Direct Numerical Simulation of Cellular-Scale Blood Flow in 3D Microvascular Networks

A High-Fidelity Computational Model for Predicting Blood Cell Trafficking and 3D Capillary Hemodynamics in Retinal Microvascular Networks

Purpose

To present a first principle-based, high-fidelity computational model for predicting full three-dimensional (3D) and time-resolved retinal microvascular hemodynamics taking into consideration the flow and deformation of individual blood cells.

Methods

The computational model is a 3D fluid-structure interaction model based on combined finite volume/finite element/immersed-boundary methods. Three in silico microvascular networks are built from high-resolution in vivo motion contrast images of the superficial capillary plexus in the parafoveal region of the human retina. The maximum tissue area represented in the model is approximately 500 × 500 µm2, and vessel lumen diameters ranged from 5.5 to 25 µm covering capillaries, arterioles, and venules. Blood is modeled as a suspension of individual blood cells, namely, erythrocytes (RBC), leukocytes (WBC), and platelets in plasma. An accurate and detailed biophysical modeling of each blood cell and their flow-induced deformation is considered. A physiological, pulsatile boundary condition corresponding to an average cardiac cycle of 0.9 second is used.

Results

Detailed quantitative data and analysis of 3D retinal microvascular hemodynamics are presented, and their relationship to RBC flow dynamics is illustrated. Blood velocity is shown to have temporal oscillations superimposed on the background pulsatile variation, which arise because of the way RBCs partition at vascular junctions, causing repeated clogging and unclogging of vessels. Temporal variations in RBC velocity and hematocrit are anti-correlated in a given vessel, but their time-averaged distributions are positively correlated across the network. Whole blood velocity is 65% to 85% of RBC velocity, with the discrepancy related to the formation of an RBC-free region, adjacent to the vascular endothelium and typically 0.8 to 1.8 µm thick. The 3D velocity and RBC concentration profiles are shown to be oppositely skewed with respect to each other, because of the way that RBCs "hug" the apex of each bifurcation. RBC deformation is predicted to have biphasic behavior with respect to vessel diameter, with minimal cell length for vessels approximately 7 µm in diameter. The wall shear stress (WSS) exhibits a strongly 3D distribution with local regions of high value and gradient spanning a range of 10 to 80 dyn/cm2. WSS is highest where there is faster flow, greater curvature of the vessel wall, capillary bifurcations, and at locations of RBC crowding and associated thinning of the cell-free layer.

Conclusions

This study highlights the usefulness of high-fidelity cell-resolved modeling to obtain accurate and detailed 3D, time-resolved retinal hemodynamic parameters that are not readily available through noninvasive imaging approaches. The results presented are expected to complement and enhance the interpretation of in vivo data, as well as open new avenues to study retinal hemodynamics in health and disease.

Hemodynamic Characteristics of a Tortuous Microvessel Using High-Fidelity Red Blood Cell Resolved Simulations

OBJECTIVE

Tortuous microvessels are characteristic of microvascular remodeling associated with numerous physiological and pathological scenarios. Three-dimensional (3D) hemodynamics in tortuous microvessels influenced by red blood cells (RBCs), however, are largely unknown, and important questions remain. Is blood viscosity influenced by vessel tortuosity? How do RBC dynamics affect wall shear stress (WSS) patterns and the near-wall cell-free layer (CFL) over a range of conditions? The objective of this work was to parameterize hemodynamic characteristics unique to a tortuous microvessel.

METHODS

RBC-resolved simulations were performed using an immersed boundary method-based 3D fluid dynamics solver. A representative tortuous microvessel was selected from a stimulated angiogenic network obtained from imaging of the rat mesentery and digitally reconstructed for the simulations. The representative microvessel was a venule with a diameter of approximately 20 μm. The model assumes a constant diameter along the vessel length and does not consider variations due to endothelial cell shapes or the endothelial surface layer.

RESULTS

Microvessel tortuosity was observed to increase blood apparent viscosity compared to a straight tube by up to 26%. WSS spatial variations in high curvature regions reached 23.6 dyne/cm2 over the vessel cross-section. The magnitudes of WSS and CFL thickness variations due to tortuosity were strongly influenced by shear rate and negligibly influenced by tube hematocrit levels.

CONCLUSIONS

New findings from this work reveal unique tortuosity-dependent hemodynamic characteristics over a range of conditions. The results provide new thought-provoking information to better understand the contribution of tortuous vessels in physiological and pathological processes and help improve reduced-order models.

