Numerical investigation of variations in wall shear stress distributions at the diseased human...
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$606 Journal of Biomechanics 2006, Vol. 39 (Suppl 1) Poster Presentations The effects of blood flow on wall stress and of wall motion on blood flow, were examined in axisymmetric models of AAAs. Models based on Gaussian curves have been created with Young's modulus in the range 2.0 to 4.5 MPa and both with and without thrombus. Flow was solved in Fluent and coupled to Abaqus, using an iterative method, for the solid solution. Realistic velocity and pressure waveforms [4] were used for the boundary conditions at the inlet and outlet respectively. Results are presented comparing the flow fields and wall stresses from FSI, rigid walled models and quasi-static pressure models. References [1] R Uflacker, J Robinson. European Journal of Radiology 2001; 11: 739-753. [2] RB Galland, TR Magee. Journal of Vascular and Endovascular Surgery 1997; 14: 421-422. [3] CJ Egelhoff et al. Journal of Biomechanics 1999; 32: 1319-1329. [4] CJ Mills et al. Cardiovascular Research 1970; 4: 405-417. 14.3 Hemodynamics and Vascular Biology 5204 Mo-Tu, no. 12 (P65) Mathematical modelling of blood flow in curved arteries J.H. Siggers, S.L. Waters. School of Mathematical Sciences, University of Nottingham, Nottingham, UK Atherosclerosis, characterised by plaques, is the most common arterial dis- ease. Plaques tend to develop in regions of low mean wall shear stress (WSS), and regions where the WSS changes direction during the course of the cardiac cycle. To investigate the effect of the arterial geometry and driving pressure gradient on the WSS distribution we consider an idealised arterial model. The artery is modelled as a pipe of fixed circular cross section of radius a, with centreline lying on an arc of a circle of radius R. The blood is treated as an incompressible Newtonian fluid driven by a steady pressure gradient characterised by the Dean number, D. We assume that the flow is fully developed and seek steady solutions to the governing equations, finding the dependence of the flow and WSS distribution on D and the pipe curvature, 5=a/R. Many arteries have significant curvature (e.g. the aortic arch has :~ ~), and we consider finite, as opposed to asymptotically small, curvature here. We solve the equations for a range of values of D and 5 using a combination of analytical and numerical techniques. Although varying the curvature does not produce any qualitative change in the flows, its value has a significant quantitative effect. For physiological parameter values the WSS is minimized at the inside of the pipe bend, making this the most likely site for plaque development. The effect of finite curvature is to increase the WSS there, indicating that the risk of plaque development would be overestimated by considering only the weak curvature limit. References [1] J.H. Siggers, S. L. Waters, Steady flows in pipes with finite curvature. Phys. Fluids 2005; 17(7): 077102. 5359 Mo-Tu, no. 13 (P65) A bond graph approach to analysis of effects of arteriosclerosis on cardiovascular system's performance A.A. Nikooyan, A.A. Zadpoor, A.R. Arshi. Biorobotics and Virtual Reality Research Laboratory, Department of Biomedical Engineering, Amirkabir University of Technology, Hafez Ave., Tehran, Iran Arteriosclerosis disease generally occurs in the aged people. It can be simply defined as hardening of the arteries and arterioles wall. The arteriosclerosis can lead to some major problems such as hypertension which substantially overloads the heart. Furthermore, it can adversely affect the aortic valve by reducing the elasticity of the aortic root. Regardless of the way the arte- riosclerosis develops, pathological effects of it are very important in analysis of performance of the cardiovascular system. In this paper, we try to study the undesirable effects of arteriosclerosis disease on performance of the human cardiovascular (CV) system. A bond-graph model of cardiovascular system is developed in which effect of arterioscle- rosis in performance of the cardiovascular system is taken into account. The new model is an improvement of our previously developed model. The original model is a bond-graph model of cardiovascular system at physiological state [1]. In that model, the most important complexities of the CV system such as pulsatile blood flow and elasticity of the blood vessel's wall were considered. However, the natural pace making of the heart is not considered and instead, a synthetic signal, similar to the natural one, is introduced to the model. Arteriosclerosis is modeled in the system by reducing compliance of the blood vessel's wall particularly in critical sites such as aortic root. The pulsatile