Effects of wall shear stress and its gradient on tumor cell adhesion in curved microvessels

Tumor cell adhesion to vessel walls in the microcirculation is one critical step in cancer metastasis. In this paper, the hypothesis that tumor cells prefer to adhere at the microvessels with localized shear stresses and their gradients, such as in the curved microvessels, was examined both experimentally and computationally. Our in vivo experiments were performed on the microvessels (post-capillary venules, 30–50 μm diameter) of rat mesentery. A straight or curved microvessel was cannulated and perfused with tumor cells by a glass micropipette at a velocity of ~1mm/s. At less than 10 min after perfusion, there was a significant difference in cell adhesion to the straight and curved vessel walls. In 60 min, the averaged adhesion rate in the curved vessels (n = 14) was ~1.5-fold of that in the straight vessels (n = 19). In 51 curved segments, 45% of cell adhesion was initiated at the inner side, 25% at outer side, and 30% at both sides of the curved vessels. To investigate the mechanical mechanism by which tumor cells prefer adhering at curved sites, we performed a computational study, in which the fluid dynamics was carried out by the lattice Boltzmann method , and the tumor cell dynamics was governed by the Newton’s law of translation and rotation. A modified adhesive dynamics model that included the influence of wall shear stress/gradient on the association/dissociation rates of tumor cell adhesion was proposed, in which the positive wall shear stress/gradient jump would enhance tumor cell adhesion while the negative wall shear stress/gradient jump would weaken tumor cell adhesion. It was found that the wall shear stress/gradient, over a threshold, had significant contribution to tumor cell adhesion by activating or inactivating cell adhesion molecules. Our results elucidated why the tumor cell adhesion prefers to occur at the positive curvature of curved microvessels with very low Reynolds number (in the order of 10⁻²) laminar flow.     

Mathematical analysis of mural thrombogenesis. Concentration profiles of platelet-activating agents and effects of viscous shear flow.

The concentration profiles of adenosine diphosphate (ADP), thromboxane A2 (TxA2), thrombin, and von Willebrand factor (vWF) released extracellularly from the platelet granules or produced metabolically on the platelet membrane during thrombus growth, were estimated using finite element simulation of blood flow over model thrombi of various shapes and dimensions. The wall fluxes of these platelet-activating agents were estimated for each model thrombus at three different wall shear rates (100 s-1, 800 s-1, and 1,500 s-1), employing experimental data on thrombus growth rates and sizes. For that purpose, whole human blood was perfused in a parallel-plate flow chamber coated with type l fibrillar human collagen, and the kinetic data collected and analyzed by an EPl-fluorescence video microscopy system and a digital image processor. It was found that thrombin concentrations were large enough to cause irreversible platelet aggregation. Although heparin significantly accelerated thrombin inhibition by antithrombin lll, the remaining thrombin levels were still significantly above the minimum threshold required for irreversible platelet aggregation. While ADP concentrations were large enough to cause irreversible platelet aggregation at low shear rates and for small aggregate sizes, TxA2 concentrations were only sufficient to induce platelet shape change over the entire range of wall shear rates and thrombi dimensions studied. Our results also indicated that the local concentration of vWF multimers released from the platelet alpha-granules could be sufficient to modulate platelet aggregation at low and intermediate wall shear rates (less than 1,000 s-1). The sizes of standing vortices formed adjacent to a growing aggregate and the embolizing stresses and the torque, acting at the aggregate surface, were also estimated in this simulation. It was found that standing vortices developed on both sides of the thrombus even at low wall shear rates. Their sizes increased with thrombus size and wall shear rate, and were largely dependent upon thrombus geometry. The experimental observation that platelet aggregation occurred predominantly in the spaces between adjacent thrombi, confirmed the numerical prediction that those standing vortices are regions of reduced fluid velocities and high concentrations of platelet-activating substances, capable of trapping and stimulating platelets for aggregation. The average shear stress and normal stress, as well as the torque, acting to detach the thrombus, increased with increasing wall shear rate. Both stresses were found to be nearly independent of thrombus size and only weekly dependent upon thrombus geometry. Although both stresses had similar values at low wall shear rates, the average shear stress became the predominant embolizing stress at high wall shear rates.     

