INTRODUCTION

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THE TOTAL ARTERIAL compliance of the systemic arterial tree is an important determinant of the cardiac load. Alterations in the total arterial compliance are linked to various physiological (aging) or pathological (hypertension) states, and thus the estimation of total arterial compliance has long interested clinicians and researchers of cardiovascular physiology (4, 6, 7, 9, 18-20).

The most widely used and accepted method is the diastolic decay time method (DTM), which, on the basis of the two-element windkessel model (4), fits a monoexponential curve to the time decay of the diastolic pressure (9, 10). To avoid problems that arise when aortic pressure does not decay monoexponentially, the area method was suggested (7). Under most conditions, the two methods yield identical results. Although the diastolic decay time and area methods are simple to use, they can only be applied when flow in diastole is zero, limiting them to measurements in the ascending aorta only. Another inconvenience of the diastolic decay and area methods is that they require knowledge of the diastolic aortic pressure waveform, which, at present, is difficult to obtain accurately noninvasively.

Recently, Stergiopulos et al. (11) proposed the pulse pressure method (PPM) for estimating arterial compliance. The PPM is based on simultaneous measurements of flow and pulse pressure (see detailed description of the method in METHODS), but it does not necessitate knowledge of the whole pressure pulse and it does not require zero flow in diastole. Therefore, it may be more adapted to in vivo applications. The PPM was tested for a variety of simulated physiological and pathological conditions using an extensive nonlinear distributed model of the arterial tree (13). Comparison with six other compliance estimation methods, including the decay time and area methods, showed that overall the PPM is the most accurate method (12). Good correlation, however, was found between the PPM estimates and the DTM estimates. We have never tested, however, the use of the PPM in the intact animal.

In the present study we evaluate the performance of the PPM using data from canine experiments under control conditions and under total aortic occlusion at different aortic locations. Because in the intact animal compliance is unknown in an absolute sense, we chose to compare the PPM with the DTM, the latter being generally accepted as a standard method for estimating total arterial compliance. The results will be used to: 1) assess the applicability of the PPM in vivo, and 2) evaluate the relative contribution of the proximal aorta on the total compliance of the arterial tree.

	METHODS

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Pulse pressure method. For an extensive description of the PPM, we refer the reader to the original article (11). In brief, the PPM, shown schematically in Fig. 1, is implemented as follows. From the ratio of mean pressure over mean flow we derive peripheral resistance. Then, using measured flow as input to the two-element windkessel, we fit the predicted pulse pressure to the actual pulse pressure by adjusting compliance. Compliance adjustment is done by a simple "trial and error" type of approach knowing, however, that lower compliance yields larger pulse pressures. From that, a few iterations always suffice. The value of the compliance (C) that gives the closest fit of the pulse pressure is the best estimate of the compliance.

View larger version (19K): [in this window] [in a new window]   Fig. 1.   Schematic diagram of pulse pressure method (PPM). Mean pressure (Pm) over mean flow yields value of total peripheral resistance (R). PPa, measured pulse pressure; PPd, pulse pressure predicted by two-element windkessel (WK) model using measured flow as input. Two-element WK is formed by the known R and an assumed compliance value (C). Iterative scheme searches for value of C that yields the closest agreement between PPa and PPd. This is the best estimate of total arterial compliance.

Experimental data. The aortic pressure and flow waveforms used in this study were obtained earlier in seven closed-chest anesthetized dogs (14, 17). The dogs weighed from 16.3 to 22.7 kg (mean 19.0 kg). Flow was measured with an implanted electromagnetic flow probe on the ascending aorta. Pressure was measured with a catheter tip manometer introduced into the femoral artery and moved to the same aortic location as the flow probe at the day of the experiment. A typical set of simultaneously measured aortic pressure and flow recordings under control conditions is shown in Fig. 1. The hemodynamic data for each dog under baseline conditions are given in Table 1. Aortic pressure and flow were also measured under several different conditions. The abdominal and thoracic aorta were occluded by an inflatable balloon at four locations: at aortic trifurcation (A), between trifurcation and level of the diaphragm (B), at the diaphragm (C), and at the level of the proximal descending thoracic aorta (D). The location of the aortic occlusions is shown schematically in Fig. 2. The purpose of the aortic occlusions was to augment wave reflections and change the topology of wave reflection sites. For details regarding the experimental procedure, the reader is referred to the original articles (14, 17).

