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Pulmonary artery hemodynamics with varying degrees of valvular stenosis: an in vitro study
Journal of Biomechanics 31 (1998) 1153—1161
Pulmonary artery hemodynamics with varying degrees of valvular stenosis: an in vitro study Hsing-Wen Sung *, Tsui-Lieh Hsu, Chi-How Hsu , Jer-Chen Hsu Department of Chemical Engineering, National Central University, Chung-Li, Taiwan, Republic of China Division of Cardiology, Veterans General Hospital-Taipei Taiwan, Republic of China Received 6 July 1998
Abstract The study was to investigate the effects of varying degrees of valvular stenosis on the hemodynamics of the main (MPA), left (LPA), and right (RPA) pulmonary arteries. Particle flow visualization was used to examine the flow patterns in a series of pulmonary artery models manufactured out of glass. These glass models were made based on the geometry of the porcine pulmonary arteries with dilatation in the MPA and LPA. Also, detailed pressure mappings in the models were conducted using a side-hole catheter. As the valve became stenotic, a jet-like flow was observed in the MPA. A higher degree of valvular stenosis corresponded to a narrower jet. This jet-like flow was noted to deflect away from the centerline and impinge on the roof of the dilated MPA. Additionally, a notable pressure gradient across the deflected jet-like flow in the direction of its radius of curvature was seen. Moreover, secondary flows started to appear in the dilated MPA. This suggested that the change in geometry in the MPA, due to its dilatation, had a marked effect on the pulmonary artery hemodynamics. In the LPA and RPA, the strengths of the secondary flows increased as the valve became more stenotic. The flow patterns observed in the LPA appeared to be more disturbed than in the RPA, due to the poststenotic, dilatation present in the LPA. Pressure recovery along the axial direction in the MPA was observed for all the stenotic valves studied. As the degree of valvular stenosis increased, the transvalvular energy loss increased. Moreover, it was observed that the energy loss decreased progressively as the flow traveled downstream. This tendency was consistent with the phenomenon of pressure recovery observed in the pressure measurement. The study demonstrates the importance of analyzing biological flows from a three-dimensional viewpoint. 1998 Elsevier Science Ltd. All rights reserved. Keywords: Valvular pulmonic stenosis; Poststenotic dilatation; Flow pattern; Pressure field; Secondary flow
1. Introduction It was clinically observed that valvular pulmonic stenosis is the most common form of obstruction in the pulmonary circulation (Sahn and Anderson, 1982). The complications of valvular pulmonic stenosis such as tricuspid regurgitation, pulmonary hypertension, and right ventricular hypertrophy reduce the efficiency of the heart. Hoffman (1969) reported that severe valvular pulmonic stenosis often causes death. In valvular pulmonic stenosis, the leaflets of the valve are thickened and domed (Weyman et al., 1975). It was reported that this anomaly may modify the pulmonary artery hemodynamics (Murphy et al., 1987; Yoo and Choi, 1989). Therefore,
* Corresponding author. Tel.: 886 3 422 7151 ext. 4228; fax: 00886 3 425 2296; e-mail: [email protected]
it is suggested that fundamental knowledge of the hemodynamics in the main (MPA), left (LPA) and right (RPA) pulmonary arteries may be used to support accurate diagnosis of valvular pulmonic stenosis. Because of the technical difficulties in obtaining sufficiently accurate and well-resolved hemodynamic data in vivo, most studies directed towards an understanding of the characteristics of the arterial hemodynamics have been carried out in vitro. Detailed flow patterns in an in vitro pulmonary artery model with varying degrees of valvular pulmonic stenosis have been previously studied in Yoganathan’s laboratory (Philpot et al., 1985; Sung et al., 1990; Yoganathan et al., 1986). However, the following simplifications were made in their test model when compared to a real pulmonary artery in vivo. The test model used in their studies was two-dimensional; the MPA, LPA, and RPA were in the same plane. Additionally, dilatation of the MPA and LPA, which is often
0021-9290/98/$ — see front matter 1998 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 1 - 9 2 9 0 ( 9 8 ) 0 0 1 1 5 - 8
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observed clinically with the valvular pulmonic stenosis (Kirshenbaum, 1987; Yoo and Choi, 1989), was disregarded in their test model. It is expected that such simplifications of the test model would vary the local flow fields to some extent. To the best of our knowledge, the exact three-dimensional geometry of the human pulmonary artery, particularly for those with poststenotic dilatation, is still not available in the literature. Therefore, in a previous study, we used the porcine pulmonary arteries procured from pigs (approximately 6-month-old and 70—80 kg) as our test models to further understand the effects of varying degrees of valvular stenosis on the pulmonary artery hemodynamics (Hsu et al., 1998). To make the MPA and LPA dilated as clinically observed in valvular pulmonic stenosis, an epoxy fixation technique was employed. A three-dimensional echocardiographic reconstruction method for color Doppler flow mapping was used to examine the flow fields in the test models. It was observed that the change in geometry in the MPA, due to its dilatation, had a marked effect on the pulmonary artery hemodynamics. Although color Doppler flow mapping is useful in semi-quantitatively describing the flow patterns in the pulmonary artery, it can only image one-dimensional flow fields. Data such as vortices and secondary flows cannot be observed by color Doppler flow mapping. To further comprehend the effects of varying degrees of valvular stenosis on the pulmonary artery hemodynamics in a three-dimensional format, particle flow visualization was used to examine the flow fields in a series of glass models. These glass models were made based on the geometry of the porcine pulmonary arteries used in our previous study. Also, detailed pressure mappings in the test models were conducted using a side-hole catheter.
