Abstract
Castiglioni, P., R. Tommasini, M. Morpurgo, and M. Di Rienzo. Modulation of pulmonary arterial input impedance during transition from inspiration to expiration. J. Appl. Physiol. 83(6): 2123–2130, 1997.—We investigated whether respiration influences pulmonary arterial input impedance during transition from inspiration to expiration in five anesthetized, spontaneously breathing dogs. Impedance (Z) was separately assessed for heart beats occurring in inspiration, in expiration, and during the transition from inspiration to expiration (transitional beat). Transitional beats were scored by the ratio between the fraction of beat falling in expiration and the total beat duration [expiratory fraction (E_{fr})] to quantify their position within the transition. In transitional beats, input resistance linearly increased with E_{fr}; Z modulus at the heartrate frequency (f_{HR}) decreased up to −50% for E_{fr} = 50%. Z phase at f_{HR} was greater than in inspiration for E_{fr}<40% and lower for E_{fr} >50%. Unlike blood flow velocity, mean value and first harmonic of pulmonary arterial pressure were correlated to E_{fr} and paralleled the changes of input resistance and Z at f_{HR}. This indicates that respiration influences Z through modifications in arterial pressure. The evidence of important respiratory influences on Z function may help the pathophysiological interpretation of dysfunctions of the right heart pumping action, such as the socalled cor pulmonale.
 pulmonary circulation
 pulmonary blood pressure
 pulmonary blood flow
 intrapleural pressure
the pulmonary arterial input impedance (Z), defined as the ratio between the oscillations in blood pressure and blood flow at the entrance of the pulmonary circulation, is a quantitative coupling index between the right ventricle (RV) and the pulmonary vascular bed in the frequency domain (12). Because of the low values of pulmonary arterial pressure (PAP), the pulmonary input Z should be influenced by the changes in intrathoracic pressure associated with breathing. Surprisingly, the available literature does not report any significant difference between the average Z values of heart beats occurring during the inspiratory and expiratory phases of respiration, both at rest (3,11) and during exercise (8). These studies, however, have not considered the pulmonary Z during the transition between inspiration (I) and expiration (E), namely, during the fraction of respiratory cycle characterized by marked changes in intrathoracic pressure.
In the present study, we focused on this unexplored issue by evaluating the pulmonary arterial input Z during the transition from I to E in spontaneously breathing dogs. To interpret the results obtained by the above analysis, we also separately investigated the influences of respiration on blood pressure and blood flow, i.e., on the individual determinants of the input Z.
METHODS
Animal preparation, data acquisition, and beat classification.
The experiments were performed on five mongrel dogs. Anesthesia was induced by pentobarbital sodium (an initial bolus of 25–30 mg/kg iv followed by 0.07 mg ⋅ kg^{−1} ⋅ min^{−1}infusion). Dogs were studied while they were in the right lateral position on a surgical table. They were intubated and then breathed spontaneously throughout the experiments.
PAP and bloodflow velocity (FV) were obtained via a highfidelity MikroTip catheter (SVPC684A, 8 Fr; Millar Instruments) with pressure and velocity sensors at the same location. The catheter was advanced into the main pulmonary artery via the right jugular vein. Use of the integrated catheter avoided the surgical opening of the thorax for the implantation of a perivascular flowmeter, thus simplifying the experimental setup. It should be noted that with this approach blood flow is expressed in terms of FV (in cm/s) and that the derived parameters are velocityderived input resistance (R_{I}) and Z. Nichols and O’Rourke (12) discussed in detail the differences between use of FV or use of flowvolume in expressing the Z modulus. According to these authors, use of flow volume has the benefit of familiarity and leads to Z moduli expressed in the same units of the hydraulic resistance. Nevertheless, these authors recommend the use of FV and point out that expressing Z modulus in terms of FV has a number of advantages, in particular when comparisons are made between animals or when comparisons are made in the same artery under different circumstances in which the artery dilates or constricts.
In two dogs, intrapleural pressure (IPP) was also determined by means of a catheter inserted into the pleural space through the fifth or sixth intercostal spaces. Airflow was measured with a heated meshscreen pneumotachograph. All signals were sampled at 200 Hz and digitized through an analogtodigital converter (HP 6942A). The average duration of each recording was 80.8 s.
