Microvascular Bifurcations Research Articles

Clot Accumulation in 3D Microfluidic Bifurcating Microvasculature Network.

The microvasculature, which makes up the majority of the cardiovascular system, plays a crucial role in the process of thrombosis, with the pathological formation of blood clots inside blood vessels. Since blood microflow conditions significantly influence platelet activation and thrombosis, accurately mimicking the structure of bifurcating microvascular networks and emulating local physiological blood flow conditions are valuable for understanding blood clot formation. In this work, we present an in vitro model for blood clotting in microvessels, focusing on 3D bifurcations that align with Murray's law, which guides vascular networks by maintaining a constant wall shear rate throughout. Using these models, we demonstrate that microvascular bifurcations act as sites facilitating thrombus formation compared to straight models. Additionally, by culturing endothelial cells on the luminal surfaces of the models, we show the potential of using our in vitro platforms to recapitulate the initial clotting in diseases involving endothelial dysfunction, such as Thrombotic Thrombocytopenic Purpura.

In Silico Design of Heterogeneous Microvascular Trees Using Generative Adversarial Networks and Constrained Constructive Optimization.

Designing physiologically adequate microvascular trees is of crucial relevance for bioengineering functional tissues and organs. Yet, currently available methods are poorly suited to replicate the morphological and topological heterogeneity of real microvascular trees because the parameters used to control tree generation are too simplistic to mimic results of the complex angiogenetic and structural adaptation processes invivo. We propose a method to overcome this limitation by integrating a conditional deep convolutional generative adversarial network (cDCGAN) with a local fractal dimension-oriented constrained constructive optimization (LFDO-CCO) strategy. The cDCGAN learns the patterns of real microvascular bifurcations allowing for their artificial replication. The LFDO-CCO strategy connects the generated bifurcations hierarchically to form microvascular trees with a vessel density corresponding to that observed in healthy tissues. The generated artificial microvascular trees are consistent with real microvascular trees regarding characteristics such as fractal dimension, vascular density, and coefficient of variation of diameter, length, and tortuosity. These results support the adoption of the proposed strategy for the generation of artificial microvascular trees in tissue engineering as well as for computational modeling and simulations of microcirculatory physiology.

Dependence of cell-free-layer width on rheological parameters: Combining empirical data on flow separation at microvascular bifurcations with geometrical considerations.

When blood flows through vessel networks, red blood cells (RBCs) are typically concentrated close to the vessel center line, creating a lubrication layer near the vessel wall. As RBCs bind oxygen, the width of this cell-free layer (CFL) impacts not only the blood rheology inside the vasculature, but also oxygen delivery to the tissues they perfuse and, hence, their function. Existing attempts to relate the width of the CFL to the rheological properties of the blood and the geometrical properties of the vessel are based on an analysis of the forces acting on RBCs suspended in the blood. However, the complexity of interactions in the blood makes this a challenging task. Here, we propose an alternative, two-step approach to derive such a functional relationship. First, we extend widely accepted empirical fits describing the minimum flow fraction needed for RBCs to enter a daughter vessel downstream of a microvascular bifurcation so that it depends not only on the diameter and discharge haematocrit of the parent vessel, but also on its average shear rate. Second, we propose a simple geometrical model for the minimum flow fraction based on the cross-sectional blood flow profile within the parent vessel upstream of the bifurcation-considering uniform, parabolic, and blunt velocity profiles-and derive the leading-order approximation to this model for small CFL widths. By equating the functional relationships obtained using these two approaches, we derive expressions relating the CFL width to the vessel diameter, discharge haematocrit, and mean shear rate. The resulting expressions are in good agreement with available in vivo data and represent a promising basis for future research.

Margination and adhesion dynamics of tumor cells in a real microvascular network.

In tumor metastasis, the margination and adhesion of tumor cells are two critical and closely related steps, which may determine the destination where the tumor cells extravasate to. We performed a direct three-dimensional simulation on the behaviors of the tumor cells in a real microvascular network, by a hybrid method of the smoothed dissipative particle dynamics and immersed boundary method (SDPD-IBM). The tumor cells are found to adhere at the microvascular bifurcations more frequently, and there is a positive correlation between the adhesion of the tumor cells and the wall-directed force from the surrounding red blood cells (RBCs). The larger the wall-directed force is, the closer the tumor cells are marginated towards the wall, and the higher the probability of adhesion behavior happen is. A relatively low or high hematocrit can help to prevent the adhesion of tumor cells, and similarly, increasing the shear rate of blood flow can serve the same purpose. These results suggest that the tumor cells may be more likely to extravasate at the microvascular bifurcations if the blood flow is slow and the hematocrit is moderate.