Relation between hematocrit partitioning and red blood cell lingering in a microfluidic network

Despite increased interest in the effect of lingering red blood cells (LRBCs) on the heterogeneous hematocrit distribution in the microcirculation, quantitative data on LRBCs before and after the lingering event are still limited. The aim of the study was to investigate the relation between red blood cell (RBC) lingering and hematocrit partitioning in a microfluidic model of a microvascular bifurcation in the limit of low hematocrit conditions (tube hematocrit <10%). To this end, the classification of LRBCs was performed based on timing, position, and velocity of the RBCs. The investigation provided statistical information on the velocity, shape, and orientation of LRBCs as well as on their lateral distribution in the parent and daughter vessels. LRBCs traveled predominantly close to the centerline of the parent vessel, but they marginated close to the distal wall in the daughter vessels. Differently than the RBC flow observed in the smallest vessels, no influence of lingering events on the local hematocrit partitioning was observed in our experiments. However, importantly, we found that LRBCs flowing in the daughter vessel after lingering may be connected to reverse hematocrit partitioning in downstream bifurcations by influencing the skewness of the hematocrit distribution in the daughter vessel, which relates to the so-called network history effect.

The effect of the endothelial surface layer on cell-cell interactions in microvessel bifurcations

Red blood cells (RBCs) carry oxygen and make up 40-45% of blood by volume in large vessels down to 10% or less in smaller capillaries. Because of their finite size and large volume fraction, they are heterogeneously distributed throughout the body. This is partially because RBCs are distributed or partitioned nonuniformly at diverging vessel bifurcations where blood flows from one vessel into two. Despite its increased recognition as an important player in the microvasculature, few studies have explored how the endothelial surface layer (ESL; a vessel wall coating) may affect partitioning and RBC dynamics at diverging vessel bifurcations. Here, we use a mathematical and computational model to consider how altering ESL properties, as can occur in pathological scenarios, change RBC partitioning, deformation, and penetration of the ESL. The two-dimensional finite element model considers pairs of cells, represented by interconnected viscoelastic elements, passing through an ESL-lined diverging vessel bifurcation. The properties of the ESL include the hydraulic resistivity and an osmotic pressure difference modeling how easily fluid flows through the ESL and how easily the ESL is structurally compressed, respectively. We find that cell-cell interaction leads to more uniform partitioning and greatly enhances the effects of ESL properties, especially for deformation and penetration. This includes the trend that increased hydraulic resistivity leads to more uniform partitioning, increased deformation, and decreased penetration. It also includes the trend that decreased osmotic pressure increases penetration.

Reconstructing microvascular network skeletons from 3D images: What is the ground truth?

Structural changes to microvascular networks are increasingly highlighted as markers of pathogenesis in a wide range of disease, e.g. Alzheimer's disease, vascular dementia and tumour growth. This has motivated the development of dedicated 3D imaging techniques, alongside the creation of computational modelling frameworks capable of using 3D reconstructed networks to simulate functional behaviours such as blood flow or transport processes. Extraction of 3D networks from imaging data broadly consists of two image processing steps: segmentation followed by skeletonisation. Much research effort has been devoted to segmentation field, and there are standard and widely-applied methodologies for creating and assessing gold standards or ground truths produced by manual annotation or automated algorithms. The Skeletonisation field, however, lacks widely applied, simple to compute metrics for the validation or optimisation of the numerous algorithms that exist to extract skeletons from binary images. This is particularly problematic as 3D imaging datasets increase in size and visual inspection becomes an insufficient validation approach. In this work, we first demonstrate the extent of the problem by applying 4 widely-used skeletonisation algorithms to 3 different imaging datasets. In doing so we show significant variability between reconstructed skeletons of the same segmented imaging dataset. Moreover, we show that such a structural variability propagates to simulated metrics such as blood flow. To mitigate this variability we introduce a new, fast and easy to compute super metric that compares the volume, connectivity, medialness, bifurcation point identification and homology of the reconstructed skeletons to the original segmented data. We then show that such a metric can be used to select the best performing skeletonisation algorithm for a given dataset, as well as to optimise its parameters. Finally, we demonstrate that the super metric can also be used to quickly identify how a particular skeletonisation algorithm could be improved, becoming a powerful tool in understanding the complex implication of small structural changes in a network.

Analysis of the Suitability of an Effective Viscosity to Represent Interactions Between Red Blood Cells in Shear Flow

Many methods to computationally predict red blood cell damage have been introduced, and among these are Lagrangian methods that track the cells along their pathlines. Such methods typically do not explicitly include cell-cell interactions. Due to the high volume fraction of red blood cells (RBCs) in blood, these interactions could impact cell mechanics and thus the amount of damage caused by the flow. To investigate this question, cell-resolved simulations of red blood cells in shear flow were performed for multiple interacting cells, as well as for single cells in unbounded flow at an effective viscosity. Simulations run without adjusting the bulk viscosity produced larger errors unilaterally and were not considered further for comparison. We show that a periodic box containing at least 8 cells and a spherical harmonic of degree larger than 10 are necessary to produce converged higher-order statistics. The maximum difference between the single-cell and multiple-cell cases in terms of peak strain was 3.7%. To achieve this, one must use the whole blood viscosity and average over multiple cell orientations when adopting a single-cell simulation approach. The differences between the models in terms of average strain were slightly larger (maximum difference of 6.9%). However, given the accuracy of the single-cell approach in predicting the maximum strain, which is useful in hemolysis prediction, and its computational cost that is orders of magnitude less than the multiple-cell approach, one may use it as an affordable cell-resolved approach for hemolysis prediction.

