D. Sekhane et al. / Journal of Advanced Research in Physics 6(2), 021604 (2016) 1 Image-based Computational fluid dynamics (CFD) Modeling cerebral blood flow in the Circle of Willis Djalal Sekhane 1,*, Karim Mansour 1,2 1 Laboratory of Electronic Materials Study for Medical Applications, Brothers Mentouri University, Algeria 2 Medical School of Constantine, University Constantine 3, Algeria Abstract Understanding the blood flow in cerebral arterial tree have a major importance to apprehend the mechanisms of the transport of blood in the cortex. Recently, the use of Computational Fluid Dynamics (CFD) combined with medical imaging methods has increased. In this work we investigate the influence of the change of heart rate on the different hemodynamic parameters. Numerical simulations based on 3D Navies-Stokes laws used to calculate and estimate the values of the hemodynamic parameters investigated. The study concentrates on the Circle of Willis (CW), the base of cerebral vasculature network. The 3D geometry has extracted from MRI images (3D TOF) obtained from GE Signa HDtx MRI with TE=3.1 ms, TR=25 ms, thickness=1.4 mm, the arterial network was reconstructed using 3DSlicer. Afterwards the CW was isolated for the simulation. We use pulsatile laminar incompressible flow assumptions to resolve 3D Navies-Stokes equations using COMSOL Multiphysics software in the proposed geometry. We consider that the blood is a Newtonian fluid with the physical parameters: dynamic viscosity µ = 4e-3 Pa*s and density ρ = 1060 Kg/m 3. Submitting the Circle Of Willis to different heart rates under pulsatile laminar incompressible flow we found The values of pressure were ranged between [100-123] mmhg, and the Wall shear stress between [0-6] Pa with no correlation between the artery pressure and the flow indicating that there is no quantitative effect on the vessels. The results found may help to understand the mechanisms of transport inside the vessels and the mechanisms of regulation inside the cerebral blood tree. Once finalized and valid, this model could be used to estimate potential variation of structural and mechanical parameters to some arterial disease. Keywords Cerebral blood flow, COMSOL Multiphysics, MRI, Circle of Willis, Newtonian Fluid. I. INTRODUCTION KNOWLEDGE of blood flow inside the cerebral arteries has a major importance to understand of the mechanisms of blood transport in the human brain. The brain blood supply is provided by the Common Carotid Arteries (CCAs) and the Vertebral Arteries (VAs) [1]. These arteries are considered as the parent arteries of major segments in the brain. In the base of the brain, we can find the Internal Carotid Arteries (ICAs) and the Basilar Artery (BA) relied by the Posterior Communication Arteries (PCoAs) and Anterior Communication Arterie (ACoA) to form the circle of Willis (CW) (fig. 1). As function, the CW is known by its compensatory mechanisms in the case of stenosis or the occlusion of the ICA or the BA [2]. Hemodynamics known as the blood flow dynamics inside the vessels has important role in the development of several cerebral strokes, like aneurysms [3] and Ischemic strokes [4]. However, the knowledge of the different hemodynamic factors is required to understand the mechanisms of the genesis and progression of different cerebro-vascular pathologies. Fig.1 Anatomy of the Circle of Willis The medical imaging has known a big advancement in the last decades. The advancement can be seen in quality of acquisition and images modalities. However, the current imaging modalities have some limitations to provide reliable hemodynamic information. With this handicap, it seems to be necessary to use patient specific Computational Fluid Dynamics (CFD) [5]. This choice can be justified by the ability of this method to provide effective and safe information of flow factors basing on some important assumptions like blood viscosity, aneurysm and artery wall and inlet boundary conditions during the simulations [6-7]. The aim of this work is to present preliminary data processing pipeline focussing on the extraction of a 3D patient specific smooth geometric model from MRI imaging and estimate hemodynamic factors using CFD. Manuscript received August 2, 2016. * Corresponding author (djalalsekhane@gmail.com)
2 D. Sekhane et al. / Journal of Advanced Research in Physics 6(2), 021604 (2016) II. MATERIAL AND METHODS A. Vascular model In order to study different hemodynamic factors inside the major segments of the CW, we performed a time of flight (TOF) magnetic resonance angiography (MRA) sequence for a young person using GE HDxt system (General Electric Healthcare). The parameters used are: time of repetition TR=25 ms, time of echo TE=3.1 ms, flip angle: 20, slice thickness 1.4 mm to obtain 152 slices of reconstruction matrix 512*512 voxels, covering the volume of interest. After gathering the images of angiographic sequence, a 3D patient-specific model of the major vessels was obtained. After the geometry reconstruction the vessels of the CW were truncated (Fig. 2). simulations were performed, using heart rates of 66 beats per minute (bpm), 73 bpm and 92 bpm for the investigation of the different hemodynamic factors inside the CW. The factors studied are: the pressure, wall shear stress and the velocity streamlines. The boundaries conditions used are shown in