Calculation of systemic vascular resistance, used for hemodynamic decision-making, is based on central venous pressure taken as the downstream pressure. However, during circulatory arrest, arterial pressure decreases to a plateau higher than central venous pressure, the critical closing pressure (Pcrit). The authors assessed in humans undergoing arrest whether two-compartment and pressure-dependent conductivity models better estimate arterial pressure decay and Pcrit than a single-compartment model, and whether Pcrit corresponds to Pcrit calculated with the heart beating.

Aortic pressure decay was fitted to single-compartment, two-compartment, and pressure-dependent conductivity models using specified time intervals during arrest and natural diastole in 10 patients during defibrillator implantation.

Although all models closely predicted Pcrit with an arrest of > or = 7s, both two-compartment and pressure-dependent conductivity models better estimated pressure decay than a single-compartment model. However, Pcrit calculated from natural diastolic pressure decay was greater (53 mmHg +/- 15.6) than Pcrit 15 s (26.6 mmHg +/- 7.8, P = 0.001) and 30 s (23.9 mmHg +/- 7.1, P = 0.001) during arrest, and also greater than Pcrit calculated for the same time interval during initial arrest.

Thus, during arrest, Pcrit can be closely predicted after > or = 7 s, regardless of the model; two-compartment and pressure-dependent conductivity models provide a better fit than a single-compartment model, and actual Pcrit is much less than Pcrit calculated with the heart beating. Irrespective of uncertainties in whether Pcrit calculated with the heart beating or during arrest is the "true" Pcrit prevailing physiologically, linear vascular resistance is markedly less when substituting Pcrit for central venous pressure as the downstream pressure.

CLASSIC physiology considers right atrial pressure the downstream pressure of the systemic circulation,1and therefore uses central venous pressure for linear calculation of systemic vascular resistance to help differentiate circulatory disturbances, assess vasomotor tone, and guide cardiovascular therapy.

However, the arterial system as a whole, as well as regional arterial circulations,2–4behave like a Starling resistor in several settings, since blood flow ceases at positive arterial pressures well above venous pressure.2–8Such an arterial pressure has been designated critical closing pressure (P^{crit}).2,9Since P^{crit}is altered by vasoactive drugs6,10–12and tissue warming,13,14this behavior is thought to be caused by arteriolar tone9,10,15and/or tissue pressure surrounding the vasculature.11,16In humans undergoing evoked circulatory arrest during implantation of a cardioverter/defibrillator (ICD), arterial pressure showed a monoexponential decay and did not equilibrate with venous pressure in 14 patients for as long as 20 s, which could be suggestive of a “vascular waterfall.”17Accordingly, the concept of central venous pressure as the downstream pressure of the arterial circulation18appears too simple. Furthermore, it is of interest whether systemic arterial P^{crit}can be determined in the intact circulation from analysis of the diastolic pressure decay, and be considered the downstream pressure of the arterial circulation.

Methodologically, an answer to this question could be complicated by the fact that multiple parallel channels likely affect arterial pressure decay after cessation of systemic blood flow, possibly making modeling of pressure decay by a single monoexponential function too imprecise. Conceivably, the thoracic aortic windkessel and the peripheral arterial system have different but superimposed pressure decay characteristics, and the downstream pressure of the cerebral circulation also could differ from that of other vascular territories.19,20Finally, as vascular diameters decrease after cessation of blood flow, arterial pressure decay during circulatory arrest might become a function of vascular diameter and hence pressure. Thus, to estimate P^{crit}in the intact circulation, it is a prerequisite to know what mathematical model sufficiently reflects arterial pressure decay during circulatory arrest. Furthermore, it must be clarified to what extent P^{crit}, calculated or measured during a nonphysiological situation such as circulatory arrest, corresponds to a P^{crit}calculated from the diastolic arterial pressure decay with the circulation intact.

Accordingly, using high-frequency digitization of aortic pressure measurements by micromanometry and curve fitting techniques, we assessed in humans undergoing circulatory arrest which of several mathematical models best predicts arterial pressure decay and P^{crit}; whether arterial P^{crit}during circulatory arrest, as extrapolated or measured from the arterial pressure decay, corresponds to arterial downstream pressure calculated in the intact circulation with the heart beating; and how P^{crit}determined this way would affect calculation of vascular resistance in a linear model.