Predicting capillary vessel network hemodynamics in silico by machine learning

Blood velocity and red blood cell (RBC) distribution profiles in a capillary vessel cross-section in the microcirculation are generally complex and do not follow Poiseuille's parabolic or uniform pattern. Existing imaging techniques used to map large microvascular networks in vivo do not allow a direct measurement of full 3D velocity and RBC concentration profiles, although such information is needed for accurate evaluation of the physiological variables, such as the wall shear stress (WSS) and near-wall cell-free layer (CFL), that play critical roles in blood flow regulation, disease progression, angiogenesis, and hemostasis. Theoretical network flow models, often used for hemodynamic predictions in experimentally acquired images of the microvascular network, cannot provide the full 3D profiles either. In contrast, such information can be readily obtained from high-fidelity computational models that treat blood as a suspension of deformable RBCs. These models, however, are computationally expensive and not feasible for extension to the microvascular network at large spatial scales up to an organ level. To overcome such limitations, here we present machine learning (ML) models that bypass such expensive computations but provide highly accurate and full 3D profiles of the blood velocity, RBC concentration, WSS, and CFL in every vessel in the microvascular network. The ML models, which are based on artificial neural networks and convolution-based U-net models, predict hemodynamic quantities that compare very well against the true data but reduce the prediction time by several orders. This study therefore paves the way for ML to make detailed and accurate hemodynamic predictions in spatially large microvascular networks at an organ-scale.

Angiogenic Microvascular Wall Shear Stress Patterns Revealed Through Three-dimensional Red Blood Cell Resolved Modeling

The wall shear stress (WSS) exerted by blood flowing through microvascular capillaries is an established driver of new blood vessel growth, or angiogenesis. Such adaptations are central to many physiological processes in both health and disease, yet three-dimensional (3D) WSS characteristics in real angiogenic microvascular networks are largely unknown. This marks a major knowledge gap because angiogenesis, naturally, is a 3D process. To advance current understanding, we model 3D red blood cells (RBCs) flowing through rat angiogenic microvascular networks using state-of-the-art simulation. The high-resolution fluid dynamics reveal 3D WSS patterns occurring at sub-endothelial cell (EC) scales that derive from distinct angiogenic morphologies, including microvascular loops and vessel tortuosity. We identify the existence of WSS hot and cold spots caused by angiogenic surface shapes and RBCs, and notably enhancement of low WSS regions by RBCs. Spatiotemporal characteristics further reveal how fluctuations follow timescales of RBC "footprints." Altogether, this work provides a new conceptual framework for understanding how shear stress might regulate EC dynamics in vivo.

Circulating cellular clusters are associated with thrombotic complications and clinical outcomes in COVID-19

We sought to study the role of circulating cellular clusters (CCC) -such as circulating leukocyte clusters (CLCs), platelet-leukocyte aggregates (PLA), and platelet-erythrocyte aggregates (PEA)- in the immunothrombotic state induced by COVID-19. Forty-six blood samples from 37 COVID-19 patients and 12 samples from healthy controls were analyzed with imaging flow cytometry. Patients with COVID-19 had significantly higher levels of PEAs (p value<0.001) and PLAs (p value = 0.015) compared to healthy controls. Among COVID-19 patients, CLCs were correlated with thrombotic complications (p value = 0.016), vasopressor need (p value = 0.033), acute kidney injury (p value = 0.027), and pneumonia (p value = 0.036), whereas PEAs were associated with positive bacterial cultures (p value = 0.033). In predictive in silico simulations, CLCs were more likely to result in microcirculatory obstruction at low flow velocities (≤1 mm/s) and at higher branching angles. Further studies on the cellular component of hyperinflammatory prothrombotic states may lead to the identification of novel biomarkers and drug targets for inflammation-related thrombosis.

