Effect of blood flow on near-the-wall mass transport of drugs and other bioactive agents: a simple formula to estimate boundary layer concentrations

Transport of bioactive agents through the blood is essential for cardiovascular regulatory processes and drug delivery. Bioactive agents and other solutes infused into the blood through the wall of a blood vessel or released into the blood from an area in the vessel wall spread downstream of the infusion/release region and form a thin boundary layer in which solute concentration is higher than in the rest of the blood. Bioactive agents distributed along the vessel wall affect endothelial cells and regulate biological processes, such as thrombus formation, atherogenesis, and vascular remodeling. To calculate the concentration of solutes in the boundary layer, researchers have generally used numerical simulations. However, to investigate the effect of blood flow, infusion rate, and vessel geometry on the concentration of different solutes, many simulations are needed, leading to a time-consuming effort. In this paper, a relatively simple formula to quantify concentrations in a tube downstream of an infusion/release region is presented. Given known blood-flow rates, tube radius, solute diffusivity, and the length of the infusion region, this formula can be used to quickly estimate solute concentrations when infusion rates are known or to estimate infusion rates when solute concentrations at a point downstream of the infusion region are known. The developed formula is based on boundary layer theory and physical principles. The formula is an approximate solution of the advection-diffusion equations in the boundary layer region when solute concentration is small (dilute solution), infusion rate is modeled as a mass flux, and there is no transport of solute through the wall or chemical reactions downstream of the infusion region. Wall concentrations calculated using the formula developed in this paper were compared to the results from finite element models. Agreement between the results was within 10%. The developed formula could be used in experimental procedures to evaluate drug efficacy, in the design of drug-eluting stents, and to calculate rates of release of bioactive substances at active surfaces using downstream concentration measurements. In addition to being simple and fast to use, the formula gives accurate quantifications of concentrations and infusion rates under steady-state and oscillatory flow conditions, and therefore can be used to estimate boundary layer concentrations under physiological conditions.     

Flow in an arteriosclerotic blood vessel with rigid permeable wall

This paper concerns the fluid-mechanical study of the effects of permeability of the wall of an arteriosclerotic blood vessel by idealizing the tissue space as a porous medium bounding the blood vessel and the arteriosclerotic blood vessel as a constricted axisymetric tube of slowly but arbitrarily varying cross-secton. An analytical solution in the general case is obtained by perturbation technique and several important particular geometries of constriction are discussed as special cases. Numerical results for the effects of permeability on the wall shear stress and filtration velocity are shown graphically.     

Dynamic Local Distensibility of Living Arteries and its Relation to Wave Transmission

The dynamic local distensibility of the abdominal aorta was measured in 11 anesthetized dogs by recording simultaneously phasic pressure and instantaneous intravascular cross-sectional area, utilizing a special transducer. Axial motion of the vessel wall was recorded using a modification of the same transducer. A nonlinear relationship was found to exist between area and pressure in most cases studied. Fourier analysis was performed on data from eight experiments in order to obtain frequency characteristics of distensibility. In roughly half of the cases, Fourier analysis revealed that pressure variations displayed a phase lead over area variations for frequencies up to 10 Hz. This phenomenon was ascribed to viscoelastic properties of the vessel wall and the magnitude of the phase leads roughly matched those found in vitro by others. The behavior of the vessel wall in these instances was correctly predicted by the dynamic formula for distensibility, derived by others from wave transmission theory in which absence of axial wall motion is assumed. In these experiments, axial motion of the wall was found to be virtually absent. In the other half of the cases, the reverse situation was obtained: a phase lead of area variations over pressure variations for frequencies up to 15 Hz. In those cases a craniocaudal axial displacement of the vessel wall was observed with each systole, amounting to around 1 mm. The finding of the phase leads was partially explained by a dynamic formula for distensibility, developed by us from the theory of wave transmission in which free axial motion of the wall is a chosen boundary condition. The sign and order of magnitude of the phase leads were correctly predicted by the theoretical formula, but there was a disagreement on the frequency range in which they occurred. We concluded that additional forces, not yet considered in theoretical treatments, are operative on the aortic wall, which account for this lack of agreement. The frequency dependent properties of distensibility in vivo cannot be compared to those obtained in vitro in those cases in which there is axial displacement of the vessel wall of the same order of magnitude as the radial extensions.     

