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Flow characteristics around proximal and distal stenoses in a series of tandem stenosed vessels
Journal of Biomechanics ∎ (∎∎∎∎) ∎∎∎–∎∎∎
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Flow characteristics around proximal and distal stenoses in a series of tandem stenosed vessels Hyung Kyu Huh a, Woo Rak Choi a, Hojin Ha b, Sang Joon Lee a,n a Center for Biofluid and Biomimic Research, Department of Mechanical Engineering, Pohang University of Science and Technology, Pohang 790-784, South Korea b Postech Biotech Center, Pohang University of Science and Technology, Pohang 790-784, South Korea
art ic l e i nf o
a b s t r a c t
Article history: Accepted 14 July 2016
The flow characteristics around the proximal and distal stenoses in tandem vessel models are experimentally investigated with varying flow rates (Q¼ 0.25, 0.5, 1.0 L/min), interspacing distances (L¼3, 6, 10 of diameter D) and severities (S ¼50%, 75% reduction in diameter). When the interspacing L is larger than 10 D, no fluid-dynamic interaction is observed. The flow between the proximal and distal stenoses becomes stabilized (turbulence intensity of o 3%) as the interspacing distance decreases. When the severity S is 75%, the transition from laminar to turbulent flow occurs at a flow rate higher than 0.5 L/ min, although the interspacing distance L is 3 D. Formation of recirculation flow is restricted by the presence of distal stenosis as the interspacing distance decreases. In this case, the flow between the stenoses is focused on the central region. The center-line velocity at the neck of the distal stenosis is approximately 10–15% higher than that of the proximal stenosis with equal severity of S ¼50%. When the inlet flow is center-focused, the lengths of the recirculation and the jet core behind the distal stenosis increase with decrease in interspacing distance L. When the inlet flow is turbulent, the transition from laminar to turbulent flow occurs early as the interspacing distance L is reduced. When the upstream proximal stenosis exhibits increased severity, the pressure drop is measured to be 20% compared with that when the severity of the downstream distal stenosis is increased at the flow rate of Q¼ 1.0 L/min. & 2016 Elsevier Ltd. All rights reserved.
Keywords: Tandem stenosis Hemodynamics Recirculation Severity Interspacing distance
1. Introduction Atherosclerosis is well known as the key cause of heart attacks, strokes, and peripheral vascular diseases. Previous studies have reported that the hemodynamic characteristics in arterial blood vessels are closely associated with the cause, progress, and prognosis of atherosclerosis (Blankenhorn and Hodis, 1993; Williams and Tabas, 1995). The morphological and functional expression levels of endothelial cells in blood vessels are regulated by wall shear stress (Hahn and Schwartz, 2009), especially to low and oscillating shear stresses (Caro et al., 1971; Ku et al., 1985; Myers et al., 2001). Bifurcation or stenosis geometry can cause localized recirculation or flow disturbances in blood vessels. In particular, the flow is disturbed and separated from the crest of the stenosis when blood passes through a stenosed vessel. Additionally, vortex shedding and transition from laminar to turbulent flow occur in the poststenosis region, depending on the flow conditions (Bluestein et al., n
Corresponding author. Fax: þ 82 54 279 3199. E-mail address: [email protected] (S.J. Lee).
1999; Bluestein et al., 1997). The wall shear stress in the poststenosis region yields low and oscillating values when localized recirculation and flow transition occur. Hence even arteries with mild stenosis may demonstrate transitional flow or turbulence, as previously reported by Clark (1976) and Ahmed and Giddens (1983). Considering the above aspects, stenosis in arterial vessels is one of the main parameters for the development of the secondary stenosis distal to the primary one (Rathish Kumar et al., 2002). These tandem stenoses are observed in arteries with diffused atherosclerosis or arterial dysplasia(Bertolotti et al., 2006; Lee, 1994). The stenosis in carotid bifurcation and ipsilateral extracranial stenosis in tandem with intracranial atherosclerotic disease occupies approximately 20% and 50% of the symptomatic cerebral ischemia, respectively (NASCET, 1991). However, the main contributing stenosis for such symptoms are not clearly identified, because the related hemodynamic information about tandem stenosis is insufficient yet. In addition, tandem stenosis formed extracranially and intracranially in the carotid artery is difficult to separately access for clinical treatments (Li et al., 2010). Thus, tandem stenting of both stenoses (Tsutsumi et al., 2003) or carotid
http://dx.doi.org/10.1016/j.jbiomech.2016.07.014 0021-9290/& 2016 Elsevier Ltd. All rights reserved.
Please cite this article as: Huh, H.K., et al., Flow characteristics around proximal and distal stenoses in a series of tandem stenosed vessels. Journal of Biomechanics (2016), http://dx.doi.org/10.1016/j.jbiomech.2016.07.014i
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endarterectomy and percutaneous transluminal angioplasty using a Y-shaped shunt tube have been adopted to treat multiple stenoses simultaneously (Terada et al., 1998). However, it is burden for both surgeons and the patients, when one of the stenoses is located intracranially. Therefore, detailed understanding about the hemodynamic features of tandem stenosis is crucial for proper clinical diagnosis or treatment of circulatory vascular diseases. The flows behind a single stenosis are characterized by the inlet flow Reynolds number (Re ¼ ρUD=μ ¼ ρQ D=μA) where, U, and A indicate the density, inlet velocity, and cross-sectional area of the stenosis model, and critical Reynolds number Recr of the given experimental conditions. When Reo Recr, the flow is laminar and the length of the recirculation zone is increased as Re increases. When Re4 Recr, the laminar flow is transited to turbulent flow, and the length of the recirculation zone decreases as Re increases. Recr is around 400 for flows behind a stenosis with 50% severity (Ha and Lee, 2014; Vétel et al., 2008). Similar criteria is expanded to the tandem stenosis. Lee (1994) numerically analyzed the effect of severity on the recirculation, pressure drop, wall shear stress, and vorticity distribution for a steady laminar flow. Later on, Lee et al. (2003) reported similar works on pulsatile and turbulent flows. Pulsatile laminar flows passing through a tandem stenosed vessel were numerically investigated by Rathish Kumar et al. (2002). Karayannacos et al. (1977) reported that the pressure drop caused by multiple stenoses was the sum of the pressure drops for individual stenoses with minor dependence upon the interspacing distance between stenoses. Seeley and Young (1976) demonstrated that the interspacing distance (L) plays a significant role in pressure drops. Li et al. (2010) simulated the hemodynamic effect of tandem carotid artery stenosis to facilitate clinical decisions for carotid endarterectomy. Research of Bertolotti et al. (2006) evaluated the pressure drop and peak systolic velocity ratio through echoDoppler functional diagnosis with comparison of steady-flow simulation results with steady and pulsatile flow experiments. Although various numerical simulations have studied the hemodynamic effects of tandem stenosis on the pressure drop or wall shear stress, detailed information on the flow characteristics in tandem stenosed vessels under turbulent flow conditions is still lacking. In the current study, the hemodynamic characteristics of flows around the proximal and distal stenoses in tandem stenosis models with varying interspacing distance L, severity S, and flow rate Q are quantitatively investigated using particle image velocimetry (PIV) technique under in vitro condition. The centerline velocity, laminar-to-turbulent flow transition, vorticity contour, and recirculation zone are compared to identify the effects of the flow behind the proximal stenosis on the flow around the distal stenosis and vice versa.