## Materials and Methods

### Patients

After approval by the local ethics committee (Medical Faculty, Universität Duisburg-Essen, Essen, Germany) and informed written consent, 10 consecutive patients (9 men, 1 women; age, 63.3 yr ± 6.3 SD; weight, 83.1 kg ± 10; height, 175.7 cm ± 6.3) scheduled for ICD implantation under general anesthesia were studied. All patients had essential hypertension and were on antihypertensive therapy. Nine patients had three-vessel coronary artery disease. One patient had dilated cardiomyopathy, three patients had ischemic cardiomyopathy, and one patient had idiopathic ventricular fibrillation. Functionally, two patients had mild heart failure (New York Heart Association Class I or II), three patients had moderate heart failure (New York Heart Association Class III), but no patient had severe heart failure (New York Heart Association Class IV).

### General Procedures

After premedication with 1 mg oral flunitrazepam, both on the evening and the morning before ICD implantation, a five-lead electrocardiography system was applied to monitor heart rhythm. For continuous measurement of arterial pressure and blood sampling, a radial artery catheter was inserted under local anesthesia. General anesthesia was induced by fentanyl 5 μg/kg (Fentanyl DeltaSelect; Delta Select GmbH, Dreinach, Germany) and etomidate 0.3 mg/kg (Hypnomidate; Janssen- Cilag, Neuss, Germany), and followed by rocuronium 0.6 mg/kg (Esmeron; Organon Teknika, Oberschleißheim, Germany). After tracheal intubation, patients were mechanically ventilated with 100% oxygen in air. Normocarbia was repeatedly confirmed by arterial blood gas analysis. Anesthesia was maintained by fentanyl infusion and inhaled isoflurane in concentrations not exceeding 0.8% end-tidal.

For central venous pressure measurements and blood sampling, a triple-lumen catheter was inserted *via* the right internal jugular vein, and its position close to the right atrium was confirmed by intravascular electrocardiography. For measurements of thermodilution cardiac output, a pulmonary catheter was advanced. To measure thoracic aortic pressure, a precalibrated (37°C), micromanometer-tipped 0.014-inch wire (ComboWire, Volcano Corporation, San Diego, CA) was inserted *via* the left radial artery using a 6-French introducer (Cordis Medizinische Apparate GmbH, Johnson & Johnson, Langenfeld, Germany) and a 4-French guidance catheter (Cordis Medizinische Apparate GmbH, Johnson & Johnson). The micromanometer was always positioned in the thoracic aorta, approximately 3 cm downstream from the origin of the left subclavian artery, as verified by fluoroscopy.

Patients received either a single-chamber (n = 3), double-chamber (n = 2), or biventricular ICD (n = 5). To assess ICD function, ventricular fibrillation was induced by 1.0 J T-wave triggered shocks and successfully terminated by internal shocks in all patients.

### Measurements and Data Sampling

Heart rate was recorded from an electrocardiogram. Thoracic aortic, radial artery, central venous, and pulmonary artery pressures were measured by electromanometry relative to barometric pressure and referenced to the midthoracic plane. To eliminate ventilation-induced oscillations of intrathoracic pressures, mechanical ventilation was stopped before and during ventricular fibrillation.

To minimize offset errors, electric calibration was verified by exposing the micromanometer to defined pressures in a calibration device at 37°C (pressure calibrator; Hugo Sachs, March-Hugstetten, Germany) before insertion. After data acquisition, potential offsets of aortic pressure measured by the micromanometer and of central venous pressure were checked by withdrawing the micromanometer into the radial artery and immersing it into the superior caval vein through the central venous catheter.

Cardiac output before induction of ventricular fibrillation was measured in triplicate by thermodilution, and results were averaged. Cardiac index and systemic vascular resistance index were calculated using standard formulae.

Signals were recorded continuously on a strip chart thermoarray recorder (Dash-8x; Astro-Med, West Warwick, RI) and stored on tape (RD-145T DAT Data Recorder; TEAC, Wiesbaden-Erbenheim, Germany). In parallel, data were digitized online at 1 kHz per channel using a high-performance data acquisition system (PowerLab 8/30; AD Instruments GmbH, Spechbach, Germany).

