most popular representation of respiratory mechanics obtained by this technique [13,14]. The interest in enhancement of the diagnostic power of the interrupter technique results from its numerous advantages,
Corresponding author. Tel.: +48 71 3206329; fax: +48 71 3214277. ´ E-mail address: [email protected] (I. Jabłonski). 0169-2607/$ – see front matter © 2010 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.cmpb.2010.11.003
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as low hardware requirements, easy procedure, short time of measurement, and minimal requirements regarding patient co-operation. To date, it has been documented that the IT is well suited for patients suffering from chronic respiratory diseases, and especially for monitoring young patients – newborns and pre-school children [15,16]. A possible step in dissemination of such monitoring is related to eHealth and the implementation of the IT in telemedical systems [17]. Simplified assumptions (immediate compensation between alveolar and mouth pressures after interruption, constant airway resistance, lack of dynamic phenomena) explain why Rint overestimates airway resistance by about 30% [14,16,18,19]. This fact, together with limited repeatability, results in moderate interest and clinical use of the method [14,20]. Simultaneously, fast valves and good dynamics of contemporary medical transducers enable one to observe dumped oscillatory transients of the pressure signal. These transients measured for dogs and humans have been used to analyse the power spectra of pressure, and then to compare them to corresponding input impedances resulting from the FOT [4,11,21]. For both techniques, the characteristics with resonance and antiresonance peaks have been obtained. It is hypothesized that the first peak (around 50 ÷ 150 Hz) reflects the interaction between lung tissue and air volume, and the second one (from about 150 up to even 600 Hz), depending among others on airway walls compliance and respiratory gas properties, corresponds to a quarter-wave resonance in the airway duct [11,21,22]. Variations in frequency indices characterizing these peeks can be used to detect diagnostically relevant changes of respiratory impedance [4,22,23]. Although the published shapes of the power spectra from the IT and impedances from the FOT are in good agreement, the real respiratory properties could not be known in the reported investigations and the accuracy of retrieving complex respiratory mechanics from IT measurements is still in question. Additionally, one should be aware that these two techniques cannot be strictly compared to each other because an active excitation (oscillatory pressure generated by loudspeakers) together with a respiratory system response (oscillatory flow) are taken into account to calculate input impedance by FOT [24], whereas using the IT with the passively induced transient state only pressure oscillations are analysed when computing the power spectrum [11]. Moreover, it has been shown that the diagnostic relevance between the indexes of IT in the time domain and FOT is poor [25]. Broadening the IT by analyses in the frequency domain by Romero et al. [21] and Frey et al. [4,22] seems to be a promising direction, and currently is the area of investigations [23,26]. Despite pioneer experimental results of Frey et al. [5,11] on interrelations between the frequency indexes and the mechanical status of the lungs, there is still a lack of comparative analysis which would quantify this relationship. Imprecise physical–mathematical description of the respiratory system and its behaviour during a short-term airflow interruption is another question that conditions the accuracy and repeatability of the method. Typical one- or two-element representations, including airway resistance (Raw ) or resistive (Rrs ) and compliant (Crs ) properties of the whole system [12,13,27], are not suitable for the object responding with complex traces (i.e. damped transient oscillations of airway
opening pressure) on quasi-step excitation by valve closure. Such reduction in applied description for the IT experiment resulted also directly in the amount of information obtained during its realizations. For this reason, including the postinterrupter transient states into protocol of data processing in the time and/or frequency domain could be thought of as a next step in the real system inspection. But such attempts have been mainly concentrated on the mathematical parameterisation of the measurement data set or on the generation of non-parametric spectral characteristics, and then searching for their interrelations with the mechanical status of the lungs [22,23]. Meanwhile, concluding on research findings, Frey and Kraemer suggested the need of more precise modelling of the respiratory system for the IT [4], to improve the quality of measurements and also the comprehension of processes during airflow cessation. In this context, complex – forward (used for simulations) and reduced – inverse (proper for parameter estimation) analogues proposed in [28,29] give more detailed insight into parametrical and structural characteristics of interruption and its explanations. The aim of this work is to analyse the possibility of accurate assessment of the respiratory input impedance, called from here the interrupter impedance Zint (by analogy to interrupter resistance), using the IT. A preliminary study with a six-element model proposed by DuBois [6] and more complex analogues have given satisfactory results [28,30]. In this work a complex model for the respiratory system, including a morphology-based bronchial tree structure, has been applied to simulate pressure and flow courses during spontaneous breathing and expiratory flow interruption. To calculate the impedance, both signals next to and during occlusion have been analysed. The model is linear, so the computed spectrum can be compared to the theoretical impedance values (i.e. the true input impedance of the model) and the accuracy of the method has been assessed. Simulations make it also possible to find an optimal range of the analysed samples and to investigate the impact of measurement noise on the determined impedance.
2.
Methods
2.1.