Red Blood Cell Partitioning Using a Microfluidic Channel with Ladder Structure

This study investigated the partitioning characteristics of red blood cells (RBCs) within capillaries, with a specific focus on ladder structures observed near the end of the capillaries. In vitro experiments were conducted using microfluidic channels with a ladder structure model comprising six bifurcating channels that exhibited an anti-parallel flow configuration. The effects of various factors, such as the parent channel width, distance between branches, and hematocrit, on RBC partitioning in bifurcating channels were evaluated. A decrease in the parent channel width resulted in an increase in the heterogeneity in the hematocrit distribution and a bias in the fractional RBC flux. Additionally, variations in the distance between branches affected the RBC distribution, with smaller distances resulting in greater heterogeneity. The bias of the RBC distribution in the microchannel cross section had a major effect on the RBC partitioning characteristics. The influence of hematocrit variations on the RBC distribution was also investigated, with lower hematocrit values leading to a more pronounced bias in the RBC distribution. Overall, this study provides valuable insights into RBC distribution characteristics in capillary networks, contributing to our understanding of the physiological mechanisms of RBC phase separation in the microcirculatory system. These findings have implications for predicting oxygen heterogeneity in tissues and could aid in the study of diseases associated with impaired microcirculation.

Flow Heterogeneity and Factors Contributing to the Variability in Retinal Capillary Blood Flow

Purpose

Capillary flow plays an important role in the nourishment and maintenance of healthy neural tissue and can be observed directly and non-invasively in the living human retina. Despite their importance, patterns of normal capillary flow are not well understood due to limitations in spatial and temporal resolution of imaging data.

Methods

Capillary flow characteristics were studied in the retina of three healthy young individuals using a high-resolution adaptive optics ophthalmoscope. Imaging with frame rates of 200 to 300 frames per second was sufficient to capture details of the single-file flow of red blood cells in capillaries over the course of about 3 seconds.

Results

Erythrocyte velocities were measured from 72 neighboring vessels of the parafoveal capillary network for each subject. We observed strong variability among vessels within a given subject, and even within a given imaged field, across a range of capillary flow parameters including maximum and minimum velocities, pulsatility, abruptness of the systolic peak, and phase of the cardiac cycle. The observed variability was not well explained by "local" factors such as the vessel diameter, tortuosity, length, linear cell density, or hematocrit of the vessel. Within a vessel, a moderate relation between the velocities and hematocrit was noted, suggesting a redistribution of plasma between cells with changes in flow.

Conclusions

These observations advance our fundamental understanding of normal capillary physiology and raise questions regarding the potential role of network-level effects in explaining the observed flow heterogeneity.

Red blood cell lingering modulates hematocrit distribution in the microcirculation

The distribution of red blood cells (RBCs) in the microcirculation determines the oxygen delivery and solute transport to tissues. This process relies on the partitioning of RBCs at successive bifurcations throughout the microvascular network, and it has been known since the last century that RBCs partition disproportionately to the fractional blood flow rate, therefore leading to heterogeneity of the hematocrit (i.e., volume fraction of RBCs in blood) in microvessels. Usually, downstream of a microvascular bifurcation, the vessel branch with a higher fraction of blood flow receives an even higher fraction of RBC flux. However, both temporal and time-average deviations from this phase-separation law have been observed in recent studies. Here, we quantify how the microscopic behavior of RBC lingering (i.e., RBCs temporarily residing near the bifurcation apex with diminished velocity) influences their partitioning, through combined in vivo experiments and in silico simulations. We developed an approach to quantify the cell lingering at highly confined capillary-level bifurcations and demonstrate that it correlates with deviations of the phase-separation process from established empirical predictions by Pries et al. Furthermore, we shed light on how the bifurcation geometry and cell membrane rigidity can affect the lingering behavior of RBCs; e.g., rigid cells tend to linger less than softer ones. Taken together, RBC lingering is an important mechanism that should be considered when studying how abnormal RBC rigidity in diseases such as malaria and sickle-cell disease could hinder the microcirculatory blood flow or how the vascular networks are altered under pathological conditions (e.g., thrombosis, tumors, aneurysm).

Anomalous Diffusion of Deformable Particles in a Honeycomb Network

Transport of deformable particles in a honeycomb network is studied numerically. It is shown that the particle deformability has a strong impact on their distribution in the network. For sufficiently soft particles, we observe a short memory behavior from one bifurcation to the next, and the overall behavior consists in a random partition of particles, exhibiting a diffusionlike transport. On the contrary, stiff enough particles undergo a biased distribution whereby they follow a deterministic partition at bifurcations, due to long memory. This leads to a lateral ballistic drift in the network at small concentration and anomalous superdiffusion at larger concentration, even though the network is ordered. A further increase of concentration enhances particle-particle interactions which shorten the memory effect, turning the particle anomalous diffusion into a classical diffusion. We expect the drifting and diffusive regime transition to be generic for deformable particles.

