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Int. J. Experimental and Computational Biomechanics, Vol. 1, No. 2, 2009

Experimental investigation of carotid artery haemodynamics in an anatomically realistic model Nicolas A. Buchmann* and Mark C. Jermy Centre for Bioengineering, Department of Mechanical Engineering, University of Canterbury, Christchurch 8140, New Zealand E-mail: [email protected] E-mail: [email protected] *Corresponding author

Chuong V. Nguyen Department of Mechanical and Aerospace Engineering, Monash University, Victoria 3800, Australia E-mail: [email protected] Abstract: Fluid mechanic forces play a key role in the early development and progression of cardiovascular diseases, which predominantly occurs in areas of disturbed flow and low wall shear stress (WSS). In the present study, we perform particle image velocimetry (PIV) measurements in an anatomically realistic transparent flow phantom of a human carotid artery. Steady blood flow conditions are simulated and a novel interfacial PIV technique (iPIV) is introduced to measure WSS with increased spatial resolution and accuracy compared to conventional methods. The branching of the carotid artery introduces significant secondary flow motion with flow separation and reversal only occurring in the external carotid artery. Wall shear stress is measured along the inner and outer vessel walls and is on average higher in the internal carotid and lower in the external carotid artery. Furthermore, results are compared to those in a geometrical idealised model and with previously published WSS data. Keywords: wall shear stress; WSS; particle image velocimetry; PIV; carotid artery; haemodynamic; patient specific; experimental bimechanics. Reference to this paper should be made as follows: Buchmann, N.A., Jermy, M.C. and Nguyen, C.V. (2009) ‘Experimental investigation of carotid artery haemodynamics in an anatomically realistic model’, Int. J. Experimental and Computational Biomechanics, Vol. 1, No. 2, pp.172–192. Biographical notes: Nicolas A. Buchmann received his MSc in Mechanical Engineering from Darmstadt University of Technology, Germany. He is currently a PhD candidate in the Centre for Bioengineering at the Department of Mechanical Engineering, University of Canterbury, New Zealand. Mark C. Jermy received his PhD in 1997 from the University of Kent, UK. He currently holds a position as a Senior Lecturer at the Department of Mechanical Engineering, University of Canterbury, NZ. Copyright © 2009 Inderscience Enterprises Ltd.

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Chuong V. Nguyen received his MSc in Civil and Environmental Engineering from Ritsumeikan University, Japan. Currently, he is a PhD candidate at Monash University, Australia.

1

Introduction

Atherosclerosis is a systemic proliferation and inflammatory vascular disease, which leads to arterial wall remodelling and narrowing (stenosis) due to intima thickening and vascular plaque formation. In its most severe form, atherosclerosis can lead to complete vessel occlusion through thrombosis and is a major cause of stroke and ischemic infarction. The causative factors that contribute to the formation of atherosclerosis have been studied extensively (Caro et al., 1971; Ku et al., 1985b; Zarins et al., 1983) and haemodynamic factors are identified as an important determinant in the localised development of atherosclerosis and vascular plaques. The pathology of atherosclerosis is complex, involving the endothelial cells and vascular smooth muscle layer and their response to low and oscillating wall shear stress (WSS), flow separation and departure from unidirectional flow (Chatzizisis et al., 2007; Traub and Berk, 1998). One of the predominant sites of chronic atherosclerotic lesion formation is the carotid artery. The most important haemodynamic phenomena are observed where the vessel branches into the internal carotid artery (ICA) and external carotid artery (ECA) and the carotid sinus. The vessel wall has strong curvatures in these areas and a transverse pressure gradient develops due to centrifugal forces, which in turn favours flow separation, secondary flow vorticity and spatially and temporally varying WSS. Experimental studies by Zarins et al. (1983) demonstrated that atherosclerosis in the carotid artery strongly correlates with the haemodynamic environment. To characterise such complex flows and their interaction with the vessel wall and relation to atherosclerosis, various experimental and computational methods are available for diagnosis and treatment (Taylor and Draney, 2004). Modern non-invasive techniques capable of measuring in-vivo blood flow include Doppler and ultrasound-based techniques (Vennemann et al., 2007) as well as echo particle image velocimetry (Kim et al., 2004). Techniques such as magnetic resonance imaging (MRI) or computed tomography (CT) provide high-resolution data of the arterial geometry and the three-dimensional velocity field can be measured with phase contrast MRI. A review of recent MRI velocimetry techniques in physiology and engineering is given by Elkins and Alley (2007). The complex flow pattern within the carotid artery is rather difficult to observe and spatial and temporal resolution in MRI are relatively coarse. This permits only a qualitative comparison with other measurement techniques (Botnar et al., 2000; Marshall et al., 2004) and numerical and experimental in-vitro techniques are used for a more detailed haemodynamic study. Due to its flexibility and ability to provide complete three-dimensional data, numerical approaches are widely used for the study of carotid artery haemodynamics (Botnar et al., 2000; Perktold and Resch, 1990; Rindt et al., 1990) and to investigate the effects of non-Newtonian behaviour (Perktold et al., 1991a, 1991b) and distensible walls (Karner et al., 1999; Zhao et al., 2000) to model more physiologically realistic flow conditions. Both Newtonian flow (Gijsen et al., 1999; Perktold et al., 1991b) and