Tortuosity triggers platelet activation and thrombus formation in microvessels

Tortuous blood vessels are often seen in humans in association with thrombosis, atherosclerosis, hypertension, and aging. Vessel tortuosity can cause high fluid shear stress, likely promoting thrombosis. However, the underlying physical mechanisms and microscale processes are poorly understood. Accordingly, the objectives of this study were to develop and use a new computational approach to determine the effects of venule tortuosity and fluid velocity on thrombus initiation. The transport, collision, shear-induced activation, and receptor-ligand adhesion of individual platelets in thrombus formation were simulated using discrete element method. The shear-induced activation model assumed that a platelet became activated if it experienced a shear stress above a relative critical shear stress or if it contacted an activated platelet. Venules of various levels of tortuosity were simulated for a mean flow velocity of 0.10?cm s(-1), and a tortuous arteriole was simulated for a mean velocity of 0.47?cm s(-1). Our results showed that thrombus was initiated at inner walls in curved regions due to platelet activation in agreement with experimental studies. Increased venule tortuosity modified fluid flow to hasten thrombus initiation. Compared to the same sized venule, flow in the arteriole generated a higher amount of mural thrombi and platelet activation rate. The results suggest that the extent of tortuosity is an important factor in thrombus initiation in microvessels.     

Numerical simulation of sinusoidal flow in a straight elastic tube: effects of phase angles

Numerical simulations of flow in straight elastic (moving wall) tubes subjected to a sinusoidal pressure gradient were performed for conditions prevailing in large and medium sized arteries. The effects of varying the phase angle between the pressure gradient and the tube radius, the amplitude of wall motion, and the unsteadiness parameter (alpha) on flow rate and wall shear stress were investigated. Mean and peak flow rates and shear stresses were found to be strongly affected by the phase angle between the pressure gradient and the tube radius with greater sensitivity at higher diameter variation and higher alpha. In large artery simulations (alpha = 12), means flow rate was found to be 60% higher and peak flow rate to be 73% higher than corresponding rigid tube values for certain phase angles, while a threefold increase in mean wall shear stress and sevenfold increase in peak wall shear stress were observed in a sensitive phase angle range. Significant reversal in the wall shear stress direction occurred in the sensitive phase angle range even when there was negligible flow rate reversal. All effects were greatly diminished in simulations of medium sized vessels (alpha = 4). Some experimental evidence to support the predictions of a strong effect of phase angle on wall shear stress in large vessels is presented. Finally, physiological implications of the present work are discussed from a basis of aortic input impedance data, and a physical explanation for the extreme sensitivity of the flow field to small amplitude wall motion at high alpha is given.     

The hemodynamic and embolizing forces acting on thrombi--II. The effect of pulsatile blood flow

A previous analysis (Basmadjian, J. Biomechanics 17, 287-298, 1984) of the embolizing forces acting on thrombi in steady Poiseuille flow has been extended to pulsatile blood flow conditions in the major blood vessels. We show that for incipient and small compact thrombi up to 0.1 mm height, the maximum embolizing stresses can be calculated from the corresponding 'quasi-steady' viscous drag forces and measured maximum wall shear. Their magnitude is from 5 to 30 times (tau w)Max, the maximum wall shear stress during the cardiac cycle in the absence of thrombi. For larger thrombi, inertial and 'history' effects have to be taken into account, leading to embolizing stresses in excess of 100 Pa (1000 dyn cm-2).     

