This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.Atherosclerosis shows predilection in regions of coronary arteries with hemodynamic
particularities as, local disturbances of Wall Shear Stress (WSS) in space and time, and locally high concentrations of lipoprotein. Six, image-based human deceased, Right Coronary Arteries (RCA) are used to elucidate, a) Low Density Lipoprotein (LDL) transport under steady flow and b) oscillating flow (no mass
transfer). A semi-permeable nature of the arterial wall computational model is incorporated with hydraulic conductivity and permeability treated as WSS dependent. The 3D reconstruction technique is a combination
of angiography and IVUS. LDL is elevated at locations where WSS is low. Under steady flow conditions the area-averaged normalized LDL concentration over the RCAs, using shear dependent water infiltration and endothelial permeability is 9.6 % higher than at entrance. However, under constant water infiltration and endothelial permeability this value is only 3.2 %. High Oscillating Shear Index (OSI) and low average WSS nearly co-locate. Approximately 630000 grid nodes proved to be sufficient enough to accurately describe the oscillating flow and the LDL concentration within the RCAs

3rd Micro and Nano Flows Conference (MNF2011)

Fytanidis, DK

Giannoglou, GD

Papaioannou, VC

Soulis, JV

English

Brunel University Research Archive

3rd Micro and Nano Flows Conference Thessaloniki, Greece, 22-24 August 2011 - 1 -   Oscillating shear index, wall shear stress and  low density lipoprotein accumulation in human RCAs  Johannes V. SOULIS 1,*, Dimitrios K. FYTANIDIS1,  Vassilios C. PAPAIOANNOU1, George D. GIANNOGLOU 2  * Corresponding author: Tel: ++302310994837; Fax: ++302310994837; Email:  jvsoulis@med.auth.gr 1: Fluid Mechanics, Demokrition University of Thrace, Greece 2: Cardiovascular Engineering and Atherosclerosis Laboratory,  1st Cardiology Department, Aristotle University of Thessaloniki, Greece    Abstract Atherosclerosis shows predilection in regions of coronary arteries with hemodynamic particularities as, local disturbances of Wall Shear Stress (WSS) in space and time, and locally high concentrations of lipoprotein. Six, image-based human deceased, Right Coronary Arteries (RCA) are used to elucidate, a) Low Density Lipoprotein (LDL) transport under steady flow and b) oscillating flow (no mass transfer). A semi-permeable nature of the arterial wall computational model is incorporated with hydraulic conductivity and permeability treated as WSS dependent. The 3D reconstruction technique is a combination of angiography and IVUS. LDL is elevated at locations where WSS is low. Under steady flow conditions the area-averaged normalized LDL concentration over the RCAs, using shear dependent water infiltration and endothelial permeability is 9.6 % higher than at entrance. However, under constant water infiltration and endothelial permeability this value is only 3.2 %. High Oscillating Shear Index (OSI) and low average WSS nearly co-locate. Approximately 630000 grid nodes proved to be sufficient enough to accurately describe the oscillating flow and the LDL concentration within the RCAs.    .   Keywords: Averaged Wall Shear Stress, Oscillating Shear Index, LDL Transport, Right Coronary Artery    1. Introduction   Elucidating the blood flow and the transport of macromolecules in the cardiovascular system is essential in understanding the genesis and progression of atherosclerosis (Fatouraee, et al., 1998). The association between low Wall Shear Stress (WSS) and accumulation of macromolecules, leading to atherosclerosis, may be mediated through effects on transport properties and mass transport. Endothelial cells sense and respond to cyclic mechanical stretching imposed to them through various biomechanical factors i.e. static pressure and WSS. Regional variations in the permeability of arterial endothelium may contribute to the localization of atherosclerosis (Ogunrinade, et al., 2002). The luminal surface LDL concentration is affected by the flow infiltration, which in turn is affected by the deformation of the arterial wall. An increased permeability to LDL, as it is the case of increased plasma LDL concentration, increases atherosclerosis (Nielsen, et al., 1996). Higher permeability of the endothelium caused excessive influx of LDL to the subendothelial layer. A shear stress-dependent three-pore model (Olgac, et al., 2009) was applied for the left coronary artery in its healthy and atherosclerotic state showing that the location of the plaque in the diseased state corresponds to one of the sites with predicted elevated LDL concentration in the healthy state.     