人口流动条件下血管壁运动的数学模型

根据血管人口流动条件,从血液流动、血管壁运动、血液－血管壁耦合运动３个方面出发,推导出血管壁运动的数学模型,通过理论分析与实例计算,进一步明确了模型的物理意义。     

粘弹性血管入口区域内血管壁与血液耦合运动的研究

从血液流动、血管壁运动、血液－血管壁耦合运动三方面出发,建立了粘弹性血管发展流动的数学模型。导出了一组血液流动的速度分布、压力分布公式以及管壁位移公式。理论分析与数值计算都表明：（１）入口区域内血液流动的速度分布、压力分布与管壁的粘弹性无关;（２）管壁运动的位移公式中,Ａ、Ｂ、Ｃ、Ｄ、Ｅ各项都具有特定的物理意义;（３）完全弹性问题可视为本文公式的特殊情况。     

关于血管入口流动公式的进一步研究

为进一步研究前文［１］提出的粘弹性血管入口流动公式,以一组狗的胸主动脉参数为实例进行分析与讨论。结果表明,（１）公式中Ａ、Ｂ、Ｃ、Ｄ、Ｅ各项对管壁运动位移的影响规律为：当ｘ／ＲｎＲ＜Ｌｘ时,Ｄ、Ｅ的影响是主要的,而Ａ、Ｂ、Ｃ可忽略不计;当ｘ／ＲｎＲ＞Ｌｘ时,就必须考虑Ａ、Ｂ、Ｃ、Ｄ、Ｅ的联合作用。（２）定常、非定常状态下粘弹性血管的运动呈现一定的规律：当ｘ／ＲｎＲ＜０．１６时,管壁位移变化显著,当ｘ／ＲｎＲ＞０．１６时,管壁位移变化平稳。同时,相同条件下,弹性血管的位移变化幅值大于粘弹性血管。（３）粘弹性血管的运动不仅与它的径向、轴向位置有关,而且与血液对血管的作用力有关。     

动脉硬化仿真模拟分析

目的：通过对血管中血液流动对血管的影响及血液内低密度脂蛋白（sLDL）微粒行为的模拟分析,研究动脉粥样硬化产生的血流动力学原因。方法：第一步,使用流体力学软件CFD,建立动脉血管弯曲分叉仿真模型;第二步,分析血液流动特性,跟踪血液中15—25纳米尺度范围类的sLDL粒子在动脉分叉模型中的流体力学行为,研究sLDL在血液流速稳定下在血管中的空间分布及流场特征分布。结果：血管起始段出现压强很高的区域。在动脉血管弯曲内侧处及分岔处的分支外侧血液流动较慢,并且在这些部位出现压强较高的区域。在血管弯曲外侧处及分岔点处,sLDL与血管壁发生碰撞的几率较其它位置较高,粒子在血管上沉积高发区域在这些部位呈斑块状分布。讨论及结论：在血管起始段的高压,可能是导致这一部分血管损伤,并进而引起动脉硬化形成的主要原因;在动脉血管弯曲外侧处及分岔点处出现的高压低速血流分布,一方面增大了血液中包括sLDL粒子在内的致病因子与血管壁的接触时间,另一方面则引起这些部位血清的侧漏加强,出现所谓的’浓度极化’现象,从而导致这些部位出现高浓度的sLDL分布,增大sLDL粒子与血管壁的接触几率;粒子在血管上沉积高发区域往往存在于动脉血管分岔点处,而在血管弯曲外侧处也有较高几率沉淀,呈斑状分布;长期性轻微性振动的剪切压力的作用使多数血管内皮细胞性质改变,促进动脉硬化形成。在动脉血管起始段、弯曲处及分岔点处血液的高压低速分布、sLDL粒子的高沉积率及低剪切应力等是动脉硬化产生及演化的重要因素.     

