Abstract
The aim of this study was to examine whether the spectral characteristics of tidal flow waveform reflect the interaction between the control of breathing and lung mechanics in 10 healthy infants (H), 10 infants with a history of wheezing disorders (W), and 10 infants with chronic lung disease (CLD). From the flow waveform, we calculated a shape index, the harmonic distortion (k _{d}), which quantifies the extent to which a periodic signal deviates from a sine wave. Thek _{d} of the entire tidal flow waveform did not significantly discriminate between diagnostic groups. However,k _{d} was sensitive to maturation: it increased from 0.26 at 1 mo to 0.37 at 6 mo of age (P < 0.002). Furthermore, the frequency (f) spectra of the flow (V˙) amplitudes between 0.13 and 10 Hz followed a power law:V˙(f) ∼f ^{−s}, where s(slope) is the exponent in the power law. The exponent of the healthy infants s(H) was 4.24 [95% confidence interval (CI) = 0.2] at 1 mo, 4.39 (CI = 0.16) at 6 mo, and 4.35 (CI = 0.19) at 12 mo and not significantly changing with age. The mean value ofs(W) was marginally lower (4.09 ± 0.28;P < 0.05) than that of s(H). The means(CLD) was significantly lower (3.04 ± 0.31;P < 0.001). Lower values of s and higher values of k _{d} indicate an increased complexity of the feedback mechanisms determining tidal flow waveform and may be associated with disease.
 respiratory function tests
 control of breathing
 respiratory mechanics
it has been proposed that simple tidal flow indexes, such as the ratio of time to peak tidal expiratory flow (Tptef) to expiratory time (Te) (Tptef/Te) (13), which can be assessed noninvasively (e.g., Refs. 6, 10,13), may contain information regarding airway mechanics in infants. However, the early phase of expiration is not only determined by respiratory mechanics but, to a large extent, by the postinspiratory activity of the respiratory muscle drive (19). Ueda et al. (18) demonstrated a close correlation between Tptef/Te and the pressure 100 ms after airway occlusion at onset of inspiration, a measure of inspiratory drive in infants. Furthermore, Thomas et al. (16, 17) have recently shown in infants that inspiratory and expiratory phases are related to respiratory drive, peripheral chemoreceptor sensitivity, and sleeping patterns in infants. Thus inspiratory and expiratory waveforms are closely related, and the expiratory waveform is not independent of breathing frequency, inspiratory waveform, and inspiratory offswitch mechanisms (3,8, 11, 12). Thus it seems more appropriate to consider the whole flow waveform as an integrated output of the neural respiratory oscillator in the brain stem, reflecting its interaction with the various chemo and stretchreceptor feedback mechanisms and the passive mechanical properties of the lung and the chest wall.
Therefore, instead of analyzing the expiratory flow waveform using simple indexes (e.g., Tptef/Te) based on limited information, one should define and use parameters that are more suitable to characterize the tidal flow wave as the output of an integrated control system. The neurorespiratory control system is a highly complex feedback system that maintains a certain dynamic equilibrium in health. In disease, this dynamic equilibrium may become disturbed if one of its components, for example the mechanical properties of the airways or the chemo or stretchreceptor feedback, is altered. We hypothesize that such a disturbance to the system leads to a concomitant change in the shape of the periodic flow waveform. Changes in the shape of a periodic waveform must in turn be reflected in the spectral characteristics of the waveform.
Accordingly, the aims of this study were 1) to develop simple indexes that are suitable to characterize the shape and hence the spectral features of the tidal flow waveform in the frequency domain; 2) to assess whether these new parameters are sensitive to alterations in respiratory control and/or lung mechanics because of developmental changes and disease; and 3) to test whether these indexes are more reliable and robust descriptors of the changes in respiratory control and/or airway mechanics than Tptef/Te, which is one of the most commonly used tidal flow indexes.
METHODS
The study includes analysis of data obtained from both new experiments and newly analyzed tidal flow data sets from previously published studies on Tptef/Te (1, 4,5). First, we examined tidal flow waveforms of 10 healthy infants during development at the ages of 1, 6, and 12 mo. Based on these data, we introduced two new indexes derived from the tidal flow waveform in the frequency domain. We then compared the breathtobreath variabilities of the new parameters with that of Tptef/Te calculated from the same series of tidal flow data.