Computational model for flow interruption
A complex model for the respiratory system during flow interruption has been implemented in the Matlab-Simulink environment (The MathWorks, USA). It consists of six dynamic, lumped parameter submodels representing successive components of the system and a model of the interrupter (Fig. 1). The chest wall (W) is specified by chest wall compliance in series with tissue inertance and resistance (the R–I–C structure). An inherent (and invisible in Fig. 1) part of this subsystem is a pressure source, modelling inspiratory muscle. It generates exponentially rising and falling pressure with the inhalation to exhalation time ratio of 1/3 and the breathing rate of 0.25 Hz [31] (see Appendix A). The lung (L) is modelled as a viscoelastic structure of the second order [32] and the pressure between these two blocs is the pleural pressure (Ppl ). The acinar airways (AC), connected to the lung at the point of
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 1 ( 2 0 1 1 ) 115–125
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Fig. 1 – A Simulink model for the respiratory system during flow interruption, including the chest wall (W), the lung (L), the accinar airways (AC), the conductive airways (CN), the trachea (T), and the upper airways (UP).
P(g) = Ppl + Pc (g),
Fig. 2 – Electrical circuit modelling a single generation of conductive airways (see text for notation).
alveolar pressure (Pa ), are included similarly to the chest wall, as a single compartment with cumulative resistance, compliance and inertance representing airway generations from 16 to 23 (the so-called silent zone) [33]. The most complex part of the model is the structure of the intrathoracic conductive airways (CN, generations 1–15), being subject to pleural pressure and taking into account symmetrical bifurcations described by Weibel [34]. Each of 65,534 airways is represented again by the R–I–C structure, however, due to a parallel arrangement of the identical tubes in every generation, cumulative parameters and two differential equations are used to model such segment [35]. As an example, an electrical circuit representing the gth airway generation is shown in Fig. 2, together with the resulting model Eqs. (1)–(5) and their Simulink implementation (Fig. 3). dQ(g + 1) P (g) , = i dt Icn (g)
(1)
dPc (g) Qc (g) , = dt Ccn (g)
(2)
Pi (g) = P(g + 1) − Rcn (g)Q(g + 1) − Pc (g) − Ppl ,
(3)
Qc (g) = Q(g + 1) − Q(g),
(4)
(5)
where Q are flows, P are pressures, and the subscript cn labels cumulative parameters of the given generation of conductive airways. Each submodel cooperates with its neighbours connected in series, returning flow Q(g + 1) and pressure P(g) calculated from the input flow Q(g) and pressure P(g + 1), using common Ppl . The trachea (T) is no longer influenced by Ppl , so it is represented as a separate R–I–C block, likewise the upper airways (UP). The shutter valve closes for 100 ms after about a 10% decrease of the maximal expiratory flow. Its resistance both rises from 10−3 to 106 kPa/(L/s), and drops back, during 20 ms [21] (see Appendix A). The values of model parameters were collected from the literature and adjusted, when needed, to reproduce empirical IT results more precisely both in the time and frequency domains (see Appendix A for details). All the values are in accordance with physiological and clinical findings, and are a kind of consensus between numerous experimental and modelling reports, which provide some ranges for the parameters introduced in the model. Detailed protocol and discussion of the modelling methodology for the interrupter technique, and
Fig. 3 – A Simulink submodel of a single conductive airway generation (see text for notation).
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also its consequences for further analysis of this method, were given in [28,29]. Numerical simulations of spontaneous breathing with expiratory flow interruption were performed for the reference parameter values (Normal state), mild constriction of intrathoracic conductive airways (generations 1–15, Airway constriction), and cheeks supported externally by hands to reduce their compliance (Cheeks supported). Differential equations were solved with the Dormand–Prince algorithm and the relative tolerance of 10−6 . Two respiratory cycles (each of 4 s) were simulated and the second one, deprived of transient states resulting from inaccurate initial conditions, was chosen for further analyses. Flow interruption lasted 100 ms, from 1.85 s to 1.95 s during passive expiration. To avoid distortion artefacts resulting from a finite sampling frequency of A/D converters, analog antialiasing filters are used in real measurements. An antialiasing filter was implemented in the computational model as follows. Firstly, during simulations, the flow and pressure signals were oversampled at the frequency of 100 kHz. This reduced a highfrequency energy leakage (related to the fast dynamics of the interrupter valve) into the samples. Then the FIR (linear phase, Kaiser window) lowpass digital filter with a passband from 0 to 400 Hz and a stopband from 600 Hz (order of 1462 and attenuation of 50 dB) was applied to the simulated data [36,37]. In the end, the filtered samples were decimated with the factor of 100, yielding the final sampling frequency of 1 kHz, a typical value during IT measurements. This enabled calculation of the discrete impedance spectrum up to 500 Hz.
2.2.
Calculation of input impedance
The structure of the linear model was taken into consideration when preparing a procedure for the computation of theoretical impedance Zth of the respiratory system for the three sets of parameter values, whereas the simulated and lowpass-filtered signals of flow and pressure were used to calculate interrupter impedance. Firstly, using the definitions of impedance for individual lumped resistive (ZR = R), inductive (ZI = jωI) and capacitive elements (ZC = 1/jωC), arranged in an appropriate net representing the scheme of electrical equivalent of the respiratory system, and the rules of their serial and parallel connections in the circuit, the theoretical input impedance of the model (Zth ) for a chosen range of frequencies (f = ω/2) was calculated. Secondly, the power spectral density of pressure GPP and the cross power spectral density of flow and pressure GQP were estimated using the Welch averaged periodogram method and the Hanning window, and finally the interrupter impedance Zint was calculated at every frequency as follows [38]: Zint (f ) =
GPP (f ) . GQP (f )
(6)
The accuracy of interrupter impedance assessment was determined by comparing its values with the theoretical ones in the range from 10 to 400 Hz: ıZint =
zint − zth × 100%, zth
(7)
where ıZint is the relative error of the measurement and zint and zth are vectors with interrupter and theoretical impedance values at this frequency range. It is obvious that the information content changes along the measured signals and the optimal time range of the pressure and flow samples used for impedance calculation can be searched. Ranges including 100, 125, 200, and 400 samples used to identify the impedance (i.e. 100–400 ms, regarding the sampling rate of 1 kHz) were investigated by shifting them sample-by-sample in the neighbourhood of flow interruption and calculating ıZint . Results of this part of study made it possible to propose the optimal range of samples as well as its location along the simulated data (see Section 3), and they were used in further analyses.