Design optimization of vena cava filters: an application to dual filtration devices

Pulmonary embolism (PE) is a significant medical problem that results in over 300,000 fatalities per year. A common preventative treatment for PE is the insertion of a metallic filter into the inferior vena cava that traps thrombi before they reach the lungs. The goal of this work is to use methods of mathematical modeling and design optimization to determine the configuration of trapped thrombi that minimizes the hemodynamic disruption. The resulting configuration has implications for constructing an optimally designed vena cava filter. Computational fluid dynamics is coupled with a nonlinear optimization algorithm to determine the optimal configuration of a trapped model thrombus in the inferior vena cava. The location and shape of the thrombus are parametrized, and an objective function, based on wall shear stresses, determines the worthiness of a given configuration. The methods are fully automated and demonstrate the capabilities of a design optimization framework that is broadly applicable. Changes to thrombus location and shape alter the velocity contours and wall shear stress profiles significantly. For vena cava filters that trap two thrombi simultaneously, the undesirable flow dynamics past one thrombus can be mitigated by leveraging the flow past the other thrombus. Streamlining the shape of the thrombus trapped along the cava wall reduces the disruption to the flow but increases the area exposed to low wall shear stress. Computer-based design optimization is a useful tool for developing vena cava filters. Characterizing and parametrizing the design requirements and constraints is essential for constructing devices that address clinical complications. In addition, formulating a well-defined objective function that quantifies clinical risks and benefits is needed for designing devices that are clinically viable.     

An experimental and theoretical study on the dissolution of mural fibrin clots by tissue-type plasminogen activator.

During thrombolytic therapy and after recanalization is achieved, reduction in the volume of mural thrombi is desirable. Mural thrombi are known to contribute to rethrombosis and reocclusion. The lysis rate of mural thrombi has been demonstrated to increase with fluid flow in different experimental models, but the mechanisms responsible are unknown. An experimental and a theoretical study were developed to determine the contribution of outer convective transport to the lysis of mural fibrin clots. Normal human plasma containing recombinant tissue-type plasminogen activator (tPA; 0.5 microg/mL) was (re)perfused over mural fibrin clots with fluorescently labeled fibrin at low arterial, arterial, or higher wall shear stresses (4, 18, or 41 dyn/cm(2), respectively) and lysis was monitored in real time. Flow accelerated lysis, but significantly only at the highest shear stress: The average lysis front velocity was 3 x 10(-5) cm/s at 41 dyn/cm(2) vs. almost half of that at the lower shear stresses. Confocal microscopy showed fibrin fibers dissolving only in a narrow region close to the surface when permeation velocity was predicted to be low. A heterogeneous transport-reaction finite element model was used to describe mural fibrinolysis. After scaling the effects of outer and inner convection, inner diffusion, and chemical reactions, a simplified inner diffusion/reaction model was used. Correlation to fibrin lysis data in purified systems dictated higher rates of plasmin(ogen) and tPA adsorption onto fibrin and a decreased catalytic rate of plasmin-mediated fibrin degradation, compared with published parameters. At each shear stress, the model predicted a temporal pattern of lysis of mural fibrin (similar to that observed experimentally), and protease accumulation in a narrow fibrin region and significant lysis inhibition by plasma alpha(2)-antiplasmin (according to the literature). Increasing outer convection accelerated mural fibrinolysis, but the model did not predict the big increase in lysis rate at the highest shear stress. At higher than arterial flows, additional mechanisms not accounted for in the current model, such as fibrin collapse at the fibrin front, may regulate the lysis of mural clots and determine the outcome of thrombolytic therapy.     

Volume flow and wall shear stress quantification in the human conjunctival capillaries and post-capillary venules in vivo

Understanding the mathematical relationships of volume blood flow and wall shear stress with respect to microvessel diameter is necessary for the study of vascular design. Here, for the first time, volume flow and wall shear stress were quantified from axial red blood cell velocity measurements in 104 conjunctival microvessels of 17 normal human volunteers. Measurements were taken with a slit lamp based imaging system from the post capillary side of the bulbar conjunctiva in microvessel diameters ranging from 4 to 24 micrometers. The variation of the velocity profile with diameter was taken into account by using a profile factor function. Volume flow ranged from 5 to 462 pl/s with a mean value of 102 pl/s and gave a second power law best fitting line (r=0.97) deviating significantly from the third power law relation with diameter. The estimated wall shear stress declined hyperbolically (r=0.93) from a maximum of 9.55 N/m(2) at the smallest capillaries, down to a minimum of 0.28 N/m(2) at the higher diameter post capillary venules. The mean wall shear stress value for all microvessels was 1.54 N/m(2).     