The “patient-specific” geometry is used in several works, (Steinman, 2002). The importance of low WSS and high Oscillating Shear Index (OSI) in atherosclerosis is reported (Chatzizisis, et al., 2008). The regional 3rd Micro and Nano Flows Conference Thessaloniki, Greece, 22-24 August 2011 - 2 - differences of WSS and the OSI was examined with flow sensitive 4D MRI (Frydrychowicz, et al., 2009).     The numerical research work uses semi-permeable arterial wall (no transmural flow or mass transfer) to study the steady mass transport patterns in RCAs focusing on the effects of geometric features using shear dependent endothelial properties with six image-based diseased RCAs (angiography and IVUS reconstruction technique). Furthermore, the RCAs are analyzed, also including grid scale effects, to elucidate the relation between the two flow properties namely, the time-Average Wall Shear Stress (AWSS) and the OSI (no mass transfer).   2.	Methods 2.1. Geometries, grid dependence     A combination of angiography and IVUS is utilized for the 3D reconstruction of six human RCAs. All ultrasound data was digitized by a frame-grabber and the end-diastolic images were selected. In the gated sequence of IVUS images, the lumen border was semi-automatically detected. Each contour was assigned equidistantly at the 3D reconstructed catheter path. The output consists of lumen contours which are perpendicularly positioned onto the reconstructed 3D catheter path, (Giannoglou, et al., 2007). Table 1 gives the geometrical details of the tested human RCA models.    2.2. Equations for steady flow and mass      problem, boundary conditions The code solves the governing Navier-Stokes flow equations and the mass transport of LDL equation in steady form. The numerical scheme utilizes an implicit formulation of the governing partial differential equations. The assumptions made about the nature of the flow are that it is 3D, laminar, isothermal, with no external forces applied on it. The arterial wall is comprised from non-elastic and permeable material. The blood is considered as non-Newtonian fluid obeying power law. The coupling of fluid dynamics and solute dynamics at the endothelium was achieved by the Kedem-Katchalsky equation (Kedem, et al., 1958). A mesh sensitivity study was performed to solve LDL convection-diffusion equation for No 1 RCA, Fig 1.The final mesh adopted for this vessel was comprised form 635000 grid nodes.   Fig. 1. Maximum normalized LDL con-centration versus grid nodes for No1 RCA      Table 1. Geometrical details of the tested six human RCA models  The applied endothelium boundary condition  Vessel 1 Vessel 2 Vessel 3 Central vessel length (cm) 8.79  7.38  7.63  Inlet equivalent radius (mm) 1.93 2.04 1.82 Outlet equivalent radius (mm) 1.73 1.37 1.58 Min equivalent radius (mm) 1.03 1.25 1.38 Max equivalent radius (mm) 2.12 2.25 2.35  Vessel 4 Vessel 5 Vessel 6 Central vessel length (cm)    8.96  8.05  8.59 Inlet equivalent radius (mm) 1.67 2.00 1.23 Outlet equivalent radius (mm) 1.26 0.96 0.93 Min equivalent radius (mm) 1.08 0.90 0.93 Max equivalent radius (mm) 1.82 2.20 1.28 3rd Micro and Nano Flows Conference Thessaloniki, Greece, 22-24 August 2011 - 3 - at the semi-permeable aortic walls is (Soulis et al., 2008),  www CKnCD-VC  ∂ ∂               (1)  Cw (mg/ml) denotes LDL wall concentration, Vw (m/sec) the blood infiltration velocity, n the direction normal to the wall, the LDL diffusivity D is considered as isotropic and equals 15×10-12 m/s2 and K (m/sec) is the permeability coefficient (overall mass transfer coefficient) of LDL at the arterial wall. The above equation 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. The Vw is calculated (Soulis et al., 2008; Sun, et al., 2007; Khakpour et al., 2008; Curry, et al., 1984; Karner, et al., 2000) as,  5933]10x7931.2)015.0ln(10x392.0[)(V12w12ww--           (2)                                         τw (N/m2) is the WSS, The above equation states that low WSS results into decreased Vw velocity. For the shear dependent K coefficient, the following equation is used (Stangeby, et al., 2002),  (3)  Kconst is the constant permeability coefficient (=2.0×10-10 m/s), Co (=1.3 mg/ml) the uniform constant LDL concentration at inlet. The inlet flow condition is set 0.17 m/s.  2.3. Equations for the oscillating flow     problem    For the oscillating flow problem, the governing Navier-Stokes equations are solved in unsteady form and the arterial wall is comprised from non-elastic and impermeable material. The pulse period T (sec) of this waveform is 1.0 sec, Fig. 2.     