Respiratory gating improves correlation between pulse wave transit time and pulmonary artery pressure in experimental pulmonary hypertension

Objective. Since pulse wave transit time (PWTT) shortens as pulmonary artery pressure (PAP) increases it was suggested as a potential non-invasive surrogate for PAP. The state of tidal lung filling is also known to affect PWTT independently of PAP. The aim of this retrospective analysis was to test whether respiratory gating improved the correlation coefficient between PWTT and PAP. Approach. In each one of five anesthetized and mechanically ventilated pigs two high-fidelity pressure catheters were placed, one directly behind the pulmonary valve, and the second one in a distal branch of the pulmonary artery. PAP was raised using the thromboxane A2 analogue U46619 and animals were ventilated in a pressure controlled mode (I:E ratio 1:2, respiratory rate 12/min, tidal volume of 6 ml kg−1). All signals were recorded using the multi-channel platform PowerLab®. The arrival of the pulse wave at each catheter tip was determined using a MATLAB-based modified hyperbolic tangent algorithm and PWTT calculated as the time interval between these arrivals. Main results. Correlation coefficient for PWTT and mean PAP was r = 0.932 for thromboxane. This correlation coefficient increased considerably when heart beats either at end-inspiration (r = 0.978) or at end-expiration (r = 0.985) were selected (=respiratory gating). Significance. The estimation of mean PAP from PWTT improved significantly when taking the respiratory cycle into account. Respiratory gating is suggested to improve for the estimation of PAP by PWTT.


Introduction
Pulmonary hypertension (PH) is known to cause right and global heart failure, and is associated with a high oneyear mortality (Humbert et al 2022).In current guidelines, pulmonary hypertension (PH) is defined as a mean pulmonary artery pressure (mPAP) above 20 mmHg measured by invasive right heart catheterization at rest (Humbert et al 2022).Unfortunately, current non-invasive methods like echocardiography or magnetic resonance imaging (MRI) are not accurate enough to confirm the diagnosis of PH or to serve for follow-up (Ibrahim et al 2015, Galiè et al 2016, Schäfer et al 2018).Therefore, the determination of pulse wave transit time (PWTT) by means of electrical impedance tomography and MRI has been proposed as a non-invasive surrogate for pulmonary artery pressure (PAP) (Proença et al 2016).
In a previous publication we described a negative linear correlation between the PWTT and systolic pulmonary artery pressure (sPAP), mPAP and diastolic pulmonary artery pressure (dPAP) over a wide range of pressures in a porcine model of acute PH (Mueller-Graf et al 2021) and found this surrogate promising for monitoring of mPAP.Besides the expected rather large PAP-induced changes in PWTT, we also noticed a range of PWTT values (10-15 ms) for one corresponding PAP value, which resulted in a blurring of the dot plots of PWTT over PAP.For this reason a rather low average correlation coefficient of 0.712 was found (Mueller-Graf et al 2021).In a subsequent analysis of changes in PWTT under resting conditions (with unaltered PAP), we described an inspiratory shortening and an expiratory prolongation of the PWTT (Mueller-Graf et al 2023).Interestingly, these changes were independent of the current PAP, calculated for the respective heartbeat.Therefore, we thought it would be valuable to investigate, whether considering the current tidal lung filling (respiratory gating) could improve the correlation so that PWTT could become a better surrogate for PAP.