2.3. Analysis of noise impact on impedance measurement The accuracy of impedance measurement by interrupter technique depends not only on data processing algorithms but also on disturbances present in the recorded flow and pressure, such as measurement random noise or physiological artefacts. The effect of random noise disturbing the measured signals was analysed using the Monte Carlo method. An approach consisting in averaging impedances calculated from a few successive respiratory cycles had been reported [11], so in this study it was assumed that four sets of occlusion data would be used to compute one interrupter impedance spectrum. The Monte Carlo analysis covered 100 simulations of such measurement, each one consisting of four occlusions. Consecutive realizations of Gaussian noise characterized by a standard deviation equal to 0.5% of typical sensor ranges (±20 L/s for a pneumotachometer and ±2 kPa for a pressure transducer) were added to the simulated data, then low-pass filtered and used to compute Zint . Finally, mean values and standard deviations for the impedance spectrum were calculated at each analysed frequency.
3.
Results
Synthetic measurement data generated with the model are presented in Fig. 4. The valve occlusion begins after about a 10% decrease of the maximal expiratory flow and then the flow is stopped. At this time period, pressure rises to about 0.15 kPa indicating damped oscillations in the initial phase. Differences between signals representing different states of respiratory mechanics are well visible, particularly in the pressure transients. The observed trends are also in accordance with clinical and theoretical findings and well reproduce three zones which are typical for post-interrupter behaviour of the respiratory system in the time domain [22,39]. The first one, with a rapid change in mouth pressure (Pao ), is thought to be proportional to airway resistance. This period is followed by the oscillatory transient of Pao , reflecting the movement of gas down to the respiratory tract. The process arises from the kinetic to potential energy transfer, thus with interactions between inertial and compliant properties of the system and gas contained in it. The last section, a slow rise in pressure Pao , is ascribed to both the relax-
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Fig. 4 – Synthetic data of flow and pressure generated with the model for the respiratory system during flow interruption (flows for the normal state and cheeks supported are virtually undistinguishable). Vertical lines at the bottom zoomed panel indicate the optimal range of analysed samples.
ation of respiratory muscle and pendelluft in the airways [22,39,40]. As quite intuitive and relevant to clinical observations, the cheeks supporting is connected with modification of elastic properties in the upper airway segment, whereas asthmatic-like conditions of airway constrictions can manifest in increased airway resistance and decreased airway wall compliance and respiratory gas inertance in the bronchial tree. First condition influences mainly oscillatory profile of Pao just after occlusion, and this procedure is used for improving the reliability of the classical IT algorithm [41,42]. According to that, the twofold decrease of Cup produces higher frequency oscillations of the output Pao (Fig. 4). Furthermore, obstructive pathologies cause the decrease of airflow measured at the mouth (Qao ) and simultaneous increase in the pressure level (Pao ) [23,26], which also occurs during simulations with the complex model. On the other hand, changes of reactance properties (inertances, compliances) along the bronchial tree reshape the zone of postoclussional transient response (Fig. 4). The error of interrupter impedance assessment in the range from 10 to 400 Hz was dependent both on the width of the analysed range of samples and the location of the first sample. Minimal errors for the four ranges and three states of respiratory mechanics are shown in Table 1. These results suggest that the optimal range is situated between 100 and
Fig. 5 – Dependence of the error of interrupter impedance assessment on the position of the first sample for the case of 125 samples analysed.
200 samples included (i.e. between 0.1 and 0.2 s, since the signals are sampled at 1 kHz), whereas the largest errors have been obtained when using 400 samples. The error is sensitive not only to the width of the range but also to its position with respect to the occlusion. Fig. 5 demonstrates that only a specific location of the analysed samples assures minimal inaccuracy. What is interesting, for the first three cases the optimal location of samples is such that the centres of the ranges (around 1.865 s) are placed very close to the rapid jump of pressure (at 1.858 s). Additionally, when the right boundary of the range considerably goes beyond the rapid drop of pressure (as for 400 samples in Table 1), the accuracy decreases. Following these outcomes, the optimal range of the analysed samples has been proposed as centred around 1.865 s and almost not exceeding the time of the pressure drop, i.e. 190 samples between 1.77 and 1.96 s (see Fig. 4). To assure a 5 Hz resolution in the frequency domain, the flow and pressure vectors, after windowing, were additionally supplemented by zeros to reach exactly 200 samples (the zero-padding method). Impedances Zint calculated from the samples of flow (Qao ) and pressure (Pao ) belonging to the optimal range (1.77–1.96 s) have been compared to the theoretical values Zth for the three states of respiratory mechanics (Figs. 6–8). The interrupter and theoretical impedances are in very good agreement regarding both the real and imaginary parts, particularly in the region of antiresonance peaks. The impact of measurement noise on the accuracy of interrupter impedance determination, yielded by Monte Carlo
Table 1 – Minimal errors (ıZint ) of impedance assessment for different numbers of analysed samples (NS ), and related optimal time periods. NS
Normal state
100 125 200 400
7.4% 6.4% 7.9% 14.5%
Airway constriction 7.6% 5.6% 5.2% 11.8%
Cheeks supported 8.9% 7.4% 7.8% 15.1%
Optimal time period (s) 1.817 ÷ 1.916 1.806 ÷ 1.934 1.762 ÷ 1.961 1.568 ÷ 1.967
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Fig. 6 – Comparison of calculated interrupter impedance Zint to theoretical input impedance Zth for the normal state of respiratory mechanics.
