Influence of Oscillating Flow on LDL Transport and Wall Shear Stress in the Normal Aortic Arch

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/38015819 Influence of Oscillating Flow on LDL Transport and Wall Shear Stress in the Normal Aortic Arch ArticleinThe Open Cardiovascular Medicine Journal · September 2009 DOI: 10.2174/1874192400903010128·Source: PubMed CITATIONS 26 READS 812 6 authors, including: Johannes Vassiliou Soulis Democritus University of Thrace 120 PUBLICATIONS1,672 CITATIONS SEE PROFILE George Giannoglou Aristotle University of Thessaloniki 152 PUBLICATIONS5,419 CITATIONS SEE PROFILE Vassilios Papaioannou Centre for Research and Technology Hellas 36 PUBLICATIONS193 CITATIONS SEE PROFILE All content following this page was uploaded by Johannes Vassiliou Soulis on 20 May 2014. The user has requested enhancement of the downloaded file. 128 The Open Cardiovascular Medicine Journal, 2009, 3, 128-142 1874-1924/09 2009 Bentham Open Open Access Influence of Oscillating Flow on LDL Transport and Wall Shear Stress in the Normal Aortic Arch J. Soulis1,*, G. Giannoglou2, M. Dimitrakopoulou1, V. Papaioannou1, S. Logothetides3 and D. Mikhailidis4 1Fluid Mechanics, School of Engineering, Demokrition University of Thrace, Xanthi, Greece 2AHEPA University General Hospital, 1st Cardiology Department, Aristotle University of Thessaloniki, Thessaloniki, Greece 3AHEPA Physics Department, Aristotle University of Thessaloniki, Thessaloniki, Greece 4Dept. of Clinical Biochemistry (Vascular Prevention Clinics) and Dept. of Surgery, Royal Free Hospital campus, University College Medical School, University College London, London, UK Abstract: Lipid accumulation in the aortic wall is an important factor in the development of atherosclerosis. The Low Density Lipoprotein (LDL) at the surface of the endothelium in relation to Wall Shear Stress (WSS) in the normal human aortic arch under unsteady, normal flow and mass conditions was computationally analysed. Concave sides of the aortic arch exhibit, relatively to the convex ones, elevated LDL levels at the surface of the endothelium for all time steps. At the peak systolic velocity, the LDL level reaches a value 23.0% higher than that at entrance in the ascending-descending aorta region. The corresponding LDL levels at the surface of the endothelium for the near minimum entrance velocity instant reaches 26.0%. During the cardiac cycle, the highest area averaged normalized LDL taken up as compared to the lowest one is 0.69%. WSS plays an important role in the lipid accumulation. Low WSS regions are exposed to high LDL levels at the surface of the endothelium. Regions of elevated LDL levels do not necessarily co-locate to the sites of lowest WSS. The near wall paths of the velocities might be the most important factor for the elevated LDL levels at the surface of the endothelium. Keywords: Unsteady Low-density lipoprotein Transport, Wall Shear Stress, Atherosclerosis, Aortic Arch. 1. INTRODUCTION Lipid accumulation in the aortic wall is an important factor in the development of atherosclerosis. Disturbed blood flow and occurrence of atherosclerotic plaques at certain sites of human arteries are strongly correlated [1]. The flow of blood and the transport of macromolecules in the vascular system [2] are essential to understand atherogenesis [3]. Biomechanical factors, such as Wall Shear Stress (WSS), blood viscosity and flow velocity, may be responsible for the localization and progression of atherosclerosis [4, 5]. Besides the spatial distribution of flow parameters, their temporal variation during the cardiac cycle has been proposed as an atherogenic factor [6]. Complex configuration of the vessel promotes flow disturbances with low time-averaged WSS and high shear stress temporal oscillations during the cardiac cycle [6]. The application of unsteady flow constitutes a challenging issue, since it demands computational power and analysis time. The WSS may affect endothelial permeability [7]. Regional variations in the permeability of arterial endothelium may contribute to the localization of atheroscle- *Address correspondence to this author at the Fluid Mechanics, School of Engineering, Demokrition University of Thrace, 67100 Xanthi, Greece; Tel: ++302541079617; Fax: ++302310994838; E-mail: [email protected] rosis [8, 9]. Luminal surface level of Low Density Lipoprotein (LDL) transport across the artery wall is considered to be important in atherogenesis [10, 11]. Elevated LDL colocalize with known sites of atherosclerotic plaque development, [2]. Atherosclerotic regions are also low WSS regions and consequently it was difficult to determine whether it was low WSS, abnormal mass transfer or both that were contributing to atherosclerosis [2]. Oscillating flow on LDL transport in the arterial wall showed that the steady flow assumption is inadequate and the instantaneous hemodynamic conditions have important influence on LDL transmural transport in arteries with disturbed and complicated flow patterns [12]. The accumulation of LDL in vascular areas featuring a highly disturbed flow was examined, [13]. Geometrical parameters such as curvature and variations of the luminal section strongly influence the LDL within the wall. Realizing that the research produced in macromolecular transport in curved 3D blood vessels was rare, steady and unsteady flows and mass simulation was analyzed [14]. The effect of near-wall blood flow velocity and plasma filtration velocity across the arterial wall on luminal surface concentration of LDL and the uptake of tritium-cholesterol