### Mathematical Modeling and Curve Fitting Techniques of Thoracic Aortic Pressure Decay

The aortic pressure decay in each individual patient was modeled using three different models, both during episodes of evoked ventricular fibrillation and during diastole of the heartbeat preceding ventricular fibrillation (fig. 1). The endpoint of each model was the pressure asymptote resulting from curve fitting techniques encompassing the diastole preceding circulatory arrest, and from data sets acquired during ventricular fibrillation with time intervals spanning complete diastolic length and 3, 7, 10, 15, 20, and 30 s. Accordingly, this resulted in calculated pressure asymptotes related to diastole with the heart beating, as well as to different time intervals of ventricular fibrillation, and 240 data sets were assessed in 10 patients (8 data acquisition sets per patient × 3 models × 10 patients).

In addition, to assess the potential impact on calculated P^{crit}values of pressure waves reflected from the arterial periphery to the thoracic aorta, P^{crit}with the circulation intact was also calculated using half of diastole (early and late). Furthermore, these values and those obtained from fitting pressure decay over the complete diastole were compared with P^{crit}values calculated during initial circulatory arrest, with an interval equivalent to diastolic length. For analysis of diastolic pressure decay with the heart beating, a starting point of curve fitting approximately 30 ms after aortic valve closure (dicrotic notch) was chosen; *i.e* ., obvious wave reflections in the aortic pressure tracing had faded.

For comparison, and since this model has been described in the literature,17aortic pressure decay was modeled first as a single-compartment (*i.e* ., a monoexponential function) according to the following:

where P^{i}is the initial pressure at time (t) zero, τ is the time constant of arterial pressure decay, and P^{crit}is the nonzero asymptote.

Also, to account for potential effects of two parallel pressure decay channels (two compartments) with two different time constants (*i.e* ., a central thoracic aortic windkessel and a peripheral arterial vascular compartment), a biexponential function was fitted according to the following:

where P^{i}and P^{crit}have the same meaning as in the previous paragraph, and the terms containing P^{1}and P^{2}reflect the contributions of two compartments, with possibly different decay time constants τ^{1}and τ^{2}.

Finally, to also account for a diameter (pressure)–dependent effect on vascular conductivity of aortic pressure, we fitted the aortic pressure decay to the solution of an equation derived from a windkessel and decaying *via* a pressure-dependent vascular diameter (pressure-dependent conductivity model). Here, an elastic response of vascular diameter to pressure was assumed, and a linear approximation to the Hagen-Poiseuille law21was used. The corresponding equation can be solved to yield:

Again, P^{i}and P^{crit}have the same meaning as in the previous paragraph, b reflects the response of arterial conductivity to pressure, and τ is the time constant of arterial pressure decay.

As a measure of goodness of fit and to compare the three models used, the sum of the squared differences (χ^{2}) between measured aortic pressure and the pressure calculated from the respective curve fitting functions for each data point were calculated for each individual data set and each curve fitting model, allowing comparison of medians between models.

### Statistical Analysis

Data are reported as means ± SD or medians, as appropriate. Aortic pressure, central venous pressure, and pressure asymptotes were compared using one-way repeated measures ANOVA and the Student *t* test. P^{crit}calculated for different intervals within a model was compared by Student *t* test for paired data. Since the goodness of fit (χ^{2}) of the three different models is not normally distributed, these data are presented as median and interquartile ranges, and the nonparametric Wilcoxon signed-rank test was used to compare potential differences between the three models. The following *a priori* null hypotheses were tested:

There is no difference in the means of values of cardiovascular variables (thoracic aortic, central venous, and calculated P^{crit}) when compared over time during circulatory arrest and between the three models, critical closing pressures calculated with the heart beating when compared to P^{crit}during circulatory arrest, and vascular resistance index using central venous pressure when compared to vascular resistance index using P^{crit}calculated for 15 and 30 s of circulatory arrest or with the heart beating. An alpha error *P* of less than 0.05 was considered statistically significant.