Fig. 8 – Comparison of calculated interrupter impedance Zint to theoretical input impedance Zth for the cheeks externally supported.
model for the respiratory system during flow interruption was developed and implemented in the Matlab–Simulink environment. Performed simulations yielded synthetic flow and pressure signals related to the known states of respiratory mechanics and thus to the known impedances of the model. Finally, the calculated interrupter impedance could be compared with its theoretical values. Using both signals of flow and pressure recorded before and during occlusion seems to be superior to the approach when only pressure is analysed. Doing this, one provides real and imaginary parts of respiratory impedance, certainly containing more exhaustive information about respiratory mechanics than the pressure power spectrum alone. It is known that using the interrupter technique the values of acoustic antiresonance frequencies are influenced by geometrical dimensions
Fig. 7 – Comparison of calculated interrupter impedance Zint to theoretical input impedance Zth for the mild constriction of intrathoracic conductive airways.
analysis, is illustrated in Fig. 9. Both real and imaginary parts of impedance are assessed quite correctly at lower frequencies (to about 150 Hz), however a greater distortion of calculated impedance caused by the noise present in the measured signals should be expected at higher frequencies in real experiments.
4.
Discussion
In the present study the possibility of input impedance measurement using the interrupter technique, as well as the accuracy of such approach, were analysed. To be able to optimize the method and to assess its correctness, the complex
Fig. 9 – Effect of noise present in flow and pressure data on the accuracy of interrupter impedance assessment (mean ± one standard deviation, SD).
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of the shutter [22], and their amplitudes by the speed of shutter closure [21]. Nevertheless, relative changes during provocation tests (lung function tests causing airway narrowing by inhaled methacholine or histamine) should not be significantly influenced by these facts, because the shutter properties remain unchanged during examinations [4]. Most of real phenomena in the respiratory system are nonlinear. Among other things, the rapid drop of flow during occlusion modifies airway resistance (the primary component of the real part of respiratory impedance Zrs ), and the jump and fluctuations of pressure modify diameters of flexible airways, thus both their resistances and compliances (contributing to the real and imaginary parts of Zrs ). It has been also reported that flows higher than 0.1 L/s cause the decrease in the coherence function [11]. Despite this, a linear model was used, since this approach assures a proper calculation of theoretical impedance originally defined for linear systems. Nevertheless, one should be aware that this simplification could lead to overstated results, giving only a preliminary assessment of the measurement method. On the other hand, the inability to calculate Zint correctly from the data generated by a linear model would question the method itself, so this had to be done first. Having promising results, the next stage of investigations ought to take into account these nonlinear effects. One of the most interesting findings is that the minimal error of impedance calculation is obtained when the central sample from the analysed range lies near the jump of pressure and when the region of pressure drop accompanied by the highly damped flow oscillations is excluded from the analysis (see Table 1). In fact, the central sample is located at about 1.865 s. Comparing it with the time when the valve occlusion begins (1.85 s), a shift of 0.015 s is observed, equal exactly to the time resulting from the delay caused by the Kaiser filter used as the antialiasing filter (its order of 1462 at the sampling frequency of 100 kHz is equivalent to the shift of 0.01462 s). The symmetrical location of the analysed samples around the pressure jump and oscillations makes additionally that these data are least deformed by the Hanning window with the values close to 1 in this region. The rapid increase of the error when taking into calculations samples covering the end of occlusion demonstrates that the selected window should not contain the both pressure jumps simultaneously. This agrees also with the protocols of procedures applied by Romero et al. [21] and Frey at al. [22] or in the theoretical work by Bates at al. [39] who analysed the postinterrupter pressure and flow data in the frequency or time domain with only one of the slope’s directions (upward step – valve closing). Interrupter impedance was calculated in the frequency range from 10 to 400 Hz where, as reported by others, antiresonance peaks are expected. Simulations with undisturbed flow and pressure data (Figs. 6–8) have shown that the inaccuracy is virtually negligible. When random noise is present in the data, impedance at frequencies to about 150 Hz is still precisely assessed, however the accuracy of Zint reconstruction decreases for higher frequencies (Fig. 9). This effect can be explained by energy content in the frequency spectrum of the analysed signals. As depicted graphically by Frey et al. [11], the power spectra of pressure and flow decrease with frequency, and the first considerable drop is located at about 150 Hz, reducing the signal-to-noise ratio (SNR) at higher frequencies.