Currently, neither publications investigating the direct effects of ventilation on PWTT in the lungs nor any publications on how to improve the determination of the surrogate parameter PWTT for estimating PAP i.e. by a filtering based on the respiratory cycle could be found.However, when looking at pulse wave velocity (PWV) as a surrogate for PAP, respiratory gating was suggested as a means to optimize the estimation of PWV in the pulmonary artery by MRI (Bradlow et al 2007).The authors of this study did not test, whether the correlation between PWV and PAP was affected by ventilation and the respective PAPs were not measured.The endexpiratory gating used in their study accepted cardiac cycles only if the diaphragm was within 7-8 mm of the previously defined end-expiratory diaphragmatic position (Bradlow et al 2007).This approach was used to minimize motion artifacts due the movement of lungs and heart within the chest since the resolution of the MRI images relies on repetitive measurements.Unexpectedly, the calculated PWV values did not differ whether respiratory gating was used or not.Additionally, in several other publications respiratory gating is recommended to improve image resolution of MRI, computed tomography scan and of Single-photon emission computed tomography in the context of PH (Colvin et al 2014).Thus, to the best of our knowledge the effect of the respiratory status, neither in terms of tidal lung filling, functional residual capacity, alveolar ventilation nor respiratory rate on PWTT and PWV in PH is known.
Except for the above mentioned few publications dealing with PWTT and PWV in the pulmonary circulation, particularly in PH, these surrogate parameters have mostly been investigated in the systemic circulation (Hirata et al 2006, Nilsson et al 2014).Despite the theoretical fact that PWTT correlates linearly with systemic blood pressure, PWV and PWTT are not reliable enough for clinical estimation of blood pressure for the following reasons: (1) a high inter-individual variation requiring calibration (Gaddum et al 2015, Mukkamala et al 2015), (2) sympathetic nervous activation affecting arterial stiffness (Nardone et al 2018), (3) while elastin determines arterial elasticity at low blood pressures, whereas collagen (400 times stiffer) contributes to the elasticity at high blood pressures, making blood pressure estimation over a wide range difficult or even impossible (Mukkamala et al 2015) and (4) difficulty in determining the exact time of pulse arrival (Solà et al 2009).
Due to these limitations PWV is not used to estimate blood pressure, but to determine arterial stiffness in the systemic circulation, a predictor of an individual's risk of atherosclerosis (Milan et al 2019).In clinical guidelines, a value of 10 m s −1 for femoral carotid PWV is considered the cut-off for atherosclerosis (Townsend et al 2015).One most likely reason for PWV-based estimations of blood pressure not reaching clinical routine might be the ubiquitous availability and speed of oscillometric blood pressure measurements in almost every situation (Forouzanfar et al 2015).
Despite the above-mentioned limitations for the systemic circulation, we believe that PWTT could become a valuable surrogate for PAP because of the limited availability of non-invasive PAP measurements by other methods.Therefore, the accuracy of this surrogate should be improved to make its clinical application more likely.We tested whether respiratory gating could increase the accuracy of this surrogate.
Ventilation has a particular strong effect on PWTT in the pulmonary circulation.Therefore, we aimed to eliminate this cofactor by respiratory gating and thereby improving the coefficient for the correlation between PWTT and PAP.