nature of the flow as well as fluid-solid interaction is considered in the model. Governing differential equations of the model are derived and a MATLAB code is developed for simulation of the model. Simulations are carried out and a comparison is made between simulation results and widely available experimental data. It is shown that there is a good agreement between simulations results and experimental data. References [1] A.A. Zadpoor, A.R. Arshi, A.A. Nikooyan. A bond graph approach to the modeling of fluid-solid interaction in cardiovascular system's pulsatile flow. In: Proceedings of the 27th Annual International Conference of the IEEE in Medicine and Biology Society (EMBC05), Shanghai, China, 1-4 September, 2005. 7097 Mo-Tu, no. 14 (P65) Hemodynamic simulation of the effect of asymmetric entry velocity profile on wall shear stress in carotid bifurcation model Z. Ding 1, S. Yang 1, X. Zhu 2, '~ Wang 1. 1Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai, China, 2Image Center, No. 1 Hospital, Suzhou University, Suzhou, Jiangsu Province, China Up to now, in experimental and numerical simulation of carotid bifurcation under entry flow wave condition of common carotid, it is assumed that the entry velocity profile is symmetric. Clinical observations and analysis of 50 specimens show that the common carotid bends gradually with age. The asym- metric entry velocity profile has been observed through numerical analysis in a curved tube, using LDA in the phantom and using MRI clinically. The pictures of flow visualization in the phantom with a curvature-adjustable common carotid show that, with the same flow volume (Re=400), when the entry peak velocity deviated outwards or inwards by d/6 from the axis (d is the diameter of the common carotid), the area of separation zone in the sinus in the former case is four times that in the latter case. In these two cases, numerical simulations in a TF-AHCB model under physiological pulsatile flow conditions show that the differences in the size of the 0-3 10-3 Pa shear stress region on the outer wall of the sinus were very obvious during the diastole. The (inward or outward) tilting of the entry velocity profiles led to the formation of low shear stress regions on the inner wall of the sinus close to the bifurcation apex during the diastole. Sometimes, the low shear stress regions on the inner wall even became connected with those on the outer wall, forming an annulus. The greater the deviating distance of the peak velocity is from the axis, the stronger the above-mentioned results. The study shows that besides bifurcation geometry and entry flow waveform, the asymmetry of entry velocity profile is also a significant factor influencing the flow fields and the distribution of wall shear stress in the carotid sinus. 6830 Mo-Tu, no. 15 (P65) Numerical investigation of variations in wall shear stress distributions at the diseased human carotid artery bifurcation M.N. Baksh, M.Z. Bidhandi. University of Science and Technology, Tehran, Iran From clinical practice, it is known that the non-divider side of carotid sinus is very sensitive for the development of atherosclerotic lesions. Because of drastic consequences of a severely narrowed carotid artery bifurcation, there is a need for detecting mild stenosis, less than 25% area reduction, in a very early stage of the atherosclerotic disease. Wall shear stress plays a significant role in the formation of early atherosclerotic lesions; however these quantities are difficult to measure in vivo. The computerized simulation of the homodynamic behaviour of blood flow in the 3-D model of 25% and 35% stenosed carotid artery with different varying angles and varying mass flow rates at the entrance of CCA has been studied. The non-Newtonian fluid flow in the carotid bifurcation is investigated by using finite volume method to solve the three-dimensional Navier-Stokes equations coupled with a non-Newtonian constitutive model, in which the shear thinning behaviour of blood is described by the Kuang-Luo (K-L) equations. The results show that at the apex of bifurcation junction, because of noticeable changes in blood flow pattern as well as presence of flow separation, recirculation regions, the probability of deposition of atherosclerotic plaque would increase especially on the posterior wall of carotid sinus, due to low wall shear stress. The presence of stenosis will produce two definite regions in ICA especially near the non-divider side. The first region locates in sinus region which incorporates high WSS and the second region is out of the sinus with low WSS. These considerable variations in WSS and turbulence in downstream of stenosis region can cause a series of non-physiologic phenomena which may ultimately result in brain stroke.