Second, we compared the new indexes obtained from healthy infants with measurements in infants with wheezing disorders (10 infants) and chronic lung disease (CLD) of prematurity (10 infants). To quantify the degree of airway obstruction, we performed forced flowvolume loops using the rapid thoracic compression (RTC) technique in each group.
Third, to assess whether any of the tidal flow waveform parameters were associated with altered airway mechanics, we reanalyzed data from previously published bronchial challenge studies (1, 5). Histamine challenge tests were performed as previously described in healthy infants (1, 5), and the data were reanalyzed using our new indexes.
Experimental Study
Subjects.
We analyzed tidal flow waveforms in 10 healthy infants, each measured at the ages of 1, 6, and 12 mo; 10 infants with a known history of wheezing disorders [mean age, 13.9 ± 1.6 (SD) mo] asymptomatic at the time of measurement; and 10 infants with CLD of prematurity [mean postnatal age, 8.1 ± 7.2 (SD) mo and gestational age, 27.7 ± 2.4 wk]. The mean inspired O_{2} fraction of the CLD group was 29.1 ± 6.1%, whereas in all other groups it was 21%. The characteristics of these infants are given in Table1. In the 10 healthy infants, 14 histamine challenge tests were performed (in 4 infants at 2 different ages). The studies were authorized by the Ethics Committee of the Hammersmith Hospital, London, UK, where the measurements were performed. Parental consent was obtained for all studies.
Measurements.
All infants were sedated by using a maximal dose of 150 mg/kg triclofos sodium. Partial expiratory flow at functional residual capacity (V˙_{max FRC}) was measured by using the RTC technique (5). The supine infants wore an inflatable polythene thoracoabdominal jacket (Medical Engineering Department, Royal Postgraduate Medical School, London, UK) with arms out. Flow was measured by using a face mask (size 1, Rendell Baker Soucek, Ambu International, Bath, Avon, UK) and a Fleisch no. 1 (Gould) pneumotachograph equipped with a differential pressure transducer (MP45, Validyne, Northridge, CA). The linearity of the pneumotachograph was found to be accurate within 2% up to flows of 1 l/s. The frequency response of the flow transducer was flat up to 12 Hz. The flow signals were lowpass filtered (hardware filter, cutoff at 20 Hz), sampled at 100 Hz using a 12bit analogtodigital converter, and processed by using the RASP software (Physiologic, Newbury, UK).
In all infants, tidal flow sequences of 8–10 s and forced expiratory flows were recorded by using the RTC technique described in detail previously (5). After a series of initial RTC measurements to determine the optimal jacket pressure, 10 RTC recordings were carried out at endtidal inspiration using this optimal jacket pressure, and the corresponding V˙_{max FRC} was calculated. The mean value of all technically satisfactoryV˙_{max FRC} was determined. Transcutaneous Po _{2} (TMC3, Radiometer, Copenhagen, Denmark) and transcutaneous arterial O_{2} saturation (Biox 3740, Omeda, Omaha, NE) were measured. The head position was kept fixed between forced flow measurements and tidal breathing measurements. For both techniques, we used the same face mask and putty ring.
Bronchial challenge tests.
As previously described (5), after the baseline measurements in the healthy infants, we administered histamine in doubling concentrations until V˙_{max FRC} decreased by at least 30%. Sequences of tidal breathing were recorded and analyzed before and after the bronchial challenge test.
Analysis of tidal flow signals.
