flow dynamics and wall shear stress downstream of a...

17th International Symposium on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 07-10 July, 2014

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Flow dynamics and wall shear stress downstream of a stenosis in a

compliant blood vessel

Patrick H. Geoghegan1,*, Mark C. Jermy1

1: Department of Mechanical Engineering, University of Canterbury, Christchurch, New Zealand

* correspondent author: [email protected] Abstract Atherosclerosis is a vascular disease, which causes a remodelling of the arterial wall leading to restriction (stenosis) by thickening of the intima and the formation of vascular plaque through the deposition of fatty materials. This remodelling alters the compliance of the artery stiffening the arterial wall locally. A common location for this to occur is in the carotid artery, which supplies blood to both the brain and the face. It can lead to complete occlusion of the artery in the extreme case and is a major cause of stroke and ischemic infarction. Stroke is the third largest cause of death in the U.S.A., but even if not fatal it can cause coma, paralysis, speech problems and dementia. Atherosclerosis causes a change in the local hemodynamics. It can produce areas of flow separation and low wall shear stress (WSS), which can lead to endothelial dysfunction and to promotion of plaque growth. Several investigations have been made numerically into stenosed arterial geometries with rigid walls and some work modelling the fluid structure interaction (FSI) in compliant geometries. Although there is some experimental work available in compliant geometries representing stenosis, further work needs to be done to provide data that can be used to validate computational results. In this work particle image velocimetry (PIV) is used to investigate the flow field and WSS through, and downstream of, a 3.2 times life size compliant silicone phantom of a stenosed common carotid artery. Comparisons are also made with results obtained in a compliant phantom of a healthy artery. A healthy geometry is shown to have a peak WSS of 1.4Pa. At the throat of the stenosis peak WSS is shown to increase to 33.29Pa. The jet exiting the stenosis is shown to interact with a surrounding reverse flow region occurring downstream from the stenosis throat. This causes a breakdown of the flow during the cardiac cycle, which leads to minimum WSS of -1.75Pa being observed. These events will have a detrimental impact on the endothelial cell structure in the arterial lumen. 1. Introduction Atherosclerosis is caused by the formation of atherosclerotic plaque, which causes a progressive constriction of the arterial wall. Atherosclerosis is most serious when it affects the carotid or coronary arteries. In the carotid artery, it can lead to stroke, the third largest cause of death and the largest cause of long-term disability in the western world. In the coronary artery it causes coronary heart disease (CHD) which causes 650 000 fatalities a year in the U.S.A alone (Mautner et al. 1994). It can produce areas of flow separation and low wall shear stress, which can lead to endothelial dysfunction and to promotion of plaque growth. Wall shear stress (WSS) is a major influence on the structure of the endothelium (Traub and Berk 1998; Chatzizisis et al. 2007). In the main vasculature, in regions void of arterial geometry change, the arterial vessel diameter changes to maintain a normal physiological WSS ~1-2Pa (Traub and Berk 1998). A long-term increase in WSS experienced in an artery results in vasodilation followed by a remodelling of the artery to a larger diameter with the same arterial structure. A low WSS causes a thickening of the intimal layer (producing a stenosis) to re-establish a normal WSS (Ku 1997). In-vitro modelling with artificial flow phantoms allows the fluid mechanics of the circulatory system to be studied without the ethical and safety issues associated with animal and human experiments. Extensive work has been performed using both experimental and computational techniques to study rigid models representing the arterial system. Computational methods, in which the equations governing the flow and the elastic walls are coupled, are maturing. There is a lack of experimental data in compliant arterial systems to validate the numerical predictions. Previous work in a compliant model representing a symmetric stenosis in the common carotid artery (CCA) (Geoghegan et al. 2013, 2012a) has shown Kelvin–Helmholtz instabilities to occur in the shear layer between the main jet exiting the stenosis and the reverse flow region surrounding it between 0–2.5 D (where D=unstenosed diameter) longitudinally downstream from the