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rigid-wall (Karner et al., 1999) assumptions are now widely used for the carotid artery bifurcation. Furthermore, numerical approaches readily facilitate haemodynamic studies in diseased carotid artery bifurcations with varying degrees of stenosis such as presented by Lovald et al. (2009). The advantage of numerical models is the accessibility of the full three-dimensional flow field, WSS and spatial and temporal gradients as well as the choice of complex geometries and fluid-structure coupling. Laminar flow predominates in the healthy carotid artery, but in cases of complex or diseased geometries, flow can become unstable or undergo transition to low Reynolds number turbulence. In recent direct numerical simulations in carotid bifurcation models, Fischer et al. (2007) reported the formation of time-dependent small-scale turbulent structures and vortex shedding. Early experimental work used flow visualisation techniques (Motomiya and Karino, 1984; Zarins et al., 1983) and laser Doppler velocimetry (LDA) for quantitative measurements in idealised models (Ding et al., 2001; Gijsen et al., 1996; Ku et al., 1985a; Zarins et al., 1983). Idealised models of the carotid artery, however, represent only a population average and tend to omit interesting flow features observed in real arteries. The geometry of an individual carotid artery differs markedly from the population average (Ding et al., 2001; Thomas et al., 2005) and the local haemodynamic environment and plaque growth is influenced by the individual vessel geometry (i.e., ‘geometrical risk factors’) (Friedman et al., 1983; Nguyen et al., 2008; Perktold and Resch, 1990; Thomas et al., 2005). Detailed LDV measurements in such anatomically realistic geometries, reconstructed from post-mortem data were presented by Liepsch (2002) and Liepsch et al. (1998). Due to the pointwise nature of LDV measurements, the full three-dimensional (and instantaneous) velocity and WSS maps are difficult to obtain and can only be obtained with considerable experimental effort. An alternative is the whole field measurement technique, particle image velocimetry (PIV), which can provide velocity and WSS maps with high spatial and temporal resolution. Unlike in other physiological flow problems, the application of PIV to the carotid artery has received little attention in the past. Bale-Glickman et al. (2003) performed planar PIV measurements in adjacent planes in a diseased carotid bifurcation model, and most recently, Vétel et al. (2009) conducted stereoscopic PIV measurements in a physiologically realistic carotid artery. Both studies reported complex three-dimensional flow structures and onset of flow instabilities for higher physiological Reynolds numbers and steady flow. The derivation of WSS from PIV data has also been demonstrated by Zhang et al. (2008) for flow through a modelled anastomosis, yet to the best of the authors’ knowledge, no such studies exist for the carotid artery. In summary, high resolution measurements of the flow structure and WSS distribution in the carotid artery are necessary in the validation of numerical models and characterisation of flow instability and transition to turbulence. Due to the complex vascular geometry, the use of measuring techniques with high spatial resolution such as PIV is desirable. The objective of this work is to investigate haemodynamic factors in a physiological realistic carotid bifurcation model by means of planar PIV. The carotid artery geometry is obtained from MRI data and reproduced in a transparent flow phantom. In this paper, only steady flow conditions are considered as they are typical to patients with chronic heart failure with a rotary blood pump delivering continuous steady flow (Vétel et al., 2009). An overview of the model construction and experimental procedure is given in Section 2.