The primary aim of the analysis was to develop a method to characterize the waveform of the flow signal. Because the flow signal in the time domain does not appear to follow a simple shape (e.g., a sinusoid), we analyzed the shape in the frequency domain. In particular, we examined the relationship between breathing frequency and its higher harmonics, which are the frequency components of the signal at integer multiples of the breathing rate. The harmonics can be calculated by using the fast Fourier transform (FFT) algorithm applied to one or more periods of the signal. The FFT is invariably applied to several individual breathing cycles, and the individual spectra are then ensemble averaged. Unfortunately, the time period of the breathing cycle can vary by 20–50% from cycle to cycle. One solution is to find the longest cycle and zero pad all other cycles to obtain blocks of data having the same number of time points. When the spectra of these blocks are ensemble averaged, the resulting spectrum will be a smeared version of the individual spectra, because frequency of breathing with the highest energy content would vary from block to block. If, on the other hand, the FFT is applied to the entire signal, spectral leakage will occur, as the breathing frequency will not be the same in the individual cycles. In both cases, the frequency dependence of the higher harmonics will be masked by these effects. To avoid these problems, we first isolated all individual respiratory flow cycles using a zerocrossing detection algorithm that identifies the beginning and the end of a cycle. The number of data points (N_{i} , where i is the cycle number) was different for the different cycles. Because we were interested in the shape of the spectra (rather than the absolute frequencies), instead of zero padding the time domain data and using FFT of the same length for all cycles, we applied the discrete Fourier transform of window lengthN_{i} (MATLAB, 5.0, MATHWORKS) to the individual flow cycles. We then analyzed the power spectra of the individual respiratory cycles based on the two methods described below. No filtering or windowing was used, as these operations affect the shape of the spectra. However, to smooth the spectra, we applied a twopoint box car averaging technique. The above analysis was then repeated for each respiratory cycle of a single recording. This method allowed us to define parameters (see below) that can characterize the shape of the power spectra on a cyclebycycle basis and then calculate the average and variability of these parameters.
Interpretation of Flow Signal Harmonics
We examined two methods of characterizing the shape of the flow signal as expressed by the frequency dependence of the higher harmonics in the flow signal. These methods are the 1) power law analysis (e.g., Refs. 7, 9) and the 2) harmonic distortion method (15, 20).
Power law analysis.
As an example, Fig. 1 shows the tidal waveform of a healthy 6moold infant. The corresponding power spectra of the tidal flow signals (Fig. 1) of the infant are shown in Fig.2. The spectra apparently decrease linearly on the loglog graph. Thus the logarithm of the harmonics of the flow signals appears to be linearly related to the logarithm of frequency. Indeed, a linear regression provides good fit to the data, as shown in Fig. 2. This can be formally written as
Harmonic distortion.
The extent to which a periodic signal deviates from a single sine wave can also be characterized by the socalled harmonic distortion index (k _{d}), defined as the square root of the relative power in the signal above the fundamental frequency (15,20). In other words, k _{d} is the square root of the ratio of the sum of the squares of the higher harmonic amplitudes above the fundamental frequency F and the sum of the squares of all amplitudes. The k _{d} is usually specified in percent. For example, the harmonic distortion of a sine wave is obviously zero, whereas that of a triangular wave is 37%. Higher values of k _{d} indicate the presence of stronger harmonic components in the signal and, hence, a shape in the time domain that deviates more from an ideal sinusoidal wave.
Statistical Analysis
In individual infants, s, k _{d}, and Tptef/Te were calculated for each respiratory cycle and averaged (mean) for the whole flow signal. In healthy infants, the group means (and 95% confidence interval) of the parameters s, k _{d}, and Tptef/Te were calculated for the 1, 6, and 12moold groups. Because the healthy infant groups at 1, 6, and 12 mo consisted of longitudinal data sets, we tested age dependence of the paramaters s, k _{d}, and Tptef/Te by using paired ttests. Because there were only three age groups and the main change was in the first 6 mo of age, we used paired ttests instead of ANOVA statistics.
We compared the infants with CLD and the infants with wheezing disorders with the healthy infants of similar ages. The s, k _{d}, and Tptef/Te in the infants with CLD were compared with those in the healthy infants at the age of 6 mo, whereas the wheezy infants were compared with healthy infants at the age of 12 mo (see Tables 13). The mean postconceptional as well as postnatal ages of the compared groups were not statistically different.
To compare the breathtobreath variability of the parameterss, k _{d}, and Tptef/Te, the coefficient of variation (CV) for all respiratory cycles around the mean value was calculated and expressed in percentage of the mean CV for each individual subject. For each group, the mean CV was calculated for each parameter. Within these particular groups, the CVs of s, k _{d}, and Tptef/Te were compared by using a pairedttest because the mean CVs of the various physiological and diagnostic groups were not expected to be similar. However, to account for the effect of multiple comparisons, we set the limits of theP value to 0.01 instead of the usual 0.05.
