Oscillatory flow in human arteries

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/235957879 Oscillatory flow in human arteries Conference Paper · November 2010 DOI: 10.1109/itab.2010.5687787 CITATION 1 READS 382 4 authors: Dimitrios K. Fytanidis Argonne National Laboratory 50 PUBLICATIONS598 CITATIONS SEE PROFILE Johannes Vassiliou Soulis Democritus University of Thrace 120 PUBLICATIONS1,673 CITATIONS SEE PROFILE Vassilios Papaioannou Centre for Research and Technology Hellas 36 PUBLICATIONS193 CITATIONS SEE PROFILE George Giannoglou Aristotle University of Thessaloniki 152 PUBLICATIONS5,421 CITATIONS SEE PROFILE All content following this page was uploaded by Vassilios Papaioannou on 05 June 2014. The user has requested enhancement of the downloaded file. Abstract—Although genetic factors seem to be important, basic mechanisms related to arterial wall cell malfunction, which leads to atherosclerosis formation, depend on the blood flow properties. The present study correlates the factors simulating pulsatile blood flow in the human arteries (aortic arch) using patient-specific geometry. Using numerical techniques we examine the relation between time-Averaged Wall Shear Stress (AWSS) and Oscillatory Shear Index (OSI). The velocity vector oscillates and at the same time alters its direction in places with low AWSS values. Low AWSS and high OSI values do not always collocate. Regional differences between AWSS magnitude and OSI may answer the question as to where atherosclerotic lesions predominately develop and progress at specific aortic regions. This analysis gives information for deeper understanding of the atherosclerosis mechanisms. I. INTRODUCTION HE blood flow properties, such as low/high Wall Shear Stress (WSS) and macromolecules transport through human arteries are shown to be important factors for endothelial dysfunction [1], [2]. Complex geometry and pulsating flow in the human aortic arch lead to different spatial and temporal changes in the WSS. The advances of computerized image processing technology and the improved resolution of medical imaging processes, forced researchers to use more realistic geometries. Thus, “patientspecific” geometry is used in several works; suggestively the works of [3], [4], [5]. A general fully computerized algorithm of 3D geometry reconstruction using CT or MRI images data for biomedical applications was published [6]. The importance of low WSS and high Oscillating Shear Index (OSI) in atherosclerosis is reported in [7]. The regional differences of WSS and the OSI in the aortic arch was examined by flow sensitive 4D MRI, [8]. They report that these vessel wall parameters may help to explain where lesion develop and progress in the aorta. In the present study a semi-automatic computerized methodology was used in order to reproduce the 3D geometry of a healthy middle-aged male’s aortic arch and a computational model is applied in order to elucidate the Manuscript submitted on the 10th of June 2010. Dimitrios K. Fytanidis, is with Fluid Mechanics Devision, Faculty of Engineering, Democrition University of Thrace, 67100 Xanthi, GREECE. (Phone: ++302310260011, Fax: ++302310994837, e-mail: [email protected]). Johannes V. Soulis is, is with Fluid Mechanics Devision, Faculty of Engineering, Democrition University of Thrace, 67100 Xanthi, GREECE. (e-mail: [email protected]). Vasilios. C. Papaioannou is with Fluid Mechanics Devision, Faculty of Engineering, Democrition University of Thrace, 67100 Xanthi, GREECE. (e-mail: [email protected]). George D. Giannoglou 1st Cardiology Department, Cardiovascular Engineering and Atherosclerosis Laboratory, AHEPA General Hospital, Aristotelion University of Thessaloniki, GREECE. ([email protected]). relation between the two transient flow properties namely, the time-Average Wall Shear Stress (AWSS) and the OSI. II. MATERIALS AND METHODS A. Geometry Reconstruction The commercial software Mimics is used in order to reconstruct the 3D aortic arch geometry after 2D CT digital image processing, Fig 1. 