主动脉弓及分支血管内非稳态血流分析
刘莹, 章德发, 毕勇强, 王梦洪. 主动脉弓及分支血管内非稳态血流分析. 36(4): 432-439LIU Ying, ZHANG De-fa, BI Yong-qiang, WANG Meng-hong. Analysis of Unsteady Blood Flow in the Human Aortic Bifurcation. Applied Mathematics and Mechanics, 36(4): 432-439&&
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主动脉弓及分支血管内非稳态血流分析
1. 南昌大学 机电工程学院, 南昌 330031
2. 南昌大学 第一附属医院 心血管科, 南昌 330006
作者简介: 刘莹(1957—),女,江西吉水人,教授,博士,博士生导师(通讯作者. E-mail:).
基金:国家自然科学基金()
运用流体力学中的三维非定常Navier-Stokes方程作为血液流动的控制方程,并采用计算流体力学方法对人体主动脉弓及分支血管内非Newton(牛顿)血液黏度模型下血流进行瞬态数值模拟.分析了一个心动周期内不同时刻血流动力学特征参数的分布对动脉粥样硬化斑块形成的影响,并与Newton血液黏度模型下的血管壁面压力和壁面切应力特征参数进行对比.结果表明:与Newton血液模型相比,非Newton血液模型下血流分布更符合真实血流特性;在心动收缩期,分支血管外侧壁附近存在面积较大的低速涡流区,该区域内血管壁面压力与壁面切应力具有较大的变化量,血液中的血小板、脂质和纤维蛋白等易沉积,血管内壁易疲劳损伤并发生血管重构,促使动脉粥样硬化斑块形成;而在心动舒张期,分支血管内血流速度分布均匀,血管壁面压力与壁面切应力变化量较小,血管壁受到较小的应力作用,对动脉粥样硬化斑块形成的作用较小.
主动脉分支;
非Newton血液;
动脉粥样硬化斑块
中图分类号:Q66;O351
文献标志码:A
文章编号:15)04-0432-08
Analysis of Unsteady Blood Flow in the Human Aortic Bifurcation
LIU Ying1,
ZHANG De-fa1,
BI Yong-qiang1,
WANG Meng-hong2
1. School of Mechanical and Electrical Engineering, Nanchang University, Nanchang 330031, P.R.China
2. Department of Cardiology, the First Affiliated Hospital, Nanchang University,Nanchang 330006, P.R.China
Fund:The National Natural Science Foundation of China()
Based on the 3D unsteady Navier-Stokes equations as the governing equations, the blood flow in the human aortic bifurcation was simulated by means of the non-Newtonian blood model with the computational fluid dynamics method. The influence of blood flow characteristic parameter distributions on the formation of atherosclerotic plaques at the feature points within a cardiac cycle was investigated, and a comparison of the wall pressure and wall shear stress parameters was made between the Newtonian blood model and the non-Newtonian blood model. The results show that, compared to the Newtonian blood model, the non-Newtonian blood model is more suitable for the description of real blood flow characteristics. Larger blood stagnation areas, more complex wall pressure and wall shear stress distributions exist around the lateral walls of the bifurcation blood vessels during the systolic cycle, more probably causing deposition of fat particles, platelets and fibrin in the blood vessels which are liable to wall injury and reconstruction, in turn formation of atherosclerotic plaques. However, smaller blood stagnation areas, less changes of wall pressure and wall shear stress distributions happen around the lateral walls of the bifurcation blood vessels during the diastolic cycle, with less influence on the formation of atherosclerotic plaques.