Red blood cell dynamics in extravascular biological tissues modelled as canonical disordered porous media

The dynamics of blood flow in the smallest vessels and passages of the human body, where the cellular character of blood becomes prominent, plays a dominant role in the transport and exchange of solutes. Recent studies have revealed that the microhaemodynamics of a vascular network is underpinned by its interconnected structure, and certain structural alterations such as capillary dilation and blockage can substantially change blood flow patterns. However, for extravascular media with disordered microstructure (e.g. the porous intervillous space in the placenta), it remains unclear how the medium's structure affects the haemodynamics. Here, we simulate cellular blood flow in simple models of canonical porous media representative of extravascular biological tissue, with corroborative microfluidic experiments performed for validation purposes. For the media considered here, we observe three main effects: first, the relative apparent viscosity of blood increases with the structural disorder of the medium; second, the presence of red blood cells (RBCs) dynamically alters the flow distribution in the medium; third, symmetry breaking introduced by moderate structural disorder can promote more homogeneous distribution of RBCs. Our findings contribute to a better understanding of the cell-scale haemodynamics that mediates the relationship linking the function of certain biological tissues to their microstructure.

Hematocrit skewness along sequential bifurcations within a microfluidic network induces significant changes in downstream red blood cell partitioning

There has been a wealth of research conducted regarding the partitioning of red blood cells (RBCs) at bifurcations within the microvasculature. In previous studies, partitioning has been characterized as either regular partitioning, in which the higher flow rate daughter channel receives a proportionally larger percentage of RBCs, or reverse partitioning, in which the opposite occurs. While there are many examples of network studies in silico, most in vitro work has been conducted using single bifurcation. When microfluidic networks have been used, the channel dimensions are typically greater than 20 μm, ignoring conditions where RBCs are highly confined. This paper presents a study of RBC partitioning in a network of sequential bifurcations with channel dimensions less than 8 μm in hydraulic diameter. The study investigated the effect of the volumetric flow rate ratio (Q*) at each bifurcation, solution hematocrit, and channel length on the erythrocyte flux ratio (N*), a measure of RBC partitioning. We report significant differences in partitioning between upstream and downstream bifurcations even when the flow rate ratio remains the same. Skewness analysis, a measure of cell distribution across the width of a vessel, strongly suggests that immediately following the first bifurcation most RBCs are skewed toward the inner channel wall, leading to preferential RBC perfusion into one daughter channel at the subsequent bifurcation even at higher downstream flow rate ratios. The skewness of RBC distribution following the first bifurcation can either manifest as enhanced regular partitioning or reverse partitioning at the succeeding branch.

Neurovascular coupling: motive unknown

In the brain, increases in neural activity drive changes in local blood flow via neurovascular coupling. The common explanation for increased blood flow (known as functional hyperemia) is that it supplies the metabolic needs of active neurons. However, there is a large body of evidence that is inconsistent with this idea. Baseline blood flow is adequate to supply oxygen needs even with elevated neural activity. Neurovascular coupling is irregular, absent, or inverted in many brain regions, behavioral states, and conditions. Increases in respiration can increase brain oxygenation without flow changes. Simulations show that given the architecture of the brain vasculature, areas of low blood flow are inescapable and cannot be removed by functional hyperemia. As discussed in this article, potential alternative functions of neurovascular coupling include supplying oxygen for neuromodulator synthesis, brain temperature regulation, signaling to neurons, stabilizing and optimizing the cerebral vascular structure, accommodating the non-Newtonian nature of blood, and driving the production and circulation of cerebrospinal fluid (CSF).

Lingering Dynamics of Type 2 Diabetes Mellitus Red Blood Cells in Retinal Arteriolar Bifurcations

It has been proven that the deformability of red blood cells (RBC) is reduced owing to changes in mechanical properties, such as diabetes mellitus and hypertension. To probe the effects of RBC morphological and physical parameters on the flow field in bifurcated arterioles, three types of RBC models with various degrees of biconcave shapes were built based on the in vitro experimental data. The dynamic behaviors of the RBCs in shear flow were simulated to validate the feasibility of the finite element-Arbitrary Lagrangian-Eulerian method with a moving mesh. The influences of the shear rate and viscosity ratios on RBC motions were investigated. The motion of RBCs in arteriolar bifurcations was further simulated. Abnormal variations in the morphological and physical parameters of RBCs may lead to diminished tank-tread motion and enhanced tumbling motion in shear flow. Moreover, abnormal RBC variations can result in slower RBC motion at the bifurcation with a longer transmit time and greater flow resistance, which may further cause inadequate local oxygen supply. These findings would provide useful insights into the microvascular complications in diabetes mellitus.