2. Materials and methods 2.1. Test models and test valves Four glass flow-through pulmonary artery models with varying degrees of dilatation in the MPA and LPA were used in the study (Fig. 1). The dimensions of these glass models were determined based on the geometry of the porcine pulmonary arteries used in a previous study (Hsu et al., 1998). Trileaflet prosthetic tissue valves (Baxter Healthcare Corp., Irvine, CA, USA) were applied to represent the normal, mild, moderate, and severely stenotic pulmonary valves. The trileaflet tissue valve was used because its performance paralleled that of a stenotic pulmonic valve by ballooning outward and having a relatively symmetric opening (Weyman et al., 1977). As per the porcine pulmonary arteries used in our previous study, these trileaf-
Fig. 1. Schematic drawing of the glass pulmonary artery models with their corresponding geometric dimensions tested in the study.
let tissue valves were made axisymmetrically stenotic by sewing their three commissures together with thin black polyester thread. The valve areas of the normal, mild, moderate, and severe stenosis tested in the study were 2.8, 2.1, 1.0, and 0.5 cm, respectively. The reason for selecting these valve opening areas was based on the clinical classification of the severity of valvular pulmonic stenosis: over 1.0 cm for mild, 0.5—1.0 cm for moderate, and less than 0.5 cm for severe (Kirshenbaum, 1987). 2.2. Flow apparatus The study was conducted in a pulse duplicator system. The system was able to mimic the realistic flow and pressure waveforms observed on the right side of the human heart. Details of the pulse duplicator system used in the study can be found elsewhere (Yoganathan et al., 1986). The experiments were performed at a heart rate of 70 beats min\. For cases of the normal, mild, and moderately stenotic valves, the experiments were conducted at a cardiac output of 4.8—5.3 l min\. However, it was not possible to maintain such a high flowrate for a prolonged period of time with the severely stenotic valve, without physically damaging it. The flowrate used for the severely stenotic valve was, therefore, diminished to 3.2—3.5 l min\. Clinically, it was reported that the cardiac output through a severely stenotic valve is limited (Schlant, 1978), so this situation is not non-physiologic. In the study, the flow was split 50/50 (volumetric) between the LPA and RPA. The blood-analog fluid used in the study was an aqueous glycerin solution with a viscosity of 3.5 cP and a density of 1.05 g cm\ at room temperature. 2.3. Particle flow visualization Pulsatile flow visualization was applied to examine the pulmonary artery hemodynamics. Polystyrene
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particles (&300 lm in diameter, Amberlite ion exchange resin, Rhom and Hass Co., Philadelphia, PA, USA) were suspended in the blood-analog fluid and reflected by a white light, thus illuminating the flow fields. The flow fields, together with the flow waveform displayed on an oscilloscope, were recorded on-line by a video camera. The results were then analyzed off-line at distinct instants over a cardiac cycle (Fig. 2).
Electronics). A similar system was used to measure the downstream pressure simultaneously. However, the downstream pressure measurement was conducted via a side-hole catheter attached to a blood pressure transducer. The position of the catheter-tip, parallel to the MPA wall, was controlled by the thin metal wires through the test model. The positions where the downstream pressures were measured are shown in Fig. 3.
2.4. Transvalvular pressure drop measurement
2.5. Effective orifice area and transvalvular energy loss calculations
As shown in Fig. 3, the upstream pressure was measured at a wall tap 50 mm proximal to the test valve, using a blood pressure transducer (Statham P23ID, Gould Electronics, Cleveland, OH, USA) which was connected to an amplifier (Universal2+ Amplifier, Gould
Clinically, the geometric area of a stenotic valve cannot be accurately measured. Therefore, the evaluation of valvular stenosis in the cardiac catheterization laboratory routinely involves a calculation of effective orifice area based on pressure drop and flow across a valve. The effective orifice area of each test valve was calculated by the Gorlin—Gorlin formula (Gorlin and Gorlin, 1951). The transvalvular energy loss, a measure of the work load for the heart resulting from the stenotic pulmonic valve, was calculated throughout the entire cardiac cycle as follows (Knott et al., 1988) :
E" q *p/450 dt# q *p/450 dt# q *p/450 dt, forward flow
Fig. 2. Schematic drawing of the five distinct instants (acceleration phase, peak systole, deceleration phase, early diastolic phase, and late diastolic phase) over a cardaic cycle from which flow patterns were analyzed.
closing flow
(1)
leakage flow
where E, q, *p and t are the transvalvular energy loss (J), flow rate (l min\), pressure drop (mmHg), and integration time (s), respectively. The integration constant shown in the equation, 450, results from dimensional conversion. The three terms on the right-hand side of Eq. (1) are the energy losses during the forward-flow period, closing-flow period, and leakage-flow period (Fig. 2), respectively.
3. Results
Fig. 3. Schematic drawing of the positions where pressures were measured in the pulmonary artery models. The upstream pressure was measured at a wall tap 50 mm proximal to the test valve, while the downstream pressure was measured simultaneously at distinct positions via a side-hole catheter attached to a blood pressure transducer. The x’s in the figure are the measurement positions.
Examples of the flow visualization results and their schematic descriptions for the normal valve are shown in Fig. 4a—e. In the MPA, during the acceleration phase (Fig. 4a), flow that emerged from the valve was relatively evenly distributed. A region of flow separation was observed immediately distal to the valve near the sinus area. At peak systole (Fig. 4b), the instantaneous flow rate increased and a broad central flow was seen in the MPA. No significant secondary flows were observed. During the deceleration phase (Fig. 4c), the intensity of the broad central flow seen at peak systole decreased. In the LPA and RPA, during the acceleration phase, the flows were evenly distributed. No secondary flows were observed. However, during the peak systole (Fig. 4d) and deceleration phases, significant secondary flows were seen in
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Fig. 4. Results of flow visualization for the normal valve obtained in the MPA (a) during the acceleration phase, (b) at peak systole, and (c) during the deceleration phase and (d) obtained in the LPA at peak systole. (e) Schematic descriptions of the flow patterns at peak systole.
both daughter branches. Generally, the flow fields observed during the peak systole and deceleration phases were more disturbed than those seen during the acceleration phase in all three branches (Fig. 4a—c). During the early diastolic phase, the flow distal to the valve disappeared. The flow field remained disturbed until the late diastolic phase. Changes in flow patterns in the MPA were observed as the degree of valvular stenosis increased. A jet-like flow was observed distal to the stenotic valve. A higher degree of valvular stenosis corresponded to a narrower jet. It was noted that the jet-like flow deflected away from the
centerline and hit the roof of the dilated MPA (Fig. 5a—c). As the severity of dilatation in the MPA increased, the tendency of the jet-like flow hitting the roof of the MPA became more prominent, thus resulting in a larger region of flow separation underneath the jet. In addition, an increase in the curvature of the dilated MPA correlated with an increase in the disturbed nature of the overall flow fields. Moreover, secondary flow patterns started to appear in the dilated MPA (Fig. 5b and c). However, the axial velocity component (v ) observed in the secondary X flow patterns was significantly greater than its radial (v ) P and circumferential (v ) velocity components. F
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In the LPA and RPA, the strengths of the secondary flows increased as the valve became more stenotic (Fig. 5d). The flow patterns observed in the LPA appeared to be more disturbed than in the RPA, due to the poststenotic dilatation present in the LPA. Again, the flow fields observed during the peak systole and deceleration phases were more disturbed and had larger regions of flow separation than during the acceleration phase (Fig. 5a—c). Additionally, a higher degree of valvular stenosis corresponded to a more disturbed flow field in all three branches.