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The direct measurement of WSS is difficult in complex flows such as in the carotid artery and one method is to estimate its value from the velocity gradient near the wall. In principle, the PIV velocity fields can be differentiated to yield the field of velocity gradients. However, several sources of errors such as imaging errors (e.g., optical distortion, light reflections and low tracer density near the wall) and systematic errors (peak fitting algorithm, image interpolation, etc.) cause signal truncation and greatly affect the velocity estimation near stationary walls. These errors are further amplified when computing the velocity gradients and even in well-executed PIV experiments, a relatively low error can lead to substantial errors in the velocity derivatives (Luff et al., 1999). Accurate determination of differential quantities from DPIV data is crucial for an accurate haemodynamic assessment, and as such, some methods for overcoming these difficulties have been proposed previously (Karri et al., 2009; Luff et al., 1999; Theunissen et al., 2008). In this paper, we present the application of a new interfacial particle image velocimetry (iPIV) technique for WSS measurements in the carotid artery model. The technique estimates the velocity gradient directly from the recorded particle images without calculating the velocity field. Thus, the propagation of systematic PIV processing errors is avoided, which leads to increased measurement accuracy and data fidelity. A description of the iPIV technique relevant to the current work is given in Section 2.4. Results are presented in Section 3 in the form of velocity maps in the bifurcation plane and at several cross-sectional planes in the carotid sinus. WSS is measured along the inner and outer vessel walls and compared with previously published data. Finally, results are compared to an idealised model under similar flow conditions to contrast the effect of geometrical variation.

2

Method

2.1 Carotid artery geometry and flow phantom The geometry of the carotid bifurcation model was generated from MRI data of the left common carotid artery (CCA), ICA and ECA of a healthy male volunteer. The image slices were acquired on a GE MR scanner (3T, Signa) with a 2D time-of-flight sequence. A total of 84 parallel images were obtained with a slice spacing of 1.2 mm and an in-plane resolution of 0.47 mm. Details on the image segmentation and 3D lumen reconstruction can be found in Moore (2008). The resulting anatomically realistic carotid bifurcation geometry is shown in Figure 1. The surface exhibits true in-vivo characteristics and topological variations that lead to differences in cross-sectional areas and asymmetry. The geometry of the idealised carotid artery used for comparison is that of Buchmann and Jermy (2007). The model geometry was derived from population averaged data given by Ding et al. (2001) and reconstructed as a solid computer model. This idealised model geometry consists of circular cross-sections and is symmetric with regard to the plane of bifurcation. Compared with the idealised model, the physiological model exhibits some out-of-plane curvature, a smaller branching angle, a shorter carotid sinus and a more gradual tapering of the common carotid towards the bifurcation (i.e., bifurcation region). Both model geometries are illustrated in Figure 3 and a summary of the dimensions and flow parameters is given in Table 1.

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Figure 1

Reconstructed carotid artery geometry comprising the CCA, ICA and ECA, (a) coronal view (b) axial view

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Transparent silicone flow phantom of the anatomically realistic carotid artery bifurcation

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A physical prototype of both carotid bifurcation geometries was created in water-soluble plaster using rapid prototyping. The geometries were scaled to approximately 2.8 times life size, which allowed for a higher effective spatial resolution in the velocity and WSS measurements. The prototypes were then embedded in a clear silicone (Dow Corning, Sylgard 184) and dissolved after curing, yielding the transparent replica of the flow passage. Barbed connectors were inserted at the model outlet to provide connectivity with the flow circuitry. The model construction was identical for both models and is described in more detailed in Buchmann and Jermy (2007). The final flow phantoms were rectangular with flat sidewalls and an example is shown in Figure 2 for the realistic carotid bifurcation. Figure 3

Location of the spanwise planes S1–S5 and the bifurcation region, (a) idealised (b) patient specific geometry Idealised model

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2.2 Experimental set-up and flow conditions The flow phantoms were installed in a recirculating steady flow loop as shown in Figure 4. Flow was supplied by a constant head tank and conducted to the test section through a straight pipe of length L = 75 D to ensure fully developed flow at the entrance of the test section (confirmed by initial PIV measurements). Flow rates upstream and downstream of the test section were measured with an electromagnetic flow meter and two rotameters. The individual flow rates in the two daughter branches were adjusted by altering the downstream flow resistance. Flow was collected in a downstream tank and pumped back to the header tank via a centrifugal pump. The in-vivo flow rate was measured with phase contrast MRI and for the steady flow simulations, peak and mean flow in the CCA were 13.93 ml/s and 8.97 ml/s, respectively. The corresponding Reynolds numbers ( Re = 4Q / πDV ) were 453 for mean and 704 for peak systolic flow using a blood viscosity of V = 3.5 ⋅10−6 m 2 /s. The division of flow into the daughter branches varied over time with an average division of approximately 7:3 (internal:external). Measurements in the idealised model were taken at Re = 400 and Re = 700.