cardiac cycle;
aortic bifurcation;
non-Newtonian blood;
atherosclerotic plaque
引言随着人们生活条件的改善, 生活规律与饮食结构发生了巨大的变化, 使得动脉粥样硬化、脑卒中和动脉炎等血管类疾病的发病率呈逐年上升趋势.研究已证实[, ], 人体血液循环系统中血流动力学特征参数, 如血管壁受到的交变应力、复杂血流分布等均与血管类疾病的形成具有密切关系.Piskin等[]研究了不同入口血流速度对颈动脉内血流动力学特征参数分布的影响.梅立泉等[]将血液认为是定常流动的Newton流体, 采用计算流体力学方法(CFD)研究了分叉血管中动脉狭窄对血液流动的影响, 分析了狭窄率对动脉粥样硬化形成的作用.王晓曦分析了冠状动脉内局部血流动力学分布及对斑块的影响, 研究了冠状动脉内局部血流动力学特征参数分布情况及冠状动脉粥样硬化病变形成、发展的血流动力学机制[].早期血液流动数值模拟研究一般将血液近似看作定常Newton流体, 而血液实际上是以脉动形式流动的非Newton流体.在进行瞬态数值模拟研究过程中, 当剪切应变率处于0~100 s-1区域内时, 血液的黏度系数随剪切应变率减小而增加, 血液具有一定的“ 屈服” 应力, 表现出较明显的非Newton特性, 导致交变应力区及低速涡流区的面积发生明显变化, 为动脉粥样硬化斑块的形成与发展提供有利条件[].因此, 选取血液为脉动形式流动的非Newton流体, 采用CFD技术从血流动力学方面分析动脉粥样硬化、脑卒中和动脉炎等血管类疾病的发病机理具有重要意义.本文采用计算流体力学方法对一个心动周期内人体正常主动脉弓及分支血管中血流动力学进行瞬态数值模拟, 分析了一个心动周期内Newton血液模型和非Newton血液模型下主动脉弓及分支血管内血流动力学特征参数的分布情况, 以探讨一个心动周期内不同时刻主动脉弓及分支血管内血流动力学特征参数的分布与动脉粥样硬化斑块形成机理的关系.1 资料与方法1.1 一般资料采用NX8.0建立了具有几何锥度的主动脉弓及分支血管模型.主动脉弓及分支血管包括主动脉弓、外侧头臂干动脉、左颈总动脉和左锁骨下动脉, 其内径分别为5 mm、3.5 mm、3.0 mm和2.8 mm, 锥度角均为2° .其中K1, K2为外侧头臂干动脉(brachiocephalic artery)近心端, K3, K4为左颈总动脉(left common carotid artery)近心端, K5, K6为左锁骨下动脉(left subclavian artery)近心端, K7, K8为降主动脉(descending aorta)近心端, 如所示.图1Fig. 1 图1 主动脉弓与分支血管模型Fig. 1 The model of the aortic bifurcation采用ICEM对主动脉弓及分支血管进行网格划分, 为提高边界层区域的计算精度, 在边界层处采用3层逐渐加密的三棱柱网格, 其它区域则采用四面体网格来划分.1.2 方法假设血液为绝热、不可压缩的黏性非Newton流体, 并忽略血管壁的影响[].取血液生理压力
P为13 339 Pa, 血液密度ρ 为1 056 kg/m3, 血液黏度模型为Carreau-Yasuda模型[].设定主动脉弓及分支血管的入口速度为所示的瞬态血流速度, 各出口压力均设为0 Pa, 血液流动控制方程为流体力学中的三维非定常Navier-Stokes方程[, ].图2Fig.2 图2 入口速度随时间变化曲线图Fig.2 Curve of the inlet velocity1) 三维非定常Navier-Stokes方程 ρ?u?t+(u·?)u=-?P+?τ, (1) ?·u=0, (2)式中, u为血流动三维速度矢量, P为流场内压强, ρ 为血液的密度, τ 为应力张量.2) Carreau-Yasuda血液黏度模型表达式 μ=μ∞+(μ0-μ∞)[1+(λγ)z](n-1)/z, (3)式中,
μ为动力黏度, 单位为Pa· s, 低剪切黏度
μ0为0.022 Pa· s, 高剪切黏度
μ∞为0.002 2 Pa· s, 时间常数
λ为0.110 s, 幂律指数