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Fig. 10 – Effect of noise present in flow and pressure data on the accuracy of interrupter impedance assessment (mean ± one standard deviation, SD) by Monte Carlo procedure covering 1000 simulations: (A) oversampling at 100 kHz and (B) oversampling at 1 MHz.
Nevertheless, using the IT, the frequency zone including typical antiresonance peaks can be examined exactly enough, especially as the noise level used in the simulations was relatively high. The higher SNR in relation to the FOT is especially useful for increasing the frequency range for Zint enough to include the higher frequency antiresonances [5]. The obtained results could not be considerably improved by greater number of iterations in the Monte Carlo procedure. The example with 1000 repetitions of computer simulations gave the characteristics shown in Fig. 10A. On the other hand, the improved accuracy of Zint reconstruction was observed for the increased oversampling of Pao and Qao signals. Data acquisition at 1 MHz sampling rate narrowed the range of uncertainty of Zint assessment at higher frequencies (Fig. 10B). Characteristic glitches, observed also in the input impedance calculated from the FOT [7], are now reduced. They are the consequences of the filtration procedure and the accuracy of implementation of
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the analog antialiasing filter in the digital platform. This experiment reveals that it should be possible to reconstruct accurately the interrupter impedance also at higher frequencies when using an appropriate analog filter. Also the experimental finding that oscillatory pressure transients after flow interruption are sensitive to the change in lung volume ought to be taken into considerations when analysing the accuracy of respiratory input impedance measurement by interrupter technique [22]. The mechanical properties of the respiratory system are directly related to the lung volume, and this inevitably produces additional Zint variability, which can be evaluated during further model studies. Some existing analogies with the FOT should be helpful in this research [43]. At this stage of research it is difficult to address the problem of the impact of respiratory system nonlinearities on the accuracy of Zint measurement. According to the best knowledge of the authors, non-linear complex simulation models for the IT have not been analysed so far. This work proves, however, that input respiratory impedance can be precisely assessed by IT in case of the linear system, and this sets the direction of future studies – now it is justified to repeat the same analysis with a nonlinear model. Taking into account that the complex linear model presented here represents empirical signals very well, one can expect that the effects of nonlinearities will not be significant.
5.
Conclusions
The possibility of input impedance measurement using the interrupter technique instead of the FOT was analysed in this work. The advantage of this approach stems from its technical simplicity as well as from the fact that measurements can be performed breath by breath with minimal cooperation of a subject, which makes it particularly useful for the examination of children and infants, or in internet-based home monitoring systems. Both, real and imaginary parts of respiratory impedance can be measured in contrast to former analyses yielding only the power spectrum of the pressure
transients. Simultaneously, other authors have shown that the acoustic antiresonance phenomena are sensitive to airway mechanics and its change during the provocation tests. The results convince that the input respiratory impedance can be calculated using flow and pressure measured by IT, at least when the effects of nonlinear phenomena in the respiratory system can be neglected and the examination is focused on the antiresonance peak features. Although there are some interesting questions open, e.g. the cause of inability to Zint reconstruction from postocclusional data recorded in the time range of valve reopening, the main goal – the feasibility and precision assessment of the input interrupter impedance estimation – was achieved. These calculations were conducted for a case of the standard hardware configuration in the IT (shutter valve and pressure and flow transducer placed in the measurement path), in contrast to the wave-tube technique application postulated by Frey et al. [5,11]. Also the analysis in the frequency domain may be supplementary to the traditional measurement of the interrupter resistance performed in the time domain. Then it is enough to supplement the existing IT equipment with dedicated numerical algorithms appropriately processing flow and pressure data. This idea has influenced our activities when developing a telemedical system for the monitoring of patients suffering from pulmonary diseases. In this system, beside standard spirometry, also the IT is included, with the measurement results transmitted to a medical server via the Internet, phone or a GSM network. The IT analysis of respiratory impedance will broaden capabilities of the system without extending its electronic structure. Satisfactory results when retrieving impedance from the IT measurements have been achieved assuming that the respiratory system is linear. This implies necessity of further work and simultaneously encourages us to continue the investigations. A few succeeding steps can be anticipated, each of them motivated by successful completion of the previous one. First, the impact of respiratory nonlinearities on the impedance measurement should be assessed. Then the sensitivity and specificity of Zint to pathological changes ought to be examined. Finally, an effort to solve the inverse prob-
Table A1 – Values of conductive airway parameters at the Normal state of the respiratory system. Generation number g 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Rcn (kPa/(L/s)) −3
1.46 × 10 3.90 × 10−3 2.24 × 10−3 1.49 × 10−3 9.83 × 10−3 12.0 × 10−3 14.6 × 10−3 16.4 × 10−3 37.8 × 10−3 42.2 × 10−3 44.3 × 10−3 43.2 × 10−3 33.3 × 10−3 23.7 × 10−3 15.9 × 10−3 10.1 × 10−3
Icn (kPa/(L/s2 )) −6
416 × 10 414 × 10−6 140 × 10−6 51.0 × 10−6 189 × 10−6 136 × 10−6 97.5 × 10−6 67.0 × 10−6 56.6 × 10−6 32.1 × 10−6 21.3 × 10−6 13.7 × 10−6 7.80 × 10−6 4.29 × 10−6 2.26 × 10−6 1.17 × 10−6
Ccn (L/kPa) 28.5 × 10−4 3.12 × 10−4 5.10 × 10−4 3.48 × 10−4 1.75 × 10−4 2.10 × 10−4 2.40 × 10−4 2.70 × 10−4 2.92 × 10−4 3.22 × 10−4 3.57 × 10−4 4.00 × 10−4 4.99 × 10−4 6.65 × 10−4 8.64 × 10−4 11.8 × 10−4
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Table A2 – Values of upper (indexed up) and accinar (indexed ac) airway parameters at the Normal state of the respiratory system. Upper airways Rup (kPa/(L/s)) Iup (kPa/(L/s2 )) Cup (L/kPa)
Accinar airways 22.7 × 10 625 5 × 10−3
−3
Rac (kPa/(L/s)) Iac (kPa/(L/s2 )) Cac (L/kPa)
1.2 × 10−3 2.7 × 10−7 0.43
lem, i.e. to elaborate an identification algorithm for concluding quantitatively about respiratory mechanics from Zint , can be undertaken.