Animal model and anesthesia
The study was approved by the governmental ethical board for animal research (Landesamt für Landwirtschaft, Lebensmittelsicherheit und Fischerei, Mecklenburg-Vorpommern, Germany; No: 7221.3-1-037/19) and was carried out in accordance with the EU-directive 2010/63/EU and the Animal Research: Reporting of In Vivo Experiments guidelines 2.0 (ARRIVE 2.0) (Du Percie Sert et al 2020).The data obtained during the induction of pulmonary hypertension has been presented before.However, in this previous analysis data were not assessed using respiratory gating, since the investigators were not aware of the significant effects that ventilation has on PWTT (Mueller-Graf et al 2021).The data of these same animals under resting conditions were analyzed to describe the effect of ventilation on the correlation between PWTT and PAP and have recently been published, too Mueller-Graf et al (2023).Of the six animals studied, the data of five healthy German Landrace pigs (24,4-48,3 kg, 12-15 weeks old) were of sufficient quality to be processed further.Detailed information about the animal model, anesthesia, preparation and catheterization can be found in the above-mentioned previous publication (Mueller-Graf et al 2021).

Instrumentation
For PAP measurement, a 7.5 Fr thermodilution pulmonary artery catheter was inserted into the proximal left pulmonary artery through an 8.5 Fr vascular sheath (both Arrow, Teleflex, Wane, USA) placed in the right external jugular vein.Two 5 Fr Mikro-Tip™ Millar pressure catheters SPR-350 (Millar Instruments Inc., Houston, Texas) were surgically placed in the right internal jugular vein and advanced into the left pulmonary artery, the tip of the first one placed immediately behind the pulmonary valve (proximal) and that of the second one in a peripheral branch of the pulmonary artery (distal, figure 1).The correct positions of all intravascular catheters were verified by posterior-anterior x-ray taken with the C-Arm Ziehm Vision (Ziehm Imaging, Nuremberg, Germany).

Ventilation
The pigs were intubated endotracheally (ID 7.0 mm) and mechanically ventilated in a pressure-controlled mode using a Dräger Primus ventilator (Dräger Medical, Lübeck, Germany).Positive end-expiratory pressure (PEEP) was individually adjusted to obtain a transpulmonary pressure just above zero as recommended by Talmor, where transpulmonary pressure (Ptrans) was calculated as the difference between airway pressure and esophageal pressure (Talmor 2006).Inspiratory pressure was individually adjusted to achieve a tidal volume of approximately 6 ml kg −1 .The ratio of inspiration to expiration time was fixed at 1:2.Respiratory rate was adjusted to maintain end-tidal partial pressure of CO 2 at 5 ± 0.4 kPa.Airway pressure was measured at the heat moisture exchange filter using a disposable pressure sensor in conjuction with a PowerLab 16/35 (ADInstruments, Dunedin, New Zealand).Esophageal pressure was recorded by the same device and the same pressure sensor connected to a NutriVent multifunctional nasogastric catheter (Sidam Group, San Glacomo Roncole, Italy) positioned according to x-ray and Baydur (Baydur et al 1982).

Induction of pulmonary hypertenstion
The thromboxane A2 (TXA) analogue U46619 (Enzo Life Sciences Science GmbH, Lörrach, Germany) was administered at doses of up to 0.15 μg kg −1 min −1 to induce pulmonary hypertension by pulmonary vasoconstriction (Mosing et al 2015).In addition, temporary hypoxic vasoconstriction was induced by reducing FiO2 from 21% to 15% using Nitrogen (ALPHAGAZ™, Air Liquide Deutschland, Düsseldorf, Germany) (Hlastala et al 2004).The data presented here were the ones gathered during the recovery period after the respective PH inductions.

Data acquisition
Data were acquired at 10 kHz using bridge transducer amplifiers in combination with the respective hardware PowerLab 16/35 and software LabChart 8 (both ADInstruments, Dunedin, New Zealand).Data showing obvious mechanical noise caused by catheters bouncing within the pulmonary artery or against the pulmonary valve were excluded from the analysis.Additionally, data containing premature heart beats were also excluded automatically.

Data processing
Stored data were exported from LabChart in a Matlab-compatible format (MATLAB TM R2022a, The MathWorks, Inc., Natick, Massachusetts USA).The times of pulse arrival (t PA ) at the proximal and distal catheters were estimated parametrically using a hyperbolic tangent fitting algorithm derived from Solá et al [18].An analysis of each heartbeat was performed on a segment centered at the wavefront and with a duration of five times the rising edge of the systolic upstroke (figure 2).The segment's mean was removed for curve fitting and added back afterward.Segments were multiplied by a hamming window to reduce the fitting-algorithm's sensitivity to the data at the segment edges.The values in the periods before and after the rising edge were fixed to the values of the respective minimum and maximum.To improve the estimation of the time of pulse arrival, a case distinction focusing on the incoming part of the wave was added to the proposed function.Thereafter, the hyperbolic tangent function contained two different slopes where parameter A represents the amplitude of the modeled wavefront and μ the position of the inflection point, ν and σ control the slopes of the wavefront, and parameter C determines the offset (supplemental figure 1).The hyperbolic tangent function was fitted to each wavefront of the pressure curves by method of least squares.The time of reaching a threshold of 25% of the total model amplitude was defined as t PA at the proximal and distal catheter, respectively (see figure 1).PWTT was then calculated as the time difference between the distal and the proximal t PA .End-expiratory and end-inspiratory cardiac cycles were defined as those complete last heartbeats (from the beginning of the systole until the end of the diastole) falling within the respective phase (inspiration or expiration) of the respiratory cycle.