178 Figure 4

N.A. Buchmann et al. Schematic diagram of the experimental apparatus showing the test section and optical arrangement Upper Reservoir

Flowmeter

Temp. Controller

Valve

Optics 120mJ Nd:YAG Laser

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Note: Arrows indicate the flow direction.

Blood flow was simulated with an aqueous glycerin mixture of kinematic viscosity −6 V = 13.1 ⋅10 m 2 /s and density ρ = 1.15 g/cm3 at 20°C. At a composition of 39% water and 61% glycerin b.w., the liquid had the same refractive index as the silicone flow phantom and thus optical distortion were minimised during the imaging of the three-dimensional and curved flow passage.

2.3 Velocity measurements Planar PIV was used to measure blood flow velocities in the plane of bifurcation and cross-sectional planes as indicated in Figure 3. The PIV system consisted of a pulsed 120mJ Nd:YAG laser (New Wave Solo XT), a digital CCD camera (Kodak Megaplus 1.0) and optics to form a light sheet of approximately 1 mm thickness. The optical set-up is shown in Figure 4. The camera was positioned perpendicular to the model sidewall to allow for a normal (distortion free) viewing of the illuminated flow passages. To measure the secondary flow structure, the camera was positioned under an angle such that the test section could be viewed through the wedged corner seen in Figure 2. The working liquid was seeded with 10 μm hollow glass spheres

( ρ = 1.1 g/cm3 )

and sequential images of the illuminated particles were recorded on

1,008 × 1,018 pix2 frames at a rate of 14 Hz. A total of 100 image pairs were recorded from which a pixel averaged background image was calculated. The background image was used to locate the fluid-wall interface and for later calculations of the WSS. The background image was subsequently subtracted from each recording to remove image noise and light reflections. The resulting particle images were processed with an adaptive multigrid cross-correlation algorithm described elsewhere (Buchmann and Jermy, 2008). Magnification (M = 0.055 − 0.25) and time delay (Δt = 500 − 2, 600 μs) were adjusted depending on the flow conditions and measurement plane location. The interrogation windows overlapped by 75% and a

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single iterative refinement step was used, resulting in an average vector spacing of four pixels (or approximately 40 vectors across the model diameter). Finally, the outof-plane vorticity ( ωz ) was calculated by equating the circulation within a region of interest (i.e., 3 × 3, 5 × 5) to the product of the averaged vorticity and the area of the region of interest (Raffel et al., 1998).

2.4 WSS measurements This section gives a brief overview of the iPIV technique for the WSS measurements used in the current work. A more complete description of the technique is given in Buchmann et al. (2008) and Nguyen and Wells (2006). Using the above described background images, the wall interface can be described with a piecewise spline curve as shown in Figure 5(a) for the case of the outer ICA wall. Once the wall location is found, a near-wall region of constant height N (typically 80 pixels) is specified in the physical domain. An orthogonal curvilinear grid is then generated within this region and mapped to a rectangular domain using conformal transformation to preserve orthogonality [Figure 5(b)]. The particle images are interpolated onto the rectangular grid with subpixel accuracy using a two-dimensional cardinal interpolation function (Scarano, 2002). The resulting particle images in Figure 5(c) can then be processed with a standard PIV method or with iPIV detailed hereafter. If the flow moves predominantly parallel to the wall, a 1D correlation function between the two images can be computed at every horizontal position n within an interrogation region of width and height (M , N ) (Figure 6). RU ,n =

1 M

M

∑ (I

m =1

1, m , n

)(

− I1,m ,n ⋅ I 2,m +U ,n − I 2,m ,n

)