## Results

### Aortic and Central Venous Pressure Changes During Circulatory Arrest

After induced circulatory arrest, aortic pressure decreased in a time-dependent fashion, as shown in figure 1A. From a diastolic aortic pressure of 66 mmHg ± 14, aortic pressure decreased to 27.5 mmHg ± 6.9 and 25.4 mmHg ± 7.1 after 15 and 30 s, respectively. Central venous pressure increased to 14.6 mmHg ± 3.8 over the course of 10 s, but did not change significantly thereafter. Thus, even at the end of 30 s of circulatory arrest, a substantial gradient remained between arterial pressure and central venous pressure, with a mean difference of approximately 10 mmHg, as shown in figure 2.

### Calculation of P^{crit}During Circulatory Arrest

All models applied for fitting the arterial pressure decay during circulatory arrest were able to predict P^{crit}. Using a single-compartment model, the values of the pressure asymptote and measured arterial pressure after 30 s of circulatory arrest were within 1 mmHg (fig. 3A). Using data sets of shorter durations for curve fitting, calculated P^{crit}was significantly greater but still quantitatively close to aortic pressure measured 30 s after circulatory arrest (fig. 3A). In particular, a time frame of ≥ 7 s of circulatory arrest was sufficiently accurate to within 4.5 mmHg aortic pressure 30 s after circulatory arrest.

All models used for curve fitting yielded a similar P^{crit}with a maximum mean difference between models of less than 0.8 and 1.5 mmHg (fig. 3B) for 30- and 15-s periods of circulatory arrest, respectively (table 1). Furthermore, there were only small differences between models in the goodness of fit, as expressed by χ^{2}(table 1). Of note, however, is that both the two-compartment and the pressure-dependent conductivity model yielded a significantly better goodness of fit than the single-compartment model (table 1).

### Critical Closing Pressure Calculated in the Intact Circulation with the Heart Beating

Arterial downstream pressure calculated from the diastolic aortic pressure decay (mean duration, 694 ms ± 148) as the pressure asymptote with the heart beating yielded mean values between 47.6 and 56.8 mmHg for the 3 models used (table 1).

Of note, these values were significantly and markedly different from the P^{crit}calculated during circulatory arrest; *e.g* ., for time intervals of 15 and 30 s (fig. 4), irrespective of the model used (table 1). In particular, for the single-compartment approach, P^{crit}averaged 56.8 mmHg ± 16.2 with the heart beating, but 39.8 mmHg ± 12.6 for the same interval of pressure decay during circulatory arrest (*P* = 0.004). For the two-compartment model, P^{crit}averaged 53 mmHg ± 15.6 with the heart beating, but 38.9 mmHg ± 12.3 for the same interval during circulatory arrest (*P* = 0.022). Furthermore, P^{crit}calculated with the heart beating was also significantly greater than P^{crit}calculated during circulatory arrest for data sets using intervals of 3, 7, 10, 15, and 30 s (*P* = 0.002 or less).

To also assess the potential impact on P^{crit}of early and late diastolic time intervals, we compared calculated P^{crit}derived from analysis of complete, early, and late diastolic pressure decay to one another and to P^{crit}calculated during circulatory arrest for the same (complete diastole) time interval. There was no difference in the values of P^{crit}with any model of fit when comparing values using complete, early, and late diastole (table 2).

However, regardless of diastolic duration used for analysis and regardless of the model used, P^{crit}calculated from diastolic intervals were always significantly greater than during initial circulatory arrest (table 2).

### Calculation of Vascular Resistance as a Function of Downstream Pressure

As expected, calculation of vascular resistance index in a linear model using as the downstream pressure either central venous pressure, P^{crit}calculated for 30 s of circulatory arrest, or P^{crit}with the heart beating yielded markedly and significantly different vascular resistances, as depicted in figure 5. In particular, systemic vascular resistance index using central venous pressure as the downstream pressure was almost three times greater than when using P^{crit}calculated with the heart beating as the downstream pressure.