Statistics
Linear regression analysis was performed with the least square method and the respective correlation coefficient calculated using SigmaPlot 12.0 (Systat Software, Inc., San Jose, California, USA).For each linear regression F-tests were performed and a p-value calculated.After Fisher's-Z transformation, weighted mean correlation for each group was calculated and retransformed into an r coefficient (Field 2005).A standard error for the correlation coefficient was calculated as recommended (Field 2005).Repeated measurement ANOVA Figure 2. Pulse wave transit time (PWTT) between the proximal and distal pulmonary artery.The proximal pressure curve is shown in blue, the distal one in red.Solid lines represent the respective pulmonary artery pressures in mmHg.Local pulse arrival times were determined by the inflection points of the fitted hyperbolic tangent curve for t < μ (blue and red dotted lines) and marked by respective blue and red dots.Pulse wave transit time (PWTT) was calculated as the time difference between the arrival times at the distal and the proximal measurement site (dashed vertical lines).
(rmANOVA) was used to detect statistically significant differences in the calculated correlation coefficients (p 0.05).

Results
PEEP was 8 mmHg in two, 5 mmHg in two pig and 7 mmHg in one pig.To test which threshold was most suitable for PWTT estimation in our dataset, 5 thresholds between 15% and 35% in steps of 5% were analysed.
All heartbeats for TXA-induced PH of each animal are presented for each one of the respective threshold values in the supplemental figures 2-6.Supplemental figure 7 provides a synopsis for one animal and all tested thresholds.When the threshold was set to 15% or even lower, the respiratory effect on the PWTT was not detectable anymore.When the threshold was 30% or above, in some animals the PWTT became unphysiologically short or even negative, which we considered implausible.Within the range of 20%-30% we were able to obtain rather stable and reproducible results.In addition to this more qualitative analysis a quantitative analysis was performed.Linear regression for mPAP and PWTT was performed for all animals in TXA-induced PH and average R was calculated for each threshold (table 1) R was best for a threshold value of 25%.Therefore, this threshold was selected, and all subsequent analyses were performed using this threshold.
Respiratory gating improved the correlation coefficient between PAP and PWTT significantly, especially for mPAP and dPAP (table 2).Those two correlations improved in both experimental conditions, TXA-and hypoxia-induced PH.Gating also improved the correlation between sPAP and PWTT in hypoxia-induced but not in TXA-induced PH.
Figures 3 and 4 display all heart beats analyzed in this study for PH induction by TXA and by hypoxia (figures 3 and 4).The mean linear correlation coefficient for PAP and PWTT was calculated for both types of PH regardless of the state of inspiration (ungated) and as the last expiratory heartbeat (end-expiratory gating), or as the last inspiratory heartbeat (end-inspiratory gating, table 1).In the Supplemental material all correlation coefficients and their characteristics are presented (supplemental tables 1-3).The slope of the linear regression for PWTT and mPAP showed interindividual variations.For example, the slope for mPAP and PWTT varied between the 5 animals in hypoxia-induced pulmonary hypertension for all heartbeats between 0.256 and 0.546 (Supplemental Material table 3B).