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Fig. 6a—d show that maximum transvalvular pressure drops measured, at distinct positions distal to the valve, for varying degrees of valvular pulmonic stenosis. It was noted that the maximum pressure drops increased with increasing degree of valvular stenosis. Generally, the transvalvular pressure drops decreased with increasing distance from the valve along the axial direction for all the stenotic cases. This indicated that the pressure measured distal to the valve was recovered as the flow traveled farther downstream.
Fig. 5. Results of flow visualization for the severely stenotic valve obtained in the MPA (a) during the acceleration phase, (b) at peak systole, and (c) during the deceleration phase and (d) obtained in the LPA at peak systole. (e) Schematic descriptions of the flow patterns at peak systole.
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Fig. 6. Maximum transvalvular pressure drops measured at distinct positions in the MPA for the (a) normal, (b) mild, (c) moderate, and (d) severely stenotic valves. ‘n’ means number of cardiac cycles analyzed.
The differences between the pressure measured at each distinct position and the lowest pressure measured in the MPA, for each studied case at peak systole, are presented in Fig. 7a—d. The areas shaded in the figure represent where the minimal pressures occurred at each downstream location (i.e. positions A, B, C, and D). As shown in the figure, the shaded area in each studied case corresponded to the course of the jet-like flow seen in the flow visualization. Also, a notable pressure gradient across the jet-like flow in the direction of its radius of curvature was seen, for all the stenotic valves studied. The results of the maximum transvalvular pressure drop measured at position A and its Gorlin-derived effective orifice area for the normal, mild, moderate, and severely stenotic valves are presented in Table 1. As shown in the table, the Gorlin-derived effective orifice areas for varying degrees of stenotic valves correlated well with their actual valve opening areas (r"0.99). Also, the transvalvular pressure drops measured inversely related to the Gorlin-derived effective orifice areas. Fig. 8 illustrates the transvalvular energy losses for varying degrees of valvular pulmonic stenosis during the forward-flow, closing-flow, and leakage-flow periods obtained at distinct positions distal to the valve. Generally, the energy loss during the forward-flow period was the greatest and that during the closing-flow period was the lowest for all the valves investigated. As the degree of valvular stenosis increased, the total energy loss increased. However, it was noted that the total energy loss decreased progressively as the flow traveled downstream. This tendency was consistent with the phenomenon of pressure recovery observed in the pressure measurement.
Fig. 7. Differences between the pressure measured at each distinct position and the lowest pressure measured in the MPA for the (a) normal, (b) mild, (c) moderate and (d) severely stenotic valves. ‘n’ means number of cardiac cycles analyzed.
Table 1 Valve opening areas (VOA), Gorlin-derived effective orifice areas (EOA), and maximum transvalvular pressure drops (*P) for varying degrees of valvular pulmonic stenosis Degree of stenosis
VOA (cm)
EOA (cm)
*P (mmHg)
Normal Mild Moderate Severe
2.8 2.1 1.0 0.5
2.4 1.8 0.8 0.4
19.7 41.7 106.8 141.5
Fig. 8. Transvalvular energy losses for varying degrees of valvular pulmonic stenosis during the forward-flow, closing-flow, and leakage—flow periods obtained at distinct positions distal to the valve.
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4. Discussion As aforementioned, particle flow visualization may reveal the three-dimensional characteristics of flow patterns and color Doppler flow mapping and one-dimensional (axial component) characteristics. Generally, the axial flow patterns visualized by particle flow visualization in the glass models were comparable to those imaged by color Doppler flow mapping in the porcine pulmonary arteries obtained in a previous study (Hsu et al., 1998), in spite of the rigidity of the glass models used. It is believed that the influence of the distensibility of the pulmonary artery bifurcation on its general hemodynamics is limited. In an in vitro study of the effect of the arterial wall distensibility on the flow characteristics in a carotid bifurcation, Anayiotos et al. (1994) reported that the general flow features in the rigid and compliant models were comparable. For the normal valve, the flow observed in the MPA was relatively evenly distributed (Fig. 4a—c). This is consistent with the clinical observations documented in the literature. Reuben et al. (1970), examining five normal humans with a hot-film anemometry, found the velocity profiles in the MPA to be approximately flat. Additionally, with a multiplane TEE transducer, Sloth et al. (1994) performed Doppler velocity measurements in the human pulmonary artery of eight healthy volunteers. They reported that the mean temporal velocity profile in the MPA was virtually flat. As the valve became stenotic, a jet-like flow was observed in the MPA (Fig. 5a—c). This observation agrees with the clinical report. Murphy et al. (1987) studied patients with valvular pulmonic stenosis and described the blood flow pattern in the MPA as a jet surrounded by flow disturbance. The jet-like flow was noted to deflect away from the centerline and impinge on the roof of the dilated MPA (Fig. 5a—c). This phenomenon was also observed clinically. In a ventriculographic inspection of the flow patterns in patients with valvular pulmonic stenosis, it was reported that a jet of contrast emerged from the stenotic valve and hit the roof of the dilated MPA (Yoo and Choi, 1989). Nevertheless, because of disregarding the poststenotic dilation in the MPA, this phenomenon was not seen in the studies of Yoganathan’s laboratory. This suggested that the change in geometry in the MPA, due to its dilatation, had a marked effect on the pulmonary artery hemodynamics. The phenomenon of the deflection of the poststenotic jet away from the centerline was also reflected in the results of our pressure measurement. Giving that the radius of curvature of the jet stream distal to a stenotic valve is r. Consider a volume element within the jet stream as shown in Fig. 9. Assume that the axis of the volume element is inclined at an angle h from the vertical. Denote the density, mass, tangential velocity, cross section, and height of the volume element by o, m, º, dA,
Fig. 9. Schematic drawing of the momentum balance on a volume element within the jet stream distal to a stenotic valve.