z为0.644, Carreau-Yasuda指数n为0.392, γ 为剪切应变率; 取Newton血液黏度模型的黏度为常数&#x003 =0.003 5Pa· 血液黏度随剪切应变率变化趋势如所示.图3Fig. 3 图3 非Newton与Newton血液模型的黏度曲线图Fig. 3 Viscosity curves of the Newtonian and non-Newtonian blood models假设心脏每秒输出血量为Q, 血液在主动脉弓及分支血管内平均流速v=Q/π R2, 根据Reynolds(雷诺)数公式Re=ρ vD/&#x003 , 则主动脉弓及分支血管内Reynolds数为Re=2ρ Q/π R&#x003 , 其中, ρ 为血液密度, v为流体流动速度, D为血管内径, R为血管半径, &#x003 为血液黏度.通常, 平静时正常人体平均每次心脏跳动血液输出量为70 ml, 心率为1.25 次/s, 则Re=1 071< 2 300, 血流为层流.2 结果一个心动周期为0.8 s, 瞬态数值模拟计算时间步长为10 ms, 得到一个心动周期内主动脉弓及分支血管中不同时刻的血液动力学特征参数分布情况.2.1 血流速度分析为非Newton血液模型下各特征时刻 (血流加速期0.05 s, 正峰值期0.19 s, 收缩期0.30 s, 负峰值期0.54 s)的血流流线图.由图可知, 在血流加速期(0.05 s), 分支血管内血流速度大小与主动脉弓内血流速度相近, 方向与管壁平行.在入口血流正峰值期(0.19 s)和收缩期(0.30 s), 分支血管内血流流速低, 且在分支血管近心端外侧壁附近均出现了面积不同的低速涡流区.在负峰值期(0.54 s), 血管处于舒张期, 分支血管内血流流线少、流速低, 表明心动舒张期流经分支血管内的血液流量相对心动收缩期减少.因此, 在心动收缩期, 变化的血流对血管壁作用效果增强, 分支血管内出现复杂血流分布, 易引起血管内皮细胞受损, 影响内皮细胞的形态和功能, 加速血小板的局部黏附和血管平滑肌细胞的增殖、凋亡, 从而促进动脉粥样硬化斑块的形成.图4Fig. 4 图4 心动周期内各特征时刻点的血流流线分布图Fig. 4 Streamline distribution of blood flow in a cardiac cycle为主动脉弓及分支血管在t=0.19 s时各分支血管截面的速度分布云图.为了较直观地比较各截面速度分布, 统一设定标值为0~1.6 m/s.由图可发现, 在外侧头臂干动脉纵截面(a-a1)分支血管外侧出现低速涡流区域, 主动脉弓内血流流速最大, 且峰值偏移到血管的边缘, 表明头臂干动脉对主动脉弓内血液起到重要的分流作用.左颈总动脉及左锁骨下动脉纵截面b-b1 和c-c1 内中心血流速度较a-a1处小, 且出现低速涡流区域的面积较小.图5Fig. 5 图5 t=0.19 s时主动脉弓及分支血管各截面速度云图Fig. 5 Velocity contour of blood flow at 0.19 s in the cross section2.2 血管壁面压力分析为一个心动周期内Newton血液模型(N)和非Newton血液模型(F)在各特征点的壁面压力值随时间变化曲线图.在心动收缩期, 分支血管壁面压力的变化率和变化量均较大.分支血管内侧(K2, K4, K6)壁面压力随入口血流流速的增大而增大, 而外侧(K1, K3, K5)随入口血流流速增大而减小.当入口血液流速达到正峰值时, 分支血管内外两侧的壁面压力均出现局部突变, 且外侧壁面压力为负突变, 内侧为正突变.而在心动舒张期, 随着入口血液流动速度的减小, 血管壁面压力并没有出现明显的变化且逐渐趋于稳定, 最终达到生理压力.另外, 整个心动周期内, 降主动脉近心端(K7, K8)壁面压力均在生理压力附近小幅度波动.低壁面压力易引起下游远端血管内血液流动动力不足, 下游血管壁组织出现缺氧、缺营养物质等现象, 为动脉粥样硬化斑块的形成提供有利条件[].而高壁面压力可破坏血细胞结构, 血细胞的通透性增强, 细胞内部分脂质混杂于血液中, 且流经低速涡流区时, 易沉积并诱发动脉粥样硬化斑块的形成.图6Fig. 6 图6 一个心动周期内各特征点血管壁面压力值变化曲线图Fig. 6 Curves of wall pressure at the feature points in a cardiac cycle对比N和F模型下壁面压力分布可知, 在心动收缩期, F模型外头臂干动脉近心端(K1, K2)处壁面压力出现较大变化幅度(K1点处F模型为12 840 Pa, N模型为12 950 Pa; K2点处F模型为14 260 Pa, N模型为14 090 Pa), 而左颈总动脉及左锁骨下动脉的近心端(K3, K4和K5, K6)的变化幅度均比N模型小.