Acknowledgment This work was financed from the Resources for Polish Science in 2007–2010 as the research and development project (No.: R01 028 03).
Appendix A. Values of parameters used in the complex model for the Normal state of the respiratory system are brought together in Tables A1–A3. They describe the lumped properties of the conductive airways including the trachea as generation 0 (Table A1), upper and accinar airways (Table A2), and lung and chest wall tissues (Table A3). Structure and parameter values of the upper airway model were deduced according to [44–47]. The main basis for the parameters of conductive and accinar airways was the paper by Lambert [48]. Originally, it presented the parameters of the airway area – transmural pressure characteristics for the bronchial tree generations together with airway lengths. From these characteristics airway areas and elementary compliances were calculated at 0.5 kPa transmural pressure (being equivalent to the Functional Residual Capacity, FRC), and then, using appropriate formulas [35,48], airway resistances, compliances and inertances of separate airways were computed. These data were aggregated for each generation (0–23), taking into account the parallel arrangement of identical airways in every segment [35], yielding Rcn (g), Ccn (g), and Icn (g) for the conductive region (g: 0–15), whereas the parameters of generations 16–23 (accinar airways) were further combined into cumulative Rac , Cac , and Iac , having in mind their serial distribution. The properties of lung and chest wall tissues were taken from [49]. After the basal values of the parameters had been implemented in the model, preliminary simulations of flow
interruptions were analysed both in the time and frequency domain. The pressure oscillations were in good accordance with empirical data published (e.g. [22,23,26]), however, to reproduce better the respiratory impedance spectrum (central frequencies and widths of resonance and antiresonance peeks), values of some parameters were manually modified. Lambert has extrapolated his data from measurements of big airways to higher generations and this is why they are less reliable. It has been found for example, that they give too small resistances of peripheral airways [49]. Thus, the resistances and inertances of conductive airways were iteratively increased and compliances decreased (according to their distinct dependences on cross-section area [35] and changes during airway constriction [50]) to mimic the published respiratory impedances or power spectra [4,21–23]. The final values used in the model are summarized in Tables A1–A3. Conditions of Airway constriction were simulated by twofold increase of Rcn and 1.5-times decrease of Icn and Ccn (generations 1–15) in relation to the Normal state [50]. The state of Cheeks supported uses only modified Cup , equal half of the normal value. The respiratory drive was implemented as the changes of pressure (Pm ) generated by respiratory muscle, similarly to the work by Lutchen et al. [31]. Its time trace, consisting of two exponential slopes with various time constants ( 1 = 0.11 s and 2 = 0.22 s), was imitated for every respiratory cycle of duration time equal to 4 s. Depending on the actual time (t) within the following respiratory cycle, this pressure is given as:
−t for 0 < t ≤ 1.3 s, 1 t − 1.3 = Apm exp − for 1.3 < t ≤ 4 s, −2 Pm = Apm 1 − exp
Pm
(A1)
where the amplitude of muscle pressure Apm = 0.4 kPa. The interrupter valve was simulated with a timevarying resistance Rv , switched within 0.02 s between its minimal (Rmin = 0.001 kPa/(L/s) – fully open) and maximal (Rmax = 1 × 10−6 kPa/(L/s) – fully closed) values, according to the formulas:
Rv =Rmin +
Ar 1 + sin 225 (t − tint ) − 2 2
Rv =Rmin +
Ar 1 + sin 225 (t − tint ) + 2 2
when closing,
when opening, (A2)
where Ar = Rmax − Rmin and tint denotes the time within a respiratory cycle when the interrupter manoeuvre starts.
references Table A3 – Values of lung (indexed l) and chest wall (indexed w) parameters at the Normal state of the respiratory system, including viscoelastic properties (indexed ve). Chest wall Rw (kPa/(L/s)) Cw (L/kPa) Iw (kPa/(L/s2 ))
Lungs −3
41 × 10 2.0 2.6 × 10−4
Rl (kPa/(L/s)) Cl (L/kPa) Rlve (kPa/(L/s)) Clve (L/kPa)
8.0 × 10−3 2.4 0.34 3.1
[1] R. Peslin, C. Duvivier, C. Gallina, Total respiratory input and transfer impedances in humans, J. Appl. Physiol. 59 (1985) 492–501. [2] K.R. Lutchen, H. Gillis, Relationship between heterogeneous changes in airway morphometry and lung resistance and elastance, J. Appl. Physiol. 83 (1997) 1192–1201. [3] A.C. Jackson, K.R. Lutchen, Physiological basis for resonant frequencies in respiratory system impedances in dogs, J. Appl. Physiol. 70 (1991) 1051–1058.