and dr. The pressure forces normal to the top and bottom cross sections of the volume element are pdA and (p#dp)dA, respectively. A momentum balance can be written for the volume element in direction of its axis assuming that flow is steady and viscous forces are neglected. (p#dp) dA!pdA!mg cos h"ma , (2) where g and a are the acceleration of gravity and the normal acceleration in curvilinear motion, respectively. This assumption may be valid for flow at peak systole that is often considered to be quasi-steady because the blood is neither accelerating nor decelerating at this moment. Substitution of m"odAdr, a "º/r, and cos h"dy/dr in Eq. (2) gives dpdA!ogdAdy"odAdrº/r.
(3)
Dividing Eq. (3) by dAdr and in the limit of drP0, *p/*r!og*y/*r"oº/r.
(4)
If the gravitational force on the volume element can be neglected, Eq. (4) can be simplified *p/*r"oº/r.
(5)
As shown in the flow visualization, the streamlines that emerged from the normal valve were primarily straight (Fig. 4b). This indicated that the curvature of these streamlines is infinite (rPR). From Eq. (5), it can be inferred that *p/*rP0 or there is no pressure gradient across the MPA flow. In contrast, for a stenotic valve, the jet stream distal to the valve was found to deflect toward the roof of the dilated MPA. This suggested that the curvature of this jet stream is finite (r'0). Therefore, it can be deduced that, again from Eq. (5), *p/*r'0 or there is a pressure gradient across the deflected jet in the direction of its radius of curvature. These phenomena were consistent with the results obtained in our pressure measurement (Fig. 7a—d).
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The phenomenon of pressure recovery observed in the pressure measurement for all the stenotic valves (Fig. 6b—d) can be understood in terms of the results observed in the flow visualization study. As shown in the flow visualization study, the axial velocity component (v ) of the poststenotic jet was significantly greater than its radial (v ) and circumferential (v ) components. Assum F ing that the viscous and gravitational forces can be ignored, the equation of motion in cylindrical coordinate along the axial direction (z!component) can be simplified (Bird et al., 1960) *p/*z+!o(v *v /*z#*v /*t). (6) Integrating Eq. (6) with respect to z and subsequently substituting in the continuity equation, A v "A v "q, gives p !p "1/2 ov [1!(A /A )]#o dq/dt dz/A, (7) where the subscripts 1 and 2 represent the upstream and downstream positions, respectively, along a stream line, and A and q are the flow area and volumetric flowrate, respectively (Fig. 10). Eq. (7) is the Bernoulli equation under pulsatile flow condition. At peak systole, the blood flow is often considered to be quasi-steady (dq/dt+0). Hence, ignoring the 2nd term on the right-hand side, Eq. (7) may be written as
p !p "1/2 ov [1!(A /A )]. (8) Eq. (8) related the maximum transvalvular pressure drop (p !p ) measured at peak systole for varying degrees of valvular pulmonic stenosis and its downstream velocity (v ) and the downstream-to-upstream flow area ratio (A /A ). The results of flow visualization study revealed that the jet-type flow distal to a stenotic valve broadened progressively as it traveled downstream by entraining the surrounding fluid (i.e. A /A increased with increasing distance distal to the valve as depicted in Fig. 10). Additionally, as per the continuity equation, it can be inferred that the downstream velocity, v , declined gradually as the jet-type flow broadened progressively. Therefore, the maximum transvalvular pressure drop measured at peak systole decreased as the jet-type flow traveled downstream. This may explain the phenomenon of pressure recovery along the axial direction observed for all the
stenotic valves studied (Fig. 6b—d). Additionally, the more severe the valvular stenosis, the more perceptible was the pressure recovery. The flow during the deceleration phase was more disturbed and had a larger region of flow separation than during the acceleration phase, even though the instantaneous flowrates during these two instants were equivalent. These results seemed to confirm the conclusion drawn by Nerem and Seed (1972) in an in vivo study of the arterial flow disturbances. This phenomenon can be known by the pulsatile Bernoulli equation derived in Eq. (7). As shown in the equation, during the acceleration phase (dq/dt'0), the instantaneous pressure drop (p !p ) tends to be favorable which may stabilize the flow fields. In contrast, during the deceleration phase (dq/dt(0), the instantaneous pressure drop (p !p ) tends to be adverse which may destabilize the flow fields. Therefore, the flow during the deceleration phase was more disturbed and had a larger region of flow separation than during the acceleration phase. No significant secondary flows were observed in the MPA for the normal valve. However, as the valve became stenotic, significant secondary flows started to appear in the MPA, due to its curvature present in the dilated MPA. Additionally, the more severe the valvular stenosis, the more perceptible was the secondary flow pattern. However, this phenomenon was not observed in the studies of Yoganathan’s laboratory, again because of disregarding the poststenotic dilatation in the MPA. The presence of secondary flows in a curved tube has been discussed previously (Chandran et al., 1979). The strengths of the secondary flows in the LPA and RPA increased as the degree of valvular stenosis increased. Due to the poststenotic dilation in the LPA, the flow observed in the LPA was more disturbed than in the RPA. In conclusion, significant changes in both flow patterns and pressure fields were observed in the pulmonary artery, as its valve became stenotic. These changes in pulmonary artery hemodynamics may be used to support accurate diagnosis of valvular pulmonic stenosis through both blood pressure measurements and non-invasive flow imaging. It is expected that the exact three-dimensional geometry of the human pulmonary artery may be different from that of the porcine pulmonary artery to some extent. Therefore, one must use caution in extrapolating these results to physiologic hemodynamics. This study, however, demonstrates the importance of analyzing biological flows from a three-dimensional viewpoint.
Acknowledgements
Fig. 10. Schematic drawing of the flow areas (A , A ) and velocities (v , v ) proximal and distal to a stenotic valve. X X
This work was supported by grants from the National Science Council of the Republic of China (NSC85-2331B-075-072 and NSC86-2314-B-075-035).