Application of machine learning in predicting blood flow and red cell distribution in capillary vessel networks

Capillary blood vessels in the body partake in the exchange of gas and nutrients with tissues. They are interconnected via multiple vascular junctions forming the microvascular network. Distributions of blood flow and red cells (RBCs) in such networks are spatially uneven and vary in time. Since they dictate the pathophysiology of tissues, their knowledge is important. Theoretical models used to obtain flow and RBC distribution in large networks have limitations as they treat each vessel as a one-dimensional segment and do not explicitly consider cell-cell and cell-vessel interactions. High-fidelity computational models that accurately model each individual RBC are computationally too expensive to predict haemodynamics in large vascular networks and over a long time. Here we investigate the applicability of machine learning (ML) techniques to predict blood flow and RBC distributions in physiologically realistic vascular networks. We acquire data from high-fidelity simulations of deformable RBC suspension flowing in the networks. With the flow and haematocrit specified at an inlet of vasculature, the ML models predict the time-averaged flow rate and RBC distributions in the entire network, time-dependent flow rate and haematocrit in each vessel and vascular bifurcation in isolation over a long time, and finally, simultaneous spatially and temporally evolving quantities through the vessel hierarchy in the networks.

Vascular bifurcation influences the protein corona composition on nanoparticles and impacts their cellular uptake

The protein corona (PC) that forms on nanoparticles (NPs) after in vivo injection influences their biodistribution, pharmacokinetics, and cell interaction. Although injected NPs traverse vascular networks, the impact of vascular features on the protein corona composition is mainly unexplored. Using an in vitro flow model that introduces bifurcations, a common feature of blood vessels, we show that vessels are not passive bystanders in the formation of the PC but that their features play active roles in defining the PC on NPs. The addition of bifurcation significantly increased the amount of proteins associated with NP. The bifurcation's introduction also changed the PC's composition on the NPs and affected the NP interactions with cells. Correlation analysis and modeling showed that these changes in the PC are mediated by both the branching and diameter reduction associated with vessel bifurcation and the resulting change in flow rate. The results indicate that blood vessel structures play an active part in the information of the PC, and their role should be studied critically for a better understanding of the PC and its biological implications.

A computational study of red blood cell deformability effect on hemodynamic alteration in capillary vessel networks

Capillary blood vessels, the smallest vessels in the body, form an intricate network with constantly bifurcating, merging and winding vessels. Red blood cells (RBCs) must navigate through such complex microvascular networks in order to maintain tissue perfusion and oxygenation. Normal, healthy RBCs are extremely deformable and able to easily flow through narrow vessels. However, RBC deformability is reduced in many pathological conditions and during blood storage. The influence of reduced cell deformability on microvascular hemodynamics is not well established. Here we use a high-fidelity, 3D computational model of blood flow that retains exact geometric details of physiologically realistic microvascular networks, and deformation of every one of nearly a thousand RBCs flowing through the networks. We predict that reduced RBC deformability alters RBC trafficking with significant and heterogeneous changes in hematocrit. We quantify such changes along with RBC partitioning and lingering at vascular bifurcations, perfusion and vascular resistance, and wall shear stress. We elucidate the cellular-scale mechanisms that cause such changes. We show that such changes arise primarily due to the altered RBC dynamics at vascular bifurcations, as well as cross-stream migration. Less deformable cells tend to linger less at majority of bifurcations increasing the fraction of RBCs entering the higher flow branches. Changes in vascular resistance also seen to be heterogeneous and correlate with hematocrit changes. Furthermore, alteration in RBC dynamics is shown to cause localized changes in wall shear stress within vessels and near vascular bifurcations. Such heterogeneous and focal changes in hemodynamics may be the cause of morphological abnormalities in capillary vessel networks as observed in several diseases.

A few upstream bifurcations drive the spatial distribution of red blood cells in model microfluidic networks

The physics of blood flow in small vessel networks is dominated by the interactions between Red Blood Cells (RBCs), plasma and blood vessel walls. The resulting couplings between the microvessel network architecture and the heterogeneous distribution of RBCs at network-scale are still poorly understood. The main goal of this paper is to elucidate how a local effect, such as RBC partitioning at individual bifurcations, interacts with the global structure of the flow field to induce specific preferential locations of RBCs in model microfluidic networks. First, using experimental results, we demonstrate that persistent perturbations to the established hematocrit profile after diverging bifurcations may bias RBC partitioning at the next bifurcations. By performing a sensitivity analysis based upon network models of RBC flow, we show that these perturbations may propagate from bifurcation to bifurcation, leading to an outsized impact of a few crucial upstream bifurcations on the distribution of RBCs at network-scale. Based on measured hematocrit profiles, we further construct a modified RBC partitioning model that accounts for the incomplete relaxation of RBCs at these bifurcations. This model allows us to explain how the flow field results in a single pattern of RBC preferential location in some networks, while it leads to the emergence of two different patterns of RBC preferential location in others. Our findings have important implications in understanding and modeling blood flow in physiological and pathological conditions.