The tandem stenosis model can be mathematically described by the following cosine-form equation (Ahmed and Giddens, 1983): h zπi rðzÞ ¼ 1 δc 1 þ cos ; DrzrD R D
ð1Þ
where R and D represent the radius and diameter of the vessel, and r and z indicate the radial and axial coordinates, respectively. The percentage of the vessel constriction δc is 0.25 and 0.5, which corresponds to the reduction of 50% and 75% in vessel diameter. The length of each stenosis section is 2 D for all stenoses, and the interspacing distances L between the proximal and distal stenoses are 3, 6, and 10 D. Conduit of 15 D in length is attached in front of the proximal stenosis and behind the distal stenosis. Nine different tandem stenosis models with a combination of interspacing distances (L ¼3, 6, 10 D) and severities [proximal and distal stenoses with S¼ 50% diameter (P50_D50), proximal S¼ 50%, distal S ¼75% (P50_D75) and proximal S¼ 75%, distal S ¼50% (P75_D50)] are made of hardened acrylic. See Supplementary S1. Flow rates of Q ¼0.25, 0.5, 1.0 L/min are selected for flow visualization and PIV experiment. These flow rates correspond to the Reynolds numbers of 187, 375, and 750, respectively. A working fluid is stored in a reservoir that can hold up to 4 L of the liquid for stabilization and circulated through a closed flow circuit by a 15 W centrifugal pump, while the flow rate is precisely controlled with a valve. An electromagnetic flow meter (VN10, Wintech Process, Korea) is used to measure the flow rate during the experiments (Fig. 1). For pressure measurements, two pressure taps of 2 mm in diameter are installed at 130 mm upstream of the proximal stenosis and 130 mm downstream of the distal stenosis. The pressure drop across the stenosis is measured using a U-tube manometer. Detailed information of PIV velocity field measurements and turbulence intensity estimation are available in Supplementary S2. Three adjacent velocity vectors normal to the surface of the vessel was obtained and used to calculate the wall shear stress.
3. Results 3.1. Flow characteristics behind the proximal stenosis 3.1.1. Effect of interspacing distance The mean velocity fields of the flow behind the proximal stenosis for L¼3 and 10 D at Q¼0.25 L/min are shown in Fig. 2a for P50_D50. A recirculation flow formed in the post-proximal stenosis region is extended up to the X/D 8 from the crest (X/D¼0) of the proximal stenosis when L ¼10 D. The size of the
2. Methods The blood-mimicking working fluid is prepared by mixing 1% distilled water, 20% glycerol, and 79% saturated aqueous sodium iodine (NaI) by volume (Deutsch et al., 2006). The kinematic viscosity measured using a viscometer (LVDV2 þ Pro, Brookfield, USA) is approximately 2.8 70.005 cSt (cSt), while the density of the fluid ρf is 1.06 g/m3. NaI is added to the working fluid to obtain a refractive index of n¼ 1.491 70.001, corresponding to the refractive index of the acrylic stenosis model. The refractive index of the working fluid is measured using an Abbe refractometer (ATAGO, Japan). The working fluid is seeded with polymethylmethacrylate (PMMA) fluorescence particles (PMMA-Rhodamine-B particles, Dantec Dynamics, Denmark) with an average diameter of 20–50 mm and the density of the particles ρp are 0.98 g/m3. The concentration of the seeded tracer particles is approximately 0.01 wt%.
Fig. 1. (a) Schematic of a tandem stenosis composed of the proximal stenosis of 50% severity and distal stenosis of 75% severity. (b) Experimental setup of the present study.
Please cite this article as: Huh, H.K., et al., Flow characteristics around proximal and distal stenoses in a series of tandem stenosed vessels. Journal of Biomechanics (2016), http://dx.doi.org/10.1016/j.jbiomech.2016.07.014i
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Fig. 2. Comparison of mean velocity fields in the P50_D50 model with interspacing distance L ¼3D (upper) and 10D (lower) at a flow rate of Q ¼0.25 L/min (a) and Q¼ 1.0 L/min (b) according to the nondimensional position X/D. Flow visualization images are magnified in the red boxes. The crest of the proximal stenosis is located at X/D¼ 0.
recirculation zone is suppressed as the L ¼3 D, and flow separation occurs at the neck of the distal stenosis. The length of the recirculation zone is gradually decreased as the flow rate increases up to Q¼1.0 L/min (Fig. 2b). Eddies are formed in the frontal bottom wall of the L ¼10 D model and it is suppressed as L ¼3 D. The jet core in the proximal stenosis is uniform and stable when L ¼3 D when the flow diverges for the case of L ¼10 D. For vertical velocity distribution around the proximal and distal stenoses, see Supplementary S3. The dimensionless centerline axial velocity uc/up,max in the P50_D50, where up,max indicates the maximum velocity at the stenosis crest(X/D¼0) linearly decreases and the decreasing rates are nearly identical, regardless of the interspacing distance L at Q¼0.25 L/min (Fig. 3a). The maximum uc in the distal stenosis is 10% higher than that in the proximal stenosis when L ¼3 or 5 D. As the inlet flow rate increases up to Q¼0.5 L/min (Fig. 3b), the centerline velocities uc of the distal stenosis are approximately 15% higher than those in the proximal stenosis. When the interspacing distance is L ¼10 D, the uc values are abruptly decreased in the downstream region X/D ¼2 to X/D ¼4 and returned to the inlet uc. At Q¼1.0 L/min (Fig. 3c), the centerline velocities are maintained up to X/D ¼3 and 2 and then abruptly decreased to the inlet uc values up to X/D¼ 4 and 5 at L ¼6 and 10 D, respectively. In both cases, the uc values in the proximal and distal stenoses are nearly identical, whereas the uc in the distal stenosis is about 15% higher for the case of L ¼3 D. Regions of high-axial velocity fluctuations (Urms) from the crests of the proximal stenosis expand along the turbulent shear layers (P50_D50, Q¼1.0 L/min). The length of the high-velocity fluctuations from the proximal stenosis is the shortest at L ¼10 D (X/D¼ 0.8). As the L is reduced to 6 D, the location of high-velocity fluctuations shifts backward to X/D¼ 2. When the distance is
Fig. 3. The effect of interspacing distance L ¼ 3D, 6D and 10D on the time-averaged centerline velocity distribution at three flow rates in the P50_D50 model: (a) 0.25, (b) 0.5 and (c) 1.0 L/min, respectively. The error bar indicates the standard deviation. The upper dashed line indicates the centerline velocity at the crest of the proximal stenosis, while the lower dashed line indicates the centerline velocity of the inlet flow. The crest of the proximal stenosis is located at X/D ¼ 0. The first period of L ¼ 3D ( ) is overlapped with L ¼6D ( ) (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.).
further decreased to L¼ 3 D, no abrupt increase in the velocity fluctuations in the central region of the stenosis model is observed (Fig. 4a). As shown in Fig. 4b, the translation from laminar to turbulent flow (where vorticity contour becomes thicker) is delayed from X/D ¼2 to 3 to X/D ¼3 to 4 when L decreases from 10 D to 6 D.
Please cite this article as: Huh, H.K., et al., Flow characteristics around proximal and distal stenoses in a series of tandem stenosed vessels. Journal of Biomechanics (2016), http://dx.doi.org/10.1016/j.jbiomech.2016.07.014i
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Fig. 4. (a) Contours of rms values of velocity fluctuations in the P50_D50 model with three different interspacing distances of L ¼ 3D, 6D and 10D at a flow rate of Q ¼1.0 L/min. (b) Mean vorticity contours in the P50_D50 model with L ¼ 3D and 6D at a flow rate of Q¼ 1.0 L/min. (c) Comparison of recirculation zone length for three interspacing distances of L ¼ 3D, 6D and 10D at a flow rate of Q¼ 1.0 L/min. The crest of the proximal stenosis is located at X/D¼ 0.
