Numerical simulation of infimal thickening in a bifurcation artery

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Thread 2. Flow-Structure Interactions

[2] V.K. Sud. Biophys. J. 2003; 84: 2638-2645. [3] O. Anwar Beg, H.S. Takhar, et al. Micropolar bioengineering fluid dynamics: a review. October 2005; in preparation. 7789 We-Th, no. 42 (P68) Effect o f meteorological parameters on aerosol number density during pre-monsoon season over Roorkee (India) D.K. Sharma & Jagdish Rai. Department of Physics, Indian Institute of

Technology, Roorkee, India Aerosol number density distribution for different size ranges have been studied in relation with some meteorological parameters (relative humidity, temperature, rainfall and wind speed) during South-East (SE) pre-monsoon (May-July 2001) at Roorkee (77053 / E, 29052 / N and 275 m at hmsl). The measurements were done with the help of Optical particle counter by exposing the particles to light. The scattered light from aerosols of different size range generates the electrical pulse of different height. The counter monitors the particle concentration in four different size ranges viz: 0.3-0.5~m, 0.5-1.0 ~m, 1.0-2.0~m and 2.0-5.0~m. These size ranges are mainly responsible for the optical effect, cloud condensation and radiation budget in the atmosphere. An analysis has been done taking the daily average number density of aerosols and meteorological parameters during pre-monsoon season. The present study indicates that the number density of aerosol is affected by the meteorological parameters. The rain has played significant role to modulate the aerosol concentration. In the month of July the concentration of aerosol was less than that from the month of June and it was maximum in May during pre-monsoon season. The large size ranges (1.0-2.0 ~m and 2.0-5.0~m) were much more effective compared to the lower size ranges (0.3-0.5~m and 0.5-1.0 ~m). The decrease of concentration for aerosols in the month of July has been attributed to the scavenging by the prevailing monsoon rain. The wind speed was not significantly effective in changing the aerosol number during this period. 6803 We-Th, no. 43 (P68) Multi-scale simulation of blood flow with the dynamical behavior o f elastic red blood cells T. Omori, S. Wada, K.-I. Tsubota, T. Yamaguchi. Department of Bioengineering

and Robotics, Tohoku University, Sendal, Japan

ductus of efferentus of the male reproductive tract and vasomotion in small blood vessels, pumping mechanisms utilized in biomedical devices such as the heart-lung machine. The most sophisticated mathematical model for the physiological fluids, is the micro-continuum rheological model, introduced by Eringen [1]. The micropolar theory has proven to be an accurate model in the simulation of various biofluid problems. However the presence of porous matrix is often encountered in biomechanics. Vascular beds, lungs, kidneys and tumorous vessels are several important examples of zones in the body where porosity has a major influence on fluid dynamical processes. However in perfused skeletal tissue structures inertial effects are boosted and Forcheimmer drag needs to be incorporated into the mathematical model for the porous medium. The purpose of the present study is to develop a mathematical model for micropolar peristaltic pumping in a 2D anisotropic non-Darcian porous medium. Such a study, which has thusfar not been reported in the scientific literature, constitutes an important extension to peristaltic non-Newtonian biofluid dynamic modelling. The effects of both bulk matrix resistance and Forcheimmer impedance are incorporated in the equations. FEM is used with a thorough examination of the interactional effects of anisotropic permeability, Forcheimmer drag, Darcian drag, micropolar viscosity ratio, amplitude ratio on the peristaltic pumping flow regime. The model described herein has various applications in hemodynamic flows in tissue zones in flexible conduits, stenosed arteries and peristaltic biomedical devices. References [1] Eringen A.C. Micropolar fluids. JAMM 1966; 16: 1-18.

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Flow-Structure Interactions 4238 Mo-Tu, no. 1 (P68) Use of fluid-structure simulations to determine pulse wave velocity in the human aorta N. Sampat, M. Gabi. Department of Fluid Machinery, Faculty Mechnaical