Continuum microhaemodynamics modelling using inverse rheology

Modelling blood flow in microvascular networks is challenging due to the complex nature of haemorheology. Zero- and one-dimensional approaches cannot reproduce local haemodynamics, and models that consider individual red blood cells (RBCs) are prohibitively computationally expensive. Continuum approaches could provide an efficient solution, but dependence on a large parameter space and scarcity of experimental data for validation has limited their application. We describe a method to assimilate experimental RBC velocity and concentration data into a continuum numerical modelling framework. Imaging data of RBCs were acquired in a sequentially bifurcating microchannel for various flow conditions. RBC concentration distributions were evaluated and mapped into computational fluid dynamics simulations with rheology prescribed by the Quemada model. Predicted velocities were compared to particle image velocimetry data. A subset of cases was used for parameter optimisation, and the resulting model was applied to a wider data set to evaluate model efficacy. The pre-optimised model reduced errors in predicted velocity by 60% compared to assuming a Newtonian fluid, and optimisation further reduced errors by 40%. Asymmetry of RBC velocity and concentration profiles was demonstrated to play a critical role. Excluding asymmetry in the RBC concentration doubled the error, but excluding spatial distributions of shear rate had little effect. This study demonstrates that a continuum model with optimised rheological parameters can reproduce measured velocity if RBC concentration distributions are known a priori. Developing this approach for RBC transport with more network configurations has the potential to provide an efficient approach for modelling network-scale haemodynamics.

Computational Characterization of Mechanical, Hemodynamic, and Surface Interaction Conditions: Role of Protein Adsorption on the Regenerative Response of TEVGs

Currently available small diameter vascular grafts (<6 mm) present several long-term limitations, which has prevented their full clinical implementation. Computational modeling and simulation emerge as tools to study and optimize the rational design of small diameter tissue engineered vascular grafts (TEVG). This study aims to model the correlation between mechanical-hemodynamic-biochemical variables on protein adsorption over TEVG and their regenerative potential. To understand mechanical-hemodynamic variables, two-way Fluid-Structure Interaction (FSI) computational models of novel TEVGs were developed in ANSYS Fluent 2019R3^® and ANSYS Transient Structural^® software. Experimental pulsatile pressure was included as an UDF into the models. TEVG mechanical properties were obtained from tensile strength tests, under the ISO7198:2016, for novel TEVGs. Subsequently, a kinetic model, linked to previously obtained velocity profiles, of the protein-surface interaction between albumin and fibrinogen, and the intima layer of the TEVGs, was implemented in COMSOL Multiphysics 5.3^®. TEVG wall properties appear critical to understand flow and protein adsorption under hemodynamic stimuli. In addition, the kinetic model under flow conditions revealed that size and concentration are the main parameters to trigger protein adsorption on TEVGs. The computational models provide a robust platform to study multiparametrically the performance of TEVGs in terms of protein adsorption and their regenerative potential.

Recent advances in blood rheology: a review

Due to the potential impact on the diagnosis and treatment of various cardiovascular diseases, work on the rheology of blood has significantly expanded in the last decade, both experimentally and theoretically. Experimentally, blood has been confirmed to demonstrate a variety of non-Newtonian rheological characteristics, including pseudoplasticity, viscoelasticity, and thixotropy. New rheological experiments and the development of more controlled experimental protocols on more extensive, broadly physiologically characterized, human blood samples demonstrate the sensitivity of aspects of hemorheology to several physiological factors. For example, at high shear rates the red blood cells elastically deform, imparting viscoelasticity, while at low shear rates, they form "rouleaux" structures that impart additional, thixotropic behavior. In addition to the advances in experimental methods and validated data sets, significant advances have also been made in both microscopic simulations and macroscopic, continuum, modeling, as well as novel, multiscale approaches. We outline and evaluate the most promising of these recent developments. Although we primarily focus on human blood rheology, we also discuss recent observations on variations observed across some animal species that provide some indication on evolutionary effects.

In vitro study on the partitioning of red blood cells using a microchannel network

To investigate the partitioning properties of red blood cells (RBCs) in the bifurcating capillary vessels, an in vitro experiment was performed to perfuse human RBC suspensions into the microfluidic channels with a width of <10 μm. Two types of microchannel geometries were established. One is a single model comprising one parent and two daughter channels with different widths, and the other is a network model that had a symmetric geometry with four consecutive divergences and convergences. In addition to the fractional RBC flux at each bifurcation, changes in hematocrit levels and flow velocity before and after the bifurcation were investigated. In the single model, non-uniform partitioning of RBCs was observed, and this result was in good agreement with that of the empirical model. Furthermore, in the network model, the RBC distribution in the cross-section before the bifurcation significantly affected RBC partitioning in the two channels after the bifurcation. Hence, there was a large RBC heterogeneity in the capillary network. The hematocrit levels between the channels differed for more than one order of magnitude. Therefore, the findings of the current research could facilitate a better understanding of RBC partitioning properties in the microcirculatory system.