Discussion
Our results suggest that respiratory gating has a significant impact on the correlation between PAP and PWTT in both types of PH, TXA-and hypoxia-induced.The use of respiratory gating helps improve the correlation coefficient between PAP and PWTT, particularly for mPAP and dPAP.By taking into account only the last cardiac cycle during inspiration or expiration, the correlation coefficient improved and resulted in a nearly linear relationship between PWTT and PAP.Interestingly, the correlation coefficient was slightly better for endexpiratory gating compared to end-inspiratory gating, but without this difference reaching significance.The effect of ventilation on the PWTT independent of the current PAP has been shown previously (Mueller-Graf et al 2023).In addition to these findings, we also found shorter PWTTs in inspiration compared to expiration in this current data analysis.The differences of 5-10 ms in the baseline measurement in the herin presented dataset are comparable to the ventilation induced changes published previously (Mueller-Graf et al 2023).Therefore, we believe that the results presented in this study are reliable and valid for estimating the improvements that can be achieved by using respiratory gating techniques in PAP estimations using PWTT as a surrogate.
Based on our previous results with the presented linear correlation between PAP and PWTT, we can also confirm with our newly presented results the validity of the linear approximation used in our model (Mueller-Graf et al 2021).It is known that PWTT becomes shorter when vessels are narrower, intravascular pressures higher, vessel walls stiffer, and distances between proximal and distal pressure sensors shorter (The Reference Values for Arterial Stiffness 2010).Such linear correlation has also been reported previously for the correlation between pulse arrival time (PAT) and PAP (Proença et al 2016).PAT, defined as the time interval between the R-peak of the Electrocardiographyand the pulse arrival in the lungs, as determined by electrical impedance tomography, yielded a correlation of r = 0.87 (Proença et al 2020).However, the respiratory status was not considered in these investigations.Therefore, it is possible that the reported correlation coefficients could have been higher had the respiratory status been considered.
We increased pulmonary arterial pressure by both, TXA and hypoxia.TXA analogon U46619 has important proinflammatory effects on the pulmonary microvasculature, such as vasoconstriction, increased permeability, and activation of neutrophils and platelets (Wright et al 1999).Despite these many effects, the TXA analogon U46619 has been recommended for inducing acute reversible and selective PH in porcine models (Goncharova et al 2021).In this particular application acute vasoconstrictive effects are mediated by precapillary vasoconstriction, in addition to some postcapillary pressure effects with concomitant moderate augmentation of capillary pressure (Walmrath et al 1997).The animals of our study demonstrated hemodynamic stability throughout the TXA-induced PH, as evidenced by consistent levels of systemic arterial pressure, heart rate, and central venous pressure (data not shown).To further validate our findings, we induced PH by ventilating the animals with hypoxic breathing gases.Hypoxia triggers reflexive hypoxic pulmonary vasoconstriction, leading to an increase in PAP as long as right ventricular pump function is not yet affected by the hypoxia (Sylvester et al 2012).Therefore, experimental PH by hypoxia is limited to shorter periods as compared to TXA and tends to be more unstable due to potential hypoxic systemic side effects.The effects of acute hypoxia on the systemic circulation are numerous, highly variable within individuals, and are dependent on the duration and extent of hypoxic damage to the organs.Consequently, it may manifest as tachycardia or bradycardia, slight increases or decreases in systemic blood pressure, and alterations in inotropy (Da Zhang et al 2014, Savla et al 2018, Yasuma andHayano 2000).In our animal model, systemic hypoxia tended to induce tachycardia and to increase the frequency of premature heartbeats, while causing a drop in systemic blood pressure.As a result, animals were generally less stable during hypoxia compared to TXA administration.We therefore had to limit the duration of PH induction by hypoxia to shorter periods compared to TXA.We also had to exclude more premature heartbeats from the data obtained during hypoxia than from those under TXA administration.The correlation coefficients obtained during hypoxic periods were slightly lower than those gathered under TXA, but this difference was not statistically significant.This finding could easily be explained by the relatively more unstable conditions during hypoxic PH.
Although PWTT is a physiological correlate of PAP, it is a parameter the measurement of which depends on definitions and technical means.In our study we used high-fidelity pressure transducers that were directly inserted into the pulmonary artery at their respective locations.Although the measured pressures were highly accurate, the actual pulse arrival is a single point in time within a continuum of physiologically changing conditions.Therefore, this step is crucial for a correct estimation of the PWTT.To determine this point we fitted a hyperbolic tangent curve to our data in the way recommended by Solà et al (2009).Thus, using this model as the only measure of t PA resulted in PWTT's of less than 10 ms, which we assumed to be physiologically impossible.Therefore, we faced several challenges adopting the hyperbolic tangent algorithm to the needs of our dataset: due to the two-stage nature of the rising slope of the pressure curve caused by the superposition of the peak systolic pressure (forward wave) and the pressure of the first systolic diffraction (reflected wave), Solà's approach achieved only a moderate fitting of the wave fronts (Mills et al 2008).To improve the fitting we modified this approach further.Since the arrival of a pulse wave is defined by its first upstroke, introducing of a mathematical case distinction could account for the the biphasic systolic upstroke, thereby taking only the first upstroke into acount.Since this case distinction is rather arbitrary we present in the supplementary material a sysnopsis of the results we obtained with thresholds of 15%, 20%, 25%, 30% and 35% (supplemental figures 1-7).The calculation of the averaged R and its respective standard error of the mean (SEM) were stable for threshold values in the range of 20% to 30%.We thus argue that within this range our results are independent of the exact threshold chosen.As R was best for 25% we decided to use this threshold for all additional estimations presented in this manuscript.
The heart-lung-interaction is a complex physiological process involving the close interplay between the cardiovascular and respiratory systems.The two systems are interconnected by the pulmonary circulation and share many cofactors including intrathoracic pressure, lung volume, preload and after load of the right and left ventricle and heart contractility.To replicate physiological ventilation and ensure the use of a minimally harmful mechanical ventilation approach, we carefully selected our respiratory settings.A typical PEEP, adjusted to meet individual needs, was determined through a PEEP titration following the methodology proposed by Talmor (2006).Tidal volume was maintained at a minimum level of 6 ml, as recommended to mitigate the risk of lung injury (Brochard et al 2017).The inspiratory-to-expiratory (I:E) ratio was set at 1:2 to align with physiological norms, considering that expiration is naturally longer, and increasing inspiratory time has been associated with a higher risk of lung injury (Müller-Redetzky et al 2015).
In the following we will focus on the effects of lung filling on the pulmonary vasculature, since we believe this has the highest impact on the ventilation-induced changes in PWTT, which are removed by respiratory gating.Changing lung volumes can effect PWTT mainly by two mechanisms: (a) pulmonary vascular resistance (PVR), and (b) an inspiratory reduced transmural pressure.
Ad (a) PVR is a function of vessel diameter and legnth.Thus, literature pertaining to PVR provides valuable insights into changes in the diameter of pulmonary vessels induced by ventilation.Total PVR, and thereby the vessel diameter is at a minimum at functional residual capacity, but increases as lung volume moves towards total lung capacity or decreases towards residual volume with PVR representing the cumulative resistance of extra-alveolar vessels and the alveolar capillaries.Therefore, with changing lung volumes both contribute to total PVR in opposite directions (Simmons et al 1961, Solà et al 2011, Suresh and Shimoda 2016).
Extra-alveolar vessels running through the lung parenchyma are mechanically attached to this tissue.As the lung expands, their diameter increases due to radial traction on the vessel walls.As a result, the resistance of these large vessels decreases at large lung volumes.However, the resistance of extra-alveolar vessels increases during lung collapse as their inherent elastic fibers recoil (Suresh andShimoda 2016, Widrich andShetty 2022).
Alveolar capillaries, including those in the corners of alveolar walls, behave in the opposite manner.When lung volume approaches functional residual capacity, alveoli are small and exert little external counterpressure on these small vessels.As a result, vessel diameter increases, resulting in lower PVR.When alveolar filling reaches total lung capacity, resistance reaches its maximum (Widrich and Shetty 2022).
In our experiment, PEEP was set according to Talmor using an esophageal catheter to obtain a slightly positive transpulmonary pressure (Talmor 2006).The personalized PEEP level aimed to balance collapsible forces within the mechanically ventilated lungs of animals under general anesthesia and muscle relaxation, resulting in an end-expiratory lung volume close to functional residual capacity or slightly above.
Having positioned the measuring catheters within the larger pulmonary arteries in our experiments, we hypothesize that inspiratory phases may cause an increase in the diameter of the pulmonary artery due to radial traction in the assesed vessels .According to the Moens-Korteweg equation, an elevated vessel diameter is expected to result in a prolongation of the PWTT (Korteweg 1878).And indeed, in our experiments, we observed a slightly longer PWTT at end-inspiration.This phenomenon might have contributed to the enhanced correlation coefficient that we report when applying respiratory gating.
Ad (b) During inspiration mechanical ventilation leads to an increase in intrathoracic pressure and thereby compresses thoracic tissues.This effect has also been used to explain changes in the PWTT within the aorta.When participants increased inthrathoracic pressure by performing a Valsalva Maneuver their PWTTs became longer .In the systemic circulation longer PWTTs occur when intrathoracic pressures are increased The increased extravascular pressure during inspiration could also be transferred to larger arteries of the lungs which would decrease the transmural pressure.This phenomen could oppose in part the vessel wall tension.This decreased transmural pressure would reduce the load on the arterial wall, resulting in a lower wall stiffness.Accoridng to the Moens-Korteweg equation this would then result in a slower PWV and a higher PWTT during inspiration, which is in line with our findings (Korteweg 1878).This explanation fits with the findings of our studyshowing an increased PWTT within the pulmonary artery during inspiration.