(1)

where the pixel coordinates are (m , n ) and I1 and I 2 are the mean intensities on each line. The 1D correlation functions is evaluated at every horizontal pixel line and the resulting correlation tables are stacked to give the correlation map RU ,n on axes of the horizontal (wall-parallel) displacement U and vertical (wall-normal) position n . Correlation peaks occur at height n with strong tracer signals and lie at horizontal positions that correspond to the tracer displacement. Thus, the correlation peaks form a ridge that lies along the wall-normal velocity profile (Figure 6). If tracer particles exist at every vertical position within the interrogation window, the peaks form a continuous ridge (i.e., time-averaging) as shown in Figure 6(b). Note that equation (1) is only applicable if the wall-normal displacement (i.e., velocity) of the tracer particles is less than their particle diameter. For larger displacements, the tracer particles leave the pixel line in the second exposure, which results in the loss of signal. The tracer displacement between the exposures can be controlled by adjusting the time separation Δt . The displacement gradient at the wall, ∂D / ∂n (pixel/pixel) is then inferred directly from the correlation map RU ,n by fitting a straight line onto the correlation peaks using a

weighted optimisation function (Buchmann et al., 2008). The measured gradient is then reverse transformed into world coordinates (curved wall) and WSS is calculated as τw = μ∂D / ∂n / Δt .

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Since the no-slip condition applies at the wall surface, the accuracy of the iPIV method (as well as for other methods) is sensitive to the accurate identification of the wall interface. In the present work, the accuracy of the identified wall position is within ±1 pixel or approximately 55 μm [see insert in Figure 5(a)], which yields an error of the estimated displacement gradient of less than ±0.02 pixel/pixel as shown in our earlier work (Buchmann et al., 2008). Figure 5

Image transformation method, (a) time-averaged background image with detected wall interface and near-wall region of height N (b) orthogonal curvilinear grid in (x, y) space and interrogation window of size (M , N ) (c) resampled near-wall image in transformed space (ξ , η ) 400

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Experimental investigation of carotid artery haemodynamics Line correlation, (a) interrogation windows for the 1st and 2nd exposure (b) 1D correlation ‘stack’, peaks lie on the same position as the displacement profile (dotted line)

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3

Results

Velocity and WSS measurements were conducted in two carotid bifurcation geometries. The physiologically realistic model represents the left carotid artery of a healthy male volunteer and the idealised carotid bifurcation model is that of Buchmann and Jermy (2007). Steady flow conditions were imposed for both models and are representative of mean and peak systolic flow (Table 1). The velocity fields were measured with planar PIV in the plane of bifurcation and at several cross-sectional planes in the carotid sinus as indicated in Figure 3. iPIV was used in the measurement of WSS in the plane of bifurcation and along the inner and outer vessel walls (Figure 3).

3.1 Primary and secondary flow structure The primary velocity fields in the bifurcation plane for peak flow are shown in Figure 7 for both models (Re = 704 and 700, respectively). For both models, sectional streamlines, which are lines tangential to the in-plane velocity vector, are parallel in the CCA, indicating fully developed flow. At the bifurcation, high-momentum axial flow moves along the divider wall into the internal and external carotid. Along the outer vessel wall, regions of low momentum fluid form, which are separated from the streamwise flow by a shear layer. For the in-vivo model, a region of reversed flow can be observed along the outer external carotid wall, whereas in the idealised model, flow reversal occurs along the outer sinus wall. In both cases, flow separation occurs proximally, but

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the streamlines do not form closed loops in which fluid particles (and thus, nutrients and blood borne agonists) would become trapped. On the contrary, flow in these regions is progressively restored to streamwise flow. Downstream, sectional streamlines converge to a bifurcation line or asymptotic trajectory as it typically occurs in free shear flows. The branching and vessel curvature of the carotid artery causes a radial pressure gradient, which introduces secondary flow formation. This instability is known as Dean instability and the formation of secondary vortex pairs depends on the vessel curvature, radius and flow velocity. The secondary flow motion in both models was measured in the cross-sectional planes in the carotid sinus for mean and peak flow as indicated in Figure 3. Figure 7

Primary velocity fields and sectional streamlines in the bifurcation plane, (a) physiological realistic model, Re = 700 (b) idealised carotid artery model, Re = 704