The statistically averaged length of the recirculation zone between stenoses (S ¼50%) is approximately 25 mm in the case of L¼ 3 D and is increased (p o0.01) to 30 and 40 mm when the distance is L ¼10 and 6 D, respectively at Q¼ 1.0 L/min (Fig. 4c). The turbulence intensity Urms/Umean of P50_D50 tandem model at Q¼0.25 L/min remains low under 3% regardless of the interspacing distance L (Fig. 5a). When Q¼0.5 L/min, the turbulence intensity for the case of L¼3 D is kept under 3% and increases up to 18% and 10% for the cases of L ¼10 and 6 D, respectively. The peak location in the turbulence intensity profile is shifted toward the downstream from X/D ¼3 to 5 as the L decreases from 10 D to 6 D (Fig. 5b). When Q¼ 1.0 L/min, the magnitude of the peak turbulence intensity for L ¼6 D increases up to 17%, whereas that for the L¼ 10 D case is maintained at 18%. The peak location is shifted upstream to X/D ¼2.5 and 3.5 for the case of L ¼10 and 6D, respectively. The turbulence intensity is kept low under 3% for the flow in the region behind the proximal stenosis with the smallest interspacing distance of L¼ 3 D. 3.1.2. Effect of severity The flow behind the proximal stenosis with S¼ 75% (P75_D50) exhibits similar flow characteristics as a result for the P50_D50 model at increased flow rate condition. The severity of the distal stenosis presents negligible influence on the flow characteristics behind the proximal stenosis. Detailed flow characteristics and explanations are presented in Supplementary S4. 3.2. Flow characteristics behind the distal stenosis 3.2.1. Effect of interspacing distance The centerline velocity at the crest of the distal stenosis (P50_D75) is the highest when L ¼3 D at Q¼ 0.25 L/min. It decreases as the L increases as shown in Fig. 6a. Lengths of jet core and the recirculation zone behind the distal stenosis decrease as the interspacing distance L increases (Fig. 6b). This inverse proportional relation also occurs at the increased flow rate of 0.5 L/min in distal stenosis with severity S ¼50% (Supplementary S4). When the flow rate Q¼1.0 L/min, the flow behind the distal stenosis is oppositely affected (proportional) by the interspacing distance L(Fig. 6c). Region of high-velocity fluctuations is shifted upstream and the length of recirculation zone is decreased at postdistal stenosis region of P50_D50 model as the interspacing distance L is shortened to 3 D. However, when the severity of the distal
stenosis is 75%, neither velocity fluctuations nor the size of the recirculation zone are affected by the interspacing distance L. 3.2.2. Effect of severity Relation between jet core length and interspacing distance is proportional when proximal stenosis severity is 75% and Q4 0.5 L/ min (Fig. 7). The area of high-vorticity values decreases as the distance L decreases. The flow entering the distal stenosis with L¼3 D and Q¼0.5 L/min presents a large velocity gradient (Fig. 7a). As a result, the flow passing through the crest of the distal stenosis is strongly center-focused compared with L ¼6 or 10 D. The flow entering the distal stenosis with L ¼3 D also presents high-velocity gradient when Q¼1.0 L/min (Fig. 7b). The spatial distributions of velocity fluctuations in the P50_D50 and P75_D50 models with L¼ 3 D at Q¼0.5 L/min are compared in Fig. 7c. High-velocity fluctuations from P75 increase the centerline velocity fluctuations at the crest of the distal stenosis by five times higher than those of P50 case. The effect of the proximal severity of the proximal stenosis on the flow behind the distal stenosis is demonstrated in the vorticity contours (Supplementary movie 1). Supplementary material related to this article can be found online at http://dx.doi.org/10.1016/j.jbiomech.2016.07.014. The flow behind the stenosis with S ¼75% is highly disturbed in the near downstream region of X/D¼0.5 to 2.0, regardless of the sequential arrangement (Fig. 8a). Highly disturbed flow behind the P75 stenosis enhances the disturbance of the flow behind the distal stenosis D50. As a result, velocity fluctuations Urms are increased up to 160 mm/s. By contrast, the velocity fluctuations of the flow behind the proximal stenosis P50 are smaller than 100 mm/s. Supplementary movie 2 shows different velocity fluctuations behind stenosis with S ¼50%. The pressure drop difference is nearly 400 Pa for the case of L ¼3 D and less than 60 Pa for L ¼6 and 10 D (Fig. 8b). The pressure drop in the P50_D75 tandem stenosis model is generally greater than that in the P75_D50 model. Supplementary material related to this article can be found online at http://dx.doi.org/10.1016/j.jbiomech.2016.07.014.
4. Discussion The flow rates selected in current study are Q¼0.25, 0.5, 1 L/ min, corresponding to the minimum, average, and maximum flow rates in the common carotid artery of normal humans (Holdsworth et al., 1999). Corresponding Reynolds numbers of Re¼187,
Please cite this article as: Huh, H.K., et al., Flow characteristics around proximal and distal stenoses in a series of tandem stenosed vessels. Journal of Biomechanics (2016), http://dx.doi.org/10.1016/j.jbiomech.2016.07.014i
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Fig. 5. The effect of interspacing distance on the turbulent intensity distribution of centerline velocity in the P50_D50 model at three flow rates of (a) 0.25, (b) 0.5 and (c) 1.0 L/min. The crest of the proximal stenosis is located at X/D ¼ 0.
375, 750 represent the laminar, transitional, and turbulent flow behind a stenosis with 50% severity, respectively. Recr decreases as the severity of the stenosis increases, indicating the earlier occurrence of turbulence behind the severe stenosis at a higher Re number flow. The size of recirculation zone formed behind the proximal stenosis is suppressed when the distance L is shorter than the length of the recirculation zone behind a single stenosis (Figs. 2a and 4c). As the interspacing distance L decreases, the distal stenosis is exposed to low and oscillatory wall shear stresses, which can cause the outbreak and growth of stenosis (Myers et al., 2001).
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Fig. 6. (a) Effect of interspacing distance L ¼ 3D, 6D and 10D on the centerline velocity distribution in the P50_D75 model at three flow rates of Q¼ 0.25 L/min. The crest of the proximal stenosis is located at X/D ¼ 0. (b) Comparison of mean velocity fields in the P50_D75 models with interspacing distances L ¼3D, 6D and 10D at a flow rate of Q¼ 0.5 L/min. (c) Comparison of velocity fluctuations of flow behind the distal stenosis of P50_D50 (left) and P50_D75 (right) models at a flow rate of Q ¼1.0 L/ min. Each arrow indicates the end of flow separation region extracted based on stream lines. The crest of the distal stenosis is located at X/D ¼ 0.
In the present study (Re 750), a recirculation flow is formed between the proximal and distal stenosis, causing low and negative wall shear stress as shown in Fig. 9a. The existence of low wall shear stress region in between proximal and distal stenoses may promote atherosclerotic growth, leading to the merge of adjacent stenoses. The suppressed recirculation zone occupies region between the proximal and distal stenoses when interspacing distance L¼ 3 D. In this case, either flow separation (recirculation zone length for
Please cite this article as: Huh, H.K., et al., Flow characteristics around proximal and distal stenoses in a series of tandem stenosed vessels. Journal of Biomechanics (2016), http://dx.doi.org/10.1016/j.jbiomech.2016.07.014i
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Fig. 8. (a) Contours of velocity fluctuations in the P75_D50 (upper) and P50_D75 (lower) models with L ¼3D at a flow rate of Q¼ 1.0 L/min. The crest of the proximal stenosis is located at X/D ¼0. (b) Pressure difference between the P75_D50 and P50_D75 models according to the interspacing distance. (c) Comparison of vertical velocity fluctuation in the distal stenosis of P50_D50, P75_D50 and P50_D75 models at different flow rates of Q¼ 0.25, 0.5 and 1.0 L/min.
Fig. 7. Spatial distributions of vorticity field behind the distal stenosis of P75_D50 models with different interspacing distances of L ¼3D, 6D and 10D at flow rates of (a) 0.5 and (b) 1.0 L/min. (c) Comparision of velocity fluctuations in the P50_D50 (upper) and P50_D75 (lower) models with L ¼ 3D at a flow rate of Q ¼0.5 L/min. The crest of the proximal stenosis is located at X/D ¼ 0.