动脉硬化仿真模拟分析

目的:通过对血管中血液流动对血管的影响及血液内低密度脂蛋白(sLDL)微粒行为的模拟分析,研究动脉粥样硬化产生的血流动力学原因.方法:第一步,使用流体力学软件CFD,建立动脉血管弯曲分叉仿真模型;第二步,分析血液流动特性,跟踪血液中15.25纳米尺度范围类的sLDL粒子在动脉分又模型中的流体力学行为,研究sLDL在血液流速稳定下在血管中的空间分布及流场特征分布.结果:血管起始段出现压强很高的区域.在动脉血管弯曲内侧处及分岔处的分支外侧血液流动较慢,并且在这些部位出现压强较高的区域.在血管弯曲外侧处及分岔点处,sLDL与血管壁发生碰撞的几率较其它位置较高,粒子在血管上沉积高发区域在这些部位呈癍块状分布.讨论及结论:在血管起始段的高压,可能是导致这一部分血管损伤,并进而引起动脉硬化形成的主要原因;在动脉血管弯曲外侧处及分岔点处出现的高压低速血流分布,一方面增大了血液中包括sLDL粒子在内的致病因子与血管壁的接触时间,另一方面则引起这些部位血清的侧漏加强,出现所谓的'浓度极化'现象,从而导致这些部位出现高浓度的sLDL分布,增大sLDL粒子与血管壁的接触几率;粒子在血管上沉积高发区域往往存在于动脉血管分岔点处,而在血管弯曲外侧处也有较高几率沉淀,呈斑状分布;长期性轻微性振动的剪切压力的作用使多数血管内皮细胞性质改变.促进动脉硬化形成.在动脉血管起始段、弯曲处及分岔点处血液的高压低速分布、sLDL粒子的高沉积率及低剪切应力等是动脉硬化产生及演化的重要因素.     

一种带有旋动流引导器的新型小口径人造血管流场的数值模拟

大尺寸人造血管的临床应用已取得很大成功,但用于冠状动脉等旁路搭桥的小口径人造血管的急性血栓堵塞问题,至今仍未解决．因此,本文设计了一种可装于小口径人造血管前的旋流导引器,以期使进入人造血管内的血流产生旋动．对带有旋流导引器的人造血管内的血流流场进行了计算机数值模拟分析,并与常规人造血管内的血流流场进行了比较．数值模拟分析揭示,这种旋流导引器的确能使人造血管内的血流产生旋动,从而改变人造血管内的血流流场和流速分布,使近壁面血液的流速和壁面剪切应力得到极大提高．本研究认为,血液在人造血管壁面的流速和壁面剪切应力的提高,可抑制小口径人造血管内急性血栓的形成,从而达到提高小口径人造血管的通畅率的目的．     

血流剪切力在动脉粥样硬化形成中的作用

血管内皮位于血管壁和血液的界面,直接与血流接触而持续受血流剪切力的作用。血管内皮细胞能感受血流机械力的变化,通过激活相应的信号通路调节血管内皮和平滑肌的结构和功能。研究发现,血液流动力的形式与动脉粥样硬化的发生发展有密切的关系。本综述将就血流剪切力与动脉粥样硬化的相互关系及作用机制的最新研究进展作简要介绍。     

磁场在观察蛙血液循环上的应用

用显微镜观察蛙蹼内血液的流动现象,目的是观察蛙蹼的血管、血流和血细胞运动.如果在蛙蹼两侧加上磁铁效果更好.具体做法是: 1.将蛙的蹼膜展放在薄木板中间的圆孔上,固定后,再移至载物台上进行观察,以见到蹼内血管、血液流动及血球运动为止.     

对“血压”概念的新看法

中学《生理卫生》课本中血压的定义是:“血液在血管内向前流动时对血管壁造成的侧压力,叫做血压。”人民卫生出版社出版的高等医药院校试用教材《生理学》(湖南医学院等十个医学院校合编)中对血压的论述是:“血管内血液对于血管壁的侧压力,称为血压。测定血压时,是以血压与大气压作比较,而用血压高过大气压的数值表示血压的高度,通常以毫米汞柱高为单位。”我对上述教材中有关血压的论述有不同看法,特提出供老师们讨论. 教材中给血压下的定义跟血压所用的单位自相矛盾。从定义看,血压是指血液对血管侧壁的压力,这个压力只涉及到压力的大小、压力的方向和压力的作用部位三方面的含义,而没有涉及到血管侧壁的受力面积,因此其中压力大小的数值无法确定,如果要知道汞柱对血管的压力数值,还必须具备血管壁的受力面积这样一个条件.才能计算出压力;     