Engineering, University Karlsruhe, Germany

Motion and deformation of Red Blood Cell (RBC) and their mechanical interaction play an important role in non-Newtonian properties of blood. The aim of this study is to investigate the rheological properties of the blood from the analysis of dynamic behavior of multiple RBCs in the flowing blood. In order to simulate the RBC behavior in the flowing blood, we built up a two-dimensional model of an elastic RBC based on the minimum energy principle. The model was constructed by surrounding the internal liquid of RBC with spring elements which resist to bending and stretch of the RBC membrane. The interaction among multiple RBCs was expressed by a potential function assigned at each nodal point on the membrane. Based on the momentum conservation and Newton's friction law, the fluid force acting on the membrane was estimated from the difference in velocity between the RBC and fluid flow. The fluid flow was determined by solving continuity and Navier-Stokes equations with FEM, where the local viscosity of the fluid was given as a function of the cell density of RBC (local hematocrit, Hct). It was assumed that the viscosity increased with increasing local Hct. The calculations of RBC behavior and fluid flow were repeated until a stable flow was obtained. The simulation was carried out for a blood flow containing 108 RBCs (mean Hct =0.31) in the straight channel with a height of 96 ~m and a length of 44 ~m. The initial flow was assumed to be a Poiseuille flow taking a parabolic velocity profile. The Reynolds number was 0.06 and the periodic boundary condition was applied to the both edges of the channel. The RBCs were carried downstream by the fluid flow with an axial migration, causing higher fluid viscosity around the central axis than that near the wall of the flow channel. As a result, the velocity profile was finally converged to that of non-Newtonian blood flow observed in experiments, taking a uniform velocity around the central axis of the channel.

In practical medical fields like cardiology and angiology, Pulse Wave Velocity (PWV) determined in vivo and its correlations to arterial stiffness and disorders of the cardio-vascular network are reported frequently and used as a medical indicator. Experimentally, the measurement is a challenge because of the complicated geometry in the periphery of the heart, complex geometry of the vascular network and due to Non-Newtonian character of blood-flow properties. Moreover the blood-flow itself is unsteady in nature. We report a method to determine PWV through fluid-structure interaction simulations conducted on a highly detailed human-based aorta model. The mechanical properties and boundary conditions are based on experiments. The commercial software packet STAR-CD, based on finite volume method, and structure mechanics software packet PERMAS, based on finite element method have been used. The fluid-structure interaction has been realised as that of pressure exchange between the aorta-wall and the fluid. With the help of the software MpCCI from Fraunhofer Institute SCAI, this exchange was carried out between STAR-CD and PERMAS. In STAR-CD the flow is characterised as 3-dimensional, laminar, incompressible and the aorta-wall is hydraulically smooth. Through the simulations we demonstrate the distensibility of the model aorta and deduce PWV through a modified BramwelI-Hill equation. Results for the PWV will be compared with values reported in literature and further computations will be proposed. The numerical simulation method of fluidstructure coupling can thus be useful for deducing important medical indicators. Moreover, such simulations can be used on in vitro distensible tubes found useful in the emerging field of tissue engineering for replacing in vivo sick arteries.

4090 We-Th, no. 44 (P68) Peristaltic pumping of micropolar fluid in porous channel - model for stenosed arteries R. Bhargava 1, S. Sharma 2, H.S. Takhar3, T.A. B6g 4, O.A. B6g 5, T.K. Hung 6.

4790 Mo-Tu, no. 2 (P68) Numerical simulation of intimal thickening in a bifurcation artery '~ Fan 1,2, W. Jiang 2, '~ Sou 2, J. Chen 2. 1Department of Bioengineering,

1Mathematics Department, liT, Roorkee, India, 2Mathematics Department, liT, Roorkee, India, 3Engineering Department, MMU, Manchester, England, UK, 4Earthquake Consultant, Manchester, UK, 5Leeds Metropolitan University, Leeds, England, UK, ~Neurosurgery, Civil Department, University of Pittsburgh, USA Peristaltic flows are involved in many biological and biomedical systems, eg., urine transport from kidney to the bladder through the ureter, the transportation of chyme in the gastro-intestinal tract, the movement of spermatozoa in the

Beihang University, Beijing, China, 2Biomechanical Engineering Laboratory, Sichuan University, Chengdu, China Intimal thickening is a complicated process from plaque formation to arteryobstructed. In this process, intimal thickening, the change of artery geometry and hemodynamics are interacted. A new numerical skill named Cell-filled method is applied to simulate the process of intimal thickening in a carotid bifurcation under critical low wall shear stress condition. The new method can overcome the limitation of previous method£ such as the discontinuous of simulation and the trouble of model re-meshing. Results showed that the low