在心动舒张期, F模型各特征点处壁面压力的变化率及变化量均小于N模型.当入口血流速度较小时, 血液黏度的剪切应变率小于100 s-1, 血液黏度系数随剪切应变率减小而增加, 血液具有一定的“ 屈服” 应力, 表现出非Newton特性, 影响血管壁面压力的分布[].2.3 血管壁面切应力分析为一个心动周期内N, F模型下各特征点的壁面切应力值随时间变化曲线图.由图可知, 在整个心动周期内, N, F模型中各特征点的壁面切应力均随入口血流流速变化而变化, 且在分支血管近心端外侧壁面切应力均小于内侧壁面切应力.在心动加速期(0.05 s), 各特征点的壁面切应力值均较小(小于1 Pa), 且在N模型下, 分支血管近心端外侧壁面切应力存在局部突变.在正峰值(0.19 s)时, 各特征点壁面切应力迅速增加并同时达到峰值, 在左锁骨下动脉的内侧
(K6)出现最大切应力, 且F模型下此处壁面切应力(28.4 Pa)较N模型(20.2 Pa)大.在心动收缩期(0.30 s), 随着入口血流流速的降低, 各特征点的壁面切应力均快速减小并趋于稳定, 且F模型下分支血管内侧壁面切应力降低幅度较N模型大.在负峰值(0.54 s)时, 壁面切应力出现局部增大的现象, 但F模型下各特征点的变化量和变化率均略小于N模型.对比N, F模型可发现, 在心动收缩期, 血管壁面切应力分布存在较大的差异, N模型切应力变化量大于F模型, 尤其是血液流速较低时, 其差异表现较明显, 非Newton血液模型下血管壁面切应力分布更流畅, 较符合真实血液的特性.图7Fig.7 图7 一个心动周期内各特征点血管壁面切应力值变化曲线图Fig.7 Curves of wall shear stress at the feature points in a cardiac cycle研究已证实[, ], 壁面切应力异常与动脉粥样硬化斑块等血管类疾病的形成与发展密切相关.在低壁面切应力(小于0.5 Pa[])作用下, 近壁面血流分布发生局部变化, 流经此处的血细胞与管壁不断摩擦、碰撞, 血小板活性增强、血管壁损伤因子分泌增多及内皮细胞活性因子分泌减少, 引起内皮细胞功能紊乱及血小板在损伤部位局部聚集与黏附, 诱发动脉粥样硬化斑块的进一步病变发展[].同样, 血管高壁面切应力(大于20 Pa)作用下, 流经此处的血细胞易被撕裂并释放出致凝剂, 在粥样硬化斑块处聚集, 进一步促使斑块的成长[]; 过高的壁面切应力可能引起动脉粥样硬化斑块稳定性发生变化, 斑块易出现破裂与脱落, 引起血管堵塞.3 结论文中对一个心动周期内不同时刻点Newton血液模型与非Newton血液模型下人体主动脉弓及分支血管中血流动力学进行了数值模拟, 对比计算结果得到以下结论:1) 一个心动周期内, 分支血管近心端外侧壁附近出现面积大小不一的血液低速涡流区, 且在心动收缩期低速涡流区域面积明显大于心动舒张期.低速涡流区内血流速度较低, 血液流态复杂, 复杂血流分布可影响血管内皮细胞的结构和功能、平滑肌细胞的增殖和凋亡, 诱发早期动脉粥样硬化斑块的形成.2) 对比研究两种血液黏度模型下的壁面压力和壁面切应力分布结果可知:① 无论是Newton血液黏度模型还是非Newton血液黏度模型下, 血管壁面在一个心动周期内存在周期性大小、方向不一的应力(壁面压力和壁面切应力)作用, 应力的突变易引起血管壁细胞因疲劳而损伤, 促进动脉粥样硬化斑块的形成.② 分支血管近心端的壁面压力在心动收缩期比心动舒张期有较大的变化量和变化率.且在心动收缩期, 分支血管近心端外侧壁面压力明显低于内侧壁面压力, 处于“ 负压” 状态, 下游易出现供血动力不足, 导致下游血管中血流速度降低, 血液中脂质与血细胞等物质的沉积, 促进动脉粥样斑块的形成.③ 与心动舒张期相比, 在心动收缩期, 分支血管近心端外侧壁面切应力变化量与变化率较大, 壁面切应力异常均易引起血管壁细胞结构和功能发生改变, 导致动脉粥样硬化斑块的形成.对比N, F模型可发现, 在心动收缩期, 血管壁面切应力分布存在较大的差异, N模型切应力变化量大于F模型, 尤其是血液流速较低时, 其差异表现较明显, 非Newton血液模型下血管壁面切应力分布更流畅, 较符合真实血液的特性.