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The secondary velocity field in the physiological carotid bifurcation is shown in Figure 8 for mean flow at Re = 453. Consistent with previous findings, very strong secondary flows are observed in the carotid sinus. At the proximal location, fluid flows through the centre of the vessel towards the flow divider wall (left to right in Figure 8) and low momentum fluid near the wall flows towards the outer sinus wall setting up an asymmetric vortex pair. The vortex pair almost vanishes at the mid-sinus location (S2) before it changes its swirling direction at the distal sinus due to changes in vessel curvature. Unlike in the idealised model (Figure 9) with a symmetric and planar bifurcation, secondary flow is asymmetric in the in-vivo geometry with only a single predominant vortex occurring in the distal sinus. In both models, the strength and centre of the vortex changes with time as the flow moves downstream and similar behaviour is observed for steady peak flow. The streamwise vorticity distribution in the physiological model is shown in Figure 10 for Re = 704. A strong shear layer exists along the inner wall and streamwise vorticity increases towards the distal internal carotid. At S5, a second and possibly third vortex occur, giving rise to a highly unstructured flow environment.

Experimental investigation of carotid artery haemodynamics Figure 8

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Secondary flow structure in the physiological carotid artery model at mean systolic flow (Re = 453)

Note: In-plane velocity vectors in the axial planes S1–S4. Figure 9

Secondary flow structure in the idealised model at mean systolic flow (Re = 400)

Note: In-plane velocity vectors in the axial planes S1–S4. Figure 10 Secondary flow structure in the physiological carotid artery model at Re = 704

Note: Sectional streamlines and streamwise vorticity in the axial planes S1–S4.

3.2 Wall shear stress WSS in the physiological carotid bifurcation model is shown in Figure 11 for Re = 704 and compared to that in the idealised model. Measured WSS is plotted against the non-dimensional wall distance s / D with s = 0 located at the proximal/mid-sinus position (see figure insert). For better comparison, WSS is normalised by its theoretical value in the CCA for fully developed flow in a straight pipe ( τnorm = 8Re ρV 2 / D 2 ) .

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Figure 11 Non-dimensional WSS in the bifurcation plane for the physiological (Re = 704) and idealised (Re = 700) model, (a) outer ICA and ECA wall (b) inner ICA and ECA wall physiological model:

idealised model:

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Comparison of WSSs along the inner and outer ICA wall at selected location (S1–S3) within the physiological and idealised carotid artery model

Model

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12.9

2

Notes: Shear stress values given in dyn/cm . Also shown are the measured values in the CCA. Data are rescaled to in-vivo dimensions ( D = 6.25 mm, 7.2 mm, V = 3.5 × 10−6 m 2 /s ) .

In the physiological carotid bifurcation, flow experiences an increase in cross-sectional area at s = −2, which results in a rapid decrease in WSS along the outer walls. Flow separation occurs along the outer external carotid wall at approximately s = −1.5 and reattaches at s = 0.5. In the ICA, flow remains attached along the outer wall. At the distal sinus (s = 1), the cross-sectional area decreases and consequently WSS increases again. Downstream of the carotid sinus WSS levels in both branches reach similar values to that in the common carotid again. At the bifurcation apex (s = 0), a stagnation point forms and WSS along the inner wall (flow divider wall) rapidly increases to values six to eight times greater than τnorm . Further downstream WSS in the physiological model decreases again to values similar to that in the CCA [Figure 11(b)]. As with the physiological model, minimum WSS values in the idealised model are present along the outer walls of

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the carotid sinus and the external branch. In marked contrast to the in-vivo model, flow separation occurs in the carotid sinus, while flow in the external carotid remains attached. Absolute shear stress values sampled at the three spanwise locations S1–S3 are listed in Table 2 for the inner and outer carotid sinus wall. Along the outer wall, shear stress in the physiological model is on average larger (5.9 dyn/cm2) than that in the idealised model (–2.0 dyn/cm2), whilst along the inner wall, WSS is on average slightly lower (59.1 dyn/cm2) than in the idealised model (78.5 dyn/cm2). Note that the presented data are rescaled to their corresponding in-vivo values using Reynolds number scaling (Buchmann and Jermy, 2007). A comparison of the WSS in the physiological model for different Reynolds numbers (453, 704) and along the inner and outer walls is shown in Figure 12. Under both flow conditions, WSS exhibits very similar behaviour along both branches. In the ECA, WSS levels are as low as –3.2 dyn/cm2 for Re = 704, and in the carotid sinus, WSS decreases down to 0.5 dyn/cm2 at the proximal sinus for Re = 453 [see insert in Figure 12(a)]. Figure 12 Non-dimensional WSS in the bifurcation plane for the physiological model at Re = 453 and Re = 704, (a) outer ICA and ECA wall (b) inner ICA and ECA wall 8 ICA, Re=704