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Journal o f Biomechanics 2006, Vol. 39 (Suppl 1)

wall shear stress cannot result in obstructing the artery, but the interaction among intimal thickening, the change of artery geometry and hemodynamics is notable. It was observed numerically that the process of intimal thickening includes two stages of "thickening" and "spreading". The most severe stenosis occurs at the outside wall of sinus and at a distance of 5 mm from bifurcation section. The location of intimal thickening and plaque shape accords with the clinical observations. 6856 Mo-Tu, no. 3 (P68) On the geometry of arterial bifurcation S.-I. Watanabe 1, T. Matsuo 1, '~ Yokoyama 2, K. Yamamoto 1. 1Faculty of

Engineering, Kanagawa Institute of Technology, Kanagawa, Japan, 2Institute of Biomaterials and Bioengineering, Tokyo Medical and Dental University, Tokyo, Japan Murray has applied minimum work concept to a theoretical analysis of blood flow trough cylindrical segment of blood vessel and derived an expression that the diameters D of blood vessels are proportional to the cube root of the flow Q which they convey, i.e. D - Q1/3. With similar consideration, the angle of vascular branching has been predicted as a function of relative sizes of the parent trunk and its branch vessels. It has been generally accepted that arterial bifurcation geometries are understandable in terms of optimization with respect to energy expenditure required for a fluid conducting system. However, some authors, who measured arterial geometries, reported significant deviation from the Murray's law. In this study, we measured vessel geometries in various part of animal body and also in chick embryo. The results were compared with theoretical predictions by Murray as well as fluid mechanics of pipe flow to understand the physiological principle governing of arterial geometry. The relationships between branching angles and diameter ratios of branch vessels were found to be statistically significant correlation, which were in qualitative agreement with the theoretical predictions by Murray. However, the arteries were found to be well winding in most organs, especially in the brain, and therefore the branching angles were defined only in the neighborhood of branch points. This fact suggests that the branching angle of arterial bifurcation is governed by local factors. 7378 Mo-Tu, no. 4 (P68) Application o f unsteady separation investigations to stenosis S.E Das, J.H. Arakeri, U. Srinivasan. Indian Institute of Science, Bangalore,

India In a stenotic artery, the flow apart from being unsteady has a spatial variation. In particular, the boundary layers are subject to high favorable and adverse pressure gradients because of the spatial and temporal variations in velocity. It is important to know where and when the boundary layer may separate or undergo transition to turbulence. An unsteady water tunnel has been designed to study the unsteady separation past a bluff body (40% blockage), which mimics the flow of blood in stenosed artery. The set up is a closed loop water tunnel which has two compartments separated by a thick glass plate. A piston, driven by a servo motor, placed at the bottom compartment follows a trapezoidal variation. We present two aspects of flow past the bluff body. One is initiation of separation for a flow that is uniformly accelerating from rest. Experiments have been done with several acceleration values. A separation process, clearly observed using LIF technique, initiates with a 'separation vortex' that eventually moves away from the body. We derive non-dimensional time scales for the formation of the separation vortex. For acceleration Reynolds number, Rea >400 the nondimensional vortex formation time, tv([al(HUo) (duldS)] 1/2, is nearly constant (-4.0), where U0 and H are the free stream velocity and height of the channel at inlet and du/dS is the non-dimensional velocity gradient at the maximum pressure gradient point. Using a convective time scale, the time of formation of vortex is 5.5(Ue/~) -1, where ~ is the boundary layer thickness ( - 3 . 7 ~ ) . One notable observation is very large residence time of fluid particles within the separation bubble, which may be relevant for the growth of stenosis. The second aspect of the flow is the instability of the separating shear layer and shedding frequency of the shear layer vortices. The Strouhal number based on upstream momentum thickness and the velocity is found to vary between 0.004 and 0.008. The study gives an insight to the flow in the post stenotic region. 7517 Mo-Tu, no. 5 (P68) Prediction of elastic membrane moving pattern in sac-type ventricular assist device using numerical simulation F. Firouzi, N. Fatouraee, S. Najarian. Biological Fluid Mechanics Laboratory,

Biomedical Engineering Faculty, Amirkabir University of technology, Tehran, Iran Implantable devices producing a pulsatile flow are among the best prototype of ventricular assist device (VAD). Sac-type implantable VAD (including sec-