The AWSS (N/m2) magnitude is defined (Stangeby et al., 2002) as, ∫T0dtSSWT1AWSS                   (4)   Fig. 2. The applied pulsewave  Another transient flow property related with the wall is the magnitude of time-Averaged WSS Vector (AWSSV) (N/m2) defined as,  ∫T0SdtSWT1AWSSV                 (5)  The OSI monitors the differences between AWSS and AWSSV values. Using these values, the OSI clarifies the WSS vector deflection from predominant blood flow direction during cardiac cycle. Thus, OSI is calculated:  dtSSWSdtSW0.1x5.0OSI T0T0∫∫        (6)  The OSI value varies from 0 (for no-cyclic variation of WSS vector) to 0.5 (for 180-degree deflection of WSS direction).   3. Results and discussion 3.1. LDL transport under steady flow Table 2 shows the area averaged normalized LDL concentration values using constant Vw and K as well as shear dependent Vw and K. Area-averaged normalized luminal surface LDL concentrations over the RCAs using constant Vw and K are of the 3.2 % order higher than that at entrance. Area-averaged normalized luminal surface LDL concentrations over the RCAs using shear dependent Vw and K values are 9.6 % higher than that at entrance.            )537.0)(e037.0(K),C(K 27.0wCoCw75.2constww  3rd Micro and Nano Flows Conference Thessaloniki, Greece, 22-24 August 2011 - 4 -  Vessel 1 Cw/Co Vessel 2 Cw/Co Vessel 3 Cw/Co Vw=0.6x10-8 m/s K=2.0x10-10 m/s 1.030 1.041 1.046 Shear dependent Vw and K 1.075 1.117 1.125   Vessel 4 Cw/Co Vessel 5 Cw/Co Vessel 6 Cw/Co Vw=0.6x10-8 m/s K=2.0x10-10 m/s 1.036 1.033 1.029 Shear dependent Vw and K 1.097 1.089 1.075  Table 2. Area averaged LDL concentration Cw/Co over RCAs using various Vw and K  Figure 3 shows the normalized luminal surface LDL concentration Cw/Co contours for the No1 RCA under, a) constant and b) shear dependent Vw and K, Eqs. (2),(3). Higher LDL values are encountered in case of shear dependent Vw and K. The normalized luminal surface LDL concentration values (=Cw/Co) of the six RCAs are shown in Fig. 4. The spatial gradients of the LDL are considerable. In low WSS regions the LDL accumulation is high. The infiltration velocity cannot flash away the LDL particles, which are then accumulated in the low WSS region. Water infiltration velocity contours for the No1 RCA vessel are shown in Fig. 5. Values range from 1.12x10-8 to 2.19x10-8 m/s. The average calculated Vw of all six RCAs is 1.6x10-8 m/s. Due to shear flow dependence between Vw and WSS, Eq. (2), increased water infiltration velocity contours occur at high WSS values (>1.0 N/m2). Permeability coefficient contours for the No1 RCA are shown in Fig. 6. Vw is shear dependent. The values range from 3.09x10-10 to 10.81x10-10 m/s.  3.2. Oscillating flow     The AWSS (N/m2), AWSSV (N/m2) and OSI contours of the No1 RCA are shown in Fig. 7,8 and 9, respectively. High AWSS is encountered at the convex parts of the curved flow regions. Low AWSS develops at the concave parts of the curved flow regions. High OSI values reveal WSS magnitude inversion during the cardiac pulse wave. High OSI values develop at the convex part of the vessel.     Typical relationship between AWSS and AWSSV over the entire No1 RCA surface is shown in Figs. 10 and 11, respectively. It is evident that increasing OSI values coexist with decreasing either WSS or AWSSV. Figure 12 shows the variation of AWSS with AWSSV. Low AWSS values differ from low AWSSV indicating substantial alteration in the WSS vector orientation.      a)  b)  Fig. 3. Normalized luminal surface LDL con-centration Cw/Co contours of the No1 RCA, a) Vw=0.6x10-8 m/s, K=2.0x10-10 m/s, b) Vw and K are shear dependent   3rd Micro and Nano Flows Conference Thessaloniki, Greece, 22-24 August 2011 - 5 -   Fig. 4. Normalized luminal surface LDL con-centration Cw/Co contours of the RCAs. Vw and K are shear dependent. The bar shows low Cw/Co values on the left. The No1 RCA is the top left one   Fig. 5. Water infiltration velocity Vw (m/s) contours for No1 RCA. K is shear dependent             Fig. 6 Permeability coefficient K (m/s) con-tours of the No1 RCA. Vw is shear dependent      Fig. 7. AWSS (N/m2) contours for No1 RCA      3rd Micro and Nano Flows Conference Thessaloniki, Greece, 22-24 August 2011 - 6 -  Fig. 8. AWSSV (N/m2) contours for No1 RCA   Fig. 9. OSI contours for No1 RCA      Fig. 10. AWSS (N/m2) versus OSI for No 1 RCA    Fig. 11. AWSSV (N/m2) versus OSI for No1 RCA    Fig. 12. AWSS (N/m2) versus AWSSV (N/m2) for No1 RCA   3.3. Grid scale effects on AWSS, AWSSV and       OSI    Figures 13a,b show grid scale effects on AWSS using sparse (~100000 nodes) and dense (~635000 nodes) grid mesh, respectively. Nearly 42.0 % of the AWSS are in the 0.2-0.4 (N/m2) range. Differences between grids appear in the 0.0-0.2 (N/m2) range. This indicates the importance of using dense grid near to low WSS flow regions (endothelium regions). At the low AWSSV range, 0.2-0.4 (N/m2), Figs. 14a,b, the differences between sparse and fine grid meshing results are prominent. However, the OSI tends to yield indifferent results between the two grid nodes for nearly all OSI ranges, Figs. 15a,b. Nearly 80.0 % of the OSI values attend values less than 0.1. Results suggest that nearly 630000 grid nodes are sufficient enough to accurately describe the OSI distribution within the RCAs under current flow and mass conditions.     