## Discussion

There is ample evidence that both the systemic circulation as well as regional vascular beds do not show a linear arteriovenous pressure gradient flow relationship with a pressure intercept near venous pressure.5–8Rather, as flow ceases, a gradient between arterial pressure and central venous pressure remains over long time periods; *i.e* ., arterial and central venous pressure do not equilibrate as expected in rigid vascular tubes. This phenomenon has been attributed to closure of vascular channels despite a positive arterial intraluminal pressure and an arteriovenous pressure gradient, and the arterial pressure prevailing was designated “critical closing pressure” (P^{crit}).2,9Since vasodilators and vasoconstrictors6,10–12as well as heating and cooling,13,14decrease and increase P^{crit}in isolated limbs, respectively, P^{crit}is thought to be related to arterial or arteriolar vascular tone and vascular collapse. In fact, an analogy has been made with the Starling resistor concept of the pulmonary circulation,3and even with a “vascular waterfall.”2,9When assessing arterial and venous pressures at 1-s intervals during episodes of ventricular fibrillation for up to 23 s, arterial pressure decay after cardiac arrest could be described by a monoexponential curve, and a mean arteriovenous pressure gradient of 13.2 mmHg remained that was not explained by a pressure gradient across the inferior caval vein at the level of the diaphragm.17

However, there are several potential problems with a single-compartment approach to derive P^{crit}. First, since arterial pressure during circulatory arrest may decay through parallel vascular channels with different time constants (*i.e* ., a central thoracic aortic windkessel and a peripheral arterial vascular compartment), and since vascular conductivity may itself depend on vascular diameter and hence pressure, it is unclear whether a single-compartment model appropriately describes the arterial pressure decay after circulatory arrest and which time frame of data sampling is required for predicting P^{crit}. Second, it is unknown whether circulatory arrest by ventricular fibrillation evokes pathophysiological changes like vasodilation or vasoconstriction that may make P^{crit}measurements obtained in this way invalid to represent P^{crit}in the intact circulation. Third, of perhaps greatest importance, it is unknown whether P^{crit}can be calculated from the diastolic arterial pressure decay in the intact circulation with the heart beating, and to what extent this value corresponds to P^{crit}measured during circulatory arrest.

Accordingly, we assessed whether two-compartment and pressure-dependent conductivity models better reflect P^{crit}than a single-compartment model. These data also served as a prerequisite for calculation of P^{crit}from the diastolic pressure decay in the intact circulation. In a second step, we assessed P^{crit}as asymptotic pressures derived from analysis of early, late, and complete diastolic pressure decay with the heart beating, and how these pressures correspond to P^{crit}measured or calculated during circulatory arrest.

### Assessment of P^{crit}During Circulatory Arrest

Our finding of a substantial arteriovenous pressure gradient remaining even after 30 s of circulatory arrest confirms the observation of Schipke *et al* .,17and our mean values of P^{crit}of approximately 25-26 mmHg are almost identical.

However, our data extend the former observation for several reasons. Although all models predicted the aortic pressure well, measured after 15 or 30 s of circulatory arrest, an interval of 7 s was already sufficient to reliably predict aortic pressure prevailing at 30 s and hence, P^{crit}. However, higher P^{crit}values were calculated with shorter intervals, suggesting that aortic pressure decay does not follow a single monoexponential function for all durations; *i.e* ., pressure decay is altered as circulatory arrest is prolonged and/or pressure/diameter decreases. Thus, our data implies that both the two-compartment and the pressure-dependent conductivity model better reflect aortic pressure decay. First, deviation of predicted pressure values from measured pressure values (χ^{2}) showed lesser values both for the two-compartment and the pressure-dependent conductivity models when compared to the single-compartment model. Second, the shorter the interval after circulatory arrest entered into the calculations, the higher the P^{crit}calculated. Considering a 30-s interval of circulatory arrest, the two-compartment model revealed a fast and a slow mean time constant of 1.7 and 14 s, respectively. This latter time constant may relate to vasodilation and/or miniscule arterial flow runoff. Together, these findings strongly argue that arterial pressure decay during circulatory arrest does not follow a monoexponential, single-compartment decline, but follows a longer time constant later during circulatory arrest.