L¼ 10, D4 3 D) or eddy formation (recirculation zone length for L¼ 3 to 10 D) occurs in the frontal neck of the distal stenosis. As a result, the center-focused flow enters the distal stenosis. The flow velocity in the central region of the vessel should increase to compensate for the opposite directional flow, that is, the recirculating flow for a fixed flow rate. The centerline velocity uc in the distal stenosis is approximately 10–15% higher than that of the proximal stenosis of same severity (Fig. 3). These results are well matched with the simulation results of Banerjee et al. (2008). The severity of the distal stenosis can be clinically overestimated by increased maximum centerline velocity obtained in the ultrasound diagnosis when two stenoses are in close proximity (Bertolotti et al., 2006). In this case, other supplementary diagnosis devices, such as angiography or fractional flow reserve, are required. The flow in the region between the proximal and distal stenoses is more stable as the interspacing distance L decreases. As shown in Fig. 5, the centerline turbulence intensity in the P50_D50 model is maintained at o3% (laminar flow), regardless of the flow rate. The laminar-to-turbulent transition is prolonged in the model with L ¼6 D compared with 10 D (Fig. 4a and b). Forward shifted
re-laminarization is induced by faster mixing and re-distribution of flow momentum. Hence, prolonged laminar to turbulent transition indicates that the flow becomes more stable. This inverse proportional relationship is observed for the case of Re4Recr, regardless of the severity of the stenosis (S.3). However, as the severity and flow rate increase, laminar-to-turbulent transition is identical, regardless of the interspacing distance. This finding indicates that Re 750 is an upper limit of the laminar-toturbulent transition shortening behind the stenosis with S ¼75%. The numerical simulation of Lee et al. (2003) exhibited similar results in the region behind the stenosis with 50% severity at Re4 1000. As the interspacing distance decreases, the flow characteristics behind the distal stenosis are increasingly affected by the flow behind the proximal stenosis. When the flow in the middle section between the proximal and distal stenoses is stable (P50_D50 and P50_D75 at Q¼ 0.25 and 0.5 L/min, P75_D50 at Q¼0.25 L/min), the increased centerline velocity in the crest of the distal stenosis increases the length of jet core and recirculation zone formed behind the distal stenosis (Fig. 8c). The flows behind the distal stenosis are also more stable in the model with L ¼3 D than with 10 D (Figs. 6a, b, and S4). This is because the center-focused inlet flow decreases the pressure drop in the middle section between the two stenoses, which increases the discharge coefficient (Reader-Harris, 2015). On the contrary, jet length and interspacing distance shows proportional relation when Re4Recr (P50_D50 and P50_D75 at Q¼1.0 L/min, P75_D50 at Q¼0.5 L/min). It is because more energy is
Please cite this article as: Huh, H.K., et al., Flow characteristics around proximal and distal stenoses in a series of tandem stenosed vessels. Journal of Biomechanics (2016), http://dx.doi.org/10.1016/j.jbiomech.2016.07.014i
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proximal stenosis. This indicates that the proximal stenosis plays a role to protect the distal stenosis from direct exposure to the high wall shear stress. Li et al. (2010) reported similar numerical simulation results on this phenomena. This indicates the importance of the geometry of the proximal stenosis post-repair, and suggests that great care should be taken during surgical operation to avoid creation of a new high wall shear stress region on the distal stenosis. The PIV measurements of flow in the tandem stenosis model with varying flow rates, interspacing distances, and severities provide essential flow characteristics in the middle section between the two stenoses and downstream of the distal stenosis. Further in-depth research about the 3D flow structures under pulsatile inlet conditions is required to correlate the flow characteristics in the tandem stenosis with biomedical diagnoses and clinical treatments.
5. Conclusions
Fig. 9. (a) Wall shear stress of P50_D50 model with L ¼3D at a flow rate of Q¼ 1.0 L/ min. Solid line indicates zero wall shear stress. (b) Wall shear stress of P50_D75 and P50_D75 models with L ¼ 3D at a flow rate of Q ¼1.0 L/min. The crest of the proximal stenosis is located at X/D¼ 0.
required to move the asymmetric flows compared with the symmetric flows (Reader-Harris, 2015) through the distal stenosis. One may conclude that the turbulent inlet flow can give rise to a highly turbulent flow behind the distal stenosis (Supplementary movie 2). In addition, the transition from laminar to turbulent flow behind the P75 stenosis is identical, regardless of the interspacing distance at a high flow rate of Q¼1.0 L/min (Fig. 6c). These findings are well matched with the numerical simulation results of Lee et al. (2003). The present experimental results on the velocity fields and pressure drop in the tandem stenoses confirm the hypothesis of Dodds and Phillips (2003) that the sequential order of the stenoses exerts a noticeable effect on the pressure drop. The flow behind a stenosis of 50% severity is stable when located in front of the stenosis with 75% severity. However, the flows become unstable behind stenosis of S ¼50% when their orders are opposite (Fig. 8a). The viscous dissipation of kinetic energy is significant when the flow is turbulent. Therefore, the pressure drop in the P75_D50 model is significant compared with the tandem stenosis model of P50_D75 (Fig. 8b). In the view point of reducing the recirculation zone, the proximal stenosis with a high-severity is more preferred. However, in the clinical point of view, the increased pressure drop may induce overload to the heart. The maximum wall shear stress in the proximal stenosis with S ¼75% is around 8 Pa s. However, the peak wall shear stress drops to 5 Pa s in the region behind the
In this study, the effects of three different flow rates (laminar, transitional, and turbulent), three interspacing distances (3, 6, and 10 D) and two severities (50% and 75%) on the flow characteristics in tandem stenosis are experimentally investigated. As the interspacing distance decreases, flows in the middle section between the proximal and distal stenoses are stabilized until the Reynolds number Re reaches the upper limit. The transition from laminar to turbulent flow is prolonged when Re4Recr. The length of the recirculation zone is restricted by the presence of distal stenosis, and flow separation occurs at the frontal neck of the distal stenosis. The flows are focused in the central region of the conduit as the recirculation flow occupies the unstenosed area. As a result, the centerline velocity at the crest of the distal stenosis is approximately 10–15% higher than that of the proximal stenosis under the same severity. This phenomenon may cause overestimation of the severity of the distal stenosis in clinical diagnosis. Furthermore, the low wall shear stress region in between the proximal and distal stenoses may promote atherosclerotic growth or merging of adjacent stenoses. The flow behind the distal stenosis is solely affected by the flow characteristics behind the proximal stenosis. When the inlet flow is a center-focused laminar flow, the lengths of the recirculation zone and jet core region increase as the interspacing distance decreases. When the inlet flow is turbulent, the transition from laminar to turbulent flow occurs earlier as the interspacing distance is shorter. As the perturbation in the proximal stenosis strongly influences the flow around the distal stenosis, the pressure drop in the tandem stenosis models depends on the sequential arrangement of severity. Severe stenosis in the upstream increases the pressure drop by 20% compared with that located in the downstream distal stenosis.
Conflict of interest None declared.
Funding This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2008-0061991).
Please cite this article as: Huh, H.K., et al., Flow characteristics around proximal and distal stenoses in a series of tandem stenosed vessels. Journal of Biomechanics (2016), http://dx.doi.org/10.1016/j.jbiomech.2016.07.014i
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Acknowledgment We thank for the support of the NRF of Korea through the Creative Research Initiatives program.
Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.jbiomech.2016.07.014.
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Hahn, C., Schwartz, M.A., 2009. Mechanotransduction in vascular physiology and atherogenesis. Nat. Rev. Mol. Cell Biol. 10, 53–62. Holdsworth, D., Norley, C., Frayne, R., Steinman, D., Rutt, B., 1999. Characterization of common carotid artery blood-flow waveforms in normal human subjects. Physiol. Meas. 20, 219. Karayannacos, P., Talukder, N., Nerem, R., Roshon, S., Vasko, J., 1977. The role of multiple noncritical arterial stenoses in the pathogenesis of ischemia. J. Thorac. Cardiovasc. Surg. 73, 458–469. Ku, D.N., Giddens, D.P., Zarins, C.K., Glagov, S., 1985. Pulsatile flow and atherosclerosis in the human carotid bifurcation. Positive correlation between plaque location and low oscillating shear stress. Arter. Thromb., Vasc. Biol. 5, 293–302. Lee, T., 1994. Steady laminar fluid flow through variable constrictions in vascular tube. J. Fluids Eng. 116, 66–71. Lee, T., Liao, W., Low, H., 2003. Numerical simulation of turbulent flow through series stenoses. Int. J. Numer. Methods Fluids 42, 717–740. Li, Z.-Y., Taviani, V., Tang, T., Sutcliffe, M.P., Gillard, J.H., 2010. The hemodynamic effects of in-tandem carotid artery stenosis: implications for carotid endarterectomy. J. Stroke Cerebrovasc. Dis. 19, 138–145. Myers, J., Moore, J., Ojha, M., Johnston, K., Ethier, C., 2001. Factors influencing blood flow patterns in the human right coronary artery. Ann. Biomed. Eng. 29, 109–120. (NASCET), N.A.S.C.E.T., 1991. Clinical alert: benefit of carotid endarterectomy for patients with high-grade stenosis of the internal carotid artery. In: Proceedings of the National Institute of Neurological Disorders and Stroke, Stroke and Trauma Division. North American Symptomatic Carotid Endarterectomy Trial. Stroke. Vol. 22, pp. 816–817. Rathish Kumar, B., Yamaguchi, T., Liu, H., Himeno, R., 2002. A numerical study of an unsteady laminar flow in a doubly constricted 3D vessel. Int. J. Numer. Methods Fluids 38, 1159–1176. Reader-Harris, M., 2015. Orifice plates and venturi tubes. In: Wolfgang, Merzkirch, Donald, Rockwell, Cameron, Tropea. (Eds.), Experimental Fluid Mechanics, Springer International Publishing (Series ISSN:1613-222X; Edition Number: 1). Seeley, B.D., Young, D.F., 1976. Effect of geometry on pressure losses across models of arterial stenoses. J. Biomech. 9, 439–448. Terada, T., Yokote, H., Kinoshita, Y., Tsuura, M., Masuo, O., Nakai, K., Itakura, T., 1998. Carotid endarterectomy and simultaneous percutaneous transluminal angioplasty for tandem internal carotid stenoses. Neuroradiology 40, 404–408. Tsutsumi, M., Kazekawa, K., Tanaka, A., Aikawa, H., Nomoto, Y., Nii, K., Sakai, N., 2003. Improved cerebral perfusion after simultaneous stenting for tandem stenoses of the internal carotid artery-two case reports. Neurol. Med. Chir. 43, 386–390. Vétel, J., Garon, A., Pelletier, D., Farinas, M.-I., 2008. Asymmetry and transition to turbulence in a smooth axisymmetric constriction. J. Fluid Mech. 607, 351–386. Williams, K.J., Tabas, I., 1995. The response-to-retention hypothesis of early atherogenesis. Arter. Thromb. Vasc. Biol. 15, 551–561.