The authors have declared that no competing interests exist.
作者声明没有竞争性利益关系
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... 研究已证实[1,2],人体血液循环系统中血流动力学特征参数,如血管壁受到的交变应力、复杂血流分布等均与血管类疾病的形成具有密切关系 ...
. ):981-997
1. State Key Laboratory of Machinery System and Vibration, Shanghai Jiao Tong University, Shanghai, 200240, P. R. China
2. Mechanical Engineering, University of Cincinnati, Cincinnati, Ohio, , USA
Abstract This paper describes formulation and implementation of the fast multipole boundary element method (FMBEM) for 2D acoustic problems. The kernel function expansion theory is summarized, and four building blocks of the FMBEM are described in details. They are moment calculation, moment to moment translation, moment to local translation, and local to local translation. A data structure for the quad-tree construction is proposed which can facilitate implementation. An analytical moment expression is derived, which is more accurate, stable, and efficient than direct numerical computation. Numerical examples are presented to demonstrate the accuracy and efficiency of the FMBEM, and radiation of a 2D vibration rail mode is simulated using the FMBEM.
... 研究已证实[1,2],人体血液循环系统中血流动力学特征参数,如血管壁受到的交变应力、复杂血流分布等均与血管类疾病的形成具有密切关系 ...
. ):717-728
Piskin, Senol 1 ;Celebi, M. Serdar 1 ;
In this study the biomechanical characteristics of a realistic carotid artery [3] are studied numerically using different inlet velocity profiles. Several experimental data measured [32] at the common carotid artery are used as inlet boundary conditions. Computation domain is generated using computed tomography (CT) data of a real patient. Three dimensional (3D) transient NS equations are solved, in this actual domain, using the proposed boundary conditions. Effects of different input conditions on the results of simulation are discussed. Main parameters such as velocity profiles, wall shear stress (WSS) and pressure distributions are investigated at the critical parts of the carotid artery such as bifurcation and sinusoidal enlargement regions. Results show that the input boundary conditions and slope/curvature discontinuities in the realistic geometry have strong relationship with the velocity, pressure and WSS distributions as expected. The most important conclusion obtained from our model is the existence of negative relation between velocity at several inner points of the internal carotid artery and velocity at the inlet of the common carotid artery. (C) 2013 Elsevier Ltd. All rights reserved.
... Piskin等[3]研究了不同入口血流速度对颈动脉内血流动力学特征参数分布的影响 ...
... 梅立泉等[4]将血液认为是定常流动的Newton流体,采用计算流体力学方法(CFD)研究了分叉血管中动脉狭窄对血液流动的影响,分析了狭窄率对动脉粥样硬化形成的作用 ...
... 王晓曦分析了冠状动脉内局部血流动力学分布及对斑块的影响,研究了冠状动脉内局部血流动力学特征参数分布情况及冠状动脉粥样硬化病变形成、发展的血流动力学机制[5] ...
... 应力,表现出较明显的非Newton特性,导致交变应力区及低速涡流区的面积发生明显变化,为动脉粥样硬化斑块的形成与发展提供有利条件[6] ...
... 应力,表现出非Newton特性,影响血管壁面压力的分布[6] ...
血栓性疾病大多发生在弯曲和血管分叉的位置附近,其形成机制和原因比较复杂,目前的研究主要集中在临床病例的治疗护理方面.临床观测表明,动脉疾病的发病机制和病变发展与血流动力学特征(如流场分布、壁面剪应力等)密切相关.采用计算流体力学方法,从血流动力学角度研究了弯曲血管中血液流动的改变对血管栓塞形成的影响.主要从血流入口初始速度、弯曲曲率半径、血管管径及血液黏度方面研究血液流动对血栓形成的影响.同时结合相关医学病例.从多学科角度分析并验证医学研究中有关血管弯曲对血栓形成机理的猜测.