A study on the non-linear flow of blood through arteries

The pulsatile flow of blood through arteries is investigated in this paper by treating the blood vessel as a thin-walled anisotropic, non-linearly viscoelastic, incompressible circular cylindrical shell; nonlinearities of the flow of blood are also paid due consideration. The displacement components of the vessel wall are obtained from the equations of equilibrium which have been linearized by employing the principle of superimposition of a small deformation on a state of known finite deformation. The influence of the wall deformation on the flow properties of blood, has been accounted for by considering suitably formulated continuity conditions. A finitedifference scheme is employed for solving the flow equations together with the boundary and initial conditions by using the locally measured values of pressure and pressure gradient. Numerical results obtained for the velocity profile of blood flowing in a canine middle descending thoracic aorta have been presented through figures.     

Heterogeneous mechanics of the mouse pulmonary arterial network

Individualized modeling and simulation of blood flow mechanics find applications in both animal research and patient care. Individual animal or patient models for blood vessel mechanics are based on combining measured vascular geometry with a fluid structure model coupling formulations describing dynamics of the fluid and mechanics of the wall. For example, one-dimensional fluid flow modeling requires a constitutive law relating vessel cross-sectional deformation to pressure in the lumen. To investigate means of identifying appropriate constitutive relationships, an automated segmentation algorithm was applied to micro-computerized tomography images from a mouse lung obtained at four different static pressures to identify the static pressure–radius relationship for four generations of vessels in the pulmonary arterial network. A shape-fitting function was parameterized for each vessel in the network to characterize the nonlinear and heterogeneous nature of vessel distensibility in the pulmonary arteries. These data on morphometric and mechanical properties were used to simulate pressure and flow velocity propagation in the network using one-dimensional representations of fluid and vessel wall mechanics. Moreover, wave intensity analysis was used to study effects of wall mechanics on generation and propagation of pressure wave reflections. Simulations were conducted to investigate the role of linear versus nonlinear formulations of wall elasticity and homogeneous versus heterogeneous treatments of vessel wall properties. Accounting for heterogeneity, by parameterizing the pressure/distention equation of state individually for each vessel segment, was found to have little effect on the predicted pressure profiles and wave propagation compared to a homogeneous parameterization based on average behavior. However, substantially different results were obtained using a linear elastic thin-shell model than were obtained using a nonlinear model that has a more physiologically realistic pressure versus radius relationship.     

A new method to model change in cutaneous blood flow due to mechanical skin irritation part II: parameter identification procedure

Mechanical skin irritation, for example a light scratch with a needle, induces histamine and neuropeptide release on the line of stroke and in the surrounding tissue. Both histamine and neuropeptides are vasodilators. They cause vasodilation by changing the contraction state of the vascular smooth muscles and hence vessel compliance. Smooth muscle contraction state is very difficult to measure in vivo. For that reason we propose in this article an identification procedure to establish an irritation law. The law gives change in vessel compliance as a function of space, time and the intensity of the stroke. We have showed that vessel compliance increases immediately after the stroke not only on the line of stroke, but also in the surrounding tissue. Then, after a short delay, vessel compliance starts decreasing in the surrounding tissue, whereas vessel compliance on the line of stroke keeps increasing. Hence, blood is transported from the surrounding tissue to the line of stroke. In this way, higher blood volume on the line of stroke can be obtained than by only changing vessel compliance locally.     