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4

Discussion

Local haemodynamic factors are understood to influence the initiation and progression of atherosclerotic plaques within the carotid artery (Caro et al., 1971; Chatzizisis et al., 2007; Traub and Berk, 1998; Zarins et al., 1983) and a variety of experimental studies have described local haemodynamics in carotid arteries using idealised and patient specific models with steady and pulsatile flow conditions (Bale-Glickman et al., 2003;

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Botnar et al., 2000; Buchmann and Jermy, 2007; Ku and Giddens, 1987; Liepsch, 2002; Zarins et al., 1983). Across the general population, a large variety in carotid artery geometry exists (Ding et al., 2001; Thomas et al., 2005) and it is understood that the local haemodynamic environment is largely influenced by the individual vessel geometry (Nguyen et al., 2008; Perktold and Resch, 1990). For example, in the present in-vivo model, the primary and secondary flow fields are markedly different from those observed in the idealised geometry model. The non-planar branching of the physiological realistic model produces a complex non-symmetric secondary velocity field with flow separation occurring predominantly in the ECA. The presence of a helical secondary flow structure in-vivo has also been reported by Houston et al. (2003). Milner et al. (1998) showed that the WSS distribution in the carotid artery is significantly influenced by the presence of secondary and helical flow pattern, which can be caused by geometrical variations, flow rate and the characteristics of the entrance flow profile. In the current study, the flow was steady and the inlet profiles were symmetric and fully developed leaving geometrical variation as the only difference between the two models. This in turn supports the existence of a ‘geometrical risk factor’ in the development of atherosclerosis (Friedman et al., 1983). It is widely accepted that the magnitude and distribution of WSS on the arterial wall is an important factor in the localised formation of atherosclerosis (Zarins et al., 1983). Measuring WSS non-invasively is difficult and Doppler ultrasound (Vennemann et al., 2007) or MRI measurements (Elkins and Alley, 2007) are mainly used for in-vivo studies, whereas experimental in-vitro studies have commonly made use of LDA measurements (Bharadvaj et al., 1982; Ding et al., 2001; Ku and Giddens, 1987). Common to all techniques are their uncertainty in measured WSS due to limited spatial resolution and/or errors in wall normal distance. While for LDA measurements, uncertainties are relatively low [down to ±1%, Durst et al. (1996)], the acquisition of complete WSS maps is rather time consuming and experimentally elaborated. The measurement of detail WSS maps by means of PIV has been demonstrated by Zhang et al. (2008) amongst others in the case of anastomosis flow, yet to the authors’ best knowledge, no such studies exist for the carotid artery bifurcation. In this work, we presented a new iPIV technique, which allows the instantaneous measurement of WSS maps along the inner and outer vessel walls with a spatial resolution of one pixel (or ∼ 55 μm) in wall normal direction. The technique’s uncertainty has been assessed by means of synthetically generated particle images, which revealed an absolute error of Δ∂U / ∂n = ±0.02 pixel/pixel

( or Δτw = ±0.28 dyn/cm2 )

(Buchmann et al., 2008).

Measured WSS is similar for both Reynolds numbers investigated in this study, however, it shows considerable differences between the two models. In the physiological model, flow separation and thus negative WSS occurs in the external carotid, while results for the idealised geometry confirm the existence of low WSS in the carotid sinus. The observation of recirculating flow and low WSS in the external carotid is not new and has already been reported by Milner et al. (1998). One of the predominant locations for atherosclerotic lesion is the carotid sinus with WSS in the physiological model being on average higher along the outer and lower along the inner sinus wall compared with the idealised geometry (Table 2).