The PAP and FV tracings were partitioned into individual waves, each referring to a single cardiac cycle. The onset of each systolic upstroke was identified on the PAP record and taken as the reference point for the partitioning. The duration of each cardiac cycle (heart interval) was obtained by measuring the time interval between consecutive reference points, and the instantaneous heart rate (f_{HR}) was computed as the reciprocal of the heart interval. The airflow signal was subdivided into individual respiratory cycles. Each cycle was defined by a sequence of I, E, and postexpiration. I and E were identified by the onset of a positive and a negative airflow respectively; postexpiration was identified by the period of zero flow between E and I.
Each pair of simultaneous PAP and FV waves (hereafter this pair will be termed “beat”) was classified according to the respiratory phase during which it occurred. This led to three categories of beats:1) inspiratory beats, which included all beats occurring entirely in I;2) expiratory beats, which included all beats occurring entirely in E; and3) transitional beats, which included the beats occurring during the transition from I to E. Moreover, for each transitional beat we computed the expiratory fraction (E_{fr}), defined as the percent ratio between the fraction of time spent by the beat in E and the total heart beat duration (Fig.1). This was done to quantify the position of the transitional beats within the transition. By definition, E_{fr}ranges between 0 and 100%. All subsequent analyses were performed separately for each category of beats, the I beats being taken as the reference condition.
Beatbybeat estimation of Z.
The preliminary step to estimate the input Z is the computation of the Fourier coefficients for each pair of PAP and FV waves. The Fourier coefficients of a single wave are mathematically defined as the coefficients of a periodic signal composed of infinite replicas of the original wave (see Ref. 10 for details). The possible occurrence of differences between start and end values of a single wave produces discontinuities in the periodic signal and may affect the accuracy of the estimation of Fourier coefficients because of the phenomenon known as aliasing. Before computing the Fourier estimates, we made a preliminary exploration of whether the characteristics of pressure and flow signals were compatible with the requirements of the Fourier analysis. The actual influence of aliasing on the spectral results was evaluated and was shown to be negligible on the first five harmonics of PAP and FV waves, namely on all the harmonics we considered in this study (see details in appendix ).
On the basis of this favorable validation, we computed the Fourier coefficients {A_{k} ,B_{k} } for each PAP and FV wave. Equations EB9 and EB10 in appendix show the mathematical expression ofA_{k} andB_{k} . From the Fourier coefficients, modulusM_{k} and phase φ_{k} of thek ^{th}harmonic were calculated for each wave by the formulasM_{k} = (A _{k} ^{2}+B _{k} ^{2})^{1/2}and φ_{k} = arctan(B_{k} /A_{k} ), with k = 1...5. The input Z modulus, ‖Z(f)‖, was computed at f = 0 Hz as the ratio between PAP and FV mean values and at multiple frequencies of the instantaneous heart rate (f = k × f_{HR}) as the ratio between the modulus of PAP and FV at thek ^{th} harmonic. Because Z was evaluated as the ratio between pressure and FV (instead of flow volume), it was expressed in dynes per second per cubic centimeters. The input Z phase, φ[Z(f)], was computed at the same frequencies (f = k × f_{HR}) as the difference between the phases of PAP and FVk ^{th} harmonics (10).
Subsequently, four parameters were derived from each estimated impedance curve Z(f): the modulus of Z(f) at f = 0 Hz [in short called input resistance (R_{I})]; modulus and phase of Z at the frequency of the instantaneous heart rate, ‖Z(f_{HR})‖ and φ[Z(f_{HR})], respectively; and the characteristic Z modulus (Z_{C}), estimated by averaging the Z modulus between 2 and 12 Hz, as suggested by Bergel and Milnor (1). For each respiratory cycle, the differences between the estimates of the above four parameters in the transitional beat and in the inspiratory beat (the reference) were computed. The differences ΔR_{I}, Δ‖Z(f_{HR})‖, and ΔZ_{C} were then normalized with respect to the value in I to minimize variability between animals. Results of these four parameters were shown as a function of E_{fr}.
Heart rate, pressure, and flow during the transition.
To facilitate the interpretation of the results stemming from the analysis of Z, we also evaluated the effects of the transition from I to E on three factors that influence the Z estimation: heart rate, PAP, and FV.
The reason why we investigated heart rate is apparent if one considers that changes in Z(f_{HR}) can be due not only to a change in the Z curve, Z(f), but also to mere changes in the frequency where Z(f) is evaluated, i.e., to changes in the f_{HR}. To estimate whether the latter possibility occurred in our study, we computed the difference between f_{HR} in the transitional beat and in reference to each respiratory cycle and plotted the difference vs. E_{fr}.