3rd Micro and Nano Flows Conference Thessaloniki, Greece, 22-24 August 2011 - 7 - a)  b)  Fig. 13. Percentage distribution of AWSS (N/m2) for No1 RCA using, a) sparse grid and b) fine grid   a)  b)  Fig. 14. Percentage distribution of AWSSV (N/m2) for No1 RCA using, a) sparse grid and b) fine grid   a)  b)  Fig. 15. Percentage distribution of OSI for No1 RCA using, a) sparse grid and b) fine grid   4. Finer scale studies  Figures 7-12 express the variation of the engineering-oriented performance parameters AWSS, AWSSV and OSI, over the arterial surface, together with their inter-relationships. Figures 7, 8 and 9 show that a majority of the locations have low values of AWSS, AWSSV and OSI, respectively. As might be expected, these regions are basically coincident for AWSS and AWSSV and, hence, the latter quantities stand in the linear relationship, shown in Fig. 12. However, Figs. 9-11 suggest that the OSI regions are essentially complementary, which observation is suggestive, broadly, of two regimes, i) low OSI (below about 0.1), over which AWSS or AWSSV vary widely, and ii) low AWSS or AWSSV (below about 0.4 and 0.3 Pa respectively), over which OSI varies widely. These two putative regimes co-exist, or merge, in a region of parameter space where there is noticeable scatter of the points. The preceding discussion is predicated upon correlated macro-scale observables only. We therefore 3rd Micro and Nano Flows Conference Thessaloniki, Greece, 22-24 August 2011 - 8 - suggest that the observed “degeneracies” might be “raised” by data acquired form studies of the micro-scales of length and time, beyond the current scope, for which study a non-continuum such, as a Lattice Boltzmann equation solver might be necessary.    5. Conclusions    The novelty of this research work lies in the 3D patient specific RCA to study, a) steady mass transport patterns in which the endothelial physical properties, namely the hydraulic conductivity and the permeability, are WSS dependent and b) oscillating flow without mass transfer. The luminal surface LDL concentration at the RCA wall is flow-dependent with local variations due to geometric features. LDL is elevated at locations where WSS is low. Area-averaged normalized LDL concentration over the RCAs, using shear dependent hydraulic conductivity and permeability is 9.6 % higher than that at entrance. It is the permeability of the endothelium, which mainly determines the final amount passing through the wall.   Furthermore, the Computational Fluid Dynamics based AWSS and OSI calculation presented here provide valuable flow parameters for the description of the haemodynamics status within the RCAs. High AWSS is encountered at the convex parts of the curved flow regions. Low AWSS develops at the concave parts of the curved flow regions. High OSI and low AWSS nearly co-locate. Approximately 630000 grid nodes proved to be sufficient enough to accurately describe the LDL concentration and the OSI distribution under the applied flow and boundary conditions within the RCAs.     References Chatzizisis, Y.S., Jonas, M., Coskun,  A.U., Beigel, R., Stone, B.V., Maynard, C.,  Gerrity, R.G.,  Daley, W., Rogers,  C., Edelman E.R., Feldman C.L., Stone,  P.H., 2008. Prediction of the localization of high-risk coronary atherosclerotic plaques on the basis of low endothelial shear stress: An intravascular ultrasound and histopathology natural history study. Circulation. 26 117(8), 993-1002. Curry, F., 1984. Mechanics and thermo-dynamics of transcapillary exchange. Renkin E. American Physiological Society, Bethesda, MD. s.l.: American Physiological Society, Vol. IV. Fatouraee, N., Deng, X., De Champlain, A., Guidoin, R., 1998. 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Soulis, J.V., Giannoglou, G.D., Papaioannou, V., Parcharidis, G.E., Louridas, G.E., 2008.  Low-Density Lipoprotein concentration in the normal Left Coronary Artery tree. Biomed Eng Online, 17, 7-26.                                       Stangeby, D.K., Ethier, C.R., 2002. Computational analysis of coupled blood-wall arterial LDL transport. J. Biomech. Eng., 124(1), 1-8. Steinman, D.A., 2002. Image-based com-putational fluid dynamics modeling in realistic arterial geometries. Annals of Biomedical Engineering, 30, 483–497. Sun, N., Wood, N.B., Hughes, A.D., Thom, S.A., Xu, X.Y., 2007. Influence of pulsatile flow on LDL transport in the arterial wall. Ann. Biomed. Eng., 35(10), 1782-1790.   