Posthistamine parameters of s, k _{d}, and Tptef/Te from the bronchial challenge tests were compared with the corresponding baseline values, using a pairedttest for the whole group of healthy infants.
RESULTS
A power law behavior of flow harmonics was found in all healthy infants between 0.13 and 10 Hz. An example is shown in Fig. 2, and the mean (±SD) power spectra of all infants at the age of 6 mo is shown in Fig. 3. The respiratory cycle variability (RCV%) was found to be significantly lower in s andk _{d} than in Tptef/Te(except for k _{d} in the healthy 1moold infants) (Tables 2 and3). Longitudinal measurements of s, k _{d}, and Tptef/Te in healthy infants at the ages of 1, 6, and 12 mo revealed no change in s but a significant increase in k _{d} (P < 0.0025, power > 0.8) and decrease in Tptef/Tebetween 1 and 6 mo (P < 0.006, power > 0.8) (Table 2). There was an inverse relationship betweenk _{d} and Tptef/Te in healthy infants [log(Tptef/Te) = −0.017k _{d} − 0.12; r ^{2}= 0.51]. Although s and k _{d} appeared to be weakly correlated, this relationship did not reach a statistically significant level.
Comparing the different groups of infants, we found only a trend difference in the mean (95% confidence interval) values of sbetween infants with a history of wheezing disorders (4.35 ± 0.19) and the 12moold healthy infants (4.09 ± 0.28) (P < 0.05, power < 0.8; Table 2). There was a tendency for V˙_{max FRC} to be lower in the group with wheezing disorders (Table 1), but it was not statistically significant (P = 0.07). However, s was highly significantly lower in infants with CLD (3.84 ± 0.31;P < 0.001, power > 0.8) compared with the group of healthy 6moold infants (4.39 ± 0.16) (Figs. 3 and4). The correspondingV˙_{max FRC} was also statistically lower in the group with CLD [58.4 ± 47.3 (SD) ml/s] than in the normal infants at age 6 mo [299 ± 158 (SD) ml/s] (P < 0.0002, power > 0.8). The k _{d} and Tptef/Te were not statistically different among these diagnostic groups.
Despite the fact that V˙_{max FRC} changed by >30% in all 14 healthy infants, there was no significant change ins, k _{d}, or Tptef/Teafter histamine challenge, indicating that tidal breathing parameters are not sensitive to acute changes in airway mechanics.
DISCUSSION
The primary finding of this study is that the flow harmonics of all cases studied follow a power law functional form. The exponents in the power law was sensitive to disease. We also applied another shape index, k _{d}, which was not sensitive to disease but was sensitive to maturation. Additionally, these two parameters were more robust than a widely used conventional time domain descriptor of the tidal expiratory flow waveform Tptef/Te.
The k_{d} and Power Law Harmonics in Tidal Flow Waveforms
The k _{d} was originally introduced by Suki et al. (15) and extended by Zhang et al. (20). They defined k _{d} as the square root of the relative power in the signal above the fundamental frequency. Thek _{d} characterizes the power of the harmonics in the spectrum, regardless of the distribution of the harmonics in the flow spectrum and, hence, the shape of the spectrum in the frequency domain. If, for example, the harmonic energy in the flow moves to higher frequencies because of an altered complex feedback mechanism,k _{d} would not reflect this change as long as the total power remains the same. Thus a disadvantage of usingk _{d} is that it is insensitive to the redistribution of harmonic energy in the spectrum. On the other hand, it has the advantage that it does not assume any particular shape for the spectrum, such as a power law form.