the Table 1. TABLE 1 Boundaries conditions Used in the different simulations Fluid Newtonian, Incompressible fluid Wall Rigid, with no-slip condition Boundary condition Flow Model Inlet Surrogate pulsatile flow rate waveform (3 cycles). Frequencies used: 66 bpm 73 bpm and 92 bpm. Zero pressure. Outlet Pulsatile pressure waveform (3 cycles) Frequencies used: 66 bpm 73 bpm and 92 bpm. Laminar Fig. 2 Patient-specific CW B. Blood flow simulation Inside the considered vessel geometry, the blood flow is governed by two equations: u = 0 (1) u ρ + u u = t (2) T 3 = p+ µ ( u+ ( u) ) µ ( u) I + F 2 where (1) is the continuity equation, (2) is the momentum conservation equation composed from: the inertial forces, pressure forces, viscous forces, and external forces, ρ is the density, p the pressure and u the velocity. The flow was considered laminar and the blood is supposed Newtonian, incompressible fluid with a density ρ = 1060 kg/m 3 and a dynamic viscosity µ = 4 mpa*s. During the simulation, the vascular wall was considered rigid with noslip condition. For the different simulation we have used COMSOL Multiphysics. This software is known in the research field by its steady good solver and its accurate results, also it has a good graphic resolution, that make of this software a good choice for our application. The software was used to mesh the geometry of interest giving 480812 elements, 66460 boundary elements and 582 edge. The geometrical model contains no error and no reverse elements has been found, the Absolut tolerance has been talked as default. In the different simulations we used a flow rate waveform as inlet and a pressure waveform as outlet. The physiological data was for a healthy person and obtained from our data base. The calculations have been effectuated during three cycles to insure the convergence and the stability of the solver. Three Fig. 3 Flow rate and pressure waveforms used in the simulations Fig. 3 represents the graphical representation of the physiological data of the flow rate and the pressure waveforms used in the simulation, obtained from our data base. The total time is 2.466 s the systolic time was in 1.864 s. For the flow rate the typical flow is 4.6 ml/s for the heart rate 73 bpm. III. RESULTS In the fig.4 we can see the simulation results of the heart rate 66 bpm. The fig.4 gives the WSS values resulting from the blood flow inside the different compartments of the circle of Willis, and obtained from the product of dynamic viscosity and the shear rate solution. The values of WSS were ranged
D. Sekhane et al. / Journal of Advanced Research in Physics 6(2), 021604 (2016) 3 between [0, 5] Pa, the highest values were found in two locations, the first in the internal carotid artery (ICA) in the cerebral segment, the second were found in the intersection in where the ICA, the middle cerebral artery (MCA) and middle communication artery (MCoA). Fig.4 shows the pressure distribution at the systole time on a complete circle of Willis of a young health person, the pressure takes values from 118 to 123 mmhg distributed from high pressure in the internal carotids and vertebral arteries, to low pressure localised in anterior, middle and posterior cerebral arteries. The pressure distribution seems to be normal and decrease with the decreasing of the arteries radius. Fig.4 shows the streamlines in the circle of Willis, it gives a cartography of the flow speed inside the different segments. We can see the maximum value of the blood velocity at the same zone in where the values of WSS are the highest. The areas or values of the pressure decreases the velocity values increases. of the values. the pressure distribution at the systole time is represented in the fig. 5, the pressure takes values between 103 to 106 mmhg, with a decrease of 14% in the ICA and 13% in anterior, middle and posterior cerebral arteries from the previous heart rate. The overall distribution remains unchanged with no peaks of pressure on the different segments. The streamlines speeds inside the volume of interest are shown in the fig.5. We can see that the speed is increased in the different segments, its maximum is 0.66 m/s and 1.32 m/s for a heart rate of 66 bpm and 73 bpm respectively. One should note that this values were obtained in the zones with highest values of WSS. Fig. 5 Simulation results for the heart rate 73 bpm Fig.4 Simulation results for the heart rate 66 Bpm Simulation results of the heart rate 73 bpm are represented in the fig. 5. In fig.5 the WSS values resulting from the blood flow inside the different compartments of the CW, values were ranged between 0 and 6 Pa and with an increase of 14 % from the values using heart rate 66 bpm. The values repartition remains unchanged in the different segments of the CW, but the zone in where we have a high value of WSS in the previous case are the zones concerned by the increase Fig. 6 shows the simulation results of the heart rate 92 bpm. In fig.6 the WSS has values between 0 and 6 Pa with a small change comparing to the heart rate 73 bpm. Fig.6 shows the pressure distribution at the systole time, the pressure takes values were between 100 to 103 mmhg, with a small decrease in the majority of the segments. Fig.6 shows the streamlines speeds inside the volume of interest, we can see that the speed is decreased comparing to the speed found.