View larger version (15K): [in this window] [in a new window]   Fig. 2.   Top: schematic diagram of arterial tree indicating locations of aortic (balloon) occlusions. Bottom: typical aortic pressure pulse for control conditions. Part of diastolic wave used for decay time method (DTM) and corresponding average pressure value are indicated. Abdominal and thoracic aorta were occluded by means of an inflatable balloon at 4 locations: at aortic trifurcation (A), between trifurcation and level of diaphragm (B), at diaphragm (C), and at level of proximal descending thoracic aorta (D).

Because of the nonlinear elastic properties of the arterial wall, compliance is a pressure-dependent quantity (5). In the physiological range of pressures, compliance decreases with increase in pressure. To account for the pressure dependence of compliance, we assign the value of compliance estimated by the PPM to the mean pressure (P_m) over the whole cardiac cycle. The compliance estimated by the DTM is associated to the average pressure in the diastolic portion of the wave (P_av,diast) over which a monoexponential decay function is fitted to yield the decay time and the corresponding compliance C_DTM (12). This is explained schematically in Fig. 2, bottom. We have arbitrarily chosen to apply the DTM to the last one-third of the pulse.

Seventy-eight cardiac cycles were analyzed (n = 78 cycles), out of which n = 46 were for control conditions (designated by the symbol X) and the rest were for occlusion in the aorta (A: n = 6; B: n = 11; C: n = 6; D: n = 9; see Fig. 2).

	RESULTS

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PPM versus DTM. A cumulative graph showing the comparison between the compliance estimated by the PPM (C_PPM) and the compliance estimated by the DTM (C_DTM) for all beats (control and aortic occlusions, n = 78) is shown in Fig. 3. Linear regression without an intercept yielded C_PPM = (0.893 ± 0.015) · C_DTM, r = 0.989. 

View larger version (13K): [in this window] [in a new window]   Fig. 3.   Global comparison of PPM vs. DTM compliance (CPPM and CDTM, respectively) estimates for all dogs, including control conditions and aortic occlusions.

Figure 4, top, shows mean compliance estimated by the DTM and PPM for control conditions (X) and under aortic occlusions (A-D). Table 2 gives the relative hemodynamic parameters and compliance values for control and under aortic occlusions. Compliance decreases as the occlusion site moves more proximal. But even at the most proximal site (D), compliance is still at 60% of its baseline value, showing that the proximal aorta forms the major part of the total arterial compliance. Unpaired t-tests showed that total arterial compliance is significantly different between control and occlusion at C and D (P < 0.05) but not at A and B.

View larger version (18K): [in this window] [in a new window]   Fig. 4.   Top: mean compliance as predicted by PPM and DTM (X: control; A-D: aortic occlusions; see Fig. 2). Error bars indicate SE. Bottom: mean values and standard errors of Pm and Pav,diast for control and aortic occlusions.

Paired t-tests showed that the total arterial compliance estimated by the PPM is always slightly but significantly lower than the compliance estimated by the DTM (P < 0.0001). The estimates for interventions A-D, however, were not significantly different (P > 0.05).

Part of the difference between the compliance estimates given by estimates given by the PPM and the DTM may be attributed to the pressure dependence of compliance. Figure 4, bottom, shows the mean values of P_m and P_av,diast for control and aortic occlusions. Under control conditions P_m was 80.9 ± 3.32 mmHg (means ± SE), and P_m used in the DTM was 67.1 ± 3.6 mmHg. Unpaired t-tests show that P_m was significantly augmented (P value <0.05) with respect to control only for occlusion at B, C, and D. For occlusion at the iliacs (group A) P_m decreased slightly (78 ± 6.8 mmHg, Table 1), but the difference with control was not significant (P = 0.066). As expected, the difference between P_m and P_av,diast increased as aortic occlusion sites moved closer to the heart due to a loss in compliance and increase in wave reflections.

The pressure dependence of compliance can be evidenced under control conditions, where multiple independent measurements are available, in Fig. 5. We observe that when compliance estimates by the PPM and DTM are plotted against their corresponding pressures P_m and P_av,diast, they lie on a single curve. It is clear, however, that each dog has its own compliance-pressure curve. In this particular example, dogs 71 and 78 have similar compliance-pressure curves, whereas dog 79 operates on a totally different compliance-pressure curve. This makes interanimal comparison difficult.

View larger version (15K): [in this window] [in a new window]   Fig. 5.   Evidence that PPM and DTM give compliance estimates belonging to same compliance-pressure curve. Depending on animal, compliance-pressure curves may be similar (dogs 71 and 78) or entirely different (dog 79).