Limitations
Although our study provides strong evidence for an improvement of the coefficient for the correlation between PWTT and PAP, this experiment has obvious limitations.We present data that were previously analyzed (Mueller-Graf et al 2021).When we analyzed the same data for our previous publication, inspiration and expiration were not known to affect PWTT independently of PAP.In view of the desire to keep the number of experimental animal to a minimum, we felt it was reasonable not to repeat similar experiments and insteead to present results in this manuscript that are new but based on the re-analysis of previously published data (Mueller-Graf et al 2023).
As we analyzed invasive data of multiple catheters in a porcine model, we had to perform our experiments in general anesthesia involving muscle relaxation.Therefore, it was impossible to also evaluate the effects of normal spontaneous breathing, during which intrathoracic pressures become negative.From our results during positive pressure vechanical we cannot extrapolate the type and magnitude of changes in PWTT.Irrespective of this unknown outcome we propose to apply end-expiratory and end-inspiratory gating to eliminate the potential influences of breathing on the correlation between PWTT and PAP.Despite these considerations we noticed a high intrainividual variation in the slope in the linear regresssion model.We believe that the potential use of PWTT estimation and thereby calculation of a PAP surrogate has its main advantage in the individual follow up of chronic patients with PH and the steering of an individual's therapy.Therefore, an individual specific calibration could be easily included in treatment protocols.
The measurement of pulse wave arrival is challenging as the shape of the pressure curve changes considerably from the proximal to the distal pressure transducer and with changing PAP Nakayama et al 1997, (Castelain et al 2001).In our previous analysis we used an intersecting tangent method (Mueller-Graf et al 2021).Unfortunately, this method led to inconsistent results when trying to analyze the relatively small changes in PWTT under mechanical ventilation.Therefore, in our last publication we used the more robust algorithm based on the hyperbolic tangent method (Mueller-Graf et al 2021).Since we consider this approach accurate we used it again in this study but supplemnting it with an automatic exclusion of premature heart beats and sequences of noisy signals (i.e.due to catheter bouncing against the vessel walls or the heart valves).Additionally, we implemented a case distinction technique to better replicate the changes observed in the biphasic systolic upstroke induced by pulmonary hypertension.In summary, the newly developed technique shows promise in accurately detecting subtle changes in PWTT.Moreover, it holds potential for detecting PWTT variations in systemic circulation and interpreting curves derived from alternative methods such as Electrical Impedance Tomography or MRI.It is important to note, however, that the comparability to our previous findings may be reduced by implementing this new technique.
Additionally, we must consider, that PWV changed in our model dramatically upon PH induction.The reduction of the PWTT under thromboxane and hypoxia from around 70 ms to 30 ms resulted, within the approximated distance of about 10 cm between both pressure sensors, in a dramatic increase of the PWV from around 2 to 10 m s −1 (Mukkamala et al 2015).These changes occurred with an increase of mPAP from around 20 mmHg up to 40 mmHg.For the systemic circulation Spronck et al reported an increase of PWV from about 1 m s −1 when diastolic pressure increased by 10 mmHg (Spronck et al 2015).In contrast to the findings in the systemic circulation, we observed a dramatic increase in PWV following the induction of PH.Nevertheless, it's noteworthy that PWV can surpass 10 m s −1 in patients with PH, as reported by Su et al who measured wavespeed using a Doppler flow probe in the pulmonary artery .Additionally, Kopec et al reported elevated PWV levels of 10.0 m s −1 in patients with PH compared to healthy subjects with a PWV of 3.5 m s −1 .Simulation of the pulmonary circulation and calculation of changes in PWTT upon pulmonary hypertension revealed changes in PWTT comparable with our findings, where PWTT dropped from 56 to 18 ms with an increase in pulmonary artery pressure by 25 mmHg (Figure 8 in Proença et al 2017).Taken together, the formation of PH, which stiffens the pulmonary arterial walls, is known to exceed the increase in PWV reported for systemic circulation.Therefore, we conclude for our model and results that PH induction may have affected the structure and mechanics of the pulmonary artery walls.Thus, we believe that the changes of PWTT is plausible.
Our estimation of the pulse wave arrival and thus the calculation of the PWTT is highly affected by the respective algorithm used to calculate pulse arrival.We used a hyperbolic tangent for estimating the pulse wave arrival as suggested by Solà et al (2009).To adapt this approach selectively to the early upstroke of the systole we added the above-mentioned threshold.This artificial definition of a pulse arrival might contribute to an exaggeration of the changes in PWTT induced by ventilation.However, all other definitions of a pulse arrival are also artificial and thus do not represent a physiological truth.
In addition, we are aware of the complex interaction between heart and lungs to have effects also on heartrate, vascular tone, stroke volume and cardiac output, all of which will have influenced PWTT and its relation to PAP.However, we have no data to quantify the effects of such heart-lung-interaction (Pinsky 2012, Mahmood and Pinsky 2018).