Local vs. Global Blood Flow Modulation in Artificial Microvascular Networks: Effects on Red Blood Cell Distribution and Partitioning.

Our understanding of cerebral blood flow (CBF) regulation during functional activation is still limited. Alongside with the accepted role of smooth muscle cells in controlling the arteriolar diameter, a new hypothesis has been recently formulated suggesting that CBF may be modulated by capillary diameter changes mediated by pericytes. In this study, we developed in vitro microvascular network models featuring a valve enabling the dilation of a specific micro-channel. This allowed us to investigate the non-uniform red blood cell (RBC) partitioning at microvascular bifurcations (phase separation) and the hematocrit distribution at rest and for two scenarios modeling capillary and arteriolar dilation. RBC partitioning showed similar phase separation behavior during baseline and activation. Results indicated that the RBCs at diverging bifurcations generally enter the high-flow branch (classical partitioning). Inverse behavior (reverse partitioning) was observed for skewed hematocrit profiles in the parent vessel of bifurcations, especially for high RBC velocity (i.e., arteriolar activation). Moreover, results revealed that a local capillary dilation, as it may be mediated in vivo by pericytes, led to a localized increase of RBC flow and a heterogeneous hematocrit redistribution within the whole network. In case of a global increase of the blood flow, as it may be achieved by dilating an arteriole, a homogeneous increase of RBC flow was observed in the whole network and the RBCs were concentrated along preferential pathways. In conclusion, overall increase of RBC flow could be obtained by arteriolar and capillary dilation, but only capillary dilation was found to alter the perfusion locally and heterogeneously.

Heterogeneous partition of cellular blood-borne nanoparticles through microvascular bifurcations

Blood flowing through microvascular bifurcations has been an active research topic for many decades, while the partitioning pattern of nanoscale solutes in the blood remains relatively unexplored. Here we demonstrate a multiscale computational framework for direct numerical simulation of the nanoparticle (NP) partitioning through physiologically relevant vascular bifurcations in the presence of red blood cells (RBCs). The computational framework is established by embedding a particulate suspension inflow-outflow boundary condition into a multiscale blood flow solver. The computational framework is verified by recovering a tubular blood flow without a bifurcation and validated against the experimental measurement of an intravital bifurcation flow. The classic Zweifach-Fung (ZF) effect is shown to be well captured by the method. Moreover, we observe that NPs exhibit a ZF-like heterogeneous partition in response to the heterogeneous partition of the RBC phase. The NP partitioning prioritizes the high-flow-rate daughter branch except for extreme (large or small) suspension flow partition ratios under which the complete phase separation tends to occur. By analyzing the flow field and the particle trajectories, we show that the ZF-like heterogeneity in the NP partition can be explained by the RBC-entrainment effect caused by the deviation of the flow separatrix preceded by the tank treading of RBCs near the bifurcation junction. The recovery of homogeneity in the NP partition under extreme flow partition ratios is due to the plasma skimming of NPs in the cell-free layer. These findings, based on the multiscale computational framework, provide biophysical insights to the heterogeneous distribution of NPs in microvascular beds that are observed pathophysiologically.

Study of the Partitioning of Red Blood Cells Through Asymmetric Bifurcating Microchannels

The heterogeneous distribution of red blood cells (RBCs) in the microcirculatory system is a complicated phenomenon because many factors influence how they are partitioned at microvascular bifurcations. In this study, we investigated the RBC partitioning mechanism by fabricating an in vitro experimental apparatus. The apparatus comprised a bifurcating, microfluidic channel, and the flow rate through the channels can be controlled readily over a wide range. The division turning point at which an RBC trajectory changes from one bifurcation to the other was identified via particle-tracking velocimetry on individual RBCs. The experimental results were close to the theoretical predictions and numerical simulations. The hematocrit variation before and after bifurcation was quantitatively estimated by image analysis and compared to the prediction based on Pries’ empirical model. The Zweifach–Fung effect was enhanced in the smaller fractional flow, increasing the RBC flux bias. Moreover, a cell-free layer with axial symmetry was formed in the parent channel, and an asymmetric cell-free layer was formed immediately after bifurcation. These obtained results will help clarify the RBC partitioning mechanism at microvascular bifurcations.