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stenosis exit. The instability had an axis-symmetric nature, but as peak flow rate was approached this symmetry breaks down producing instability in the flow field. The present work determines the effect of this instability further downstream from the stenosis exit (>2.5 D) in the same symmetric stenosed compliant model. A comparison is also made with data taken from a geometry representing a healthy artery 2. Experimental Methodology The thin walled stenosed compliant flow phantom (Fig. 1) was produced by the method developed in (Geoghegan et al. 2012b) and was constructed at a scale of 3.2 times life size from silicone (Dow Corning Sylgard 184) (A phantom of a healthy CCA was also produced using the same technique (Fig. 1)). The phantom internal geometry and the region of interest (ROI) studied is shown in Fig. 2. The stenosis had a restriction of 50 % by diameter and was 40mm in length with two-dimensional coordinates described by Eq. 1. The phantom had an unstenosed wall thickness (h) of 1.28±0.05 mm, which was selected to ensure that distensibility (compliance) in the phantom (in vitro) was equivalent to the human CA (in vivo) (Eq. 2 (Caro et al. 1978)). The phantom had a length of 330 mm. The Young’s modulus (E) of the compliant flow phantom, measured at 1.32x106 N/m2. To calculate the length of model required for an accurate analysis of the effect of compliance the ratio of length of model (Linvitro) to propagation wavelength (λinvitro) had to be matched to in vivo values (Eq. 3). Tab. 1 provides an overview of both the properties of the CCA and the compliant flow phantom.

Fig. 1 (top left) silicone phantom representing a stenosed carotid artery (top right) magnified view of the symmetric

stenosis region (bottom) healthy phantom geometry

Fig. 2 Schematic of flow phantom internal geometry and location of camera 1 region of interest (ROI 1) and camera 2

region of interest (ROI 2) y=2.5cos π

20x (1)

d= 1A∆A∆p= 1E h D

(2) Linvitroλinvitro

= Linvivoλinvivo

(3)


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Property CCA Healthy Flow Phantom Stenosed Flow Phantom Wall Thickness (m) 0.000617 0.00128 0.00128 Internal Diameter (m) 0.0062 0.02 0.02 Density(blood, glycerol) (kg/m3) 1060 1140 1140 Young’s Modulus (N/m2) 776 000 1 320 000 1 320 000 Time Period Oscillation (s) 1 2.92 2.92 Propagation wavelength (m) 8.25 27.26 27.26 Length (m) 0.1 0.21 0.33 Symmetric Stenosis (% by diameter) N/A N/A 50%

Tab. 1 Typical CCA (Buchmann 2010; Riley et al. 1992) and flow phantom properties A schematic of the flow circuit used during the experiments is shown in Fig. 3. The compliant phantom was placed in an external bath (g) that was pressurised using a pressure control tank (h). A physiological flow wave was produced by means of a piston pump driven by a stepper motor attached to a ball screw (a). An in-house National Instruments LabVIEW code controlled the piston system with an electromagnetic flow meter (d) (Krohne Optiflux 1300) providing a real-time feedback of flow rate to the CPU. Pressure upstream and downstream of the compliant phantom was recorded using strain gauge pressure transducers (c). A honeycomb flow straightener in a settling chamber (b) was located 75 L/D upstream and downstream of the flow phantom to ensure a symmetric Poiseuille flow profile entering the phantom (Durst et al. 2005). The fluid in the system and external bath was an aqueous glycerine solution of 39:61, by weight, which provided a refractive index that matched the silicone phantom (n=1.141) (more details on the refractive index matching procedure can be found in Geoghegan et al. (2012b)). It had a kinematic viscosity (ν) of 10.2×10-

6m2/s and a density (ρ) of 1150 kg/m3 (1. 15 g/cm3) at 20°C. The transmural pressure was set to 19.09 kPa. The fluid was seeded with nominally neutrally buoyant 10 µm hollow silver-coated glass spheres (density 1.1 g/cm3).