2D images were imported in dicom format. The Mimics creates a mesh file geometry representing the 3D aortic arch as a set of tetrahedrons. The initial coarse 3D geometry was exported in STL (stereolithography) format. Specification of well-defined boundaries is crucial in order to prepare geometry volume and surface data for grid generation. The final produced geometry is shown in Fig 2. The finally smoothed geometry was imported into the computational grid generator Gambit (Fluent Inc). The computational grid was non-uniform and highly dense near wall boundaries. Fig.1 Typical 2D scanned image B. Flow Equations The governing flow equations, Eqs 1 and 2, are solved for incompressible, isothermal and laminar flow, using the finite-volume method provided by commercial software [9], ρu ρuu p τρg t ⎛⎞ ⎟ ⎜ ∂⎟ ⎜⎟ ⎜⎛⎞ ⎝⎠ ⎟ ⎜ +∇ =−∇ +∇ + ⎟ ⎜⎟ ⎜ ⎝⎠ ∂ G GG G (1) (ρu) ρu0 t ⎛⎞ ∂⎟ ⎜ +∇ = ⎟ ⎜⎟ ⎜ ⎝⎠ ∂ G G (2) ρ is the density, u G is the velocity, p is the static pressure, τ is the shear tensor, g G is the gravity acceleration. Oscillatory Flow in Human Arteries Dimitrios K. Fytanidis, Johannes V. Soulis, Vassilios C. Papaioannou and George D. Giannoglou T Fig. 2 Aortic arch geometry Blood is examined as a non-Newtonian fluid obeying to the power law and its density is set 1058 kg/m3. According to non-Newtonian power law, blood apparent viscosity can be calculated as o n1 T/T μke S − =  (3) S is the shear rate given by j i ji u u Sxx ∂ ∂ =+ ∂∂  (4) The consistency index k is 0.00622 (kg-sn-2/m), the powerlaw index n is 0.7, T(K) and To(K) are local and reference temperatures, respectively. C. Boundary Conditions The applied velocity inlet pulse is shown in Fig. 3. The pulse period of this waveform is 800 msec. The outflow discharges were calculated using a slightly modified version of the Murray’s Law [10] and are represented in Table I. Fig. 3 The applied blood waveform at the inlet of the aortic arch D. Wall Shear Stress and Oscillating Shear Index The components of the WSS possibly have different effects upon endothelial cells. WSS diagonal components generate intercellular tension whereas the off-diagonal components contribute to intercellular shearing forces. Thus, the actual shear stress is given by () SWSS μS ⎡ ⎤ = ⎣ ⎦  (5) The time-averaged WSS magnitude (AWSS) is defined as T 0 WSS 1 AWSS dt T =∫JJJJJG (6) WSS J JJJJG is the instantaneous WSS (Pa) magnitude and T (sec) is the pulse period. Another transient flow property, related with the wall, is the magnitude of time-averaged WSS vector (AWSSV) defined as T 0 1 AWSSV WSSdt T =∫JJJJJG (7) OSI monitors the differences between AWSS and AWSSV values. Using these values, OSI clarifies the WSS vector deflection from blood flow predominant direction, during cardiac cycle. Thus, OSI is calculated by T 0 T 0 WSSdt OSI 0.5 (1 ) WSS dt =×− ∫ ∫ JJJJJG JJJJJG (8) The OSI value can vary from 0, for no-cyclic variation of WSS vector, to 0.5, for 180-degree circularly deflection of WSS direction. III. RESULTS A. Average Wall Shear Stress (AWSS) The AWSS (N/m2) contours of the aortic arch are shown in Figs. 4. The AWSS values in the main artery i.e. in the ascending aorta, aortic arch and descending aorta, vary between 0.2 N/m2 and 3.5 N/m2. In the aortic branches higher values are encountered as a matter of higher strain, due to their decreased diameters (not shown). 