Microvascular hemodynamics: System properties1.

The hemodynamics of the microcirculation reflect system properties of the involved components. The blood itself is a complex suspension of water, small and large molecules and different cell types. Under most conditions, its rheologic properties are dominated by the different behaviour of fluid and cellular compartments. When perfused through small-bore tubes or vessels, the suspension exhibits specific emergent properties. The Fahraeus-effect and the Fahreaeus-Lindqvist-effect result from the interaction of cellular particles with each other and with the vessel wall. Additional phenomena occur in vascular networks due to the uneven distribution of blood cells and blood plasma at divergent microvascular bifurcations. In order to understand microvascular hemodynamics in vivo but also in artificial microfluidic geometries it is thus necessary to recognize the pertinent system properties on the level of the blood, the microvessels and the microvascular networks or perfused structures.

A micro-scale simulation of red blood cell passage through symmetric and asymmetric bifurcated vessels

Blood exhibits a heterogeneous nature of hematocrit, velocity, and effective viscosity in microcapillaries. Microvascular bifurcations have a significant influence on the distribution of the blood cells and blood flow behavior. This paper presents a simulation study performed on the two-dimensional motions and deformation of multiple red blood cells in microvessels with diverging and converging bifurcations. Fluid dynamics and membrane mechanics were incorporated. Effects of cell shape, hematocrit, and deformability of the cell membrane on rheological behavior of the red blood cells and the hemodynamics have been investigated. It was shown that the blood entering the daughter branch with a higher flow rate tended to receive disproportionally more cells. The results also demonstrate that red blood cells in microvessels experienced lateral migration in the parent channel and blunted velocity profiles in both straight section and daughter branches, and this effect was influenced by the shape and the initial position of the cells, the hematocrit, and the membrane deformability. In addition, a cell free region around the tip of the confluence was observed. The simulation results are qualitatively consistent with existing experimental findings. This study may provide fundamental knowledge for a better understanding of hemodynamic behavior of micro-scale blood flow.

Разработка микромашинных кибернетических платформ для культивирования эндотелиальных капиллярных сетей in vitro в пространстве организованных микропотоков питательной среды

This work is devoted to the development of technology and special equipment for the cultivation of spontaneously developing functioning endothelial capillary networks in vitro as the basis of artificial cloth-like structures with desired biological properties. It is the scientific and engineering projects RFBR №94-04-13544 «Structural analysis of microvascular bifurcations" and №96-04-50991 «Cell and Tissue Engineering endothelium (formation in endothelial culture in vitro the functioning self-developing capillary networks)." The proposed technology allows the author to form three-dimensional capillary endothelial network around micro-fluidic arrays, immersed in a specially designed dynamic gel. In 2013, the Korean research team under the lea-dership Noo Li Jeon has reproduced, using a similar approach, the phenomenon of self-developing functioning endothelial capillary networks with mass transfer in vitro. It has fully confirmed the validity of the concept pro-posed in the listed projects. Using system of the mathematical modeling Matlab & Simulink and system engi-neering design Cadence Orcad it was developed simulation mathematical model and circuit diagrams experimental reactor modules, it allows to saving considerable financial resources allocated to research and de-velopment of this kind. The resulting model contains 5.4 million basic Simulink blocks and performs more than 7,000 different mathematical functions, reflecting the behavior of devices in stationary and non-stationary conditions. Device control is based on neural network technology. Portable stand-alone microcomputers cyber platform includes microfluidic matrix, generators of microflows liquid phase nutrient medium, life-support systems of endothelial culture system of automatic digital imaging process of angiogenesis, the transmission system of encrypted data over a secure radio, digital control systems. All systems are backed up multiple times, allowing the product to operate in stand-alone mode for a long time (up to a year or more).