Fig. 3 Schematic view of experimental setup (a) piston pump (b) flow straightener (c) electromagnetic flow meter (d)

laser and optics (e) camera (f) flow phantom inside external bath (g) pressure control tank (h) exit tank with weir The physiological flow wave was obtained from phase contrast magnetic resonance imaging (MRI) measurements of the time dependent in-vivo flow rate in the CCA of a healthy male volunteer (Buchmann and Jermy 2010) with maximum, minimum and mean Re of 939, 379 and 632, respectively and a Womersley number (α) of 4.54 (Fig. 4). The working fluid and pressure box fluid are an aqueous glycerine solution of 39:61, which is refractive matched to the silicone material to reduce optical distortion from wall curvatures.

a

b c

d

e

f

g

h

b


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Fig. 4 In vivo (•-) scaled carotid artery and phase averaged in vitro (-) inlet physiological flow waveform. Specific

datapoints of interest have been numbered for convenience Each ROI was recorded using a Dantec Flowsense 2MP camera with a CCD array of 1608×1208 pixel2. The 60 mm Nikon lens had an aperture size set to f/8 and a magnification of 0.2 to 0.15. This gives an estimated depth of field of 3 to 4.9 mm and a diffraction limited particle size of 12.5 to 11.9 µm. The flow was illuminated with a 40 mm high, 0.5 mm thick light sheet from a New Wave Solo 120 XT laser with a wavelength of 532 nm at 120 mJ/pulse using a series of spherical and cylindrical lenses. The PIV measurements were phase locked, recording 22 image pairs per waveform over 50 waveforms. For time oscillating flow waves, the laser pulse time delay selection is a compromise due to the difference in maximum pixel displacement for maximum and minimum flow rate. For this analysis a time delay of 650 µs was selected, which produced <3% invalid vectors at each phase. After minimum background subtraction, intensity normalisation and masking, the images were processed with an in-house code implementing 2D FFT cross-correlation (Buchmann and Jermy 2007) with iterative window sizing and displacement. The data was validated using the signal-to-mean ratio filter and normalised median test (Westerweel and Scarano 2005). WSS was calculated using the iPIV technique developed by Buchmann et al. (2009). To provide physiological relevance all velocities and WSS (τw) data in this section are in vivo scaled through Reynolds scaling using Eq. 4 and Eq. 5 respectively, with µ representing the dynamic viscosity, ρ the density, and 3.2 is the scale factor between in vitro and in vivo phantom diameter. Data on the time averaged wall shear stress (TAWSS) is also presented, which over the course of one cardiac cycle is calculated by Eq. 6. U t invivo=3.2

vinvivovinvitro

U t invitro (4)

τw,invivo=ρinvivoρinvitro

µinvivoµinvitro

3.22τw,invitro (5)

TAWSS= 1τ

τwdττ0 (6)

3. Results Fig. 5 shows an example of the instantaneous velocity vectors superimposed on a colour-contour plot of the absolute velocity (Uabs) in m/s for ROI 2, Fig. 6 shows the corresponding plot for ROI 3 at selected point in the flow waveform. The high velocity jet exiting the stenosis as previously discussed in Geoghegan et al. (2013) is shown to interact with the low velocity reverse flow region surrounding it. As flow rate increases, Kelvin-Helmholtz vortices occur between the two regions as peak flow rate is approached these vortices cause a breakdown in the flow. In Fig. 5-3 this can be seen to start to occur from x/D=2.25 onwards and completely break down when 3.25 ≤ x/D (Fig. 6-3). in previous rigid wall experiments (Vétel et al. 2008) this breakdown is shown to start occurring when 3 ≤ x/D. This suggests that the breakdown is delayed by the compliance of the flexible walls. The breakdown causes a significant reduction in velocity across the arterial diameter and a mixing of the high velocity jet and the low velocity reverse flow region surrounding it. It

1

2 3

4


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also causes a severe change in velocity magnitude between 2.75≤ x/D≤6.