Transcript of Numerical investigation of variations in wall shear stress distributions at the diseased human...
$606 Journal o f Biomechanics 2006, Vol. 39 (Suppl 1) Poster Presentations
The effects of blood flow on wall stress and of wall motion on blood flow, were examined in axisymmetric models of AAAs. Models based on Gaussian curves have been created with Young's modulus in the range 2.0 to 4.5 MPa and both with and without thrombus. Flow was solved in Fluent and coupled to Abaqus, using an iterative method, for the solid solution. Realistic velocity and pressure waveforms [4] were used for the boundary conditions at the inlet and outlet respectively. Results are presented comparing the flow fields and wall stresses from FSI, rigid walled models and quasi-static pressure models.
References [1] R Uflacker, J Robinson. European Journal of Radiology 2001; 11: 739-753. [2] RB Galland, TR Magee. Journal of Vascular and Endovascular Surgery 1997;
14: 421-422. [3] CJ Egelhoff et al. Journal of Biomechanics 1999; 32: 1319-1329. [4] CJ Mills et al. Cardiovascular Research 1970; 4: 405-417.
14.3 Hemodynamics and Vascular Biology 5204 Mo-Tu, no. 12 (P65) Mathematical modelling of blood f low in curved arteries J.H. Siggers, S.L. Waters. School of Mathematical Sciences, University of Nottingham, Nottingham, UK
Atherosclerosis, characterised by plaques, is the most common arterial dis- ease. Plaques tend to develop in regions of low mean wall shear stress (WSS), and regions where the WSS changes direction during the course of the cardiac cycle. To investigate the effect of the arterial geometry and driving pressure gradient on the WSS distribution we consider an idealised arterial model. The artery is modelled as a pipe of fixed circular cross section of radius a, with centreline lying on an arc of a circle of radius R. The blood is treated as an incompressible Newtonian fluid driven by a steady pressure gradient characterised by the Dean number, D. We assume that the flow is fully developed and seek steady solutions to the governing equations, finding the dependence of the flow and WSS distribution on D and the pipe curvature, 5=a/R. Many arteries have significant curvature (e.g. the aortic arch has
:~ ~), and we consider finite, as opposed to asymptotically small, curvature here. We solve the equations for a range of values of D and 5 using a combination of analytical and numerical techniques. Although varying the curvature does not produce any qualitative change in the flows, its value has a significant quantitative effect. For physiological parameter values the WSS is minimized at the inside of the pipe bend, making this the most likely site for plaque development. The effect of finite curvature is to increase the WSS there, indicating that the risk of plaque development would be overestimated by considering only the weak curvature limit.
References [1] J.H. Siggers, S. L. Waters, Steady flows in pipes with finite curvature. Phys.
Fluids 2005; 17(7): 077102.
5359 Mo-Tu, no. 13 (P65) A bond graph approach to analysis of effects of arteriosclerosis on cardiovascular system's performance A.A. Nikooyan, A.A. Zadpoor, A.R. Arshi. Biorobotics and Virtual Reality Research Laboratory, Department of Biomedical Engineering, Amirkabir University of Technology, Hafez Ave., Tehran, Iran
Arteriosclerosis disease generally occurs in the aged people. It can be simply defined as hardening of the arteries and arterioles wall. The arteriosclerosis can lead to some major problems such as hypertension which substantially overloads the heart. Furthermore, it can adversely affect the aortic valve by reducing the elasticity of the aortic root. Regardless of the way the arte- riosclerosis develops, pathological effects of it are very important in analysis of performance of the cardiovascular system. In this paper, we try to study the undesirable effects of arteriosclerosis disease on performance of the human cardiovascular (CV) system. A bond-graph model of cardiovascular system is developed in which effect of arterioscle- rosis in performance of the cardiovascular system is taken into account. The new model is an improvement of our previously developed model. The original model is a bond-graph model of cardiovascular system at physiological state [1]. In that model, the most important complexities of the CV system such as pulsatile blood flow and elasticity of the blood vessel's wall were considered. However, the natural pace making of the heart is not considered and instead, a synthetic signal, similar to the natural one, is introduced to the model. Arteriosclerosis is modeled in the system by reducing compliance of the blood vessel's wall particularly in critical sites such as aortic root. The pulsatile nature of the flow as well as fluid-solid interaction is considered in the model. Governing differential equations of the model are derived and a MATLAB code is developed for simulation of the model. Simulations are
carried out and a comparison is made between simulation results and widely available experimental data. It is shown that there is a good agreement between simulations results and experimental data.