Numerical simulation of red blood cell distributions in three-dimensional microvascular bifurcations

We constructed three-dimensional microvascular bifurcation models using a parent vessel of diameter 10μm and investigated the flow behavior of the red blood cells (RBCs) through bifurcations. We considered symmetric and asymmetric model types. Two cases of equal daughter vessel diameter were employed for the asymmetric models, where the first was 10μm, which is the same as the parent vessel and the second was 7.94μm, which satisfies Murray's law. Simulated blood flow was computed using the lattice Boltzmann method in conjunction with the immersed boundary method for incorporating fluid–membrane interactions between the flow field and deformable RBCs. First, we investigated the flow behavior of a single RBC through microvascular bifurcations. In the case of the symmetric bifurcation, the turning point of the fractional plasma flow wherein the RBC flow changed from one daughter vessel to the other was 0.50. This turning point was however different for asymmetric bifurcations. Additionally, we varied the initial offset of RBCs from the centerline of the parent vessel. The simulation results indicated that the RBCs preferentially flow through the branch of a larger flow ratio. Next, we investigated the distribution characteristics of multiple RBCs. Simulations indicated that the results of the symmetric model were similar to those predicted by a previously published empirical model. On the other hand, results of asymmetric models deviated from those of the symmetric and empirical models. These results suggest that the distribution of RBCs varies according to the bifurcation angle and daughter vessel diameter in a microvascular bifurcation of the size considered.

Capillary recruitment in a theoretical model for blood flow regulation in heterogeneous microvessel networks

In striated muscle, the number of capillaries containing moving red blood cells increases with increasing metabolic demand. This phenomenon, termed capillary recruitment, has long been recognized, but its mechanism has been unclear. Here, a theoretical model for metabolic blood flow regulation in a heterogeneous network is used to test the hypothesis that capillary recruitment occurs as a result of active control of arteriolar diameters, combined with unequal partition of hematocrit at diverging microvascular bifurcations. The network structure is derived from published observations of hamster cremaster muscle in control and dilated states. The model for modulation of arteriolar diameters includes length-tension characteristics of vascular smooth muscle and responses of smooth muscle tone to myogenic, shear-dependent, and metabolic stimuli. Blood flow is simulated including nonuniform hematocrit distribution. Convective and diffusive oxygen transport in the network is simulated. Oxygen-dependent metabolic signals are assumed to be conducted upstream from distal vessels to arterioles. With increasing oxygen demand, arterioles dilate, blood flow increases, and the numbers of flowing arterioles and capillaries, as defined by red blood cell flux above a small threshold value, increase. Unequal hematocrit partition at diverging bifurcations contributes to recruitment and enhances tissue oxygenation. The results imply that capillary recruitment, as observed in the hamster cremaster preparations, can occur as a consequence of local control of arteriolar tone and the resulting nonuniform changes in red blood cell fluxes, and provide an explanation for observations of sequential recruitment of individual capillaries in response to modulation of terminal arteriolar diameter.

Flow of concentrated red blood cell suspensions at micro-bifurcations: an in vitro experimental study

The aim of this work was to investigate the phaseseparation effect in vitro for channels ,20 mm and for intermediate haematocrits, that is physiological conditions under which the effect is significant. For this purpose, we use RBC suspensions, microfluidic devices modelling microvascular bifurcations and new metrologies allowing the simultaneous quantification of both blood and RBC flow rates in the three branches of the bifurcation. First, these metrologies were validated by checking that their results are consistent with mass conservation of both blood and RBCs at microbifurcations. Second, the phase separation effect was studied, and the result compared with previous experimental and numerical results (Pries et al. 1989; Doyeux et al. 2011).

Multiple red blood cell flows through microvascular bifurcations: Cell free layer, cell trajectory, and hematocrit separation

Multiple red blood cell (RBC) flows through a symmetric microvascular bifurcation model have been simulated with the two-dimensional immersed-boundary lattice-Boltzmann method. The cell free layer (CFL), the RBC separation process and trajectories, and the resulting hematocrit distributions in the daughter branches have been examined, and the effects of cell deformability, aggregation, and feeding hematocrit on the RBC separation have also been investigated. Our results show that the overall phase separation behavior is mainly related to the RBC distribution in the feeding flow (i.e., the CFL thickness). On the other hand, for individual RBCs, the hydrodynamic interaction plays a non-negligible role in determining their trajectories and destinations. A detailed examination of the flow and pressure fields in the bifurcation region indicates that the difference in flow pressure across the front and rear ends of a flowing RBC is the major driving force for the cell motion; while the shear stress on the back of a cell that has been pressed against the corner wall is responsible for the cell's slow sliding into a vessel branch. The results have also been compared with experimental studies, and reasonable agreement has been observed. The results and information from this study could be helpful for understanding the complex RBC separation process and its effects in microcirculation and relevant biomedical applications.