Doppler Optical Coherence Tomography of Retinal Circulation

Noncontact retinal blood flow measurements are performed with a Fourier domain optical coherence tomography (OCT) system using a circumpapillary double circular scan (CDCS) that scans around the optic nerve head at 3.40 mm and 3.75 mm diameters. The double concentric circles are performed 6 times consecutively over 2 sec. The CDCS scan is saved with Doppler shift information from which flow can be calculated. The standard clinical protocol calls for 3 CDCS scans made with the OCT beam passing through the superonasal edge of the pupil and 3 CDCS scan through the inferonal pupil. This double-angle protocol ensures that acceptable Doppler angle is obtained on each retinal branch vessel in at least 1 scan. The CDCS scan data, a 3-dimensional volumetric OCT scan of the optic disc scan, and a color photograph of the optic disc are used together to obtain retinal blood flow measurement on an eye. We have developed a blood flow measurement software called "Doppler optical coherence tomography of retinal circulation" (DOCTORC). This semi-automated software is used to measure total retinal blood flow, vessel cross section area, and average blood velocity. The flow of each vessel is calculated from the Doppler shift in the vessel cross-sectional area and the Doppler angle between the vessel and the OCT beam. Total retinal blood flow measurement is summed from the veins around the optic disc. The results obtained at our Doppler OCT reading center showed good reproducibility between graders and methods (<10%). Total retinal blood flow could be useful in the management of glaucoma, other retinal diseases, and retinal diseases. In glaucoma patients, OCT retinal blood flow measurement was highly correlated with visual field loss (R²>0.57 with visual field pattern deviation). Doppler OCT is a new method to perform rapid, noncontact, and repeatable measurement of total retinal blood flow using widely available Fourier-domain OCT instrumentation. This new technology may improve the practicality of making these measurements in clinical studies and routine clinical practice.     

Numerical analysis of dynamic temperature in response to different levels of reactive hyperaemia in a three-dimensional image-based hand model

Vascular reactivity (VR) is considered as an effective index to predict the risk of cardiovascular events. A cost-effective alternative technique used to evaluate VR called digital thermal monitoring (DTM) is based on the response of finger temperature to vessel occlusion and reperfusion. In this work, a simulation has been developed to investigate hand temperature in response to vessel occlusion and perfusion. The simulation consists of image-based mesh generation and finite element analysis of blood flow and heat transfer in tissues. In order to reconstruct a real geometric model of human hand, a computer programme including automatic image processing for sequential MR data and mesh generation based on the transfinite interpolation method is developed. In the finite element analysis part, blood flow perfused in solid tissues is considered as fluid phase through porous media. Heat transfer in tissues is described by Pennes bioheat equation and blood perfusion rate is obtained from Darcy velocities. Capillary pressure, blood perfusion and temperature distribution of hand are obtained. The results reveal that fingertip temperature is strongly dependent on larger arterial pressure. This simulation is of potential to quantify the indices used for evaluating the VR in DTM test if it is integrated with the haemodynamic model of blood circulation in upper limb.     

血管活动的个性化

机体内不同部位的血管功能活动均具有各自独特的性质,称为血管的个性,主要表现为不同器官或区域的血管对同一刺激的反应不尽相同,甚至截然相反。血管的这种生理学特征保证了血管能在不同部位与不同机能状态下作出不同反应,巧妙地完成血液循环系统的功能,满足机体不同部位的血供需要。血管活动的个性化是血管生理学中的一个重要问题,对这一问题的研究将有助于阐明血管活动的客观规律,对研究血管疾病的发生与发展也具有重要意义     

Blood flow in branching circulatory systems during rest and activity

On the basis of simple physical considerations the blood flow in a branching circulatory system is studied. The case of two groups of parallel vessels is treated. The vessels of the same group are supposed to be identical. The resistance of each group is determined by the resistance of each vessel in the group and by the number of vessels in the group. From the dependence of the resistance of each vessel on its radius an expression is obtained for the blood flow through each group of vessels in terms of the numbers and sizes of the vessels in each group. The number of open vessels in an organ and the radius of each of those vessels are assumed to depend on the metabolic rate of that organ. The relations so obtained, together with the expression above, are applied to derive the blood flow through an organ as a function of the metabolic rate of that organ. It is indicated that the relations obtained might describe the shifting of blood from one organ to another if the activity of one of them changes. A way is pointed out to treat neural regulation of this phenomenon.     