Please cite this article as: Huh, H.K., et al., Flow characteristics around proximal and distal stenoses in a series of tandem stenosed vessels. Journal of Biomechanics (2016), http://dx.doi.org/10.1016/j.jbiomech.2016.07.014i
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Flow characteristics around proximal and distal stenoses in a series of tandem stenosed vessels Hyung Kyu Huh a, Woo Rak Choi a, Hojin Ha b, Sang Joon Lee a,n a Center for Biofluid and Biomimic Research, Department of Mechanical Engineering, Pohang University of Science and Technology, Pohang 790-784, South Korea b Postech Biotech Center, Pohang University of Science and Technology, Pohang 790-784, South Korea
art ic l e i nf o
a b s t r a c t
Article history: Accepted 14 July 2016
The flow characteristics around the proximal and distal stenoses in tandem vessel models are experimentally investigated with varying flow rates (Q¼ 0.25, 0.5, 1.0 L/min), interspacing distances (L¼3, 6, 10 of diameter D) and severities (S ¼50%, 75% reduction in diameter). When the interspacing L is larger than 10 D, no fluid-dynamic interaction is observed. The flow between the proximal and distal stenoses becomes stabilized (turbulence intensity of o 3%) as the interspacing distance decreases. When the severity S is 75%, the transition from laminar to turbulent flow occurs at a flow rate higher than 0.5 L/ min, although the interspacing distance L is 3 D. Formation of recirculation flow is restricted by the presence of distal stenosis as the interspacing distance decreases. In this case, the flow between the stenoses is focused on the central region. The center-line velocity at the neck of the distal stenosis is approximately 10–15% higher than that of the proximal stenosis with equal severity of S ¼50%. When the inlet flow is center-focused, the lengths of the recirculation and the jet core behind the distal stenosis increase with decrease in interspacing distance L. When the inlet flow is turbulent, the transition from laminar to turbulent flow occurs early as the interspacing distance L is reduced. When the upstream proximal stenosis exhibits increased severity, the pressure drop is measured to be 20% compared with that when the severity of the downstream distal stenosis is increased at the flow rate of Q¼ 1.0 L/min. & 2016 Elsevier Ltd. All rights reserved.
Keywords: Tandem stenosis Hemodynamics Recirculation Severity Interspacing distance
1. Introduction Atherosclerosis is well known as the key cause of heart attacks, strokes, and peripheral vascular diseases. Previous studies have reported that the hemodynamic characteristics in arterial blood vessels are closely associated with the cause, progress, and prognosis of atherosclerosis (Blankenhorn and Hodis, 1993; Williams and Tabas, 1995). The morphological and functional expression levels of endothelial cells in blood vessels are regulated by wall shear stress (Hahn and Schwartz, 2009), especially to low and oscillating shear stresses (Caro et al., 1971; Ku et al., 1985; Myers et al., 2001). Bifurcation or stenosis geometry can cause localized recirculation or flow disturbances in blood vessels. In particular, the flow is disturbed and separated from the crest of the stenosis when blood passes through a stenosed vessel. Additionally, vortex shedding and transition from laminar to turbulent flow occur in the poststenosis region, depending on the flow conditions (Bluestein et al., n
Corresponding author. Fax: þ 82 54 279 3199. E-mail address: [email protected] (S.J. Lee).
1999; Bluestein et al., 1997). The wall shear stress in the poststenosis region yields low and oscillating values when localized recirculation and flow transition occur. Hence even arteries with mild stenosis may demonstrate transitional flow or turbulence, as previously reported by Clark (1976) and Ahmed and Giddens (1983). Considering the above aspects, stenosis in arterial vessels is one of the main parameters for the development of the secondary stenosis distal to the primary one (Rathish Kumar et al., 2002). These tandem stenoses are observed in arteries with diffused atherosclerosis or arterial dysplasia(Bertolotti et al., 2006; Lee, 1994). The stenosis in carotid bifurcation and ipsilateral extracranial stenosis in tandem with intracranial atherosclerotic disease occupies approximately 20% and 50% of the symptomatic cerebral ischemia, respectively (NASCET, 1991). However, the main contributing stenosis for such symptoms are not clearly identified, because the related hemodynamic information about tandem stenosis is insufficient yet. In addition, tandem stenosis formed extracranially and intracranially in the carotid artery is difficult to separately access for clinical treatments (Li et al., 2010). Thus, tandem stenting of both stenoses (Tsutsumi et al., 2003) or carotid
http://dx.doi.org/10.1016/j.jbiomech.2016.07.014 0021-9290/& 2016 Elsevier Ltd. All rights reserved.
Please cite this article as: Huh, H.K., et al., Flow characteristics around proximal and distal stenoses in a series of tandem stenosed vessels. Journal of Biomechanics (2016), http://dx.doi.org/10.1016/j.jbiomech.2016.07.014i
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endarterectomy and percutaneous transluminal angioplasty using a Y-shaped shunt tube have been adopted to treat multiple stenoses simultaneously (Terada et al., 1998). However, it is burden for both surgeons and the patients, when one of the stenoses is located intracranially. Therefore, detailed understanding about the hemodynamic features of tandem stenosis is crucial for proper clinical diagnosis or treatment of circulatory vascular diseases. The flows behind a single stenosis are characterized by the inlet flow Reynolds number (Re ¼ ρUD=μ ¼ ρQ D=μA) where, U, and A indicate the density, inlet velocity, and cross-sectional area of the stenosis model, and critical Reynolds number Recr of the given experimental conditions. When Reo Recr, the flow is laminar and the length of the recirculation zone is increased as Re increases. When Re4 Recr, the laminar flow is transited to turbulent flow, and the length of the recirculation zone decreases as Re increases. Recr is around 400 for flows behind a stenosis with 50% severity (Ha and Lee, 2014; Vétel et al., 2008). Similar criteria is expanded to the tandem stenosis. Lee (1994) numerically analyzed the effect of severity on the recirculation, pressure drop, wall shear stress, and vorticity distribution for a steady laminar flow. Later on, Lee et al. (2003) reported similar works on pulsatile and turbulent flows. Pulsatile laminar flows passing through a tandem stenosed vessel were numerically investigated by Rathish Kumar et al. (2002). Karayannacos et al. (1977) reported that the pressure drop caused by multiple stenoses was the sum of the pressure drops for individual stenoses with minor dependence upon the interspacing distance between stenoses. Seeley and Young (1976) demonstrated that the interspacing distance (L) plays a significant role in pressure drops. Li et al. (2010) simulated the hemodynamic effect of tandem carotid artery stenosis to facilitate clinical decisions for carotid endarterectomy. Research of Bertolotti et al. (2006) evaluated the pressure drop and peak systolic velocity ratio through echoDoppler functional diagnosis with comparison of steady-flow simulation results with steady and pulsatile flow experiments. Although various numerical simulations have studied the hemodynamic effects of tandem stenosis on the pressure drop or wall shear stress, detailed information on the flow characteristics in tandem stenosed vessels under turbulent flow conditions is still lacking. In the current study, the hemodynamic characteristics of flows around the proximal and distal stenoses in tandem stenosis models with varying interspacing distance L, severity S, and flow rate Q are quantitatively investigated using particle image velocimetry (PIV) technique under in vitro condition. The centerline velocity, laminar-to-turbulent flow transition, vorticity contour, and recirculation zone are compared to identify the effects of the flow behind the proximal stenosis on the flow around the distal stenosis and vice versa.