Blunted temporal activity of microvascular perfusion heterogeneity in metabolic syndrome: a new attractor for peripheral vascular disease?

A key outcome for peripheral vascular disease (PVD) is a progressive decay in skeletal muscle fatigue resistance with elevated metabolic demand. We have demonstrated that PVD in obese Zucker rats (OZR) is partially due to increased perfusion distribution heterogeneity (γ) at successive microvascular bifurcations, with its cumulative impact being an increasingly heterogeneous distribution of perfusion across terminal arterioles, leading to greater tissue ischemia. To minimize this outcome, a likely compensatory mechanism against increased γ should be an increased temporal switching at bifurcations to blunt downstream deficits. Using in situ cremaster muscle, we determined that temporal activity was lower in OZR than in LZR, and this difference was present in both proximal (1A‐2A) and distal (3A‐4A) arteriolar bifurcations. While adrenoreceptor blockade (phentolamine) improved temporal activity in 1A‐2A bifurcations in OZR, this was without impact in the distal microcirculation, where only interventions against oxidant stress (TEMPOL) and thromboxane A2 activity (SQ‐29548) were effective. Analysis of the attractor for γ indicated that it was elevated in OZR, and also exhibited a reduced range, suggesting that the ability of the microcirculation to respond to any challenge is highly restricted, and may represent the major contributor to the poor muscle performance in OZR.

Blunted temporal activity of microvascular perfusion heterogeneity in metabolic syndrome: a new attractor for peripheral vascular disease?

A key clinical outcome for peripheral vascular disease (PVD) in patients is a progressive decay in skeletal muscle performance and its ability to resist fatigue with elevated metabolic demand. We have demonstrated that PVD in obese Zucker rats (OZR) is partially due to increased perfusion distribution heterogeneity at successive microvascular bifurcations within skeletal muscle. As this increased heterogeneity (γ) is longitudinally present in the network, its cumulative impact is a more heterogeneous distribution of perfusion between terminal arterioles than normal, causing greater regional tissue ischemia. To minimize this negative outcome, a likely compensatory mechanism against an increased γ should be an increased temporal switching at arteriolar bifurcations to minimize downstream perfusion deficits. Using in situ cremaster muscle, we determined that temporal activity (the cumulative sum of absolute differences between successive values of γ, taken every 20 s) was lower in OZR than in control animals, and this difference was present in both proximal (1A-2A) and distal (3A-4A) arteriolar bifurcations. Although adrenoreceptor blockade (phentolamine) improved temporal activity in 1A-2A arteriolar bifurcations in OZR, this was without impact in the distal microcirculation, where only interventions against oxidant stress (Tempol) and thromboxane A(2) activity (SQ-29548) were effective. Analysis of the attractor for γ indicated that it was not only elevated in OZR but also exhibited severe reductions in range, suggesting that the ability of the microcirculation to respond to any challenge is highly restricted and may represent the major contributor to the manifestation of poor muscle performance at this age in OZR.

Hematocrit, viscosity and velocity distributions of aggregating and non-aggregating blood in a bifurcating microchannel

Microscale blood flow is characterised by heterogeneous distributions of hematocrit, viscosity and velocity. In microvascular bifurcations, cells are unevenly distributed between the branches, and this effect can be amplified in subsequent branches depending on a number of parameters. We propose an approach to infer hematocrit profiles of human blood flowing through a bifurcating microchannel. The influence of aggregation, induced by the addition of Dextran 2000 to the samples, is also considered. Averaged values indicate plasma skimming, particularly in the presence of red blood cell (RBC) aggregation. Using an empirical model, the hematocrit profiles are used to estimate local relative viscosity distributions. Simulations are used to predict how the non-uniform viscosity influences the velocity profiles. Comparing these data to velocity profiles of RBCs measured using particle image velocimetry provides validation of the model. It is observed that aggregation blunts velocity profiles after a long straight section of channel. Downstream of the bifurcation, skewing of the velocity profiles is detected, which is enhanced by aggregation. The proposed methodology is capable of providing hitherto unreported information on important aspects of microscale blood rheology.