Blood Tracer Kinetics in the Arterial Tree

Evaluation of blood supply of different organs relies on labeling blood with a suitable tracer. The tracer kinetics is linear: Tracer concentration at an observation site is a linear response to an input somewhere upstream the arterial flow. The corresponding impulse response functions are currently treated empirically without incorporating the relation to the vascular morphology of an organ. In this work we address this relation for the first time. We demonstrate that the form of the response function in the entire arterial tree is reduced to that of individual vessel segments under approximation of good blood mixing at vessel bifurcations. The resulting expression simplifies significantly when the geometric scaling of the vascular tree is taken into account. This suggests a new way to access the vascular morphology in vivo using experimentally determined response functions. However, it is an ill-posed inverse problem as demonstrated by an example using measured arterial spin labeling in large brain arteries. We further analyze transport in individual vessel segments and demonstrate that experimentally accessible tracer concentration in vessel segments depends on the measurement principle. Explicit expressions for the response functions are obtained for the major middle part of the arterial tree in which the blood flow in individual vessel segments can be treated as laminar. When applied to the analysis of regional cerebral blood flow measurements for which the necessary arterial input is evaluated in the carotid arteries, present theory predicts about 20% underestimation, which is in agreement with recent experimental data.     

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.     

Response of Retinal Blood Flow to Systemic Hyperoxia as Measured with Dual-Beam Bidirectional Doppler Fourier-Domain Optical Coherence Tomography

Purpose

There is a long-standing interest in the study of retinal blood flow in humans. In the recent years techniques have been established to measure retinal perfusion based on optical coherence tomography (OCT). In the present study we used a technique called dual-beam bidirectional Doppler Fourier-domain optical coherence tomography (FD-OCT) to characterize the effects of 100% oxygen breathing on retinal blood flow. These data were compared to data obtained with a laser Doppler velocimeter (LDV).

Methods

10 healthy subjects were studied on 2 study days. On one study day the effect of 100% oxygen breathing on retinal blood velocities was studied using dual-beam bidirectional Doppler FD-OCT. On the second study day the effect of 100% oxygen breathing on retinal blood velocities was assessed by laser Doppler velocimetry (LDV). Retinal vessel diameters were measured on both study days using a commercially available Dynamic Vessel Analyzer. Retinal blood flow was calculated based on retinal vessel diameters and red blood cell velocity.

Results

As expected, breathing of pure oxygen induced a pronounced reduction in retinal vessel diameters, retinal blood velocities and retinal blood flow on both study days (p<0.001). Blood velocity data correlated well between the two methods applied under both baseline as well as under hyperoxic conditions (r = 0.98 and r = 0.75, respectively). Data as obtained with OCT were, however, slightly higher.

Conclusion

A good correlation was found between red blood cell velocity as measured with dual-beam bidirectional Doppler FD-OCT and red blood cell velocity assessed by the laser Doppler method. Dual-beam bidirectional Doppler FD-OCT is a promising approach for studying retinal blood velocities in vivo.     

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.     

Effects of non-Newtonian blood and metabolic states of the blood and vessel wall on the optimum design of single vessels and the vascular bifurcation

Employing the optimality principle, we attempted to predict the effects of non-Newtonian blood and the metabolic states of individual vessel segments on the optimum vascular design. Our results implied that irrespective of the vessel caliber, the optimum flow rate of non-Newtonian blood through a cylindrical vessel is less than that of Newtonian blood by not more than some 12-13%, even though the non-Newtonian nature is within the pathologically-realistic highest range. Non-Newtonian blood does not exert the slightest degree of influence on the optimum geometry of the vascular bifurcation. In contrast, as the metabolic state of the vessel wall overwhelms that of the blood, the optimum flow through the cylindrical vessel becomes markedly increased: the optimum relative caliber of the branch of the bifurcation decreases and the optimum branching angle increases.     

Mathematical modeling of the response of a resistive vessel to pressure

The response of small arterial vessels to internal pressure makes an essential contribution to autoregulation in the vascular bed. It is believed that free cytosolic Ca²⁺ concentration plays a pivotal role in the regulation of smooth muscle contractility and hence of the vascular lumen. A simple mathematical model of blood flow in a resistive vessel is suggested. The model is based on the experimental data obtained for cerebral arteries, but may be used for any other resistive vessel. The model not only describes the regulation of the vascular lumen by transmural pressure but also shows realistic behavior of the vessel radius and cytosolic [Ca²⁺] at different rates of pressure change. Possible variations in the radius along the vessel due to the Bayliss effect are considered.     