The tandem stenosis model can be mathematically described by the following cosine-form equation (Ahmed and Giddens, 1983): h zπi rðzÞ ¼ 1 δc 1 þ cos ; DrzrD R D
ð1Þ
where R and D represent the radius and diameter of the vessel, and r and z indicate the radial and axial coordinates, respectively. The percentage of the vessel constriction δc is 0.25 and 0.5, which corresponds to the reduction of 50% and 75% in vessel diameter. The length of each stenosis section is 2 D for all stenoses, and the interspacing distances L between the proximal and distal stenoses are 3, 6, and 10 D. Conduit of 15 D in length is attached in front of the proximal stenosis and behind the distal stenosis. Nine different tandem stenosis models with a combination of interspacing distances (L ¼3, 6, 10 D) and severities [proximal and distal stenoses with S¼ 50% diameter (P50_D50), proximal S¼ 50%, distal S ¼75% (P50_D75) and proximal S¼ 75%, distal S ¼50% (P75_D50)] are made of hardened acrylic. See Supplementary S1. Flow rates of Q ¼0.25, 0.5, 1.0 L/min are selected for flow visualization and PIV experiment. These flow rates correspond to the Reynolds numbers of 187, 375, and 750, respectively. A working fluid is stored in a reservoir that can hold up to 4 L of the liquid for stabilization and circulated through a closed flow circuit by a 15 W centrifugal pump, while the flow rate is precisely controlled with a valve. An electromagnetic flow meter (VN10, Wintech Process, Korea) is used to measure the flow rate during the experiments (Fig. 1). For pressure measurements, two pressure taps of 2 mm in diameter are installed at 130 mm upstream of the proximal stenosis and 130 mm downstream of the distal stenosis. The pressure drop across the stenosis is measured using a U-tube manometer. Detailed information of PIV velocity field measurements and turbulence intensity estimation are available in Supplementary S2. Three adjacent velocity vectors normal to the surface of the vessel was obtained and used to calculate the wall shear stress.
3. Results 3.1. Flow characteristics behind the proximal stenosis 3.1.1. Effect of interspacing distance The mean velocity fields of the flow behind the proximal stenosis for L¼3 and 10 D at Q¼0.25 L/min are shown in Fig. 2a for P50_D50. A recirculation flow formed in the post-proximal stenosis region is extended up to the X/D 8 from the crest (X/D¼0) of the proximal stenosis when L ¼10 D. The size of the
2. Methods The blood-mimicking working fluid is prepared by mixing 1% distilled water, 20% glycerol, and 79% saturated aqueous sodium iodine (NaI) by volume (Deutsch et al., 2006). The kinematic viscosity measured using a viscometer (LVDV2 þ Pro, Brookfield, USA) is approximately 2.8 70.005 cSt (cSt), while the density of the fluid ρf is 1.06 g/m3. NaI is added to the working fluid to obtain a refractive index of n¼ 1.491 70.001, corresponding to the refractive index of the acrylic stenosis model. The refractive index of the working fluid is measured using an Abbe refractometer (ATAGO, Japan). The working fluid is seeded with polymethylmethacrylate (PMMA) fluorescence particles (PMMA-Rhodamine-B particles, Dantec Dynamics, Denmark) with an average diameter of 20–50 mm and the density of the particles ρp are 0.98 g/m3. The concentration of the seeded tracer particles is approximately 0.01 wt%.
Fig. 1. (a) Schematic of a tandem stenosis composed of the proximal stenosis of 50% severity and distal stenosis of 75% severity. (b) Experimental setup of the present study.
Please cite this article as: Huh, H.K., et al., Flow characteristics around proximal and distal stenoses in a series of tandem stenosed vessels. Journal of Biomechanics (2016), http://dx.doi.org/10.1016/j.jbiomech.2016.07.014i
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Fig. 2. Comparison of mean velocity fields in the P50_D50 model with interspacing distance L ¼3D (upper) and 10D (lower) at a flow rate of Q ¼0.25 L/min (a) and Q¼ 1.0 L/min (b) according to the nondimensional position X/D. Flow visualization images are magnified in the red boxes. The crest of the proximal stenosis is located at X/D¼ 0.
recirculation zone is suppressed as the L ¼3 D, and flow separation occurs at the neck of the distal stenosis. The length of the recirculation zone is gradually decreased as the flow rate increases up to Q¼1.0 L/min (Fig. 2b). Eddies are formed in the frontal bottom wall of the L ¼10 D model and it is suppressed as L ¼3 D. The jet core in the proximal stenosis is uniform and stable when L ¼3 D when the flow diverges for the case of L ¼10 D. For vertical velocity distribution around the proximal and distal stenoses, see Supplementary S3. The dimensionless centerline axial velocity uc/up,max in the P50_D50, where up,max indicates the maximum velocity at the stenosis crest(X/D¼0) linearly decreases and the decreasing rates are nearly identical, regardless of the interspacing distance L at Q¼0.25 L/min (Fig. 3a). The maximum uc in the distal stenosis is 10% higher than that in the proximal stenosis when L ¼3 or 5 D. As the inlet flow rate increases up to Q¼0.5 L/min (Fig. 3b), the centerline velocities uc of the distal stenosis are approximately 15% higher than those in the proximal stenosis. When the interspacing distance is L ¼10 D, the uc values are abruptly decreased in the downstream region X/D ¼2 to X/D ¼4 and returned to the inlet uc. At Q¼1.0 L/min (Fig. 3c), the centerline velocities are maintained up to X/D ¼3 and 2 and then abruptly decreased to the inlet uc values up to X/D¼ 4 and 5 at L ¼6 and 10 D, respectively. In both cases, the uc values in the proximal and distal stenoses are nearly identical, whereas the uc in the distal stenosis is about 15% higher for the case of L ¼3 D. Regions of high-axial velocity fluctuations (Urms) from the crests of the proximal stenosis expand along the turbulent shear layers (P50_D50, Q¼1.0 L/min). The length of the high-velocity fluctuations from the proximal stenosis is the shortest at L ¼10 D (X/D¼ 0.8). As the L is reduced to 6 D, the location of high-velocity fluctuations shifts backward to X/D¼ 2. When the distance is
Fig. 3. The effect of interspacing distance L ¼ 3D, 6D and 10D on the time-averaged centerline velocity distribution at three flow rates in the P50_D50 model: (a) 0.25, (b) 0.5 and (c) 1.0 L/min, respectively. The error bar indicates the standard deviation. The upper dashed line indicates the centerline velocity at the crest of the proximal stenosis, while the lower dashed line indicates the centerline velocity of the inlet flow. The crest of the proximal stenosis is located at X/D ¼ 0. The first period of L ¼ 3D ( ) is overlapped with L ¼6D ( ) (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.).
further decreased to L¼ 3 D, no abrupt increase in the velocity fluctuations in the central region of the stenosis model is observed (Fig. 4a). As shown in Fig. 4b, the translation from laminar to turbulent flow (where vorticity contour becomes thicker) is delayed from X/D ¼2 to 3 to X/D ¼3 to 4 when L decreases from 10 D to 6 D.