血管内血栓形成发病机制的现代概念

近年来,各种疾病并发血栓栓塞症的现象日益增多。血栓形成是术后和产后以及心脏血管系统疾病时最常见的死亡原因之一。血管内血栓形成的发病机制,尚未完全阐明。前一世纪已提出它是血流速度减慢、血管壁和血液成分的改变的后果。这设想目前仍得到承认。一、各种原因在血管内血栓形成的发病机制中的意义1.血管壁损害和血管内血栓形成:根据Cop-ley 的意见,血管内皮经常复有一层纤维蛋白簿膜,并且不断生成和破坏。这层薄膜可降低血液的粘滞性和凝固性,并阻止血液有形成分粘附于血管壁,从而保证血液循环。有人发现,纤维蛋白在血管的生理性损伤部位不断生成。Nolf 指出,     

Effect of the stress phase angle on the strain energy density of the endothelial plasma membrane

Endothelial cells are simultaneously exposed to the mechanical forces of fluid wall shear stress (WSS) imposed by blood flow and solid circumferential stress (CS) induced by the blood vessel's elastic response to the pressure pulse. Experiments have demonstrated that these combined forces induce unique endothelial biomolecular responses that are not characteristic of either driving force alone and that the temporal phase angle between WSS and CS, referred to as the stress phase angle, modulates endothelial responses. In this article, we provide the first theoretical model to examine the combined forces of WSS and CS on a model of the endothelial cell plasma membrane. We focus on the strain energy density of the membrane that modulates the opening of ion channels that can mediate signal transduction. The model shows a significant influence of the stress phase angle on the strain energy density at the upstream and downstream ends of the cell where mechanotransduction is most likely to occur.     

Numerical investigation of haemodynamics in a helical-type artery bypass graft using non-Newtonian multiphase model

The classic single-phase Newtonian blood flow model ignores the motion of red blood cells (RBCs) and their interaction with plasma. To address these issues, we adopted a multiphase non-Newtonian model to carry out a comparative study between a helical artery bypass graft (ABG) and a conventional ABG in which the blood flow is composed of plasma and RBCs. The investigation focused on the mechanism of RBC buildup in an ABG but the haemodynamic parameters obtained by single-phase and multiphase models were also compared. The aggregation of RBCs along the inside wall of a conventional ABG and at the heel of its distal anastomosis was predicted while a poor aggregation was observed along the helical ABG. In addition, RBCs were observed to gradually sediment along the gravity direction. However, the computed haemodynamic parameters by multiphase model qualitatively agreed well with those by single-phase model. It was concluded that (1) the single-phase computational fluid dynamics (CFD) is reasonable to do the computation of haemodynamic parameters in ABGs; (2) secondary flow does not definitely produce buildup of RBCs in the inside curvature, its configuration played an important role in the movement of RBCs and the dominating one-way rotating flow in a helical ABG guaranteed no buildup of RBCs on its inside wall and (3) gravity direction is important for the movement of RBCs which may help to explain why doing exercise is good for human health. This study helps to shed light on the migration of RBCs in ABGs, which cannot be explored by single-phase CFD models, and provides more understanding of the underlying flow mechanism for ABG failure.     

Assessment of human left ventricle flow using statistical shape modelling and computational fluid dynamics

Blood flow patterns in the human left ventricle (LV) have shown relation to cardiac health. However, most studies in the literature are limited to a few patients and results are hard to generalize. This study aims to provide a new framework to generate more generalized insights into LV blood flow as a function of changes in anatomy and wall motion. In this framework, we studied the four-dimensional blood flow in LV via computational fluid dynamics (CFD) in conjunction with a statistical shape model (SSM), built from segmented LV shapes of 150 subjects. We validated results in an in-vitro dynamic phantom via time-resolved optical particle image velocimetry (PIV) measurements. This combination of CFD and the SSM may be useful for systematically assessing blood flow patterns in the LV as a function of varying anatomy and has the potential to provide valuable data for diagnosis of LV functionality.     