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Pulmonary artery hemodynamics with varying degrees of valvular stenosis: an in vitro study Hsing-Wen Sung *, Tsui-Lieh Hsu, Chi-How Hsu , Jer-Chen Hsu Department of Chemical Engineering, National Central University, Chung-Li, Taiwan, Republic of China Division of Cardiology, Veterans General Hospital-Taipei Taiwan, Republic of China Received 6 July 1998
Abstract The study was to investigate the effects of varying degrees of valvular stenosis on the hemodynamics of the main (MPA), left (LPA), and right (RPA) pulmonary arteries. Particle flow visualization was used to examine the flow patterns in a series of pulmonary artery models manufactured out of glass. These glass models were made based on the geometry of the porcine pulmonary arteries with dilatation in the MPA and LPA. Also, detailed pressure mappings in the models were conducted using a side-hole catheter. As the valve became stenotic, a jet-like flow was observed in the MPA. A higher degree of valvular stenosis corresponded to a narrower jet. This jet-like flow was noted to deflect away from the centerline and impinge on the roof of the dilated MPA. Additionally, a notable pressure gradient across the deflected jet-like flow in the direction of its radius of curvature was seen. Moreover, secondary flows started to appear in the dilated MPA. This suggested that the change in geometry in the MPA, due to its dilatation, had a marked effect on the pulmonary artery hemodynamics. In the LPA and RPA, the strengths of the secondary flows increased as the valve became more stenotic. The flow patterns observed in the LPA appeared to be more disturbed than in the RPA, due to the poststenotic, dilatation present in the LPA. Pressure recovery along the axial direction in the MPA was observed for all the stenotic valves studied. As the degree of valvular stenosis increased, the transvalvular energy loss increased. Moreover, it was observed that the energy loss decreased progressively as the flow traveled downstream. This tendency was consistent with the phenomenon of pressure recovery observed in the pressure measurement. The study demonstrates the importance of analyzing biological flows from a three-dimensional viewpoint. 1998 Elsevier Science Ltd. All rights reserved. Keywords: Valvular pulmonic stenosis; Poststenotic dilatation; Flow pattern; Pressure field; Secondary flow
1. Introduction It was clinically observed that valvular pulmonic stenosis is the most common form of obstruction in the pulmonary circulation (Sahn and Anderson, 1982). The complications of valvular pulmonic stenosis such as tricuspid regurgitation, pulmonary hypertension, and right ventricular hypertrophy reduce the efficiency of the heart. Hoffman (1969) reported that severe valvular pulmonic stenosis often causes death. In valvular pulmonic stenosis, the leaflets of the valve are thickened and domed (Weyman et al., 1975). It was reported that this anomaly may modify the pulmonary artery hemodynamics (Murphy et al., 1987; Yoo and Choi, 1989). Therefore,
* Corresponding author. Tel.: 886 3 422 7151 ext. 4228; fax: 00886 3 425 2296; e-mail: [email protected]
it is suggested that fundamental knowledge of the hemodynamics in the main (MPA), left (LPA) and right (RPA) pulmonary arteries may be used to support accurate diagnosis of valvular pulmonic stenosis. Because of the technical difficulties in obtaining sufficiently accurate and well-resolved hemodynamic data in vivo, most studies directed towards an understanding of the characteristics of the arterial hemodynamics have been carried out in vitro. Detailed flow patterns in an in vitro pulmonary artery model with varying degrees of valvular pulmonic stenosis have been previously studied in Yoganathan’s laboratory (Philpot et al., 1985; Sung et al., 1990; Yoganathan et al., 1986). However, the following simplifications were made in their test model when compared to a real pulmonary artery in vivo. The test model used in their studies was two-dimensional; the MPA, LPA, and RPA were in the same plane. Additionally, dilatation of the MPA and LPA, which is often
0021-9290/98/$ — see front matter 1998 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 1 - 9 2 9 0 ( 9 8 ) 0 0 1 1 5 - 8
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observed clinically with the valvular pulmonic stenosis (Kirshenbaum, 1987; Yoo and Choi, 1989), was disregarded in their test model. It is expected that such simplifications of the test model would vary the local flow fields to some extent. To the best of our knowledge, the exact three-dimensional geometry of the human pulmonary artery, particularly for those with poststenotic dilatation, is still not available in the literature. Therefore, in a previous study, we used the porcine pulmonary arteries procured from pigs (approximately 6-month-old and 70—80 kg) as our test models to further understand the effects of varying degrees of valvular stenosis on the pulmonary artery hemodynamics (Hsu et al., 1998). To make the MPA and LPA dilated as clinically observed in valvular pulmonic stenosis, an epoxy fixation technique was employed. A three-dimensional echocardiographic reconstruction method for color Doppler flow mapping was used to examine the flow fields in the test models. It was observed that the change in geometry in the MPA, due to its dilatation, had a marked effect on the pulmonary artery hemodynamics. Although color Doppler flow mapping is useful in semi-quantitatively describing the flow patterns in the pulmonary artery, it can only image one-dimensional flow fields. Data such as vortices and secondary flows cannot be observed by color Doppler flow mapping. To further comprehend the effects of varying degrees of valvular stenosis on the pulmonary artery hemodynamics in a three-dimensional format, particle flow visualization was used to examine the flow fields in a series of glass models. These glass models were made based on the geometry of the porcine pulmonary arteries used in our previous study. Also, detailed pressure mappings in the test models were conducted using a side-hole catheter.