Fig. 5 Instantaneous absolute velocity fields (Uabs m/s) and velocity vectors in ROI 1 at data points shown in Fig. 4

1

2

3

4


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Fig. 6 Instantaneous absolute velocity fields (Uabs m/s) and velocity vectors in ROI 1 at data points shown in Fig. 4

1

2

3

4


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The WSS experienced in a stenosed geometry is drastically different from that of a healthy artery. Fig. 7 presents the temporal evolution of the WSS observed in the healthy geometry phantom. Data is taken from a single point on the artery wall (x/D = 0.25) as the WSS varied minimally along the geometry. The maximum, minimum and TAWSS was 1.4, 0.58 and 0.84 Pa respectively. Fig. 8 presents the temporal evolution of the WSS between -1.1≤x/D≤1.1 (ROI 1) and the TAWSS for the stenosed geometry. Results are presented for one wall only as there was minimal difference between the results obtained on opposite surfaces. The peak WSS occurs just before the stenosis throat at x/D= -0.1. Between 0.1≤x/D≤0.75 there is also a region of negative WSS that lasts for nearly the entire cardiac cycle; this is caused by the reverse flow observed in the recirculation region. Peak WSS rises between -1.0≤x/D≤-0.1, to a value of 33.39 Pa, this drops to 29.51 Pa at the stenosis throat (x/D=0). On the downstream wall of the stenosis WSS is shown to reduce to -0.71 Pa at x/D=0.5 then increases to -0.17 Pa at x/D=1. When comparing the maximum, minimum and time-averaged WSS magnitude observed in a straight tube phantom it can be seen that the acceleration of flow caused by the reduction in diameter, severely increases the WSS along the upstream wall of the stenosis which can lead to endothelial cell erosion (Cao and Rittgers 1998). Downstream of the stenosis throat there is a reduction from the WSS values observed in a healthy arterial geometry.

Fig. 7 Temporal evolution of the WSS in the healthy geometry phantom (red) at x/D = 0.25

Fig. 8 (left) temporal evolution of the WSS through the restriction (ROI 1) of the stenosed phantom (--) represents a

region of negative WSS (right) TAWSS along the wall of the symmetric phantom.

-1 -0.5 0 0.5 1

0

5

10

15

x/D

TAW

SS

(Pa)


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Fig. 9 presents the temporal evolution of the WSS between 2.75≤x/D≤6.25 (ROI 3) and the TAWSS for the stenosed geometry. This area is where the complete breakdown of the flow occurred due to the Kelvin-Helmholtz vortices that occurred (Fig. 6). This breakdown in the flow drastically affects the WSS compared to a healthy geometry with the introduction of a negative WSS. Between 2.75≤x/D≤4 the TAWSS≤0, it can be seen in the temporal evolution of the WSS that the WSS is below zero for nearly the entire cardiac cycle reaching a minimum of -1.75 Pa. This can lead to a reorientation of the endothelial cells affect nutrient transport through the artery. For the entire region (2.75≤x/D≤6.25) the TAWSS is less than 1 Pa which as discussed before can lead to a thickening of the intimal layer of the artery.

Fig. 9 (left) Temporal evolution of the WSS in ROI 3 of the stenosed phantom (--) represents a region of negative WSS

(right) TAWSS along the wall in ROI 3. 4. Conclusions This study has shown that the introduction of a stenosis in an arterial geometry has a major effect on the flow field and WSS experienced within the arterial lumen. A complete breakdown in the flow field is shown to occur from 2.25≤x/D. This is caused by the interaction of the jet exiting the stenosis and a surrounding reverse flow region. In the stenosis region, WSS is shown to increase from 1.4 Pa observed in a healthy geometry to 33.29 Pa, which can lead to endothelial cell erosion. Downstream from the region where flow field breakdown occurs 2.75≤x/D≤6.25, WSS is observed to reduce drastically, reaching a minimum of -1.75 Pa. This can lead to thickening of the intimal layer, and cell reorientation where the magnitude of WSS is <~1 Pa. Future work will investigate further, how the flexibility of the arterial walls influences breakdown behaviour and alters the wall shear stress experienced downstream from the stenosis exit. Further investigation will be made into the effect the rate of change of flow rate (acceleration of the flow) has on the velocity field, on the duration of the instability, and on the time at which laminar flow is re-established. 5. References Buchmann N (2010) Development of Particle Image Velocimetry for In Vitro Studies of Arterial

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Buchmann NA, Jermy MC Transient Flow and Shear Stress Measurements in an anatomical Model of the Human Carotid Artery In: 15th International Symposium of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 5th-8th July 2010.


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