were investigated [15]. These results indicate that lipids accumulate at the luminal surface in areas where blood flow velocity and WSS are low and where the permeability of the endothelial layer is enhanced. Influence of Oscillating Flow on LDL Transport and Wall Shear Stress The Open Cardiovascular Medicine Journal, 2009, Volume 3 129 There have been very few studies investigating the fluidwall coupled mass transport under oscillating flow conditions [12, 14, 16]. The current work analyzes the influence of oscillating flow and LDL mass transport patterns over the normal human aortic arch. The purpose is to elucidate the association of low WSS-elevated LDL levels at the surface of the endothelium in relation to atherosclerotic plaque localization over the physiological human aortic arch during the normal cardiac pulse. Emphasis is put into a) LDL, b) WSS, c) differentiation of the LDL and WSS between concave (outer) and convex (inner) aortic arch sides as well as into d) temporal differentiation of the LDL between end systolic and end diastolic periods. We demonstrate that due to the semi-permeable nature of the arterial walls, high LDL levels at the surface of the endothelium occur at certain regions of the normal aortic arch. 2. MATERIALS AND METHODOLOGY The 3D geometry of the normal aortic arch computational model was generated using data compiled from several sources, Fig. (1). The computational model includes the ascending aorta, descending aorta, brachiocephalic artery, left common carotid artery and left subclavian artery. The assumptions made about the nature of the flow are that it is 3D, unsteady, laminar, isothermal, with no external forces applied on it while the aortic arch wall is comprised from non-elastic and semi-permeable material. The blood is considered to be non-Newtonian fluid obeying the power law. The flow equation is coupled with the convectiondiffusion equation. The diffusion flux of LDL arises due to concentration gradients. In the absence of systematic and reliable experimental data for human arteries, we assume the molecular diffusivity D to be constant and equal to 15.0x10-12 m 2/s [9, 17]. The infiltration velocity Vw is set equal to 0.6x10-8 m/s [18]. There is a limited amount of experimental data regarding the endothelial permeability K or else mass transfer coefficient. Specifications of K values are sometimes unreliable. For current analysis purposes this value is set equal to 2.0x10-10 m/s, [9]. A typical aortic arch blood flow waveform, shown in Fig. (2), is applied over the entire entrance cross-section. The waveform mimics typical aortic blood averaged flow velocity under resting condition. From the entire velocity waveform, lasting 800.0 msec, two characteristic time-points are selected for detail analysis. The first instant refers to peak systole occurring 123 msec after the systole onset with 0.32 m/s entrance velocity. The second instant refers to near minimum entrance velocity of 0.005 m/s corresponding to 522.75 msec. The inlet based Reynolds numbers range from 3.5 (minimum) to 475 (peak). Fig. (2). Average physiological human aortic arch velocity waveform. Computational analysis results refer to inlet flow velocities of a) 0.32 m/s (peak systole) and b) 0.005 m/s (near minimum entrance velocity). Fig. (1). Aortic arch geometry and non-structured computational grid including the: ascending aorta, descending aorta, brachiocephalic artery, left common carotid artery and left subclavian artery. 130 The Open Cardiovascular Medicine Journal, 2009, Volume 3 Soulis et al. A uniform constant concentration Co of LDL is applied at the orifice of the ascending aorta. At the descending aorta, brachiocephalic artery, left common carotid artery and left subclavian artery outlets, the gradient of LDL concentration along the vessels is set equal to zero (zero flux, Newmann condition). Flow discharges are set analogous to the third power of the branching vessel inlet diameter according to Murray’s law [19]. The applied endothelium boundary condition at the semipermeable aortic walls states that the net amount of LDL per unit area passing from it to the vessel wall is determined by the difference of the mass flow carried to the vessel wall by infiltration flow and the amount of flow which diffuses back to the main vessel flow. It is known that at arterial walls the LDL concentration values are higher than those of the vessel bulk flow. Furthermore, LDL concentration increases with increasing infiltration velocity. 3. RESULTS The calculated LDL levels at the surface of the endothelium Cw are normalized with the inlet value of Co (=1.3 mg/ml). WSS contours show its magnitude and not its spatial direction. 3.1. WSS in the Ascending-Descending Aorta WSS (N/m2) magnitude contour plots for the ascendingdescending aorta of the aortic arch for the selected time instants are shown in Figs. (3a, b). The convex side of the aortic arch exhibits, relatively to the concave side, high WSS values. High WSS is encountered at the convex side of the Fig. (3). Colour-coded contour plots of the Wall Shear Stress (N/m2) magnitude for the ascending-descending aorta at a) peak systole and b) near minimum entrance velocity, respectively. Influence of Oscillating Flow on LDL Transport and Wall Shear Stress The Open Cardiovascular Medicine Journal, 2009, Volume 3 131 end ascending and early descending aorta at all pulse wave times. Particular low WSS values appear along the concave parts of the ascending-descending aorta at regions located just downstream to the left subclavian artery. 