INTRODUCTION

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SIMULTANEOUS MEASUREMENTS of arterial vessel dimensions, which reflect vessel wall distending blood pressures, and blood velocity can be noninvasively performed with magnetic resonance (MR) phase mapping, with a 30-ms temporal resolution. The resulting phase contrast images encode flow velocities, and the corresponding magnitude images can be used to measure vessel cross-sectional areas (CSAs) (11). In the main pulmonary artery (MPA), MR imaging (MRI) has been extensively used to assess changes in blood flood patterns or CSAs under normal and pathological conditions, such as pulmonary arterial hypertension (PAH) (2, 3, 7, 12, 16). In particular, significant retrograde flow during middle-to-late systole has been described and measured in PAH (12). However, flow patterns in the diastolic phase have not been studied in detail. Moreover, the coupling between the pressure waves that originate in the heart, which can be assessed by CSA variations, and the resulting flow waves have not been considered. This coupling can be viewed in the more general framework of tuning.

The tuning or resonance of a system can be defined as an optimization of the coupling of its components. The hemodynamic tuning of the pulmonary arterial circulation considers the coupling between the right ventricle (RV) and the pulmonary arterial tree, with optimized coupling leading to lowered right ventricular work. The tuning of the pulmonary arterial circulation has already been considered previously (4, 9); in particular, in the sixties, Caro and Harrisson measured blood pressure at two sites in the MPA by using needles at thoracotomy (4). Despite being unable to measure blood flow, they highlighted the likely distributed character with partial reflections of the pulmonary arterial circulation.

In this study, we used MR phase mapping to noninvasively and simultaneously assess blood flow and CSA patterns throughout the cardiac cycle in the MPA of healthy volunteers. Under physiological conditions, it has been suggested that reflected pressure waves may play a role in aortic or pulmonary blood flow patterns (18, 20). A simple theoretical model of the pulmonary arterial circulation (Fig. 1), described in this paper, explains that appropriate timing of reflected pressure waves might lead to tuning, which lowers right ventricular work. The aim of this work was to examine the hypothesis of a tuned pulmonary arterial system at rest under physiological conditions.

View larger version (10K): [in this window] [in a new window]   Fig. 1.   Sketch of the theoretical model of the pulmonary arterial circulation. The right ventricle (RV) generates a forward pressure wave (FPW) through the main pulmonary artery (MPA). Lung impedance (ZL) generates a backward pressure wave (BPW) to the RV. It is assumed that the BPW is totally reflected by a closed valve at the heart, leading then to a reflected forward pressure wave (RFPW). Both FPW and RFPW provide flow waves. In this model, the pulmonary vessels between the lung and the left atrium (LA) are neglected. Zo, MPA input impedance.

	METHODS

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Study Group

MRI Technique

Experiments were performed with a 1T Magnetom Expert Imager (Siemens, Erlangen, Germany) using a gradient system capable of generating 20 mT/m. We used the flow quantification (FQ) software provided by the manufacturer, which was previously validated (14). A slice was selected at mid-MPA, perpendicular to the vessel axis. The repetition time was 30 ms, echo time was 6 ms, and the flip angle was 30°. The field of view was 338 × 450 mm (192 × 256 pixels), slice thickness was 10 mm, encoding velocity was 150 cm/s, and the number of phases was 40 (40 consecutive measurements separated by 30 ms) starting directly after detection of an electrocardiogram trigger. The time of acquisition was <5 min. The software displayed both the magnitude and phase images (Fig. 2, A and B, respectively). We manually outlined the MPA CSA in each magnitude image of a frame. The CSA value and mean blood velocity were obtained from the outlined CSA. A region of reference, chosen at the level of the vertebral body that appeared in the slice, served as a null velocity (14).

View larger version (108K): [in this window] [in a new window]   Fig. 2.   Typical images of magnitude (A) and the corresponding phase (B) of a slice perpendicular to the MPA from 1 volunteer.

Data Analysis

Theoretical model of a tuned pulmonary arterial system. Figure 1 describes a simple theoretical model of the pulmonary arterial system. The RV is the pump, and the pulmonary arterial system is a single tube (length = l) connecting the RV and the lung impedance. The pulmonary vessels between the lung and the LA are neglected, and the LA is the end of the pulmonary circuit. ZL and Zo are lung impedance and MPA input impedance, respectively. In this model, the effect of gravity is neglected. We consider the patient to be in a supine position in the magnet.

(1)

(2)

(3)

(4)

(5)

(6)

Measurements available from MR phase mapping. CSA and blood flow values throughout a complete cardiac cycle were measured from a series of phase mapping data. CSAs were outlined in each magnitude image of the series (Fig. 2A), and the blood velocity was an average over the CSA. Both mean flow and CSA were obtained from at least two measurements.