The second method, the power law analysis, is based on the primary finding of this study. The decrease in amplitude of the harmonic components of the tidal flow waveform follows a power law, as evidenced by the linear decrease of log harmonic amplitudes vs. log frequency (e.g., Fig. 2). The negative slope of the best linear fit provides an estimate of the exponent s in the power law. The lower the amplitude of these harmonics compared with the amplitude of the fundamental frequency, the steeper the linear decrease of the harmonics and the higher the value of s. Thus s is a simple index related to the degree of the nonsinusoidal behavior present in the tidal flow signal. In our study, we found only a trend but not a significant inverse correlation between s andk _{d} in healthy infants. However, in theory,s and k _{d} are not completely independent. If the flow spectrum follows a perfect power law,k _{d} can be calculated from s. Thus s better characterizes the shape of the flow waveform. Nevertheless, in situations in which the shape deviates significantly from a power law, s loses its meaning, whereas one can still use k _{d} to characterize the complexity of the waveform. The power law behavior was characteristic of the flow signals in all infants studied, raising two fundamental questions: what determines the flow harmonics and why do the harmonics follow a power law function?
The origin of the power law behavior of the tidal flow waveform is not entirely clear. Te profiles have been reported to follow one or at most the sum of two exponents (2). The power spectrum of an exponent has an infinite number of harmonics. This spectrum on a loglog graph is flat for low frequencies and turns into a power law with a fixed exponent of s = 2 above the corner frequency corresponding to the time constant of the exponent. Our power spectra, however, do not show a broad flat portion for low frequencies. Additionally, s varies among infants, ranging from 3 to 5. Therefore, the expiratory flow and hence the passive mechanical properties of the respiratory system alone cannot produce a power law behavior of the flow spectra. It is likely that the output of the respiratory oscillator (as described in Refs. 3, 11,12) is strongly influencing the power law behavior of the flow waveform.
Changes in s and k _{d} may be interpreted from a system point of view as follows. If a linear system is driven with a sine wave, the output will also be sine wave but, in general, with a different amplitude and phase. Thus, whenever the output of the system that is driven by a sine wave is nonsinusoidal, internal nonlinearities in the system must also contribute to the output. With regard to the tidal flow signal, unfortunately, the input to the system that generates the flow signal is not known. It is very likely that the input to the respiratory oscillator is not an ideal sine wave. Therefore, the presence of a power law spectrum or ak _{d} > 0 in itself may not allow us to conclude too much about the saturation type of nonlinearities in the respiratory oscillator, because the power law may be a combination of the input and the internal nonlinearities of the system. Thus a decrease in s (stronger harmonics) or an increase ink _{d} signifies that either the input to the oscillator has become more complex or the internal nonlinearities of the system have become stronger. In either case, the internal complexity of the entire system generating the flow tidal signal would increase.
Variability of Tidal Flow Indexes
To compare breathtobreath variability of the parameterss, k _{d}, and Tptef/Te, we calculated the CV of the individual values for s, k _{d}, and Tptef/Te from cycle to cycle in the entire tidal flow signal. We found that RCV% of s andk _{d} was significantly lower than that of Tptef/Te for all groups of infants except the healthy infants at 1 mo of age (k _{d}). This indicates that the parameters s andk _{d} are more stable indexes to characterize tidal flow waveforms than Tptef/Te. We can think of two possible explanations. The variability of Tptef/Te is large, partly because its calculation is based on only three points of the expiratory part of the flow signal. From a mathematical point of view, the more data points of a complex wave are analyzed, the better the waveform can be characterized. From the point of view of signaltonoise ratio, the expected noise on Tptef/Te based on three points from the cycle can be much higher than the noise on a parameter that is estimated via some smoothing operation, such as a linear regression. Additionally, expiratory flow waveform is influenced by both the respiratory oscillator and passive mechanics of the lung and chest wall, whereas the inspiratory portion is dominated by the respiratory oscillator. Therefore, Tptef/Te may carry mixed information about passive mechanics and respiratory control. In contrast, the calculation of s andk _{d} involves the whole cycle, and, hence, they will be less noisy and, therefore, more reliable. Additionally, thek _{d} and power law indexes may be more closely related to the true physiological origin of the tidal flow waveform.