We cannot pinpoint whether this finding relates to the fact that circulatory arrest *per se* is an abnormal state likely to alter circulatory properties. Ischemia during circulatory arrest, for instance, might within seconds evoke peripheral arteriolar vasodilation, and hence measurement of a too low P^{crit}. Central venous pressure, after an initial increase after circulatory arrest, did not increase significantly after 10 s, while arterial pressure continued to further decrease very slowly. Thus, although venous compliance is certainly greater than compliance of the arterial vascular tree,22the further decline in arterial pressure after 10 s of circulatory arrest may relate to diminution of vascular tone rather than remaining arterial flow runoff, although the latter cannot be excluded. Conversely, the rapid decrease in arterial pressure with circulatory arrest could also evoke intense efferent neural sympathetic outflow and hence arteriolar vasoconstriction, giving rise to a too-high P^{crit}. Furthermore, aortic valve flutter has been described using transesophageal echocardiography during ventricular fibrillation.23Although left ventricular volume decreases during fibrillation, some aortic valve regurgitation cannot be excluded. If that were the case, aortic regurgitation in addition to peripheral arterial flow runoff could speed aortic pressure decay and shorten the decay time constant, and hence underestimate calculated P^{crit}. All these issues raise the question of whether fibrillation-induced circulatory arrest allows measurement of the P^{crit}that prevails physiologically. In any case, arterial P^{crit}measured or calculated by curve fitting after prolonged periods of circulatory arrest is lower than that with a circulatory arrest of shorter duration.

### Assessment of P^{crit}with the Heart Beating

To our knowledge, our investigation is the first to explore whether P^{crit}can be calculated from the diastolic arterial pressure decay in the intact circulation, and to what extent it corresponds to P^{crit}during circulatory arrest. With the heart beating, arterial downstream pressure calculated from the diastolic arterial pressure decay averaged between 56.8 and 47.6 mmHg, depending on the model used for curve fitting. Furthermore, the two-compartment model showed a better fit than the single-compartment model. The value obtained with the two-compartment model (53 mmHg) is substantially and significantly greater than the P^{crit}calculated during circulatory arrest (∼26 mmHg) after both 15 and 30 s. This may relate to several mechanisms. First, since part of the aortic pressure morphology is generated by reflected waves,24,25wave reflections from the arterial periphery could distort the diastolic aortic pressure decay and alter curve fitting. However, since each wave has both up and down components, this should not influence a fit over all data points with high-frequency data sampling. Furthermore, if early diastolic wave reflections were the cause of wrong estimates of P^{crit}with the heart beating, arterial P^{crit}s calculated using complete, early, and late diastole should be different. However, this was not observed, and P^{crit}s estimated from each diastolic interval (early, late, complete) did not differ significantly from one another. Second, technical noise (*i.e* ., induced by respiration or movement artifacts of the catheter) could have influenced calculations. However, this can be excluded since we digitized aortic pressure at a high frequency from a calibrated micromanometer, and the original and fitted curves were virtually superimposable. Third, the information content of the rather short diastolic interval may not fully represent a slower arterial pressure decay occurring later, as suggested by measurements and during circulatory arrest. However, this is unlikely to solely account for the observed discrepancy between the P^{crit}s calculated with the heart beating and during circulatory arrest. When comparing equal intervals, (*i.e* ., during natural diastole and after initial circulatory arrest) calculated P^{crit}with the heart beating and the circulation intact was still substantially and significantly higher. Specifically, using the two-compartment model, P^{crit}averaged 53 mmHg ± 16.6 with the heart beating but 38.9 mmHg ± 12.3 for the same duration of pressure decay during initial circulatory arrest, and 26.6 mmHg ± 7.8 15 s after circulatory arrest. Thus, even if calculation of P^{crit}from diastolic pressure decay would be hampered by not containing information about the course of pressure decay occurring later, P^{crit}is still higher than during circulatory arrest. This suggests that ventricular fibrillation itself leads to an underestimation of the P^{crit}prevailing physiologically in the intact circulation. In any case, neither arterial pressure measured during circulatory arrest nor P^{crit}calculated by curve fitting techniques during circulatory arrest can be considered equivalent to the calculated downstream pressure of the arterial system with the heart beating.