Effect of aortic occlusions on compliance. Mean compliance under control conditions estimated by the PPM method was 0.169 ± 0.007 ml/mmHg. With total occlusion at the iliacs, total compliance remains essentially unchanged (0.170 ± 0.020), suggesting that the lower limbs contribute very little to the total compliance. Compliance decreased progressively as the occlusion site moved centrally (Table 1). When total occlusion was at the proximal descending aorta (group D), mean total arterial compliance was 0.100 ± 0.007 ml/mmHg.

	DISCUSSION

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We have used aortic pressure and flow data from in vivo experiments in anesthetized dogs to compare compliance estimates obtained by the PPM and the DTM. We found a good correlation between the PPM estimates and the DTM estimates. The PPM estimates compliance at mean pressure, whereas the DTM estimates compliance at the average pressure over the diastolic portion of the wave where the DTM is applied. Therefore, given the inverse relationship between pressure and compliance in the physiological pressure range (5), PPM yields lower compliance estimates in comparison to the DTM. If the pressure dependence of compliance is taken into account, the PPM and the DTM seem to yield coherent results following the same compliance-pressure curve (Fig. 5).

Although the PPM and the DTM may seem to be both equally applicable to in vivo situations, we foresee certain advantages in the use of the PPM compared with the DTM. First, the PPM yields the compliance at mean pressure, which is most relevant from a physiological standpoint. Mean compliance and peripheral resistance are the major determinants of heart load (3). Second, the PPM requires the knowledge of aortic pulse pressure only (not even the absolute values of systolic and diastolic pressures) compared with the whole pressure curve in diastole, which is necessary for the DTM. Calibrated aortic pressure is difficult to obtain noninvasively. We may speculate that aortic pulse pressure might be able to be predicted accurately by means of noninvasive measurements (brachial sphygmomanometry, tonometric measurements in the carotids, etc.), whereas the precise diastolic pressure decay in the aorta is difficult to obtain accurately. Third, aortic flow required by the PPM may be obtained noninvasively using magnetic resonance imaging or ultrasound. Fourth, the PPM does not require zero flow in the diastole, and therefore it applies equally well at other locations and in certain pathological cases such as aortic valve regurgitation. Fifth, there is certain ambiguity as to which part of the diastolic portion of the pressure wave should be used for the DTM. Preliminary analysis has shown that the compliance estimates by the DTM do depend on the choice of the diastolic part. There is no such ambiguity for the PPM which is very robust.

Application of the compliance estimation techniques in the clinical practice requires attention with respect to certain aspects of the arterial pulse. For example, the monoexponential character of the arterial pulse may be warranted only at the very late part of the diastolic wave. Wave reflections may play a role. It seems, however, that even in case of increased wave reflections in the aorta (as in the case of aortic occlusion), the PPM method yields valid compliance estimates. The most commonly used pressure measurement in the clinic is the brachial pulse pressure which, however, cannot be used as a surrogate to aortic pulse pressure. The brachial pulse pressure is in most cases considerably greater than the aorta due to contributions of wave reflections in the upper limb.

Our results show that the proximal aorta (ascending aorta and aortic arch) is the major determinant of the total arterial compliance. Although it is accepted that proximal aortic compliance forms a large part of total arterial compliance, quantitative data have, to the best of our knowledge, not been presented. When the dog aorta was occluded at the level of the proximal descending aorta (point D), compliance was reduced from 0.169 ml/mmHg under control conditions to 0.100 ml/mmHg, a 41% decrease in value. At the same time, mean pressure increased from 80.9 mmHg under control conditions to 102.3 mmHg under total occlusion at point D. Thus, at control pressure (80.9 mmHg), mean compliance with the aorta occluded at point D would have been even larger. A good estimate of mean compliance with occlusion at point D at P_m = 80.9 mmHg can be obtained from Fig. 4, A and B: C_DTM = 0.112 for P_m,diast = 77.9 mmHg and thus, by simple linear interpolation, C(P = 80.9 mmHg) = 0.110 ml/mmHg. This means that ~65% of total arterial compliance is located in the proximal aorta and the head and upper limb vessels.

We may thus conclude that total arterial compliance is mainly determined by the properties of the proximal aorta. This may have important clinical implications. In the human aortic pulse pressure appears to be well predicted by stroke volume over compliance (2), and thus compliance is the primary determinant of pulse pressure. Pulse pressure appears to be a primary risk factor for coronary disease and cardiovascular mortality (1, 8). In this context it seems much more important to determine proximal aortic compliance than local carotid, radial, or brachial compliance. We may thus hypothesize that aortic compliance should be one of the target quantities for risk assessment and prevention of arterial disease.