... 2 方法假设血液为绝热、不可压缩的黏性非Newton流体,并忽略血管壁的影响[7] ...
Vimmr, J. 1 ;Jonasova, A. 1 ;Bublik, O. 1 ;
Considering the fact that hemodynamics plays an important role in the patency and overall performance of implanted bypass grafts, this work presents a numerical investigation of pulsatile non-Newtonian blood flow in three different patient-specific aorto-coronary bypasses. The three bypass models are distinguished from each other by the number of distal side-to-side and end-to-side anastomoses and denoted as single, double and triple bypasses. The mathematical model in the form of time-dependent nonlinear system of incompressible Navier-Stokes equations is coupled with the Carreau-Yasuda model describing the shear-thinning property of human blood and numerically solved using the principle of the SIMPLE algorithm and cell-centred finite volume method formulated for hybrid unstructured tetrahedral grids. The numerical results computed for non-Newtonian and Newtonian blood flow in the three aorto-coronary bypasses are compared and analysed with emphasis placed on the distribution of cycle-averaged wall shear stress and oscillatory shear index. As shown in this study, the non-Newtonian blood flow in all of the considered bypass models does not significantly differ from the Newtonian one. Our observations further suggest that, especially in the case of sequential grafts, the resulting flow field and shear stimulation are strongly influenced by the diameter of the vessels involved in the bypassing. Copyright (c) 2013 John Wiley & Sons, Ltd.
... 为1 056 kg/m3,血液黏度模型为Carreau-Yasuda模型[8] ...
. ):177-185
Abstract Vertebral arteries are two arteries whose structure and location in human body result in development of special flow conditions. For some of the arteries, one can observe a significant difference between flow rates in the left and the right arteries during ultrasonography diagnosis. Usually the reason of such a difference was connected with pathology of the artery in which a smaller flow rate was detected. Simulations of the flow through the selected type of the vertebral artery geometry for twenty five cases of artery diameters have been carried out. The main aim of the presented experiment was to visualize the flow in the region of vertebral arteries junction in the origin of the basilar artery. It is extremely difficult to examine this part of human circulation system, thus numerical experiments may be helpful in understanding the phenomena occurring when two relatively large arteries join together to form one vessel. The obtained results have shown that an individual configuration and diameters of particular arteries can exert an influence on the flow in them and affect a significant difference between flow rates for vertebral arteries. It has been assumed in the investigations that modelled arteries were absolutely normal, without any pathology. In the numerical experiment, the non-Newtonian model of blood was employed.
... 设定主动脉弓及分支血管的入口速度为图2所示的瞬态血流速度,各出口压力均设为0 Pa,血液流动控制方程为流体力学中的三维非定常Navier-Stokes方程[9,10] ...
... 设定主动脉弓及分支血管的入口速度为图2所示的瞬态血流速度,各出口压力均设为0 Pa,血液流动控制方程为流体力学中的三维非定常Navier-Stokes方程[9,10] ...
... 低壁面压力易引起下游远端血管内血液流动动力不足,下游血管壁组织出现缺氧、缺营养物质等现象,为动脉粥样硬化斑块的形成提供有利条件[11] ...
Abstract The purpose of this study was to investigate the hemodynamic effect of variations in the angulations of the left coronary artery, based on simulated and realistic coronary artery models. Twelve models consisting of four realistic and eight simulated coronary artery geometries were generated with the inclusion of left main stem, left anterior descending and left circumflex branches. The simulated models included various coronary artery angulations, namely, 15&, 30&, 45&, 60&, 75&, 90&, 105& and 120&. The realistic coronary angulations were based on selected patient's data with angles ranging from narrow angles of 58& and 73& to wide angles of 110& and 120&. Computational fluid dynamics analysis was performed to simulate realistic physiological conditions that reflect the in vivo cardiac hemodynamics. The wall shear stress, wall shear stress gradient, velocity flow patterns and wall pressure were measured in simulated and realistic models during the cardiac cycle. Our results showed that a disturbed flow pattern was observed in models with wider angulations, and wall pressure was found to reduce when the flow changed from the left main stem to the bifurcated regions, based on simulated and realistic models. A low wall shear stress gradient was demonstrated at left bifurcations with wide angles. There is a direct correlation between coronary angulations and subsequent hemodynamic changes, based on realistic and simulated models. Further studies based on patients with different severities of coronary artery disease are required to verify our results.