124
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 1 ( 2 0 1 1 ) 115–125
[4] U. Frey, R. Kraemer, Oscillatory pressure transients after flow interruption during bronchial challenge test in children, Eur. Respir. J. 10 (1997) 75–81. [5] U. Frey, M. Silverman, R. Kraemer, A.C. Jackson, High-frequency respiratory input impedance measurements in infants assessed by the high speed interrupter technique, Eur. Respir. J. 12 (1998) 148–158. [6] A.B. DuBois, A.W. Brody, D.H. Lewis, B.F. Burgess Jr., Oscillation mechanics of lungs and chest in man, J. Appl. Physiol. 8 (1956) 587–594. [7] A.C. Jackson, C.A. Giurdanella, H.L. Dorkin, Density dependence of respiratory system impedances between 5 and 320 Hz in humans, J. Appl. Physiol. 67 (1989) 2323–2330. [8] H. Bisgaard, B. Klug, Lung function measurement in awake young children, Eur. Respir. J. 8 (1995) 2067–2075. [9] K.R. Lutchen, K. Yang, D.W. Kaczka, B. Suki, Optimal ventilatory waveform for estimating low frequency mechanical impedance, J. Appl. Physiol. 75 (1993) 478–488. [10] D.W. Kaczka, E.P. Ingenito, K.R. Lutchen, Technique to determinate inspiratory impedance during mechanical ventilation: implications for flow limited patients, Ann. Biomed. Eng. 27 (1999) 340–355. [11] U. Frey, B. Suki, R. Kraemer, A.C. Jackson, Human respiratory input impedance between 32 and 800 Hz, measured by interrupter technique and forced oscillations, J. Appl. Physiol. 82 (1997) 1018–1023. [12] J. von Neergaard, K. Wirz, Die Messung der Strömungswiderstände in den Atemwegen des Menschen, insbesondere bei Asthma und Emphysem, Z. Klin. Med. 105 (1927) 51–82. [13] M. Gappa, A.A. Colin, I. Goetz, J. Stocks, Passive respiratory mechanics: the occlusion techniques, Eur. Respir. J. 17 (2001) 141–148. [14] A.M. Adams, C. Olden, D. Wertheim, A. Ives, P.D. Bridge, J. Lenton, P. Seddon, Measurement and repeatability of interrupter resistance in unsedated newborn infants, Pediatr. Pulmunol. 44 (2009) 1168–1173. [15] J. Stocks, Pulmonary function testing in infants, in: Encyclopaedia of Respiratory Medicine, Acad. Press, Amsterdam, 2006, pp. 564–577. [16] M. Oswald-Mammosser, A. Charloux, L. Donato, C. Albrech, J.P. Speich, E. Lampert, J. Lonsdorfer, Interrupter technique versus plethysmography for measurement of respiratory resistance in children with asthma or cystic fibrosis, Pediatr. Pulmunol. 29 (2000) 213–220. ´ [17] A.G. Polak, G. Głomb, T. Guszkowski, I. Jabłonski, B. ´ ˛ ˛ ´ Z. Swierczy ´ Kasprzak, J. Pekala, A.F. Stepie n, nski, J. Mroczka, Development of a telemedical system for monitoring patients with chronic respiratory diseases, IFMBE Proc. (Berlin) 25 (2009) 51–54. [18] J. Mead, J.L. Whittenberger, Evaluation of airway interruption technique as a method for measuring pulmonary air-flow resistance, J. Appl. Physiol. 6 (1954) 408–416. [19] A.C. Jackson, H.T. Milhorn Jr., J.R. Norman, A reevelauation of the interrupter technique for airway resistance measurement, J. Appl. Physiol. 36 (1974) 264–268. [20] B. Klug, H. Bisgaard, Measurement of lung function in awake 2–4-year-old asthmatic children during methacholine challenge and acute asthma: a comparison of the impulse oscilation technique the interrupter technique, and transcutaneous measurement of oxygen versus whole-body plethysmography, Pediatr. Pulmonol. 21 (1996) 290–300. [21] P.V. Romero, J. Sato, F. Shardonofsky, J.H.T. Bates, High-frequency characteristics of respiratory mechanics determined by flow interruption, J. Appl. Physiol. 69 (1990) 1682–1688.