Poster Presentations ondary fluid) is one of the best type of its. In the present study, in order to predict the moving pattern of elastic membrane, three different models of sactype VAD have been numerically simulated. It is done by using FEM with segregated approach and mixed Eulerian-Lagrangian formulation. The motion of the elastic membrane is assumed to be elliptical in the first model and wavy in the second one. In the third model, the time dependent pressure boundary conditions in inlet and outlet ports are added to the second model in order to real simulation as much as possible. Pressure conditions are considered equal to left atrium (in diastole phase) and aorta artery pressure (in systole phase) in a natural heart complete cycle. The results demonstrate change of movement pattern of elastic membrane dose not affect vertical stress variations onto membrane and also the effective fluid dynamics term onto membrane is fluid pressure adjacent to membrane. Comparing the results of models shows the effect of membrane movement pattern on the blood flow inside the chamber is negligible and so it can be assumed that the movement of elastic membrane follows from simple model with a good approximation. References [1] Mussivand T., Handry EJ. Progress with the HeartSaver ventricular assist device. Ann Thorac Surg 1999; 68: 785-789. [2] Firouzi E, Fatouraee N., Najarian S. The effect of elastic membrane moving pattern on the blood flow in a sac-type ventricular assist device. The 13th Nordic-Baltic Conference on Biomedical Engineering and Medical Physics, June 13-17, Umea, Sweden, 2005. [3] Firouzi E, Fatouraee N., Najarian S. Simulation of blood flow in a sac-type ventricular assist device using computational fluid dynamics. Iranian Journal of Biomedical Engineering 2005 Winter; 1(2): 129-142. 7814 Mo-Tu, no. 6 (P68) Towards early diagnosis of atherosclerosis - role of shear stress V. Kanyanta 1,2, A. Ivankovic 1. 1Department of Mechanical Engineering,

University College Dublin, Ireland, 2Science Foundation Ireland, Dublin, Ireland Introduction: This research looks at the effect of shear stress variations and shear stress gradients in a pulsatic flow (coupled with flow separation and reattachment, flow recirculation, flow stagnation and turbulence) on ECs and its role in atherogenesis. Materials and Methods: polyurethane rubber (10 mm diameter) is chosen to simulate arteries because of its recent use in vascular reconstruction, and have been proved to be more compliant. First phase was material characterisation, and then followed by ec culture inside the tubing. Ecs will then be subjected to flow conditions experienced in vivo. Shear stress measurements shall then be taken while monitoring the response of the cells over a period of time to be determined. Numerical simulations will then follow using openfoam. References [1] R.B. Healy. Shear Stress on Endothelial Cells: Microscale Fluid Dynamics. 2004; Dept of Mech and Biomedical Engineering, NUI, Galway. [2] M. Akram. Wall shear stress and early atherosclerosis: a review. A JR 2000 June; 174. [3] Kurt Lin, Molecular mechanism of endothelial growth arrest by laminar shear stress. PNAS 2000 97(17): 9385-9389. 4380 Mo-Tu, no. 7 (P68) Coupled b l o o d - w a l l modeling o f steady flow in stenotic carotid arteries E.Y Tafti, M.T. Shadpour. Faculty of Biomedical Engineering, Amirkabir

University of Technology (Tehran Polytechnique), Iran Severe arterial stenoses caused by atherosclerotic plaques, may cause critical flow conditions and arterial wall mechanical disturbances which have been related to thrombose formation, platelet activation, fatigue, compression and plaque rupture in the artery wall, which lead to major heart complications as strokes [1]. In this study, computational models of stenotic carotid arteries were analyzed with deferring geometric and mechanical parameters, taking into account the fluid-solid interactions of the blood and the artery. A linear elasticity approach is implemented in modeling the artery wall and NavierStokes equations govern the fluid domain. The idea of physiological blood supply of 5.1 ml/s is adopted, as the mean flow rate of the common carotid artery (Reynolds number is 350). An incremental boundary iteration method is used to handle the fluid-wall interactions. Results indicated that severe stenoses cause high levels of wall shear stress at the throat and low and even negative wall shear stress downstream the stenosis, increased upstream blood pressure and overall disturbed blood flow pattern downstream of the stenosis. In the artery wall, the stress pattern was shown to be highly localized and extreme values of tensile and compressive circumferential stresses occur with abrupt changes in the stenotic region. Wall compliance had a regulating effect over mechanical parameters compared to the rigid wall. It was concluded that the vulnerable site of the artery in terms of further plaque formation and growth, according to previous experimental works, is the distal side of the plaque. Wall compression and collapse were observed in severely constricted arteries.