Please cite this article as: Huh, H.K., et al., Flow characteristics around proximal and distal stenoses in a series of tandem stenosed vessels. Journal of Biomechanics (2016), http://dx.doi.org/10.1016/j.jbiomech.2016.07.014i
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Fig. 4. (a) Contours of rms values of velocity fluctuations in the P50_D50 model with three different interspacing distances of L ¼ 3D, 6D and 10D at a flow rate of Q ¼1.0 L/min. (b) Mean vorticity contours in the P50_D50 model with L ¼ 3D and 6D at a flow rate of Q¼ 1.0 L/min. (c) Comparison of recirculation zone length for three interspacing distances of L ¼ 3D, 6D and 10D at a flow rate of Q¼ 1.0 L/min. The crest of the proximal stenosis is located at X/D¼ 0.
The statistically averaged length of the recirculation zone between stenoses (S ¼50%) is approximately 25 mm in the case of L¼ 3 D and is increased (p o0.01) to 30 and 40 mm when the distance is L ¼10 and 6 D, respectively at Q¼ 1.0 L/min (Fig. 4c). The turbulence intensity Urms/Umean of P50_D50 tandem model at Q¼0.25 L/min remains low under 3% regardless of the interspacing distance L (Fig. 5a). When Q¼0.5 L/min, the turbulence intensity for the case of L¼3 D is kept under 3% and increases up to 18% and 10% for the cases of L ¼10 and 6 D, respectively. The peak location in the turbulence intensity profile is shifted toward the downstream from X/D ¼3 to 5 as the L decreases from 10 D to 6 D (Fig. 5b). When Q¼ 1.0 L/min, the magnitude of the peak turbulence intensity for L ¼6 D increases up to 17%, whereas that for the L¼ 10 D case is maintained at 18%. The peak location is shifted upstream to X/D ¼2.5 and 3.5 for the case of L ¼10 and 6D, respectively. The turbulence intensity is kept low under 3% for the flow in the region behind the proximal stenosis with the smallest interspacing distance of L¼ 3 D. 3.1.2. Effect of severity The flow behind the proximal stenosis with S¼ 75% (P75_D50) exhibits similar flow characteristics as a result for the P50_D50 model at increased flow rate condition. The severity of the distal stenosis presents negligible influence on the flow characteristics behind the proximal stenosis. Detailed flow characteristics and explanations are presented in Supplementary S4. 3.2. Flow characteristics behind the distal stenosis 3.2.1. Effect of interspacing distance The centerline velocity at the crest of the distal stenosis (P50_D75) is the highest when L ¼3 D at Q¼ 0.25 L/min. It decreases as the L increases as shown in Fig. 6a. Lengths of jet core and the recirculation zone behind the distal stenosis decrease as the interspacing distance L increases (Fig. 6b). This inverse proportional relation also occurs at the increased flow rate of 0.5 L/min in distal stenosis with severity S ¼50% (Supplementary S4). When the flow rate Q¼1.0 L/min, the flow behind the distal stenosis is oppositely affected (proportional) by the interspacing distance L(Fig. 6c). Region of high-velocity fluctuations is shifted upstream and the length of recirculation zone is decreased at postdistal stenosis region of P50_D50 model as the interspacing distance L is shortened to 3 D. However, when the severity of the distal
stenosis is 75%, neither velocity fluctuations nor the size of the recirculation zone are affected by the interspacing distance L. 3.2.2. Effect of severity Relation between jet core length and interspacing distance is proportional when proximal stenosis severity is 75% and Q4 0.5 L/ min (Fig. 7). The area of high-vorticity values decreases as the distance L decreases. The flow entering the distal stenosis with L¼3 D and Q¼0.5 L/min presents a large velocity gradient (Fig. 7a). As a result, the flow passing through the crest of the distal stenosis is strongly center-focused compared with L ¼6 or 10 D. The flow entering the distal stenosis with L ¼3 D also presents high-velocity gradient when Q¼1.0 L/min (Fig. 7b). The spatial distributions of velocity fluctuations in the P50_D50 and P75_D50 models with L¼ 3 D at Q¼0.5 L/min are compared in Fig. 7c. High-velocity fluctuations from P75 increase the centerline velocity fluctuations at the crest of the distal stenosis by five times higher than those of P50 case. The effect of the proximal severity of the proximal stenosis on the flow behind the distal stenosis is demonstrated in the vorticity contours (Supplementary movie 1). Supplementary material related to this article can be found online at http://dx.doi.org/10.1016/j.jbiomech.2016.07.014. The flow behind the stenosis with S ¼75% is highly disturbed in the near downstream region of X/D¼0.5 to 2.0, regardless of the sequential arrangement (Fig. 8a). Highly disturbed flow behind the P75 stenosis enhances the disturbance of the flow behind the distal stenosis D50. As a result, velocity fluctuations Urms are increased up to 160 mm/s. By contrast, the velocity fluctuations of the flow behind the proximal stenosis P50 are smaller than 100 mm/s. Supplementary movie 2 shows different velocity fluctuations behind stenosis with S ¼50%. The pressure drop difference is nearly 400 Pa for the case of L ¼3 D and less than 60 Pa for L ¼6 and 10 D (Fig. 8b). The pressure drop in the P50_D75 tandem stenosis model is generally greater than that in the P75_D50 model. Supplementary material related to this article can be found online at http://dx.doi.org/10.1016/j.jbiomech.2016.07.014.
4. Discussion The flow rates selected in current study are Q¼0.25, 0.5, 1 L/ min, corresponding to the minimum, average, and maximum flow rates in the common carotid artery of normal humans (Holdsworth et al., 1999). Corresponding Reynolds numbers of Re¼187,
Please cite this article as: Huh, H.K., et al., Flow characteristics around proximal and distal stenoses in a series of tandem stenosed vessels. Journal of Biomechanics (2016), http://dx.doi.org/10.1016/j.jbiomech.2016.07.014i
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Fig. 5. The effect of interspacing distance on the turbulent intensity distribution of centerline velocity in the P50_D50 model at three flow rates of (a) 0.25, (b) 0.5 and (c) 1.0 L/min. The crest of the proximal stenosis is located at X/D ¼ 0.
375, 750 represent the laminar, transitional, and turbulent flow behind a stenosis with 50% severity, respectively. Recr decreases as the severity of the stenosis increases, indicating the earlier occurrence of turbulence behind the severe stenosis at a higher Re number flow. The size of recirculation zone formed behind the proximal stenosis is suppressed when the distance L is shorter than the length of the recirculation zone behind a single stenosis (Figs. 2a and 4c). As the interspacing distance L decreases, the distal stenosis is exposed to low and oscillatory wall shear stresses, which can cause the outbreak and growth of stenosis (Myers et al., 2001).
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Fig. 6. (a) Effect of interspacing distance L ¼ 3D, 6D and 10D on the centerline velocity distribution in the P50_D75 model at three flow rates of Q¼ 0.25 L/min. The crest of the proximal stenosis is located at X/D ¼ 0. (b) Comparison of mean velocity fields in the P50_D75 models with interspacing distances L ¼3D, 6D and 10D at a flow rate of Q¼ 0.5 L/min. (c) Comparison of velocity fluctuations of flow behind the distal stenosis of P50_D50 (left) and P50_D75 (right) models at a flow rate of Q ¼1.0 L/ min. Each arrow indicates the end of flow separation region extracted based on stream lines. The crest of the distal stenosis is located at X/D ¼ 0.
In the present study (Re 750), a recirculation flow is formed between the proximal and distal stenosis, causing low and negative wall shear stress as shown in Fig. 9a. The existence of low wall shear stress region in between proximal and distal stenoses may promote atherosclerotic growth, leading to the merge of adjacent stenoses. The suppressed recirculation zone occupies region between the proximal and distal stenoses when interspacing distance L¼ 3 D. In this case, either flow separation (recirculation zone length for
Please cite this article as: Huh, H.K., et al., Flow characteristics around proximal and distal stenoses in a series of tandem stenosed vessels. Journal of Biomechanics (2016), http://dx.doi.org/10.1016/j.jbiomech.2016.07.014i
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Fig. 8. (a) Contours of velocity fluctuations in the P75_D50 (upper) and P50_D75 (lower) models with L ¼3D at a flow rate of Q¼ 1.0 L/min. The crest of the proximal stenosis is located at X/D ¼0. (b) Pressure difference between the P75_D50 and P50_D75 models according to the interspacing distance. (c) Comparison of vertical velocity fluctuation in the distal stenosis of P50_D50, P75_D50 and P50_D75 models at different flow rates of Q¼ 0.25, 0.5 and 1.0 L/min.