2. Materials and methods 2.1. Test models and test valves Four glass flow-through pulmonary artery models with varying degrees of dilatation in the MPA and LPA were used in the study (Fig. 1). The dimensions of these glass models were determined based on the geometry of the porcine pulmonary arteries used in a previous study (Hsu et al., 1998). Trileaflet prosthetic tissue valves (Baxter Healthcare Corp., Irvine, CA, USA) were applied to represent the normal, mild, moderate, and severely stenotic pulmonary valves. The trileaflet tissue valve was used because its performance paralleled that of a stenotic pulmonic valve by ballooning outward and having a relatively symmetric opening (Weyman et al., 1977). As per the porcine pulmonary arteries used in our previous study, these trileaf-
Fig. 1. Schematic drawing of the glass pulmonary artery models with their corresponding geometric dimensions tested in the study.
let tissue valves were made axisymmetrically stenotic by sewing their three commissures together with thin black polyester thread. The valve areas of the normal, mild, moderate, and severe stenosis tested in the study were 2.8, 2.1, 1.0, and 0.5 cm, respectively. The reason for selecting these valve opening areas was based on the clinical classification of the severity of valvular pulmonic stenosis: over 1.0 cm for mild, 0.5—1.0 cm for moderate, and less than 0.5 cm for severe (Kirshenbaum, 1987). 2.2. Flow apparatus The study was conducted in a pulse duplicator system. The system was able to mimic the realistic flow and pressure waveforms observed on the right side of the human heart. Details of the pulse duplicator system used in the study can be found elsewhere (Yoganathan et al., 1986). The experiments were performed at a heart rate of 70 beats min\. For cases of the normal, mild, and moderately stenotic valves, the experiments were conducted at a cardiac output of 4.8—5.3 l min\. However, it was not possible to maintain such a high flowrate for a prolonged period of time with the severely stenotic valve, without physically damaging it. The flowrate used for the severely stenotic valve was, therefore, diminished to 3.2—3.5 l min\. Clinically, it was reported that the cardiac output through a severely stenotic valve is limited (Schlant, 1978), so this situation is not non-physiologic. In the study, the flow was split 50/50 (volumetric) between the LPA and RPA. The blood-analog fluid used in the study was an aqueous glycerin solution with a viscosity of 3.5 cP and a density of 1.05 g cm\ at room temperature. 2.3. Particle flow visualization Pulsatile flow visualization was applied to examine the pulmonary artery hemodynamics. Polystyrene
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particles (&300 lm in diameter, Amberlite ion exchange resin, Rhom and Hass Co., Philadelphia, PA, USA) were suspended in the blood-analog fluid and reflected by a white light, thus illuminating the flow fields. The flow fields, together with the flow waveform displayed on an oscilloscope, were recorded on-line by a video camera. The results were then analyzed off-line at distinct instants over a cardiac cycle (Fig. 2).
Electronics). A similar system was used to measure the downstream pressure simultaneously. However, the downstream pressure measurement was conducted via a side-hole catheter attached to a blood pressure transducer. The position of the catheter-tip, parallel to the MPA wall, was controlled by the thin metal wires through the test model. The positions where the downstream pressures were measured are shown in Fig. 3.
2.4. Transvalvular pressure drop measurement
2.5. Effective orifice area and transvalvular energy loss calculations
As shown in Fig. 3, the upstream pressure was measured at a wall tap 50 mm proximal to the test valve, using a blood pressure transducer (Statham P23ID, Gould Electronics, Cleveland, OH, USA) which was connected to an amplifier (Universal2+ Amplifier, Gould
Clinically, the geometric area of a stenotic valve cannot be accurately measured. Therefore, the evaluation of valvular stenosis in the cardiac catheterization laboratory routinely involves a calculation of effective orifice area based on pressure drop and flow across a valve. The effective orifice area of each test valve was calculated by the Gorlin—Gorlin formula (Gorlin and Gorlin, 1951). The transvalvular energy loss, a measure of the work load for the heart resulting from the stenotic pulmonic valve, was calculated throughout the entire cardiac cycle as follows (Knott et al., 1988) :
E" q *p/450 dt# q *p/450 dt# q *p/450 dt, forward flow
Fig. 2. Schematic drawing of the five distinct instants (acceleration phase, peak systole, deceleration phase, early diastolic phase, and late diastolic phase) over a cardaic cycle from which flow patterns were analyzed.
closing flow
(1)
leakage flow
where E, q, *p and t are the transvalvular energy loss (J), flow rate (l min\), pressure drop (mmHg), and integration time (s), respectively. The integration constant shown in the equation, 450, results from dimensional conversion. The three terms on the right-hand side of Eq. (1) are the energy losses during the forward-flow period, closing-flow period, and leakage-flow period (Fig. 2), respectively.
3. Results
Fig. 3. Schematic drawing of the positions where pressures were measured in the pulmonary artery models. The upstream pressure was measured at a wall tap 50 mm proximal to the test valve, while the downstream pressure was measured simultaneously at distinct positions via a side-hole catheter attached to a blood pressure transducer. The x’s in the figure are the measurement positions.
Examples of the flow visualization results and their schematic descriptions for the normal valve are shown in Fig. 4a—e. In the MPA, during the acceleration phase (Fig. 4a), flow that emerged from the valve was relatively evenly distributed. A region of flow separation was observed immediately distal to the valve near the sinus area. At peak systole (Fig. 4b), the instantaneous flow rate increased and a broad central flow was seen in the MPA. No significant secondary flows were observed. During the deceleration phase (Fig. 4c), the intensity of the broad central flow seen at peak systole decreased. In the LPA and RPA, during the acceleration phase, the flows were evenly distributed. No secondary flows were observed. However, during the peak systole (Fig. 4d) and deceleration phases, significant secondary flows were seen in
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Fig. 4. Results of flow visualization for the normal valve obtained in the MPA (a) during the acceleration phase, (b) at peak systole, and (c) during the deceleration phase and (d) obtained in the LPA at peak systole. (e) Schematic descriptions of the flow patterns at peak systole.
both daughter branches. Generally, the flow fields observed during the peak systole and deceleration phases were more disturbed than those seen during the acceleration phase in all three branches (Fig. 4a—c). During the early diastolic phase, the flow distal to the valve disappeared. The flow field remained disturbed until the late diastolic phase. Changes in flow patterns in the MPA were observed as the degree of valvular stenosis increased. A jet-like flow was observed distal to the stenotic valve. A higher degree of valvular stenosis corresponded to a narrower jet. It was noted that the jet-like flow deflected away from the
centerline and hit the roof of the dilated MPA (Fig. 5a—c). As the severity of dilatation in the MPA increased, the tendency of the jet-like flow hitting the roof of the MPA became more prominent, thus resulting in a larger region of flow separation underneath the jet. In addition, an increase in the curvature of the dilated MPA correlated with an increase in the disturbed nature of the overall flow fields. Moreover, secondary flow patterns started to appear in the dilated MPA (Fig. 5b and c). However, the axial velocity component (v ) observed in the secondary X flow patterns was significantly greater than its radial (v ) P and circumferential (v ) velocity components. F
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In the LPA and RPA, the strengths of the secondary flows increased as the valve became more stenotic (Fig. 5d). The flow patterns observed in the LPA appeared to be more disturbed than in the RPA, due to the poststenotic dilatation present in the LPA. Again, the flow fields observed during the peak systole and deceleration phases were more disturbed and had larger regions of flow separation than during the acceleration phase (Fig. 5a—c). Additionally, a higher degree of valvular stenosis corresponded to a more disturbed flow field in all three branches.