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. TABLE I APPLIED OUTFLOW DISCHARGES AORTIC ARCH Qo[%] Inlet 100 Right common carotid artery 3.71 Right subclavian artery 14.92 Left common carotid artery 3.22 Left subclavian artery 6.67 Descending aorta 71.48 Fig 4. Average Wall Shear Stress (N/m2) Furthermore, the flow within the aortic branches is strongly dependent upon the geometry of the branch and its particular placement within the aorta. Thus, the right common carotid artery exhibits increased AWSS throughout the cardiac pulse, Fig. 4. In contrast, the right subclavian branch exhibits particularly low WASS. Always, low AWSS is major factor contributing to the onset and development of atherosclerosis. B. Oscillating Shear Index (OSI) The OSI reveals the WSS magnitude inversion during the cardiac pulse wave. The OSI contours of the aortic arch are shown in Figs. 5. The OSI values in the main artery i.e. in the ascending aorta, aortic arch and descending aorta, vary between 0.0 and 0.3. High OSI values are encountered at the lower part of the outer aorta descending region. Furthermore, high OSI values develop at the convex part of the ascending-descending aorta. Low OSI develops at the upper concave part of the aorta descending region. C. Average Wall Shear Stress versus Oscillating Shear Index (OSI) Typical relationship between AWSS and OSI over the entire aortic surfaces is shown in Fig. 6. It is evident that increasing OSI values coexist with decreasing WSS. However, when the AWSS values are further reduced to zero, the OSI values decrease as well. IV. DISCUSSION The calculations of AWSS and OSI presented here provide valuable flow parameters for the description of the haemodynamics status within the aorta. The purpose of this study was to perform hemodynamic analysis of human arteries (patient-specific), particularly the aorta and to analyze the relationships between AWSS and OSI. Numerical results [11], among numerous others, suggest that low WSS and high OSI tend to cause wall thickening along the inferior wall of the healthy aorta and the anterior wall of the brachiocephalic artery. In general low AWSS and high OSI are considered to be susceptible to intimal thickening. It is apparent from Fig. 6, that the lower the AWSS is, the higher the OSI values are. It is also well known that low WSS results into the development of atherosclerosis. However, when the AWSS values are further reduced to zero the OSI values decrease as well. In our analysis we present the AWSS contours (not the WSS) with the OSI contours during the cardiac pulse. Results indicate that aorta regions of high OSI do not collocate with regions of low AWSS. V. CONCLUSION The present study analyzes the factors simulating pulsatile blood flow in the human aortic arch. Using numerical techniques we examine the spatial distribution and the relation between time-AWSS and OSI. The lower the AWSS is, the higher the OSI values are. Fig 5. Oscillating Shear Index (OSI) However, both flow parameters can elucidate the preferable atherosclerosis regions within the aorta. Fig. 6 Time-average Wall shear Stress (N/m2) versus Oscillating Shear Index However, when the AWSS values are further reduced to zero the OSI values decrease as well. The velocity vector oscillates and at the same time alters its direction in places. Low AWSS and high OSI values do not always collocate. Regional differences between WSS magnitude and OSI may answer the question as to where atherosclerotic lesions predominately develop and progress at specific aortic regions. REFERENCES [1] C.R. Ethier, “Computational Modeling of Mass Transfer and Links to Atherosclerosis”, Annals of Biomedical Engineering, vol. 30, pp. 461– 471, 2002. [2] J.V. Soulis, G.D. Giannoglou, V. Papaioannou, G.E. Parcharidis and G.E. Louridas, “Low-density lipoprotein concentration in the normal left coronary artery tree,” BioMedical Engineering On Line, 2008. [3] J.A. Moore, D.A. Steinman, D.W. Holdsworth and C.R. Ethier, “Accuracy of computational hemodynamics in complex arterial geometries reconstructed from magnetic resonance imaging”, Annals of Biomedical Engineering, vol. 27, pp. 32–41, 1999. [4] D.A. Steinman, “Image-based computational fluid dynamics modeling in realistic arterial geometries,” Annals of Biomedical Engineering, vol. 30, pp. 483–497, 2002. [5] D.A. Steinman, J.S. Milner, C.J. 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