References [1] A.A. Zadpoor, A.R. Arshi, A.A. Nikooyan. A bond graph approach to the
modeling of fluid-solid interaction in cardiovascular system's pulsatile flow. In: Proceedings of the 27th Annual International Conference of the IEEE in Medicine and Biology Society (EMBC05), Shanghai, China, 1-4 September, 2005.
7097 Mo-Tu, no. 14 (P65) Hemodynamic simulation of the effect of asymmetric entry velocity prof i le on wall shear stress in carotid bifurcation model Z. Ding 1 , S. Yang 1 , X. Zhu 2, '~ Wang 1 . 1Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai, China, 2Image Center, No. 1 Hospital, Suzhou University, Suzhou, Jiangsu Province, China
Up to now, in experimental and numerical simulation of carotid bifurcation under entry flow wave condition of common carotid, it is assumed that the entry velocity profile is symmetric. Clinical observations and analysis of 50 specimens show that the common carotid bends gradually with age. The asym- metric entry velocity profile has been observed through numerical analysis in a curved tube, using LDA in the phantom and using MRI clinically. The pictures of flow visualization in the phantom with a curvature-adjustable common carotid show that, with the same flow volume (Re=400), when the entry peak velocity deviated outwards or inwards by d/6 from the axis (d is the diameter of the common carotid), the area of separation zone in the sinus in the former case is four times that in the latter case. In these two cases, numerical simulations in a TF-AHCB model under physiological pulsatile flow conditions show that the differences in the size of the 0 -3 10 -3 Pa shear stress region on the outer wall of the sinus were very obvious during the diastole. The (inward or outward) tilting of the entry velocity profiles led to the formation of low shear stress regions on the inner wall of the sinus close to the bifurcation apex during the diastole. Sometimes, the low shear stress regions on the inner wall even became connected with those on the outer wall, forming an annulus. The greater the deviating distance of the peak velocity is from the axis, the stronger the above-mentioned results. The study shows that besides bifurcation geometry and entry flow waveform, the asymmetry of entry velocity profile is also a significant factor influencing the flow fields and the distribution of wall shear stress in the carotid sinus.
6830 Mo-Tu, no. 15 (P65) Numerical investigation of variations in wall shear stress distributions at the diseased human carotid artery bifurcation M.N. Baksh, M.Z. Bidhandi. University of Science and Technology, Tehran, Iran
From clinical practice, it is known that the non-divider side of carotid sinus is very sensitive for the development of atherosclerotic lesions. Because of drastic consequences of a severely narrowed carotid artery bifurcation, there is a need for detecting mild stenosis, less than 25% area reduction, in a very early stage of the atherosclerotic disease. Wall shear stress plays a significant role in the formation of early atherosclerotic lesions; however these quantities are difficult to measure in vivo. The computerized simulation of the homodynamic behaviour of blood flow in the 3-D model of 25% and 35% stenosed carotid artery with different varying angles and varying mass flow rates at the entrance of CCA has been studied. The non-Newtonian fluid flow in the carotid bifurcation is investigated by using finite volume method to solve the three-dimensional Navier-Stokes equations coupled with a non-Newtonian constitutive model, in which the shear thinning behaviour of blood is described by the Kuang-Luo (K-L) equations. The results show that at the apex of bifurcation junction, because of noticeable changes in blood flow pattern as well as presence of flow separation, recirculation regions, the probability of deposition of atherosclerotic plaque would increase especially on the posterior wall of carotid sinus, due to low wall shear stress. The presence of stenosis will produce two definite regions in ICA especially near the non-divider side. The first region locates in sinus region which incorporates high WSS and the second region is out of the sinus with low WSS. These considerable variations in WSS and turbulence in downstream of stenosis region can cause a series of non-physiologic phenomena which may ultimately result in brain stroke.