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View larger version (15K): [in this window] [in a new window]   Fig. 3.   Typical traces of blood velocity vs. time over the MPA (A) and corresponding cross-sectional area (CSA) values (B) throughout the cardiac cycle in 1 volunteer.

Statistical Analysis

	RESULTS

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In the present study, the average value for X = 2.07 ± 0.30, and X was not significantly different from 2 (P < 0.05 ). This result validates the hypothesis of tuning of the pulmonary arterial circulation.

Table 1 represents, for each volunteer, the values and means ± SD for age, T, CSAmax, CSAmin, C, c, X, , R, Zc, ZL, and Zo. Mean CSA [(CSAmax + CSAmin)/2] and mean CSA difference (CSAmax  CSAmin) for the whole series were 7.08 × 10⁴ and 1.54 × 10⁴ m², respectively.

Figure 3 shows typical time curves of the mean blood velocity over the CSA (A) and the time curve of the MPA CSA values (B) throughout the cardiac cycle in the MPA in one representative volunteer. Both graphs reveal systolic and diastolic peaks. In addition, the flow graph reveals an end-systolic weak negative flow peak. The jagged appearance of the diastolic peak in the CSA pattern gives an order of magnitude of the measurement uncertainties. Averaged positive blood systolic and diastolic volumes from the volunteers were 63.0 and 8.3 ml, respectively.

Figure 4 represents the comparison of ZL and R using the Bland and Altman method. The mean difference between ZL and R was 7.46 Pa · s · m³, and the 95% reliability domain was ±14.15 Pa · s · m³, indicating that ZL and R were not significantly different. Figure 4 also shows that the scatter of the data points increased with the pulmonary vascular resistance. Furthermore, under 95% reliability, Zc and Zo, unlike for ZL, were significantly different from R. 

View larger version (16K): [in this window] [in a new window]   Fig. 4.   Comparison of ZL and pulmonary resistance (R) by means of the Bland and Altman method (see Ref. 1), indicating no significant difference between the parameters. Each point is calculated from 1 volunteer. Bold horizontal line just under 10, mean value of the series; dotted lines, limits of the uncertainty domain.

X was linearly related to T [according to X = 0.0036T  0.7891 (r = 0.935; Fig. 5)], indicating that tuning did depend on cardiac frequency.

View larger version (18K): [in this window] [in a new window]   Fig. 5.   Plot of the parameter X vs. the cardiac period (T) for each volunteer. Linear fitting is X = 0.0036T  0.7891, with r = 0.935, indicating a significant correlation (P < 0.01). Horizontal line, the ideal value of 2.

Figure 6 shows c vs. volunteer age. The linear fitting was c = 0.021(age) + 2.210, with r = 0.582. The c significantly increased with volunteer age. We also examined the relationship between C vs. age and mean CSA vs. age. The results were: C = 0.054(age) + 9.662 (r = 0.362) and CSA = 0.056(age) + 4.760 (r = 0.490), respectively, indicating that there was no significant correlation with age for any of these parameters.

View larger version (17K): [in this window] [in a new window]   Fig. 6.   Plot of the pressure wave velocity (c) in the MPA vs. age for each volunteer. Linear fitting is c = 0.0209(age) + 2.2096, with r = 0.582, indicating a significant correlation (P < 0.05).

	DISCUSSION

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Our results validated the hypothesis of tuning of the pulmonary arterial circulation. First, Fig. 3 illustrates flow-CSA coupling. It shows two positive systolic and diastolic peaks in both graphs. The existence of a diastolic CSA peak, and, hence, a diastolic vessel distending pressure peak, precludes the occurrence of a windkessel effect in generating the diastolic positive flow peak. This observation is in agreement with results of Patel et al. (17) and also with the experimental windkessel constant (210 ms) under physiological conditions given by Reuben (19). Thus the results are in agreement with the simple theoretical model we described in the present study, and, in particular, the presence of the windkessel effect can be neglected to a first approximation. The results provide evidence for the existence of a RFPW, which is the result of a double reflection of the FPW generated by the RV (first, a partial reflection by ZL that generates a BPW, and second, total reflection by the closed valve at the heart, which generates a RFPW). Such a mechanism can also explain the origin of the end-systolic negative peak by considering the combined roles of the BPW and the RV pressure fall after the systole. In the absence of pulmonary valve insufficiency, the backward flow is stopped by the valve closing. This suggests that it is likely that the principal site of blood volume movement is the central pulmonary vascular bed. It should also be noted that, in the CSA graph, the MPA distending effects of the BPW and RFPW are coincident; indeed, the measurement slice is placed ~0.03 m from the heart valve, and, considering that c = 3.08 m/s, on average, the estimate of the delay time between the BPW and the RFPw crossing is only 20 ms.