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Fig. 6a—d show that maximum transvalvular pressure drops measured, at distinct positions distal to the valve, for varying degrees of valvular pulmonic stenosis. It was noted that the maximum pressure drops increased with increasing degree of valvular stenosis. Generally, the transvalvular pressure drops decreased with increasing distance from the valve along the axial direction for all the stenotic cases. This indicated that the pressure measured distal to the valve was recovered as the flow traveled farther downstream.
Fig. 5. Results of flow visualization for the severely stenotic valve obtained in the MPA (a) during the acceleration phase, (b) at peak systole, and (c) during the deceleration phase and (d) obtained in the LPA at peak systole. (e) Schematic descriptions of the flow patterns at peak systole.
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Fig. 6. Maximum transvalvular pressure drops measured at distinct positions in the MPA for the (a) normal, (b) mild, (c) moderate, and (d) severely stenotic valves. ‘n’ means number of cardiac cycles analyzed.
The differences between the pressure measured at each distinct position and the lowest pressure measured in the MPA, for each studied case at peak systole, are presented in Fig. 7a—d. The areas shaded in the figure represent where the minimal pressures occurred at each downstream location (i.e. positions A, B, C, and D). As shown in the figure, the shaded area in each studied case corresponded to the course of the jet-like flow seen in the flow visualization. Also, a notable pressure gradient across the jet-like flow in the direction of its radius of curvature was seen, for all the stenotic valves studied. The results of the maximum transvalvular pressure drop measured at position A and its Gorlin-derived effective orifice area for the normal, mild, moderate, and severely stenotic valves are presented in Table 1. As shown in the table, the Gorlin-derived effective orifice areas for varying degrees of stenotic valves correlated well with their actual valve opening areas (r"0.99). Also, the transvalvular pressure drops measured inversely related to the Gorlin-derived effective orifice areas. Fig. 8 illustrates the transvalvular energy losses for varying degrees of valvular pulmonic stenosis during the forward-flow, closing-flow, and leakage-flow periods obtained at distinct positions distal to the valve. Generally, the energy loss during the forward-flow period was the greatest and that during the closing-flow period was the lowest for all the valves investigated. As the degree of valvular stenosis increased, the total energy loss increased. However, it was noted that the total energy loss decreased progressively as the flow traveled downstream. This tendency was consistent with the phenomenon of pressure recovery observed in the pressure measurement.
Fig. 7. Differences between the pressure measured at each distinct position and the lowest pressure measured in the MPA for the (a) normal, (b) mild, (c) moderate and (d) severely stenotic valves. ‘n’ means number of cardiac cycles analyzed.
Table 1 Valve opening areas (VOA), Gorlin-derived effective orifice areas (EOA), and maximum transvalvular pressure drops (*P) for varying degrees of valvular pulmonic stenosis Degree of stenosis
VOA (cm)
EOA (cm)
*P (mmHg)
Normal Mild Moderate Severe
2.8 2.1 1.0 0.5
2.4 1.8 0.8 0.4
19.7 41.7 106.8 141.5
Fig. 8. Transvalvular energy losses for varying degrees of valvular pulmonic stenosis during the forward-flow, closing-flow, and leakage—flow periods obtained at distinct positions distal to the valve.
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4. Discussion As aforementioned, particle flow visualization may reveal the three-dimensional characteristics of flow patterns and color Doppler flow mapping and one-dimensional (axial component) characteristics. Generally, the axial flow patterns visualized by particle flow visualization in the glass models were comparable to those imaged by color Doppler flow mapping in the porcine pulmonary arteries obtained in a previous study (Hsu et al., 1998), in spite of the rigidity of the glass models used. It is believed that the influence of the distensibility of the pulmonary artery bifurcation on its general hemodynamics is limited. In an in vitro study of the effect of the arterial wall distensibility on the flow characteristics in a carotid bifurcation, Anayiotos et al. (1994) reported that the general flow features in the rigid and compliant models were comparable. For the normal valve, the flow observed in the MPA was relatively evenly distributed (Fig. 4a—c). This is consistent with the clinical observations documented in the literature. Reuben et al. (1970), examining five normal humans with a hot-film anemometry, found the velocity profiles in the MPA to be approximately flat. Additionally, with a multiplane TEE transducer, Sloth et al. (1994) performed Doppler velocity measurements in the human pulmonary artery of eight healthy volunteers. They reported that the mean temporal velocity profile in the MPA was virtually flat. As the valve became stenotic, a jet-like flow was observed in the MPA (Fig. 5a—c). This observation agrees with the clinical report. Murphy et al. (1987) studied patients with valvular pulmonic stenosis and described the blood flow pattern in the MPA as a jet surrounded by flow disturbance. The jet-like flow was noted to deflect away from the centerline and impinge on the roof of the dilated MPA (Fig. 5a—c). This phenomenon was also observed clinically. In a ventriculographic inspection of the flow patterns in patients with valvular pulmonic stenosis, it was reported that a jet of contrast emerged from the stenotic valve and hit the roof of the dilated MPA (Yoo and Choi, 1989). Nevertheless, because of disregarding the poststenotic dilation in the MPA, this phenomenon was not seen in the studies of Yoganathan’s laboratory. This suggested that the change in geometry in the MPA, due to its dilatation, had a marked effect on the pulmonary artery hemodynamics. The phenomenon of the deflection of the poststenotic jet away from the centerline was also reflected in the results of our pressure measurement. Giving that the radius of curvature of the jet stream distal to a stenotic valve is r. Consider a volume element within the jet stream as shown in Fig. 9. Assume that the axis of the volume element is inclined at an angle h from the vertical. Denote the density, mass, tangential velocity, cross section, and height of the volume element by o, m, º, dA,
Fig. 9. Schematic drawing of the momentum balance on a volume element within the jet stream distal to a stenotic valve.