Computational fluid dynamic studies of leukocyte adhesion effects on non-Newtonian blood flow through microvessels

The study of the effect of leukocyte adhesion on blood flow in small vessels is of primary interest to understand the resistance changes in venular microcirculation. Available computational fluid dynamic studies provide information on the effect of leukocyte adhesion when blood is considered as a homogeneous Newtonian fluid. In the present work we aim to understand the effect of leukocyte adhesion on the non-Newtonian Casson fluid flow of blood in small venules; the Casson model represents the effect of red blood cell aggregation. In our model the blood vessel is considered as a circular cylinder and the leukocyte is considered as a truncated spherical protrusion in the inner side of the blood vessel. The cases of single leukocyte adhesion and leukocyte pairs in positions aligned along the same side, and opposite sides of the vessel wall are considered. The Casson fluid parameters are chosen for cat blood and human blood and comparisons are made for the effects of leukocyte adhesion in both species. Numerical simulations demonstrated that for a Casson fluid with hematocrit of 0.4 and flow rate Q = 0.072 nl/s, a single leukocyte increases flow resistance by 5% in a 32 microns diameter and 100 microns long vessel. For a smaller vessel of 18 microns, the flow resistance increases by 15%.     

Arterial pulse attenuation prediction using the decaying rate of a pressure wave in a viscoelastic material model

The present study examines the possibility of attenuating blood pulses by means of introducing prosthetic viscoelastic materials able to absorb energy and damp such pulses. Vascular prostheses made of polymeric materials modify the mechanical properties of blood vessels. The effect of these materials on the blood pulse propagation remains to be fully understood. Several materials for medical applications, such as medical polydimethylsiloxane or polytetrafluoroethylene, show viscoelastic behavior, modifying the original vessel stiffness and affecting the propagation of blood pulses. This study focuses on the propagation of pressure waves along a pipe with viscoelastic materials using the Maxwell and the Zener models. An expression of exponential decay has been obtained for the Maxwell material model and also for low viscous coefficient values in the Zener model. For relatively high values of the viscous term in the Zener model, the steepest part of the pulse can be damped quickly, leaving a smooth, slowly decaying wave. These mathematical models are critical to tailor those materials used in cardiovascular implants to the mechanical environment they are confronted with to repair or improve blood vessel function.     

利用LabVIEW构建血管生物反应器数据采集系统

对组织工程血管的参数监测在血管的培养过程中有着重要的意义。传统的仪表硬件系统能对反应器部分参数进行测量,但仍存在一些不足之处,本文通过分析确定血管生物反应器的监控参数,并利用虚拟仪器技术及LabVIEW软件开发平台构建了血管组织工程参数监测系统,该系统在实际应用中表明:系统简捷、运行稳定,能够监测血管的体外培养并达到了预定的精度要求。Labview的     

First-order approximation for the pressure-flow relationship of spontaneously contracting lymphangions

To return lymph to the great veins of the neck, it must be actively pumped against a pressure gradient. Mean lymph flow in a portion of a lymphatic network has been characterized by an empirical relationship (P(in) - P(out) = -P(p) + R(L)Q(L)), where P(in) - P(out) is the axial pressure gradient and Q(L) is mean lymph flow. R(L) and P(p) are empirical parameters characterizing the effective lymphatic resistance and pump pressure, respectively. The relation of these global empirical parameters to the properties of lymphangions, the segments of a lymphatic vessel bounded by valves, has been problematic. Lymphangions have a structure like blood vessels but cyclically contract like cardiac ventricles; they are characterized by a contraction frequency (f) and the slopes of the end-diastolic pressure-volume relationship [minimum value of resulting elastance (E(min))] and end-systolic pressure-volume relationship [maximum value of resulting elastance (E(max))]. Poiseuille's law provides a first-order approximation relating the pressure-flow relationship to the fundamental properties of a blood vessel. No analogous formula exists for a pumping lymphangion. We therefore derived an algebraic formula predicting lymphangion flow from fundamental physical principles and known lymphangion properties. Quantitative analysis revealed that lymph inertia and resistance to lymph flow are negligible and that lymphangions act like a series of interconnected ventricles. For a single lymphangion, P(p) = P(in) (E(max) - E(min))/E(min) and R(L) = E(max)/f. The formula was tested against a validated, realistic mathematical model of a lymphangion and found to be accurate. Predicted flows were within the range of flows measured in vitro. The present work therefore provides a general solution that makes it possible to relate fundamental lymphangion properties to lymphatic system function.