The separate behavior of PAP and FV during the transition from I to E was also investigated to clarify the individual contribution of each variable on the results obtained from the Z analysis. To this aim, we considered the mean value and modulus and phase at the first harmonic of PAP and FV. Modulations of these parameters were separately quantified during transition by following the same procedure used for the assessment of Z changes.
RESULTS
Beatbybeat estimation of Z.
Figure 2 illustrates Z(f) for I, E, and transitional beats in a typical animal (dog 4). Values at each harmonic are given as means ± SD. The Z modulus and phase were similar in I and in E. The only exception was the modulus at 0 Hz (R_{I}), which was higher in E than in I. During the transition from I to E, when the transitional beats were considered as a whole (i.e., without taking into account E_{fr}), the Z of the first harmonic was characterized by a marked reduction of the modulus and by a large variability of the Z phase. At higher frequencies, the Z phase was reduced with respect to both I and E, whereas the Z modulus was virtually unchanged.
The results of the analysis on transitional beats for the whole group of animals are depicted in Figs. 3 and4 as a function of E_{fr}. R_{I} progressively increased for augmenting E_{fr} values, whereas ‖Z(f_{HR})‖ progressively decreased for E_{fr} ranging from 0 to 50%, and thereafter symmetrically increased for E_{fr} between 50 and 100%. At E_{fr} values of ∼50%, ‖Z(f_{HR})‖ was reduced to about onehalf of the reference value on average. In no animal was this reduction less than −30%. The phase φ[Z(fHR)] was positive with respect to the reference for E_{fr} <40% and became negative for E_{fr} >50%. In reference to the Z_{C}, we did not find any clear dependence between Z_{C} and E_{fr} (Fig. 4).
Moreover, in the whole group of dogs, similar to the results obtained in the representative dog of Fig. 2, the Z phase of the transitional beats at harmonics 1, 2, 3, 4, and 5 was lower than in I for E_{fr} between 10 and 90%, whereas the Z modulus was not influenced by E_{fr} (data not shown). Because Z_{C} was estimated as the average Z between 2 and 12 Hz, the latter finding also explains the lack of any dependence of Z_{C} in relation to E_{fr}.
Heart rate, pressure, and flow during the transition.
Variations of the f_{HR} that occurred in transitional beats with respect to inspiratory beats are plotted vs. E_{fr} in Fig.5. In all animals, f_{HR} was stable throughout the transition from I to E, and this result excludes the possibility that the observed changes in Z(f_{HR}) might be due to changes in f_{HR}.
Results of the separate analysis on PAP and FV waves are illustrated in Fig. 6. Figure 6 shows the relationship between the mean value and E_{fr} and between the first harmonic modulus and phase and E_{fr}. From a comparison of these data with the results of Fig. 3, it is apparent that the behaviors of mean value, modulus, and phase of PAP during transition parallel the behaviors of R_{I} and of Z modulus and phase at f_{HR}. In contrast, no evident modulation was observed for the FVderived parameters as function of E_{fr}, apart from a slight downward linear trend in the mean value. In the analysis of harmonics 1, 2, 3, 4, and 5, we found a decrease of PAP phase for E_{fr} ranging between 10 and 90%, and no changes for PAP moduli, FV moduli, and FV phases (data not shown in Fig. 6).
DISCUSSION
A new procedure was developed for the beatbybeat analysis of pulmonary arterial input Z as a function of the respiratory cycle. This allowed us to investigate specifically the changes of Z(f) during the transition from I to E.
Through application of our procedure, we observed that the transitional beats are characterized by a large variability in Z modulus and phase at the frequency of the heart rate, Z(f_{HR}). This variability was proven not to be caused by changes of the f_{HR} but rather by changes in the Z function [Z(f)]. These changes strictly depend on the onset time of the beat during the IE transition. Specifically, the modulus of Z(f_{HR}) displays a symmetrical pattern, which is characterized by a progressive drop from its reference value for E_{fr}ranging from 0 to 50% and by an opposite progressive increase for E_{fr} ranging from 50 to 100%. This has not been previously reported in literature. In particular, Murgo and Westerhof (11) measured PAP and FV in humans to compare input Z in I and E, but they classified transitional beats into one of the two phases of respiration according to where peak systolic FV occurred. They reached the conclusion that there was no difference between I and E in the overall Z spectrum. In a more recent study (3), our group investigated the influences of respiration on Z(f) by computing input Z in dogs during I, E, and postexpiration. Only beats completely occurring in a single respiratory phase were considered in that study. Significant differences were found between postexpiration and the other two respiratory phases but not between I and E, apart from a greater R_{I} in E. In view of the symmetric nature of the relationship between ‖Z(f_{HR})‖ and E_{fr}, it is now evident why in both these studies no change in Z modulus was detected between I and E.