### Implication of P^{crit}for Vascular Resistance

Systemic vascular resistance is used clinically to reflect changes in arterial resistance so as to differentiate critical cardiovascular disturbances and to guide cardiovascular therapy. Classically, vascular resistance index is calculated in a linear model as the ratio of the arteriovenous pressure gradient and cardiac index; *i.e* ., from mean arterial and central venous pressures, ignoring pulsatile characteristics. However, changes in arterial resistance will hardly be mirrored by such an approach in the presence of a critical closing pressure, *i.e* ., under conditions where the arterial circulation behaves like a Starling resistor or a “vascular waterfall,” and central venous pressure is not the downstream pressure for the arterial circulation. In addition, changes in postarteriolar pressure by themselves alter venous pressure by redistributing peripheral blood volume.26Accordingly, to assess arterial resistance, the gradient between arterial pressure and P^{crit}, rather than to central venous pressure should be considered. Substituting P^{crit}for central venous pressure, the calculated linear vascular resistance index was much less than conventional vascular resistance, as expected. This is true when P^{crit}determined during circulatory arrest is substituted, and even more so when critical closing pressure calculated with the heart beating is substituted for central venous pressure. Irrespective of uncertainties in whether the P^{crit}calculated with the heart beating or the P^{crit}measured during prolonged circulatory arrest is the “true” P^{crit}prevailing physiologically, this is a quantitative rather than a qualitative issue. From this perspective, although the approach to use P^{crit}instead of central venous pressure for linear calculation of arterial resistance has not been supported by other data so far, it would be interesting to know to what extent vasoconstrictors, vasodilators, or diseases like sepsis, shock, or liver failure influence P^{crit}as calculated from the diastolic pressure decay. Furthermore, from a clinical perspective, one might conceive a bedside monitor able to calculate P^{crit}beat-to-beat during each diastole. Although this would fall short of impedance measurements, it might provide online an idea of prevailing arterial resistance or its changes.

Our study has limitations. First, we studied patients with a history of cardiovascular disease and receiving cardiovascular drugs. Thus, although it is unlikely that healthy patients would not show a critical closing pressure, our data could differ quantitatively from those obtained in healthy patients. Second, although general anesthesia using the opioid fentanyl and low-dose isoflurane is believed to exert only minimal effects on vascular resistance and cardiovascular reflexes in the dosages used,27,28we cannot rule out that different values of P^{crit}might be obtained during circulatory arrest in the awake state. Finally, we used a linear model for estimation of resistance, not taking into account complex pulsatile characteristics of the circulation. In this regard, further investigations should address whether measurements of vascular impedance incorporating blood velocity or flow measurements can contribute on a beat-by-beat basis.

In summary, our data show that during circulatory arrest prevailing aortic pressure and hence P^{crit}can be predicted closely by curve fitting of the aortic pressure decay over a short (≥ 7 s) time frame, regardless of the model used; that two-compartment and pressure-dependent conductivity models provide a better fit for modeling arterial pressure decay than a single-compartment model; and that calculated arterial downstream pressure with the heart beating, *i.e* ., the asymptote calculated from the diastolic pressure decay, is markedly higher than P^{crit}either measured or calculated during circulatory arrest, and this may relate to immediate pathophysiological changes evoked by circulatory arrest itself. Finally, irrespective of uncertainties in whether the P^{crit}calculated with the heart beating or the P^{crit}measured during prolonged circulatory arrest is the “true” P^{crit}prevailing physiologically, linear vascular resistance is markedly less when substituting P^{crit}for central venous pressure as the downstream pressure.

We thank Professor Dr. Gerd Heusch, Ph.D., Professor of Pathophysiology, Institut für Pathophysiology, Universität Duisburg-Essen, Universitätsklinikum Essen, Essen, Germany, for kindly reviewing our manuscript; Christof Ochterbeck, Dipl.-Ing., Klinik für Anästhesiologie und Intensivmedizin, Universitätsklinikum Essen, Essen, Germany, for skillful technical help and assistance; and Professor Dr. sc. techn. Mark E. Ladd, Ph.D., Institut für Diagnostische und Interventionelle Radiologie und Neuroradiologie, Universität Duisburg-Essen, Universitätsklinikum Essen, Essen, Germany, for English language editing.

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