Breaking symmetry in non-planar bifurcations: distribution of flow and wall shear stress

Non-planarity in blood vessels is known to influence arterial flows and wall shear stress. To gain insight, computational fluid dynamics (CFD) has been used to investigate effects of curvature and out-of-plane geometry on the distribution of fluid flows and wall shear stresses in a hypothetical non-planar bifurcation. Three-dimensional Navier-Stokes equations for a steady state Newtonian fluid were solved numerically using a finite element method. Non-planarity in one of the two daughter vessels is found to deflect flow from the inner wall of the vessel to the outer wall and to cause changes in the distribution of wall shear stresses. Results from this study agree to experimental observations and CFD simulations in the literature, and support the view that non-planarity in blood vessels is a factor with important haemodynamic significance and may play a key role in vascular biology and pathophysiology.     

血浆层对血管壁剪应力和剪应力梯度的影响

在细小血管中,由于血细胞明显的趋轴效应,管中的血液分为两个不同的区域,即具有血细胞的核心区和邻近管壁和血浆层。应用两相分层流模型,研究在相同的流量和管径下,当核心区中的血液分别为牛顿流体和Casson流体时,不同的血浆层厚度对细小血管壁剪应力和剪应力梯度的影响。结果表明,血浆层的存在对壁剪应力和壁剪应力梯度有较大影响,当血浆层厚度仅为血管半径的1％和3％时,壁剪应力梯度分别下降约10％和20％。     

The features of thrombus in a microvessel injury model and the antithrombotic efficacy of heparin,urokinase, and prostaglandin E1

In failed flap transfers and in burn injuries, superoxides and thrombi generated in the microcirculation are considered responsible for tissue injury. A dynamic and morphologic analysis of thrombus formation was conducted in a model of microvessel injury, and an analysis was made of the different antithrombotic effects of heparin, urokinase, and prostaglandin E(1). The dye-light method was used (i.e., injury of the endothelium by reactive oxygen species) to induce thrombus formation in both the arterioles and venules of the rabbit ear chamber under an intravital microscope-television system. The dynamic course of thrombus formation was observed, and the period from irradiation to complete obstruction of blood flow (i.e., time to stasis) was measured and compared in relation to various treatment conditions. Arteriolar thrombi were formed by platelet aggregation. Venular thrombi were composed of platelets and erythrocytes that gathered and adhered around leukocytes stuck to the vessel wall. Heparin treatment prolonged the time to stasis in both the arterioles and the venules. Urokinase extended the time to stasis in the venules but not in the arterioles. Prostaglandin E(1)-treatment significantly prolonged the time to stasis in the arterioles, but only high-dose prostaglandin E(1) prolonged the time to stasis in the venules. The results of this study show that endothelial damage caused by superoxides promotes the formation of thrombi that differ in composition between the arteriole and the venule and that the effectiveness of each drug varies accordingly. The authors believe that these agents can be used with increased efficacy if the two types of thrombi and the specific antithrombotic effects of each agent are considered.     

The hemodynamic forces acting on thrombi, from incipient attachment of single cells to maturity and embolization

We consider the steady fluid forces acting on a thrombus from the time of first contact of a single cell with a natural or artificial surface, through the attachment process and growth to embolization. For a hemi-spherical or cylindrical attached cell of height less than 1/100-1/20th of the channel width, shear and tensile stresses are solely dependent on viscosity and on the ratio of average fluid velocity to channel width vt/Dt (shear rate). Large values of this ratio reduce adhesion and increase embolization. The average shear stress on such cells is approximately 1-10 Pa (10-100 dyn cm2), the average tensile stress about three times higher. For other shapes and larger protrusions, stress varies with protrusion height as well. Maturing thrombi composed of cell aggregates embedded in a fibrin mesh do not appear to allow significant fluid flow through their porous structure. The interior forces are then due solely to hydrostatic pressure and initially vary directly with vt/Dt and inversely with thrombus height Hp, thus favouring embolization at an early stage and in arterial systems. Rough surfaces are identified as causing an increase in dwell-time and possibly immobilizing an unattached cell due to 'negative lift'.     