Sensitivity of Tidal Flow Indexes to Maturation
We found changes in k _{d} and Tptef/Te between 1 and 6 mo of age in longitudinal data sets of healthy infants but no changes ins. Theoretically, k _{d} and sshould be correlated; however, in our data set, we only found a nonsignificant trend. We believe that this might be a potential explanation for the inconsistent behavior of s andk _{d} during maturation. An increase ofk _{d} during development would be consistent with a higher degree of nonsinusoidal behavior of the mechanism determining tidal flow waveform, maybe with increased complexity of the neurorespiratory regulatory system. Developmental changes ofk _{d} and Tptef/Te could be explained by changes in respiratory control during the first 6 mo of life and/or by changes in lung mechanics. However, our results from the histamine challenge in these healthy infants (see below) suggest that airway mechanics do not play a major role in any of these indexes because we did not find a consistent change in any of these tidal flow parameters. Therefore, it is more likely that changes in control of breathing during development might be the dominant factor responsible for the increase in k _{d}. Additionally, based on this interpretation, the parameters s,k _{d}, and Tptef/Te are likely to be dependent on sleep stage, which we did not test in this paper. Because all measurements were made during quiet sleep, sleep stage is unlikely to explain any differences.
Tidal Flow Indexes in Disease
In disease, the situation becomes more complex. We only found marginally decreased s in infants with wheezing disorders, whereas we found s to be significantly lower in infants with CLD of prematurity. It is possible that the sensitivity of sis not enough to detect changes in mild lung disease, and larger data sets are necessary to find differences. However, s was very sensitive to the presence of severe lung disease such as CLD. TheV˙_{max FRC} in the CLD group was statistically significantly lower, indicating increased lung resistance, but the infants with wheezing disorders, who were asymptomatic at the time of measurement, had only a nonsignificant trend to decreased forced expiratory flows. Another possibility is as follows. Because most of these infants with CLD still needed oxygen at the time of measurements, it could be that the patients with CLD had additional changes in control of breathing. The indexes k _{d} and Tptef/Te were not significantly different in these groups of infants, indicating that these parameters are less sensitive to changes in the disease state.
Tidal Flow Indexes During Histamine Challenge
None of the tidal flow indexes changed consistently after histamine challenge, despite an acute change in airway obstruction as demonstrated by the fall of V˙_{max FRC} by >30%. In contrast, in a chronic state of lung disease, such as in CLD, the power law slope s decreased, consistent with an increased level of nonsinusoidal behavior of the mechanisms determining flow waveform. Thus either lung mechanics were much more severely affected by CLD than after bronchial challenge or CLD has a direct effect on respiratory control. Nevertheless, these data support the argument that the tidal flow waveform is strongly dependent on neurorespiratory control and adaptive mechanisms rather than lung mechanics.
Summary
We proposed two new indexes (k _{d},s) derived from tidal flow waveform that can characterize the complexity of the neuromechanical respiratory system by quantifying the extent to which the tidal flow waveform deviates from the shape of a single sinusoid. We found that the tidal flow harmonics follow a power law that can be characterized by a single number, the exponents. This new index and k _{d} also have a significantly smaller breathtobreath variability than Tptef/Te, making them more robust descriptors of tidal flow waveforms. We also found them to be significantly different in disease but not, however, during a histamine challenge. The results from the histamine challenge indicate that the tidal flow waveform is not significantly affected by acute changes in airway mechanics and that it is, therefore, more likely that the neurorespiratory control plays a key role in determining flow waveform. These findings are consistent with previous work (1619). To study the separate influence of control of breathing and lung mechanics on tidal flow and these parameters, future studies should employ hypoxic and/or hypercapnic challenges. Furthermore, it is important to consider that infant breathing may also inherit longrange correlations, as it has been shown by Small et al. (14). Thus the parameters s andk _{d} will have to be studied in a very long time series to get more information on the control of breathing in infants. Because s and k _{d} can be determined noninvasively, they might be useful in monitoring CLD in infants, assessing therapeutic interventions, and/or giving evidence of changes in neurorespiratory control during development and growth.
Acknowledgments
U. Frey was supported by the Swiss National Science Foundation (no. 32–51974.97), the British National Asthma Campaign, and the British Society for the Protection of Infants Life.
Footnotes

Address for reprint requests and other correspondence: U. Frey, Dept. of Paediatrics, Univ. Hospital of Berne, Inselspital 3010, Berne, Switzerland (Email: urs.frey{at}insel.ch).

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 Copyright © 2001 the American Physiological Society