Concerning the determinants of Z changes, our results indicate that the changes in Z(f) are due almost entirely to changes in PAP, whereas during the transition from I to E the modifications of mean FV are negligible. It seems reasonable to ascribe the PAP changes and the concomitant changes in Z(f) to the rapid and substantial compression of the intrathoracic gases occurring between the end of I and the start of E, which are in turn reflected by an increase in IPP. To obtain an experimental support to this hypothesis, we also computed in two dogs the input Z from the pulmonary blood pressure “purified” from the influences of changes in IPP (Fig. 7). The purified intravascular pressure was obtained by computing the transmural pressure, namely PAP − IPP, on the assumption that the increase of IPP at the start of E induces an identical change in PAP. This assumption is in line with previous observations indicating that during the ventilatory cycle pulmonary intravascular pressure and IPP undergo similar changes (4). Figure 8 shows R_{I} and Z(f_{HR}) obtained from PAP and from PAP − IPP in the two dogs. The removal of the influences of IPP from PAP resulted in the abolition of the modulation of Z(f_{HR}) and in changes in the linear relation existing between E_{fr} and R_{I}. These findings suggest that IPP exerts a major role in the genesis of Z changes.
On this basis, it remains to be explained how IPP may produce the specific pattern observed in Z during the transition from I to E. A possible explanation follows. The increase in IPP occurring during the transition superimposes on the first harmonic of the purified PAP wave a sinusoidal component with the same frequency but a different phase. The difference between phases produces a lowering in the first harmonic modulus of PAP that is more pronounced when the two components have opposite phases, i.e., when the transition from I to E occurs in the middle of the transitional beat (E_{fr} = 50%). A first support of this reasoning is given by the experimental data of Fig.9, which shows PAP, IPP, and transmural pressure of three transitional beats, along with their respective first harmonic components, for E_{fr} = 25, 51, and 80%. The maximal reduction of the PAP modulus occurs for E_{fr} = 51%, namely when the first harmonic components of IPP and transmural pressure are in counterphase.
Moreover, we theoretically verified whether the increase in IPP occurring during the transition from I to E was sufficient to explain the observed patterns in the mean value and first harmonic of PAP. This was achieved by developing the mathematical model described inappendix . The results of the simulation actually confirm that the IPP increase induced by the transition from I to E and the time of occurrence of this increase within the transitional beat (quantified by E_{fr}) may account for all the changes observed in the mean value and in the first harmonic modulus and phase of the PAP wave.
As for the biological relevance of our findings, we should consider that in the pulmonary circulation the pulsatile component of pressure and flow is an important determinant of the RV afterload. Thus variations of Z(f_{HR}) may substantially affect the RV work. The observed changes of Z(f_{HR}) are therefore likely to influence the RV dynamics. Actually, alterations of RV systolic time intervals during the transition from I to E have been previously reported by our group (14), and the present findings suggest that Z(f_{HR}) modulations may be one of the factors responsible for these alterations.
The potential clinical implications of the assessment of RV afterload through Z(f) have been recently illustrated in several papers. For instance, it has been suggested that changes in Z(f) may quantify the afterload increase that characterizes the socalled chronic cor pulmonale (5) and that Z(f) is a more sensitive indicator of vascular alterations than pulmonary vascular resistance for the assessment of pulmonary function of donor lungs before transplantation (2). Kussmaul et al. (7) showed that the ventriculararterial coupling is importantly affected by pharmacological vasodilatation of pulmonary vessels in congestive heart failure and that the pulsatile properties of the pulmonary circulation must be taken into account to understand the effects of vasodilatation on cardiac output. More recently (4), pulmonary input Z has been used to evaluate the efficacy of nitric oxide administration and that of surgical interventions in the treatment and evaluation of chronic pulmonary hypertension. During the respiratory cycle, while shifting from I to E, the impairment in the RV afterload which characterizes pulmonary diseases may be further enhanced by alterations in the geometrical and mechanical characteristics of the proximal pulmonary arteries, as suggested for chronic cor pulmonale (9).
Moreover, the evaluation of the pulmonary input Z during respiration may be important for quantifying the milkingaction effect, produced by the cyclical changes of lung volume due to respiration, on the blood circulation (5). This milking action is particularly important in the Fontan procedure when the RV is markedly hypoplastic.