Non-linear viscoelastic behavior of abdominal aortic aneurysm thrombus

The objective of this work was to determine the linear and non-linear viscoelastic behavior of abdominal aortic aneurysm thrombus and to study the changes in mechanical properties throughout the thickness of the thrombus. Samples are gathered from thrombi of seven patients. Linear viscoelastic data from oscillatory shear experiments show that the change of properties throughout the thrombus is different for each thrombus. Furthermore the variations found within one thrombus are of the same order of magnitude as the variation between patients. To study the non-linear regime, stress relaxation experiments are performed. To describe the phenomena observed experimentally, a non-linear multimode model is presented. The parameters for this model are obtained by fitting this model successfully to the experiments. The model cannot only describe the average stress response for all thrombus samples but also the highest and lowest stress responses. To determine the influence on the wall stress of the behavior observed the model proposed needs to implemented in the finite element wall stress analysis.     

Velocity and wall shear stress patterns in the human right coronary artery.

Blood flow dynamics in the human right coronary artery have not been adequately quantified despite the clinical significance of coronary atherosclerosis. In this study, a technique was developed to construct a rigid flow model from a cast of a human right coronary artery. A laser photochromic method was used to characterize the velocity and wall shear stress patterns. The flow conditions include steady flow at Reynolds numbers of 500 and 1000 as well as unsteady flow with Womersley parameter and peak Reynolds number of 1.82 and 750, respectively. Characterization of the three-dimensional geometry of the artery revealed that the largest spatial variation in curvature occurred within the almost branch-free proximal region, with the greatest curvature existing along the acute margin of the heart. In the proximal segment, high shear stresses were observed on the outer wall and lower, but not negative, stresses along the inner wall. Low shear stress on the inner wall may be related to the preferential localization of atherosclerosis in the proximal segment of the right coronary artery. However, it is possible that the large difference between the outer and inner wall shear stresses may also be involved.     

Stages of endotheliocyte differentiation in the genesis of capillaries in human prenatal morphogenesis

Blood microvessels of the functionally different human organs were studied by electron microscopy to reveal regularities of cytodifferentiation of endotheliocytes in prenatal morphogenesis. Such stages of differentiation of endotheliocytes were determined: mesenchymal cells----endotheliocytes of pre-existing capillaries ("marginal" cells, primordial endotheliocytes, mature endotheliocytes of pre-existing capillaries)----specialized types of endothelium (somatic, fenestrated, sinusoidal, sinusal types of endothelium, high endothelium of post-capillary venules).     

Stress gradients in the walls of large arteries

Elastic behavior of vascular wall, assuming the vessels to be ‘thick-walled’ and utilizing finite deformation theory, was investigated. It was found that canine carotid arterial wall is neither isotropic nor transversely isotropic. Previously, stress-strain relations were obtained for carotid arteries on the basis of membrane theory (Doyle and Dobrin, 1971). Since strain gradients across the wall are fairly steep, the applicability of such expressions, for pointwise evaluation of stress, required examination. The study indicated that these relationships between mean circumferential stress and mean extension ratio in the circumferential direction could be used to relate the specific circumferential stress value to the specific extension ratio at any designated point within the wall. From this analysis it was possible to evaluate circumferential and radial wall stresses. Both of these stresses are maximal at the inner surface of the intima. At this point the radial stress is equal to the transmural pressure and is compressive, while the circumferential stress is tensile and is 1·5 to 2 times the value of the mean stress, i.e. the product of transmural pressure and the ratio of internal radius-to-wall thickness. Both stresses are lowest at the outer edge of the adventitia. These stress distributions were considered with respect to the spacing of the elastic lamellae and the absence of discernible vasa vasora in the inner third of the wall.     