Speckle variance optical coherence tomography of blood flow in the beating mouse embryonic heart

Efficient separation of blood and cardiac wall in the beating embryonic heart is essential and critical for experiment‐based computational modelling and analysis of early‐stage cardiac biomechanics. Although speckle variance optical coherence tomography (SV‐OCT) relying on calculation of intensity variance over consecutively acquired frames is a powerful approach for segmentation of fluid flow from static tissue, application of this method in the beating embryonic heart remains challenging because moving structures generate SV signal indistinguishable from the blood. Here, we demonstrate a modified four‐dimensional SV‐OCT approach that effectively separates the blood flow from the dynamic heart wall in the beating mouse embryonic heart. The method takes advantage of the periodic motion of the cardiac wall and is based on calculation of the SV signal over the frames corresponding to the same phase of the heartbeat cycle. Through comparison with Doppler OCT imaging, we validate this speckle‐based approach and show advantages in its insensitiveness to the flow direction and velocity as well as reduced influence from the heart wall movement. This approach has a potential in variety of applications relying on visualization and segmentation of blood flow in periodically moving structures, such as mechanical simulation studies and finite element modelling. Picture : Four‐dimensional speckle variance OCT imaging shows the blood flow inside the beating heart of an E8.5 mouse embryo.     

Numerical simulation of blood flow in the left ventricle and aortic sinus using magnetic resonance imaging and computational fluid dynamics

Understanding cardiac blood flow patterns has many applications in analysing haemodynamics and for the clinical assessment of heart function. In this study, numerical simulations of blood flow in a patient-specific anatomical model of the left ventricle (LV) and the aortic sinus are presented. The realistic 3D geometry of both LV and aortic sinus is extracted from the processing of magnetic resonance imaging (MRI). Furthermore, motion of inner walls of LV and aortic sinus is obtained from cine-MR image analysis and is used as a constraint to a numerical computational fluid dynamics (CFD) model based on the moving boundary approach. Arbitrary Lagrangian–Eulerian finite element method formulation is used for the numerical solution of the transient dynamic equations of the fluid domain. Simulation results include detailed flow characteristics such as velocity, pressure and wall shear stress for the whole domain. The aortic outflow is compared with data obtained by phase-contrast MRI. Good agreement was found between simulation results and these measurements.     

Numerical analysis of pulsatile blood flow and vessel wall mechanics in different degrees of stenoses

Hemodynamics factors and biomechanical forces play key roles in atherogenesis, plaque development and final rupture. In this paper, we investigated the flow field and stress field for different degrees of stenoses under physiological conditions. Disease is modelled as axisymmetric cosine shape stenoses with varying diameter reductions of 30%, 50% and 70%, respectively. A simulation model which incorporates fluid-structure interaction, a turbulence model and realistic boundary conditions has been developed. The results show that wall motion is constrained at the throat by 60% for the 30% stenosis and 85% for the 50% stenosis; while for the 70% stenosis, wall motion at the throat is negligible through the whole cycle. Peak velocity at the throat varies from 1.47 m/s in the 30% stenosis to 3.2m/s in the 70% stenosis against a value of 0.78 m/s in healthy arteries. Peak wall shear stress values greater than 100 Pa were found for > or =50% stenoses, which in vivo could lead to endothelial stripping. Maximum circumferential stress was found at the shoulders of plaques. The results from this investigation suggest that severe stenoses inhibit wall motion, resulting in higher blood velocities and higher peak wall shear stress, and localization of hoop stress. These factors may contribute to further development and rupture of plaques.     