and dr. The pressure forces normal to the top and bottom cross sections of the volume element are pdA and (p#dp)dA, respectively. A momentum balance can be written for the volume element in direction of its axis assuming that flow is steady and viscous forces are neglected. (p#dp) dA!pdA!mg cos h"ma , (2) where g and a are the acceleration of gravity and the normal acceleration in curvilinear motion, respectively. This assumption may be valid for flow at peak systole that is often considered to be quasi-steady because the blood is neither accelerating nor decelerating at this moment. Substitution of m"odAdr, a "º/r, and cos h"dy/dr in Eq. (2) gives dpdA!ogdAdy"odAdrº/r.
(3)
Dividing Eq. (3) by dAdr and in the limit of drP0, *p/*r!og*y/*r"oº/r.
(4)
If the gravitational force on the volume element can be neglected, Eq. (4) can be simplified *p/*r"oº/r.
(5)
As shown in the flow visualization, the streamlines that emerged from the normal valve were primarily straight (Fig. 4b). This indicated that the curvature of these streamlines is infinite (rPR). From Eq. (5), it can be inferred that *p/*rP0 or there is no pressure gradient across the MPA flow. In contrast, for a stenotic valve, the jet stream distal to the valve was found to deflect toward the roof of the dilated MPA. This suggested that the curvature of this jet stream is finite (r'0). Therefore, it can be deduced that, again from Eq. (5), *p/*r'0 or there is a pressure gradient across the deflected jet in the direction of its radius of curvature. These phenomena were consistent with the results obtained in our pressure measurement (Fig. 7a—d).
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The phenomenon of pressure recovery observed in the pressure measurement for all the stenotic valves (Fig. 6b—d) can be understood in terms of the results observed in the flow visualization study. As shown in the flow visualization study, the axial velocity component (v ) of the poststenotic jet was significantly greater than its radial (v ) and circumferential (v ) components. Assum F ing that the viscous and gravitational forces can be ignored, the equation of motion in cylindrical coordinate along the axial direction (z!component) can be simplified (Bird et al., 1960) *p/*z+!o(v *v /*z#*v /*t). (6) Integrating Eq. (6) with respect to z and subsequently substituting in the continuity equation, A v "A v "q, gives p !p "1/2 ov [1!(A /A )]#o dq/dt dz/A, (7) where the subscripts 1 and 2 represent the upstream and downstream positions, respectively, along a stream line, and A and q are the flow area and volumetric flowrate, respectively (Fig. 10). Eq. (7) is the Bernoulli equation under pulsatile flow condition. At peak systole, the blood flow is often considered to be quasi-steady (dq/dt+0). Hence, ignoring the 2nd term on the right-hand side, Eq. (7) may be written as
p !p "1/2 ov [1!(A /A )]. (8) Eq. (8) related the maximum transvalvular pressure drop (p !p ) measured at peak systole for varying degrees of valvular pulmonic stenosis and its downstream velocity (v ) and the downstream-to-upstream flow area ratio (A /A ). The results of flow visualization study revealed that the jet-type flow distal to a stenotic valve broadened progressively as it traveled downstream by entraining the surrounding fluid (i.e. A /A increased with increasing distance distal to the valve as depicted in Fig. 10). Additionally, as per the continuity equation, it can be inferred that the downstream velocity, v , declined gradually as the jet-type flow broadened progressively. Therefore, the maximum transvalvular pressure drop measured at peak systole decreased as the jet-type flow traveled downstream. This may explain the phenomenon of pressure recovery along the axial direction observed for all the
stenotic valves studied (Fig. 6b—d). Additionally, the more severe the valvular stenosis, the more perceptible was the pressure recovery. The flow during the deceleration phase was more disturbed and had a larger region of flow separation than during the acceleration phase, even though the instantaneous flowrates during these two instants were equivalent. These results seemed to confirm the conclusion drawn by Nerem and Seed (1972) in an in vivo study of the arterial flow disturbances. This phenomenon can be known by the pulsatile Bernoulli equation derived in Eq. (7). As shown in the equation, during the acceleration phase (dq/dt'0), the instantaneous pressure drop (p !p ) tends to be favorable which may stabilize the flow fields. In contrast, during the deceleration phase (dq/dt(0), the instantaneous pressure drop (p !p ) tends to be adverse which may destabilize the flow fields. Therefore, the flow during the deceleration phase was more disturbed and had a larger region of flow separation than during the acceleration phase. No significant secondary flows were observed in the MPA for the normal valve. However, as the valve became stenotic, significant secondary flows started to appear in the MPA, due to its curvature present in the dilated MPA. Additionally, the more severe the valvular stenosis, the more perceptible was the secondary flow pattern. However, this phenomenon was not observed in the studies of Yoganathan’s laboratory, again because of disregarding the poststenotic dilatation in the MPA. The presence of secondary flows in a curved tube has been discussed previously (Chandran et al., 1979). The strengths of the secondary flows in the LPA and RPA increased as the degree of valvular stenosis increased. Due to the poststenotic dilation in the LPA, the flow observed in the LPA was more disturbed than in the RPA. In conclusion, significant changes in both flow patterns and pressure fields were observed in the pulmonary artery, as its valve became stenotic. These changes in pulmonary artery hemodynamics may be used to support accurate diagnosis of valvular pulmonic stenosis through both blood pressure measurements and non-invasive flow imaging. It is expected that the exact three-dimensional geometry of the human pulmonary artery may be different from that of the porcine pulmonary artery to some extent. Therefore, one must use caution in extrapolating these results to physiologic hemodynamics. This study, however, demonstrates the importance of analyzing biological flows from a three-dimensional viewpoint.
Acknowledgements
Fig. 10. Schematic drawing of the flow areas (A , A ) and velocities (v , v ) proximal and distal to a stenotic valve. X X
This work was supported by grants from the National Science Council of the Republic of China (NSC85-2331B-075-072 and NSC86-2314-B-075-035).
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