Microvascular hyperpermeability and thrombosis induced by light/dye treatment

To investigate microvascular hyperpermeability and thrombosis induced by photodynamic therapy or light/dye treatment, we quantified the initiation time for thrombus formation, thrombus growth rate, and the time for the microvessel occlusion in post-capillary venules of rat mesenteries. Under similar light/dye treatments, we also measured the microvessel hydraulic conductivity (Lp) and solute permeability (P) to TRITC-BSA (bovine serum albumin), respectively, in the same type of microvessels as for thrombosis. Under an irradiation power of 0.37 mW/mm², thrombus was initiated in 3.8 ± 0.4 min, its growth rate was 3.9 ± 0.3% of the vessel mid-plane area/min, and the microvessels were completely occluded in 29.3 ± 2.2 min (SE, n = 8). Under the same irradiation power, Lp and P increased gradually, reaching a plateau in 3–5 min. At the plateau, Lp had increased to 2.2 ± 0.2 times (n = 11), while P had increased to 4.1 ± 0.7 (n = 7) times their baseline values, respectively. Neither Lp nor P increased further after longer time exposure (up to 30 min). Comparison of the measured Lp and P data with predictions from a mathematical model for the inter-endothelial cleft suggests that an almost complete depletion of the glycocalyx layer at the luminal surface of the endothelium might be one of the structural mechanisms by which the light/dye increases microvascular permeability and induces thrombosis.     

In Vitro Recapitulation of Functional Microvessels for the Study of Endothelial Shear Response,Nitric Oxide and [Ca2+]i

Microfluidic technologies enable in vitro studies to closely simulate in vivo microvessel environment with complexity. Such method overcomes certain constrains of the statically cultured endothelial monolayers and enables the cells grow under physiological range of shear flow with geometry similar to microvessels in vivo. However, there are still existing knowledge gaps and lack of convincing evidence to demonstrate and quantify key biological features of the microfluidic microvessels. In this paper, using advanced micromanufacturing and microfluidic technologies, we presented an engineered microvessel model that mimicked the dimensions and network structures of in vivo microvessels with a long-term and continuous perfusion capability, as well as high-resolution and real-time imaging capability. Through direct comparisons with studies conducted in intact microvessels, our results demonstrated that the cultured microvessels formed under perfused conditions recapitulated certain key features of the microvessels in vivo. In particular, primary human umbilical vein endothelial cells were successfully cultured the entire inner surfaces of the microchannel network with well-developed junctions indicated by VE-cadherin staining. The morphological and proliferative responses of endothelial cells to shear stresses were quantified under different flow conditions which was simulated with three-dimensional shear dependent numerical flow model. Furthermore, we successfully measured agonist-induced changes in intracellular Ca²⁺ concentration and nitric oxide production at individual endothelial cell levels using fluorescence imaging. The results were comparable to those derived from individually perfused intact venules. With in vivo validation of its functionalities, our microfluidic model demonstrates a great potential for biological applications and bridges the gaps between in vitro and in vivo microvascular research.     

Velocity measurements in steady flow through axisymmetric stenoses at moderate Reynolds numbers

The velocity field in the neighborhood of axisymmetric constrictions in rigid tubes was investigated using laser Doppler anemometry and flow visualization. Upstream flow conditions were steady; and Reynolds numbers were in the range 500-2000, values which are representative of the larger arteries in humans. Stenoses of 25, 50 and 75% area reduction were studied. Velocity profiles are presented in sufficient detail to allow comparison with computational biofluid dynamics models. Wall shear stresses were estimated from the near wall velocity gradient, and the nature of observed poststenotic flow disturbances is discussed. Results indicate that flow disturbances of discrete oscillation frequency may be more valuable than turbulence as an indicator of early stages of stenosis development. Additionally, despite the fact that poststenotic turbulence exists for the higher degrees of stenosis and Reynolds numbers, the resulting wall shear stresses are only three to four times greater than the Poiseuille value and are considerably less than the wall shear stress within the stenosis itself.