DECREASED TEMPORAL ACTIVITY AT MICROVASCULAR BIFURCATIONS EXACERBATES PERFUSION HETEROGENEITY IN SKELETAL MUSCLE IN THE METABOLIC SYNDROME

We have demonstrated that peripheral vascular disease (PVD) in obese Zucker rats (OZR) is due to increased perfusion heterogeneity at successive microvascular bifurcations. This increased heterogeneity (γ) is longitudinally present in the microvascular network, but reflects differential contributions and effects of adrenergic constriction, elevated ROS and increased TxA2 production. The cumulative impact of increased γ is a more heterogeneous distribution of perfusion between terminal arterioles, leading to greater tissue ischemia. However, increased temporal switching at bifurcations should compensate for the increased γ, and minimize perfusion impairments. In cremaster muscle, we determined that temporal activity (the cumulative sum of absolute differences between successive values of γ, taken every 15 seconds for 5 minutes) was lower in OZR than controls, and this difference was present in both proximal (1A‐2A) and distal (3A‐4A) bifurcations. While adrenoreceptor blockade (phentolamine) improved outcomes proximally in OZR, this was without impact in the distal microcirculation, where only interventions against ROS (TEMPOL) and TxA2 (SQ‐29548) were effective. These data suggest that reduced temporal activity at microvascular bifurcations in OZR accentuates the effects of increased γ, exacerbating perfusion‐based elements underlying PVD. (NIH RR2465AR, T32 HL90610, AHA 0740129N)

A Lattice Boltzmann Method for Simulating the Separation of Red Blood Cells at Microvascular Bifurcations

A computational simulation for the separation of red blood cells (RBCs) is presented. The deformability of RBCs is expressed by the spring network model, which is based on the minimum energy principle. In the computation of the fluid flow, the lattice Boltzmann method is used to solve the Navier—Stokes equations. Coupling of the fluid-membrane interaction is carried out by using the immersed boundary method. To verify our method, the motions of RBCs in shear flow are simulated. Typical motions of RBCs observed in the experiments are reproduced, including tank-treading, swinging and tumbling. The motions of 8 RBCs at the bifurcation are simulated when the two daughter vessels have different ratios. The results indicate that when the ratio of the daughter vessel diameter becomes smaller, the distribution of RBCs in the two vessels becomes more non-uniform.

Spatial heterogeneity in skeletal muscle microvascular blood flow distribution is increased in the metabolic syndrome

Previous studies have demonstrated that the metabolic syndrome is associated with impaired skeletal muscle arteriolar function, although integrating observations into a conceptual framework for impaired perfusion in peripheral vascular disease (PVD) has been limited. This study builds on previous work to evaluate in situ arteriolar hemodynamics in cremaster muscle of obese Zucker rats (OZR) to integrate existing knowledge into a greater understanding of impaired skeletal muscle perfusion. In OZR cremaster muscle, perfusion distribution at microvascular bifurcations (γ) was consistently more heterogeneous than in controls. However, while consistent, the underlying mechanistic contributors were spatially divergent as altered adrenergic constriction was the major contributor to altered γ at proximal microvascular bifurcations, with a steady decay with distance, while endothelial dysfunction was a stronger contributor in distal bifurcations with no discernible role proximally. Using measured values of γ, we found that simulations predict that successive alterations to γ in OZR caused more heterogeneous perfusion distribution in distal arterioles than in controls, an effect that could only be rectified by combined adrenoreceptor blockade and improvements to endothelial dysfunction. Intravascular (125)I-labeled albumin tracer washout from in situ gastrocnemius muscle of OZR provided independent support for these observations, indicating increased perfusion heterogeneity that was corrected only by combined adrenoreceptor blockade and improved endothelial function. These results suggest that a defining element of PVD in the metabolic syndrome may be an altered γ at microvascular bifurcations, that its contributors are heterogeneous and spatially distinct, and that interventions to rectify this negative outcome must take a new conceptual framework into account.