3rd Micro and Nano Flows Conference Thessaloniki,

Computational analysis of coupled bloodwall arterial LDL transport.

Concentration polarization of low density lipoproteins (LDL) in the arterial system,

Critical assessment of arterial transport models.

Effect of endothelial injury and increased blood pressure on albumin accumulation in the arterial wall: a numerical study.

Effect of fluid shear stress on the permeability of the arterial endothelium.

Image-based computational fluid dynamics modeling in realistic arterial geometries.

Influence of pulsatile flow on LDL transport in the arterial wall.

Low-Density Lipoprotein concentration in the normal Left Coronary Artery tree.

Mechanics and thermodynamics of transcapillary exchange.

novel active contour model for fully automated segmentation of intravascular ultrasound images: in vivo validation in human coronary arteries,

Prediction of the localization of high-risk coronary atherosclerotic plaques on the basis of low endothelial shear stress: An intravascular ultrasound and histopathology natural history study.

Thermodynamic analysis of the permeability of biological membranes to non-electrolytes.

Three-dimensional analysis of segmental wall shear stress in the aorta by flow-sensitive four-dimensional MRI.

Transfer of low density lipoprotein into the arterial wall and risk of atherosclerosis.

Oscillating shear index, wall shear stress and low density lipoprotein accumulation in human RCAs

Oscillating shear index, wall shear stress and low density lipoprotein accumulation in human RCAs

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