Conclusions
Respiratory gating improved the coefficient for the correlation between PWTT and PAP significantly in an individual specific manner and should therefore be considered when PWTT is used as a surrogate for PAP.These results offer new insights into the mechanisms of heart-lung-interaction that should be explored further.

Figure 1 .
Figure 1.Scematic drawing of the heart with placement of the pressure transducers, both of which passing the right atrium (RA) and the right ventricle (RV).The proximal pressure transducer (blue line) was placed directly behind the pulmonary valve and the distal one (red line) in a distal branch of the left pulmonary artery (LA = left atrium, LV = left vetricle).

Table 1 .
Averaged R and its respective standard error of the mean (SEM) for TXA induced PH for thresholds 15% and 35% in 5% steps.

Table 2 .
Mean linear regression analysis is for correlation of pulse wave transit time and sPAP, mPAP and dPAP for thromboxane A2-induced pulmonary hypertension (TXA) and hypoxic hypoxia for all heartbeats (ungated), the last heartbeat during expiration (endexpiratory gating) and the last heartbeat during inspiratory (end-inspiratory gating; rmANOVA on Ranks, * p < 0.05).
* Figure 4. Scatter plot for the relation between mPAP and PWTT of each heartbeat during the recovery from pulmonary hypertension induced by thromboxane.Respiratory gating (last heartbeat during expiration in red, open triangel with tip downwoards, and last heartbeat during inspiration in blue, open triangel with tip upwoards, all other heartbeats in filled light grey dots) led to a significant increase in the correlation coeficient for mPAP and dPAP in all assesed conditions.Linear correlation was calculated by Pearsons least square method.Figure 3. Scatter plot for the relation between mPAP and PWTT showing each heartbeat after induction of a pulmonary hypertension by hypoxic ventilation with an FiO 2 between 10% and 15%.Respiratory gating (last heartbeat during expiration in red, open triangel with tip downwards, and last heartbeat during inspiration in blue, open triangles with tip upwoards, all other heartbeats in filled light grey dots) led to a significant increase in the correlation coefficient for sPAP, mPAP and dPAP in all assessed conditions.Linear correlation was calculated by Pearsons least square method.