3.2. LDL in the Ascending-Descending Aorta Contour plots of the normalized luminal surface concentration Cw/Co for the ascending-descending aorta, at the selected characteristic time instants, are shown in Figs. (4a, b). At all time instants, the concave side of the aortic arch exhibits high LDL levels compared with the convex side. Low LDL levels at the surface of the endothelium are encountered at the end ascending and the early descending convex side of the aorta, while the main convex side encounters relatively high LDL levels Figs. (5a, b). At peak systolic pressure, the lowest Cw/Co value is 1.13. High LDL values appear on the luminal surface of the wall along the concave parts of the ascending-descending aorta. Regions with elevated LDL levels at the surface of the endothelium occur at the concave ascending-descending aortic arch just downstream to the left subclavian artery. 3.3. LDL in the Brachiocephalic Artery, Left Common Carotid Artery and Left Subclavian Artery Cw/Co contour plots for the brachiocephalic artery, left common carotid artery and left subclavian artery at the specific time instants are shown in Figs. (6a, b). Elevated LDL levels at the surface of the endothelium are observed in all vessels. This is due to low flow velocities which in turn gives rise to low WSS. The particular LDL levels are strongly affected by vessel curvature. As a rule, concave parts exhibit high luminal surface LDL. However, depending upon the particular bend side and the incoming flow velocity distribution, convex parts can exhibit high LDL levels. Fig. (4). Contour plots of the normalized LDL levels at the surface of the endothelium Cw/Co for the ascending-descending aorta of the aortic arch at a) peak systole and b) near minimum entrance velocity, respectively. 132 The Open Cardiovascular Medicine Journal, 2009, Volume 3 Soulis et al. Elevated LDL regions occur at the inlet surfaces of the brachiocephalic artery, left common carotid artery as well as at the downstream regions of the left subclavian artery. 3.4. Velocity and Strain Rate for an AscendingDescending Aorta Transverse Section Velocity magnitude and strain rate distributions for an ascending-descending aorta transverse section, at peak systolic pressure and near minimum entrance velocity instant, are shown in Figs. (7 and 8), respectively. Peak systolic pressure velocities occur in regions located close to the concave part of the early descending aorta. This is due to the centrifugal forces acting on blood flow as it encounters the aorta bend. Low blood flow velocities are encountered in the concave ascending-descending aorta at regions located just downstream to left subclavian artery. Low strain rates regions cover large area, Fig. (8), shifting towards concave parts of the ascending-descending aorta. 3.5. Strain Rate and Molecular Viscosity at AscendingDescending Aorta Cross-Sections Strain rate and molecular viscosity contour plots at various aorta cross-sections for the extreme flow instant i.e. at peak systolic and at near minimum velocity entrance, are shown in Figs. (9a, b), respectively. At peak systolic pressure, in the upstream region of the descending aorta, increased molecular viscosity and low strain rates are shifted towards the concave side and cover a relatively wide area, Fig. (9a); at the same time instant, high strain rates appear at the convex side of the upstream descending aorta region. At Fig. (5). Contour plots of the normalized LDL levels at the surface of the endothelium Cw/Co for the convex side of the aortic arch at a) peak systole and b) near minimum entrance velocity, respectively. Influence of Oscillating Flow on LDL Transport and Wall Shear Stress The Open Cardiovascular Medicine Journal, 2009, Volume 3 133 near minimum entrance velocity instant, increased strain rates are also present in the above region. Throughout the aortic arch the molecular viscosity increases as the inlet flow velocity decreases, Fig. (9b). 3.6. LDL-WSS Typical relationships between LDL levels and WSS over the entire aortic arch surface at the extreme velocity instants, are shown in Figs. (10a, b). It is evident that the LDL levels at the surface of the endothelium increases with decreasing WSS. The concentration increases at a higher rate as the WSS values reduce to zero. WSS plays an important role in LDL levels at the surface of the endothelium. The dependence of LDL levels at the surface of the endothelium on WSS is higher at near minimum entrance velocity instant, Fig. 10b, than at peak velocity instant, Fig. (10a). 3.7. LDL Statistics Table 1 shows the descriptive LDL statistics for the aortic arch. The total endothelial area of the computational analyzed aortic arch is 360.69 cm2. Results, at 5 specific timepoints of the cardiac cycle, show the a) area averaged LDL levels at the surface of endothelium, b) normalized area averaged LDL levels at the surface of endothelium, c) amount of LDL taken up by all luminal aortic arch surfaces, and d) percentage LDL levels at the surface of the endothelium as compared to its lowest value taken up by all luminal aortic Fig. (6). Contour plots of the normalized LDL levels at the surface of the endothelium Cw/Co for the daughter vessels of the aortic arch at a) peak systole and b) near minimum entrance velocity, respectively. 134 The Open Cardiovascular Medicine Journal, 2009, Volume 3 Soulis et al. Influence of Oscillating Flow on LDL Transport and Wall Shear Stress The Open Cardiovascular Medicine Journal, 2009, Volume 3 135 Fig. 7. contd…. Fig. (7). 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