Fig. 7. Spatial distributions of vorticity field behind the distal stenosis of P75_D50 models with different interspacing distances of L ¼3D, 6D and 10D at flow rates of (a) 0.5 and (b) 1.0 L/min. (c) Comparision of velocity fluctuations in the P50_D50 (upper) and P50_D75 (lower) models with L ¼ 3D at a flow rate of Q ¼0.5 L/min. The crest of the proximal stenosis is located at X/D ¼ 0.
L¼ 10, D4 3 D) or eddy formation (recirculation zone length for L¼ 3 to 10 D) occurs in the frontal neck of the distal stenosis. As a result, the center-focused flow enters the distal stenosis. The flow velocity in the central region of the vessel should increase to compensate for the opposite directional flow, that is, the recirculating flow for a fixed flow rate. The centerline velocity uc in the distal stenosis is approximately 10–15% higher than that of the proximal stenosis of same severity (Fig. 3). These results are well matched with the simulation results of Banerjee et al. (2008). The severity of the distal stenosis can be clinically overestimated by increased maximum centerline velocity obtained in the ultrasound diagnosis when two stenoses are in close proximity (Bertolotti et al., 2006). In this case, other supplementary diagnosis devices, such as angiography or fractional flow reserve, are required. The flow in the region between the proximal and distal stenoses is more stable as the interspacing distance L decreases. As shown in Fig. 5, the centerline turbulence intensity in the P50_D50 model is maintained at o3% (laminar flow), regardless of the flow rate. The laminar-to-turbulent transition is prolonged in the model with L ¼6 D compared with 10 D (Fig. 4a and b). Forward shifted
re-laminarization is induced by faster mixing and re-distribution of flow momentum. Hence, prolonged laminar to turbulent transition indicates that the flow becomes more stable. This inverse proportional relationship is observed for the case of Re4Recr, regardless of the severity of the stenosis (S.3). However, as the severity and flow rate increase, laminar-to-turbulent transition is identical, regardless of the interspacing distance. This finding indicates that Re 750 is an upper limit of the laminar-toturbulent transition shortening behind the stenosis with S ¼75%. The numerical simulation of Lee et al. (2003) exhibited similar results in the region behind the stenosis with 50% severity at Re4 1000. As the interspacing distance decreases, the flow characteristics behind the distal stenosis are increasingly affected by the flow behind the proximal stenosis. When the flow in the middle section between the proximal and distal stenoses is stable (P50_D50 and P50_D75 at Q¼ 0.25 and 0.5 L/min, P75_D50 at Q¼0.25 L/min), the increased centerline velocity in the crest of the distal stenosis increases the length of jet core and recirculation zone formed behind the distal stenosis (Fig. 8c). The flows behind the distal stenosis are also more stable in the model with L ¼3 D than with 10 D (Figs. 6a, b, and S4). This is because the center-focused inlet flow decreases the pressure drop in the middle section between the two stenoses, which increases the discharge coefficient (Reader-Harris, 2015). On the contrary, jet length and interspacing distance shows proportional relation when Re4Recr (P50_D50 and P50_D75 at Q¼1.0 L/min, P75_D50 at Q¼0.5 L/min). It is because more energy is
Please cite this article as: Huh, H.K., et al., Flow characteristics around proximal and distal stenoses in a series of tandem stenosed vessels. Journal of Biomechanics (2016), http://dx.doi.org/10.1016/j.jbiomech.2016.07.014i
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proximal stenosis. This indicates that the proximal stenosis plays a role to protect the distal stenosis from direct exposure to the high wall shear stress. Li et al. (2010) reported similar numerical simulation results on this phenomena. This indicates the importance of the geometry of the proximal stenosis post-repair, and suggests that great care should be taken during surgical operation to avoid creation of a new high wall shear stress region on the distal stenosis. The PIV measurements of flow in the tandem stenosis model with varying flow rates, interspacing distances, and severities provide essential flow characteristics in the middle section between the two stenoses and downstream of the distal stenosis. Further in-depth research about the 3D flow structures under pulsatile inlet conditions is required to correlate the flow characteristics in the tandem stenosis with biomedical diagnoses and clinical treatments.
5. Conclusions
Fig. 9. (a) Wall shear stress of P50_D50 model with L ¼3D at a flow rate of Q¼ 1.0 L/ min. Solid line indicates zero wall shear stress. (b) Wall shear stress of P50_D75 and P50_D75 models with L ¼ 3D at a flow rate of Q ¼1.0 L/min. The crest of the proximal stenosis is located at X/D¼ 0.
required to move the asymmetric flows compared with the symmetric flows (Reader-Harris, 2015) through the distal stenosis. One may conclude that the turbulent inlet flow can give rise to a highly turbulent flow behind the distal stenosis (Supplementary movie 2). In addition, the transition from laminar to turbulent flow behind the P75 stenosis is identical, regardless of the interspacing distance at a high flow rate of Q¼1.0 L/min (Fig. 6c). These findings are well matched with the numerical simulation results of Lee et al. (2003). The present experimental results on the velocity fields and pressure drop in the tandem stenoses confirm the hypothesis of Dodds and Phillips (2003) that the sequential order of the stenoses exerts a noticeable effect on the pressure drop. The flow behind a stenosis of 50% severity is stable when located in front of the stenosis with 75% severity. However, the flows become unstable behind stenosis of S ¼50% when their orders are opposite (Fig. 8a). The viscous dissipation of kinetic energy is significant when the flow is turbulent. Therefore, the pressure drop in the P75_D50 model is significant compared with the tandem stenosis model of P50_D75 (Fig. 8b). In the view point of reducing the recirculation zone, the proximal stenosis with a high-severity is more preferred. However, in the clinical point of view, the increased pressure drop may induce overload to the heart. The maximum wall shear stress in the proximal stenosis with S ¼75% is around 8 Pa s. However, the peak wall shear stress drops to 5 Pa s in the region behind the
In this study, the effects of three different flow rates (laminar, transitional, and turbulent), three interspacing distances (3, 6, and 10 D) and two severities (50% and 75%) on the flow characteristics in tandem stenosis are experimentally investigated. As the interspacing distance decreases, flows in the middle section between the proximal and distal stenoses are stabilized until the Reynolds number Re reaches the upper limit. The transition from laminar to turbulent flow is prolonged when Re4Recr. The length of the recirculation zone is restricted by the presence of distal stenosis, and flow separation occurs at the frontal neck of the distal stenosis. The flows are focused in the central region of the conduit as the recirculation flow occupies the unstenosed area. As a result, the centerline velocity at the crest of the distal stenosis is approximately 10–15% higher than that of the proximal stenosis under the same severity. This phenomenon may cause overestimation of the severity of the distal stenosis in clinical diagnosis. Furthermore, the low wall shear stress region in between the proximal and distal stenoses may promote atherosclerotic growth or merging of adjacent stenoses. The flow behind the distal stenosis is solely affected by the flow characteristics behind the proximal stenosis. When the inlet flow is a center-focused laminar flow, the lengths of the recirculation zone and jet core region increase as the interspacing distance decreases. When the inlet flow is turbulent, the transition from laminar to turbulent flow occurs earlier as the interspacing distance is shorter. As the perturbation in the proximal stenosis strongly influences the flow around the distal stenosis, the pressure drop in the tandem stenosis models depends on the sequential arrangement of severity. Severe stenosis in the upstream increases the pressure drop by 20% compared with that located in the downstream distal stenosis.
Conflict of interest None declared.
Funding This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2008-0061991).
Please cite this article as: Huh, H.K., et al., Flow characteristics around proximal and distal stenoses in a series of tandem stenosed vessels. Journal of Biomechanics (2016), http://dx.doi.org/10.1016/j.jbiomech.2016.07.014i
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Acknowledgment We thank for the support of the NRF of Korea through the Creative Research Initiatives program.
Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.jbiomech.2016.07.014.
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Please cite this article as: Huh, H.K., et al., Flow characteristics around proximal and distal stenoses in a series of tandem stenosed vessels. Journal of Biomechanics (2016), http://dx.doi.org/10.1016/j.jbiomech.2016.07.014i