... 研究已证实[12,13],壁面切应力异常与动脉粥样硬化斑块等血管类疾病的形成与发展密切相关 ...
. ):164-176
1. Electrical Engineering Department, Urmia University of Technology, Urmia, Iran
2. Department of Mathematics, University of Tabriz, Tabriz, Iran
3. Research Center for Industrial Mathematics, University of Tabriz, Tabriz, Iran
Abstract Gyroscopes are one of the most interesting and everlasting nonlinear nonautonomous dynamical systems that exhibit very complex dynamical behavior such as chaos. In this paper, the problem of robust stabilization of the nonlinear non-autonomous gyroscopes in a given finite time is studied. It is assumed that the gyroscope system is perturbed by model uncertainties, external disturbances, and unknown parameters. Besides, the effects of input nonlinearities are taken into account. Appropriate adaptive laws are proposed to tackle the unknown parameters. Based on the adaptive laws and the finite-time control theory, discontinuous finite-time control laws are proposed to ensure the finite-time stability of the system. The finite-time stability and convergence of the closed-loop system are analytically proved. Some numerical simulations are presented to show the efficiency of the proposed finite-time control scheme and to validate the theoretical results.
... 研究已证实[12,13],壁面切应力异常与动脉粥样硬化斑块等血管类疾病的形成与发展密切相关 ...
Although the entire coronary tree is exposed to the atherogenic effect of the systemic risk factors, atherosclerotic lesions form at specific arterial regions, where low and oscillatory endothelial shear stress (ESS) occur. Low ESS modulates endothelial gene expression through complex mechanoreception and mechanotransduction processes, inducing an atherogenic endothelial phenotype and formation of an early atherosclerotic plaque. Each early plaque exhibits an individual natural history of progression, regression, or stabilization, which is dependent not only on the formation and progression of atherosclerosis but also on the vascular remodeling response. Although the pathophysiologic mechanisms involved in the remodeling of the atherosclerotic wall are incompletely understood, the dynamic interplay between local hemodynamic milieu, low ESS in particular, and the biology of the wall is likely to be important. In this review, we explore the molecular, cellular, and vascular processes supporting the role of low ESS in the natural history of coronary atherosclerosis and vascular remodeling and indicate likely mechanisms concerning the different natural history trajectories of individual coronary lesions. Atherosclerotic plaques associated with excessive expansive remodeling evolve to high-risk plaques, because low ESS conditions persist, thereby promoting continued local lipid accumulation, inflammation, oxidative stress, matrix breakdown, and eventually further plaque progression and excessive expansive remodeling. An enhanced understanding of the pathobiologic processes responsible for atherosclerosis and vascular remodeling might allow for early identification of a high-risk coronary plaque and thereby provide a rationale for innovative diagnostic and/or therapeutic strategies for the management of coronary patients and prevention of acute coronary syndromes.
... 5 Pa[14])作用下,近壁面血流分布发生局部变化,流经此处的血细胞与管壁不断摩擦、碰撞,血小板活性增强、血管壁损伤因子分泌增多及内皮细胞活性因子分泌减少,引起内皮细胞功能紊乱及血小板在损伤部位局部聚集与黏附,诱发动脉粥样硬化斑块的进一步病变发展[15] ...
... 5 Pa[14])作用下,近壁面血流分布发生局部变化,流经此处的血细胞与管壁不断摩擦、碰撞,血小板活性增强、血管壁损伤因子分泌增多及内皮细胞活性因子分泌减少,引起内皮细胞功能紊乱及血小板在损伤部位局部聚集与黏附,诱发动脉粥样硬化斑块的进一步病变发展[15] ...
... 同样,血管高壁面切应力(大于20 Pa)作用下,流经此处的血细胞易被撕裂并释放出致凝剂,在粥样硬化斑块处聚集,进一步促使斑块的成长[16] ...
主动脉弓及分支血管内非稳态血流分析
[刘莹1, 章德发1, 毕勇强1, 王梦洪2]}