Experimental investigation of carotid artery haemodynamics Table 3

Internal carotid artery wall shear stress

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A comparison of the current WSS values to those reported in previous studies is presented in Table 3. In steady flow studies with an idealised model, Bharadvaj et al. (1982) reported minimal and maximal experimental WSS values of –1.7 dyn/cm2 at mid-sinus and 123.5 dyn/cm2 at the distal sinus and under pulsatile flow conditions; Ku and Giddens (1987) reported time-averaged minimal and maximal WSS of –13.0 dyn/cm2 and 109.0 dyn/cm2. The current results are in the same range for both models with minimal values of –4.7 dyn/cm2 in the external carotid and maximal WSS of 98.0 dyn/cm2 at the bifurcation apex. Note that the range of values in Table 3 is probably due to variations in the idealised model geometry (e.g., y-shape versus tuning fork shape). There is also a trend, even though only for a small sample, that WSS levels in the physiological models are somewhat more moderate compared to the idealised models. For completeness, some numerical studies in idealised and physiological models are also listed in Table 3. There is a strong correlation between endothelial dysfunction and low WSS in the carotid artery. In healthy arteries, the vessel diameter adapts to the local flow environment so that mean shear stress is approximately 15 dyn/cm2 (Traub and Berk, 1998) and endothelial cells exhibit athero-protective phenotypes. In regions of low WSS and flow separation, local mass transfer to and from the arterial wall is inhibited, which leads to increased particle residence time and platelet aggregation. Furthermore, in areas of WSS below 4 dyn/cm2, the endothelial cells exhibit pro-atherogenic phenotypes (Malek et al., 1999). For example, low WSS leads to reduced WSS-induced nitric oxide synthesis, vascular smooth muscle cell proliferation, increased permeability of the endothelium and increased lipoprotein uptake. Lastly, some physiological limitations of this study have to be noted. In the present study, the arterial walls are assumed to be rigid and blood flow was modelled as a Newtonian liquid. This was justified based on previous studies by Karner et al. (1999) and Perktold et al. (1991a) who concluded that the global flow structure and stress pattern remain relatively unchanged when non-Newtonian and distensible wall properties are included in the modelling. While these assumptions are now widely accepted, the assumption of steady flow is still somewhat disputed. In the present study, the assumption of steady flow is deemed reasonable, since the time scale of one cardiac cycle (approximately one second) is considerably shorter than that of physiological processes (Wiesner et al., 1996) that are relevant in atherogenesis, which are known to occur over time scales in the order of decades. Furthermore, the study of steady flow conditions is relevant to patients with chronic heart failure that rely on continuous (i.e., steady) flow ventricular assisted devices. The study of arterial haemodynamics under these conditions is important to understand long-term effects of the implantation of these devices (Thalmann et al., 2005). Nevertheless, there is a consensus for the correlation between endothelial dysfunction and regions of high oscillating shear stress (Ku and Giddens, 1987; Zarins et al., 1983). These haemodynamic factors were not addressed in the current study and it will be interesting in future work to investigate the relation between time-averaged and steady WSS using the developed iPIV technique.

Experimental investigation of carotid artery haemodynamics

5

189

Conclusions

This work presented PIV measurements of the flow field and WSS distribution within a physiologically realistic model of the human carotid artery bifurcation. The model geometry was reconstructed from MRI time-of-flight data and reproduced in a scaled and transparent flow phantom. We have applied a new iPIV technique to accurately and instantaneously measure complete WSS maps along the inner and outer vessel walls. The presented technique estimates the local velocity gradient directly from the recorded particle images and thus reduces error propagation normally encountered in traditional PIV. The technique has an absolute error of ±0.28 dyn/cm2 and measured WSS values compared favourably with previous experimental and numerical studies. A comparison with results from an idealised carotid artery model revealed differences in WSS magnitude in both the ICA and ECA and most remarkably flow reversal in the external branch in the physiological model. It has been shown that PIV measurements cannot only provide detailed flow field information, but also detailed WSS maps. In conjunction with numerical flow simulations, PIV measurements can provide the basis for a validated and detailed understanding of the local haemodynamic factors relevant to carotid artery atherogenesis. Although only for a small sample, the present results highlight the importance of individual vessel geometry on haemodynamic factors and emphasise the need for patient specific modelling.

Acknowledgements The authors are grateful to Dr. S. Moore for providing software and advice for the surface reconstruction of the carotid artery geometry and the measurement of the cardiac flow wave. We also acknowledge C. Spence for improvements to the phantom construction procedure and proofreading of the manuscript and Dr. R. Watts and Dr. R. Keenan for assistance in obtaining the MRI data.

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