Second, X was not significantly different from 2, causing the diastolic flow peaks to be inserted at midway between the systolic flow peaks. In other words, the diastolic flows do not disturb the systolic ones, rather they are complementary. Furthermore, it has been shown (Fig. 4) that the dispersion of the X values (±0.30) was very likely due to the role of the heart frequency rather than to measurement uncertainties. The linear fitting of Fig. 4 indicates that the best tuning occurs at ~77 cardiac beats/min (at rest, under physiological conditions).

The consequence of tuning of the pulmonary arterial system is a lowering of the RV work rate. The input impedance of the MPA is reduced under tuned conditions, as can be seen from the mean values of Zo, Zc and ZL (34.31 × 10⁵, 47.37 × 10⁵, and 66.41 × 10⁵ Pa · s · m³, respectively). In particular, the comparison of Zo to ZL indicates that the order of magnitude of the lowering of the RV work is several tenths of percents (in addition, a weak windkessel effect should further contribute in reducing the RV work). Furthermore, it was also found that R and ZL were not significantly different (Fig. 4). This finding suggests that, under tuned conditions, and assuming that  is real, a rough estimate of ZL could be obtained from a pressure-to-systolic-flow ratio.

As shown in Fig. 5, vascular pulmonary tuning is cardiac frequency dependent, and it is also reasonable to suggest that the tuning might be age dependent. Age-related changes of pressure wave velocity have been shown in the aorta (15), and it has been also shown, in the MPA, that the extensibility of the vessel decreases with increasing age (10). Although the significance of the correlation was weak due to data scatter and the relatively small study population, c appeared age dependent (Fig. 6). However, it should be mentioned that, although C and CSA occur in the calculation of c, the respective fittings of C and CSA vs. age were not significant. It is thus suggested that critical parameters in the tuning of the right cardiovascular system might be used to estimate PAH, and further experiments should be carried out in patients undergoing invasive right catheterization.

Caro and Harrisson (4) investigated the hypothesis of the tuning of the arterial pulmonary circulation using an invasive method. They measured c, and hence the pressure wavelength ( = cT), and compared /4 with the anatomic distance between the pulmonary valve and the position of ZL. They found that it was one-fifth of , very near a tuning of the system. Because they could not assess flow, they could not observe the effect of pressure wave reflections. Our estimate of the length between the heart valve and the position of ZL was /4 = 0.62 m (assuming mean values of c = 3.08 m/s and T = 0.8 s). This result is greater than Caro and Harrisson's estimate (<0.3 m). The discrepancy may be mainly due to a difference in c (1.82 vs. 3.08 m/s). Our method used CSA measurements and a MPA compliance estimate. The mean value of the MPA compliance was 7.43 × 10⁸ m²/Pa (SD = 2.41 × 10⁸ m²/Pa), which is in very good agreement with the C value found in the literature [7.35 × 10⁸ m²/Pa (10.04 mm²/mmHg)] (8). Furthermore, as mentioned by Caro and Harrisson, the calculations assume the constancy of c over the entire length of the vascular bed. It is likely that the assumption is an oversimplification. Nevertheless, both estimates suggest that ZL is positioned at the level of pulmonary arterioles or capillaries, which was also concluded by Harris and Heath (9).

Our simple theoretical model was based on several assumptions. In particular, it was assumed that  was global (20), which means that the individual BPWs generated in each lung arteriolar branch were indistinguishable. We considered one BPW as being the sum of all individual BPWs and assumed that all individual BPWs were in phase. Any possible phase dispersion was neglected in this study, which, in addition to a possible reflection coefficient 100% at the heart valve, might also modify the estimates of , Zo, and ZL. Furthermore, the model did not take into account the nearest reflections at the bifurcation of large arteries, and further studies using more complex models are required to investigate this point.

Outlining MPA CSAs in magnitude images allowed an assessment of CSA variations throughout the cardiac cycle, which were equal to (±1.54/2) × 10⁴ m², on average (±11%), around a mean CSA. First, it should be noted that magnitude images provided by a phase mapping software are not optimized for accurate vessel outlining. This may explain the jagged appearance of the diastolic CSA peak (Fig. 3B). Furthermore, outlining is facilitated by the known proton inflow phenomenon, which enhances the blood signal within the vessel in MRI magnitude images. Therefore, the outlining method has limitations when the flow is weak, such as in the end-diastolic part of the cardiac cycle. Moreover, in some volunteers, we noted that the MPA CSA position might move significantly in the slice plane between the end-diastolic and -systolic phases due to the whole heart contraction and, very likely, also to individual MPA curved anatomy. CSA measurements from the first and last image frames of these volunteers might be biased and thus should be excluded.

In conclusion, the MR phase mapping technique enabled us to noninvasively demonstrate the tuning of the right cardiovascular system at rest under physiological conditions. Tuned systems and resonant phenomena playing an actual role in the working of an organ are rare (13). This tuning emphasizes the role of reflected pressure waves at the level of pulmonary arterioles. The knowledge of this tuning under physiological conditions suggests that assessment of PAH by the analysis of tuning disturbances may be relevant.