In all these instances, the quantification of the ventriculararterial coupling, as obtained by the estimation of the Z(f) during the respiratory cycle and, in particular, during the IE transition, where we showed that important Z changes occur, may be of great clinical relevance.
Acknowledgments
We thank Prof. J. MilicEmili (Montreal) for help in writing this paper.
Footnotes

Address for reprint requests: P. Castiglioni, LaRC Centro di Bioingegneria, via Gozzadini 7, I20148 Milan, Italy.

↵† Deceased November 1995.
 Copyright © 1997 the American Physiological Society
Appendix
Transitional Beats and Aliasing
The PAP and FV waveforms in the pulmonary circulation are influenced by the respiratory movements, and this may result in differences between the start and the end values of any single wave. When individual waveforms have to be analyzed by the Fourier series (as in the present study), a discrepancy between the onset and end of the waveform introduces a discontinuity that adds highfrequency components into the spectrum of the single waveform. Spectral components possibly added at frequencies higher than half the sampling rate are shifted toward lower frequencies and introduce distortion in the estimates. This error, known as “aliasing,” can be avoided only by selecting a sufficiently high sampling rate (higher than two times the maximum frequency content of the signal). Because the discontinuity between starting and ending values results in an infinite number of harmonics, a residual aliasing error is unavoidable. Thus we quantified the practical influences of aliasing on our estimates of the Fourier components.
The analysis was performed in two steps. First, we computed the differences between starting and ending (headtail) values of PAP and FV waves of each transitional beat. This was done to quantify the discontinuities actually occurred in our experimental data. Results are shown in Fig. 10 where the headtail differences (d_{PAP} and d_{FV}) are expressed as a percentage of the wave amplitude for PAP and FV. The PAP differences are close to 0% (almost no headtail difference) for E_{fr} ≈0, increase in a parabolic fashion reaching a maximum (≈80%) for E_{fr} ≈50%, and progressively return to 0% when E_{fr} approaches 100%. No appreciable headtail difference was found in the FV waves at any value of E_{fr}, thus excluding the possibility that aliasing may significantly affect the Fourier components of FV. On the basis of this finding, we continued the analysis by considering the effects of aliasing on PAP only.
In the second step of the analysis, we generated a simulated signal by summing 1) a real PAP wave characterized by the same initial and final values (this condition guarantees that the estimated Fourier components are not affected by aliasing) and 2) a sawtooth function f(t) that models possible headtail discontinuities. This function was selected because its Fourier series is known in an analytic form (12); thus it is not affected by aliasing introduced by the estimation procedure. In particular, withW the amplitude and T the duration of the real PAP wave and d_{PAP} defined as the headtail difference of the simulated signal normalized by the wave amplitude W, then the sawtooth function is given by the formula
It should be noted that the signal has an infinite number of harmonics produced by the discontinuities att =nT (see Eq. EA1 ). When the simulated signal is sampled at 200 Hz (i.e., at the same sampling frequency used in this study) components >100 Hz in f(t) are shifted toward a lower frequency band and cause aliasing.
Because the Fourier coefficients of f(t) are available in an analytic form and those of the real PAP wave can be estimated without aliasing, the true Fourier coefficients of the simulated signal are known. Therefore, we evaluated the effects of aliasing by comparing the theoretical Fourier coefficients of the simulated signal with those affected by aliasing that are estimated by the procedure used in our study.
The results, shown in Table1, point out that, even considering discontinuities larger than those actually occurring in experimental data, the aliasing error in the estimation of the modulus of the first harmonic is only 5%. This indicates that reliable Fourier coefficients can be computed also in transitional beats characterized by major headtail discontinuities in the PAP wave.
Appendix
A Mathematical Model of the IPP Influence on PAP at the Start of Expiration
In the text, we hypothesized that the changes in PAP during transitional beats might be due to the fast rise in IPP. In thisappendix, we show by means of a mathematical model that an increase of IPP resulting from the I to E transition is sufficient to explain the patterns observed in mean value and first harmonic of the PAP wave.
Let us define PAP^{I}(t), with 0 ≤ t ≤ T, the PAP waveform corresponding to a beat of duration T entirely occurring during I, and PAP^{IE}(t) the waveform corresponding to a transitional beat (assumed of the same duration T). Moreover, let IPP′(t) be the increase of IPP during the transitional beat. Because of the fast pressure rise occurring in IPP at the start of expiration, let us schematize IPP′(t) with the following stepwise function
P