[22] U. Frey, A. Schibler, R. Kraemer, Pressure oscillations after flow interruption in relation to lung mechanics, Respir. Physiol. 102 (1995) 225–237. [23] P.D. Bridge, D. Wertheim, A. Jackson, S.A. McKenzie, Pressure oscillation amplitude after interruption of tidal breathing as an index of change in airway mechanics in preschool children, Pediatr. Pulmonol. 40 (2005) 420–425. [24] D. MacLeod, M. Birch, Respiratory input impedance measurement: forced oscillation methods, Med. Biol. Eng. Comput. 39 (2001) 505–516. [25] C. Delacourt, H. Lorino, C. Fuhrman, M. Herve-Guillot, P. Reinert, A. Harf, B. Housset, Comparison of the forced oscillation technique and the interrupter technique for assessing airway obstruction and its reversibility in children, Am. J. Respir. Crit. Care Med. 164 (2001) 965–972. [26] J. Kivastik, J. Talts, R.A. Primhak, Interrupter technique and pressure oscillation analysis during bronchoconstriction in children, Clin. Physiol. Funct. Imaging 29 (2009) 45–52. [27] I. Goetz, A.F. Hoo, S. Loom, J. Stocks, Assessment of passive respiratory mechanics in infants: double versus single occlusion, Eur. Respir. J. 17 (2001) 449–455. ´ [28] I. Jabłonski, J. Mroczka, A forward model of the respiratory system during airflow interruption, Metrol. Meas. Syst. 16 (2009) 219–232. ´ [29] I. Jabłonski, J. Mroczka, Reduction of a linear complex model for respiratory system during airflow interruption, in: Proc. 32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Buenos Aires, Sept., 2010, pp. 2172–2175. ´ [30] I. Jabłonski, A.G. Polak, J. Mroczka, Methods for identification of a model of the respiratory system during airflow interruption, Meas. Automat. Control 8 (2000) 18–22 (in Polish). [31] K.R. Lutchen, F.P. Primiano Jr., G.M. Saidel, Nonlinear model combining pulmonary mechanics and gas concentration dynamics, IEEE Trans. Biomed. Eng. 29 (1982) 629–641. [32] J.H.T. Bates, M. Decramer, W.A. Zin, A. Harf, J. Milic-Emili, H.K. Chang, Respiratory resistance with histamine challenge by single-breath and forced oscillation methods, J. Appl. Physiol. 61 (1986) 873–880. [33] G. Nucci, S. Tessarin, C. Cobelli, A morphometric model of lung mechanics for time-domain analysis of alveolar pressures during mechanical ventilation, Ann. Biomed. Eng. 30 (2002) 537–545. [34] E.R. Weibel, Morphometry of the Human Lung, Springer, Berlin, 1963. [35] I. Ginzburg, D. Elad, Dynamic model of the bronchial tree, J. Biomed. Eng. 15 (1993) 283–288. [36] J.F. Kaiser, Nonrecursive digital filter design using the I0-sinh window function, in: Proc. IEEE Int. Symp. Circuits and Systems, San Francisco, April, 1974, pp. 20–23. [37] A.D. Poularikas, Signals and Systems Primer with Matlab, CRC Press, Boca Raton, 2007. [38] H. Franken, J. Cl(ment, K.P. van de Woestijne, Systematic and random errors in the determination of respiratory impedance by means of the forced oscillation technique: a theoretical study, IEEE Trans. Biomed. Eng. 30 (1983) 642–651. [39] J.H.T. Bates, P. Baconnier, J. Milic-Emili, A theoretical analysis of interrupter technique for measuring respiratory mechanics, J. Appl. Physiol. 64 (1988) 2204–2214. [40] P.D. Sly, J.H.T. Bates, Computer analysis of physical factors affecting the use of interrupter technique in infants, Pediatr. Pulmunol. 4 (1988) 219–224. [41] J.H.T. Bates, P.D. Sly, T. Kochi, J.G. Martin, The effect of a proximal compliance on interrupter measurements of resistance, Respir. Physiol. 70 (1987) 301–312. [42] F. Child, S. Clayton, S. Davies, A.A. Fryer, P.W. Jones, W. Lenney, How should airways resistance be measured in
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 1 ( 2 0 1 1 ) 115–125
[43]
[44] [45]
[46]
young children: mask or mouthpiece? Eur. Respir. J. 7 (2001) 1244–1249. C. Thamrin, K.E. Finucane, B. Singh, Z. Hantos, P. Sly, Volume dependence of high-frequency respiratory mechanics in healthy adults, Ann. Biomed. Eng. 36 (2008) 162–170. M.J. Jaeger, H. Matthys, The pattern of flow in the upper human airways, Respir. Physiol. 6 (1968–1969) 113–127. M.J. Jaeger, Effect of the cheeks and the compliance of alveolar gas on the measurement of respiratory variables, Respir. Physiol. 47 (1982) 325–340. R. Peslin, C. Duvivier, P. Jardin, Upper airway walls impedance measured with head plethysmograph, J. Appl. Physiol. 57 (1984) 596–600.
125
[47] A.G. Polak, A forward model for maximum expiration, Comput. Biol. Med. 28 (1998) 613–625. [48] R.K. Lambert, Sensitivity and specificity of the computational model for maximal expiratory flow, J. Appl. Physiol. 57 (1984) 958–970. [49] A.G. Polak, J. Mroczka, Nonlinear model for mechanical ventilation of human lungs, Comput. Biol. Med. 36 (2006) 41–58. [50] B. Morlion, A.G. Polak, Simulation of lung function evolution after heart–lung transplantation using a numerical model, IEEE Trans. Biomed. Eng. 52 (2005) 1180–1187.