4 D. Sekhane et al. / Journal of Advanced Research in Physics 6(2), 021604 (2016) of the variation of vessel radii and the bifurcation angles on the pressure and the WSS. He found that the values of WSS were high in the location in where the aneurysms are frequent, also the he gives anatomic variants known to be associated to aneurysm development. Regarding to this work, in our case, the values of WSS were low and the possibility of creation of an aneurysm is also low. However, the highest values of WSS were localised near to bifurcation and at this location, creation of an aneurysm is eventual but still far. Our results show also normal values of pressure [100, 123 mmhg], which keeps low probability for a vascular disease caused by the pressure. Varying the heart rate, the values of the different factors we have studied did not have important changes, and the values stills in the normal range. The heart rate increasing has no quantitative effect on the different on the flow, vascular resistance, and there are no correlations between the heart rate and the pressure which is in good agreement with the work of [11]. This study contains some limitation. The vascular walls were assumed to be rigid, which can be a cause of over-estimation of the WSS [3]. The blood was assumed to be a Newtonian fluid, a good approximation for large arteries. The Newtonian behaviour was largely believed to be a source of over-estimation of the values of WSS, this has been gainsaid by the work of Cebral.et al [12]. Also, because of the absence of the patient specific flow rate and pressure waveforms, we were forced to use surrogate no specific waveforms in our simulations. V. CONCLUSIONS Fig. 6 Simulation results for the heart rate 92 Bpm Heart rate increasing has no quantitative effects on the different hemodynamic factors inside the CW. This model could be used to investigate hemodynamic factors inside different arterial pathologies to understand their progression with more realistic parameters. IV. DISCUSSION In this study, we present results from the simulation of blood flow inside a complete CW, using CFD combined with patient specific images from a young person. The approach used is based on the creation of a patient specific geometry for the major cerebral arteries from angiographic magnetic resonance images (MRI), as well as assumptions about the blood characteristics and its behaviour inside the vessels. and form more reliable results we used pulsatile realistic flow rate and pressure waveforms. It is known that the WSS is involved in many pathophysiological processes related to vascular diseases [7], like aneurysms. It s suggested that high values of WSS may cause the initiation of an aneurysm, while low values facilitate the growth in the creation [8]. The pressure is also involved in many vascular diseases, like atherosclerosis defined as a deposition of plates on the vessel wall [9] and more aneurysms [6]. Where high values of pressure lead to cholesterol deposition on the carotid arteries [10]. In the work of M. S. Alnæs [3], he investigate the impacte REFERENCES [1] J. R. Cebral, C. M. Putman, M. T. Alley et al., Hemodynamics in normal cerebral arteries: qualitative comparison of 4D phase-contrast magnetic resonance and image-based computational fluid dynamics, Journal of engineering mathematics, vol. 64, no. 4, pp. 367-378, 2009. [2] Z. Vrselja, H. Brkic, S. Mrdenovic et al., Function of circle of Willis, Journal of Cerebral Blood Flow & Metabolism, vol. 34, no. 4, pp. 578-584, 2014. [3] M. S. Alnæs, J. Isaksen, K.-A. Mardal et al., Computation of hemodynamics in the circle of Willis, Stroke, vol. 38, no. 9, pp. 2500-2505, 2007. [4] C. J. Klijn, and L. J. Kappelle, Haemodynamic stroke: clinical features, prognosis, and management, The Lancet Neurology, vol. 9, no. 10, pp. 1008-1017, 2010. [5] L.-D. Jou, D. Lee, H. Morsi et al., Wall shear stress on ruptured and unruptured intracranial aneurysms at the internal carotid artery, American Journal of Neuroradiology, vol. 29, no. 9, pp. 1761-1767, 2008. [6] M. Cibis, W. V. Potters, F. J. Gijsen et al., Wall shear stress calculations based on 3D cine phase contrast MRI and computational fluid dynamics: a comparison study in healthy carotid arteries, NMR in Biomedicine, vol. 27, no. 7, pp. 826-834, 2014. [7] K. Kono, and T. Terada, Flow visualization of recurrent aneurysms after coil embolization by 3D phase-contrast MRI, Acta neurochirurgica, vol. 156, no. 11, pp. 2035-2040, 2014. [8] M. Shojima, M. Oshima, K. Takagi et al., Magnitude and role of wall shear stress on cerebral aneurysm computational fluid dynamic study
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