Numerical investigation of the non-Newtonian blood flow in a bifurcation model with a non-planar branch

The non-Newtonian fluid flow in a bifurcation model with a non-planar daughter branch is investigated by using finite element method to solve the three-dimensional Navier–Stokes equations coupled with a non-Newtonian constitutive model, in which the shear thinning behavior of the blood fluid is incorporated by the Carreau–Yasuda model. The objective of this study is to investigate the influence of the non-Newtonian property of fluid as well as of curvature and out-of-plane geometry in the non-planar daughter vessel on wall shear stress (WSS) and flow phenomena. In the non-planar daughter vessel, the flows are typified by the skewing of the velocity profile towards the outer wall, creating a relatively low WSS at the inner wall. In the downstream of the bifurcation, the velocity profiles are shifted towards the flow divider. The low WSS is found at the inner walls of the curvature and the lateral walls of the bifurcation. Secondary flow patterns that swirl fluid from the inner wall of curvature to the outer wall in the middle of the vessel are also well documented for the curved and bifurcating vessels. The numerical results for the non-Newtonian fluid and the Newtonian fluid with original Reynolds number and the corresponding rescaled Reynolds number are presented. Significant difference between the non-Newtonian flow and the Newtonian flow is revealed; however, reasonable agreement between the non-Newtonian flow and the rescaled Newtonian flow is found. Results of this study support the view that the non-planarity of blood vessels and the non-Newtonian properties of blood are an important factor in hemodynamics and may play a significant role in vascular biology and pathophysiology.     

Dynamic response of wall shear stress on the stenosed artery

The present study deals with an appropriate mathematical model of an artery in the presence of constriction in which the generated wall shear stress due to blood flow is analysed. The geometry of the stenosed arterial segment in the diseased state, causing malfunction of the cardiovascular system, is formed mathematically. The flowing blood contained in the stenosed artery is treated as non-Newtonian and the flow is considered to be two-dimensional. The motion of the arterial wall and its effect on local fluid mechanics is not ruled out from the present pursuit. The flow analysis applies the time-dependent, two-dimensional incompressible nonlinear Navier–Stokes equations for non-Newtonian fluids. The flow-field can be obtained primarily following the radial coordinate transformation, using the appropriate boundary conditions and finally adopting a suitable finite difference scheme numerically. The influences of flow unsteadiness, the arterial wall distensibility and the presence of stenosis on the flow-field and the wall shear stresses are quantified in order to indicate the susceptibility to atherosclerotic lesions and thereby to validate the applicability of the present theoretical model.     

An efficient full space-time discretization method for subject-specific hemodynamic simulations of cerebral arterial blood flow with distensible wall mechanics

A computationally inexpensive mathematical solution approach using orthogonal collocations for space discretization with temporal Fourier series is proposed to compute subject-specific blood flow in distensible vessels of large cerebral arterial networks. Several models of wall biomechanics were considered to assess their impact on hemodynamic predictions. Simulations were validated against in vivo blood flow measurements in six human subjects. The average root-mean-square relative differences were found to be less than 4.3% for all subjects with a linear elastic wall model. This discrepancy decreased further in a viscoelastic Kelvin-Voigt biomechanical wall. The results provide support for the use of collocation-Fourier series approach to predict clinically relevant blood flow distribution and collateral blood supply in large portions of the cerebral circulation at reasonable computational costs. It thus opens the possibility of performing computationally inexpensive subject-specific simulations that are robust and fast enough to predict clinical results in real time on the same day.     

Computational model for simulation of vascular adaptation following vascular access surgery in haemodialysis patients

An important number of surgical procedures for creation of vascular access (VA) in haemodialysis patients still results in non-adequate increase in blood flow (non-maturation). The rise in blood flow in arteriovenous shunts depends on vascular remodelling. Computational tools to predict the outcome of VA surgery would be important in this clinical context. The aim of our investigation was then to develop a 0D/1D computational model of arm vasculature able to simulate vessel wall remodelling and related changes in blood flow. We assumed that blood vessel remodelling is driven by peak wall shear stress. The model was calibrated with previously reported values of radial artery diameter and blood flow after end-to-end distal fistula creation. Good agreement was obtained between predicted changes in VA flow and in arterial diameter after surgery and corresponding measured values. The use of this computational model may allow accurate vascular surgery planning and ameliorate VA surgery outcomes.