Investigation of red blood cell partitioning in an in vitro microvascular bifurcation

There is a long history of research examining red blood cell (RBC) partitioning in microvasculature bifurcations. These studies commonly report results describing partitioning that exists as either regular partitioning, which occurs when the RBC flux ratio is greater than the bulk fluid flowrate ratio, or reverse partitioning when the RBC flux ratio is less than or equal to that of the bulk fluid flowrate. This paper presents a study of RBC partitioning in a single bifurcating microchannel with dimensions of 6 to 16 μm, investigating the effects of hematocrit, channel width, daughter channel flowrate ratio, and bifurcation angle. The erythrocyte flux ratio, N*, manifests itself as either regular or reverse partitioning, and time-dependent partitioning is much more dynamic, occurring as both regular and reverse partitioning. We report a significant reduction in the well-known sigmoidal variation of the erythrocyte flux ratio (N*) versus the volumetric flowrate ratio (Q*), partitioning behavior with increasing hematocrit in microchannels when the channel dimensions are comparable with cell size. RBCs "lingering" or jamming at the bifurcation were also observed and quantified in vitro. Results from trajectory analyses suggest that the RBC position in the feeder channel strongly affects both partitioning and lingering frequency of RBCs, with both being significantly reduced when RBCs flow on streamlines near the edge of the channel as opposed to the center of the channel. Furthermore, our experiments suggest that even at low Reynolds number, partitioning is affected by the bifurcation angle by increasing cell-cell interactions. The presented results provide further insight into RBC partitioning as well as perfusion throughout the microvasculature.

Computational models of cancer cell transport through the microcirculation

The transport of cancerous cells through the microcirculation during metastatic spread encompasses several interdependent steps that are not fully understood. Computational models which resolve the cellular-scale dynamics of complex microcirculatory flows offer considerable potential to yield needed insights into the spread of cancer as a result of the level of detail that can be captured. In recent years, in silico methods have been developed that can accurately and efficiently model the circulatory flows of cancer and other biological cells. These computational methods are capable of resolving detailed fluid flow fields which transport cells through tortuous physiological geometries, as well as the deformation and interactions between cells, cell-to-endothelium interactions, and tumor cell aggregates, all of which play important roles in metastatic spread. Such models can provide a powerful complement to experimental works, and a promising approach to recapitulating the endogenous setting while maintaining control over parameters such as shear rate, cell deformability, and the strength of adhesive binding to better understand tumor cell transport. In this review, we present an overview of computational models that have been developed for modeling cancer cells in the microcirculation, including insights they have provided into cell transport phenomena.

The capillary fascicle in skeletal muscle: Structural and functional physiology of RBC distribution in capillary networks

KEY POINTS

The capillary module, consisting of parallel capillaries from arteriole to venule, is classically considered as the building block of complex capillary networks. In skeletal muscle, this structure fails to address how blood flow is regulated along the entire length of the synchronously contracting muscle fibres. Using intravital video microscopy of resting extensor digitorum longus muscle in rats, we demonstrated the capillary fascicle as a series of interconnected modules forming continuous columns that align naturally with the dimensions of the muscle fascicle. We observed structural heterogeneity for module topology, and functional heterogeneity in space and time for capillary-red blood cell (RBC) haemodynamics within a module and between modules. We found that module RBC haemodynamics were independent of module resistance, providing direct evidence for microvascular flow regulation at the level of the capillary module. The capillary fascicle is an updated paradigm for characterizing blood flow and RBC distribution in skeletal muscle capillary networks.

ABSTRACT

Capillary networks are the fundamental site of oxygen exchange in the microcirculation. The capillary module (CM), consisting of parallel capillaries from terminal arteriole (TA) to post-capillary venule (PCV), is classically considered as the building block of complex capillary networks. In skeletal muscle, this structure fails to address how blood flow is regulated along the entire length of the synchronously contracting muscle fibres, requiring co-ordination from numerous modules. It has previously been recognized that TAs and PCVs interact with multiple CMs, creating interconnected networks. Using label-free intravital video microscopy of resting extensor digitorum longus muscle in rats, we found that these networks form continuous columns of linked CMs spanning thousands of microns, herein denoted as the capillary fascicle (CF); this structure aligns naturally with the dimensions of the muscle fascicle. We measured capillary-red blood cell (RBC) haemodynamics and module topology (n = 9 networks, 327 modules, 1491 capillary segments). The average module had length 481 μm, width 157 μm and 9.51 parallel capillaries. We observed structural heterogeneity for CM topology, and functional heterogeneity in space and time for capillary-RBC haemodynamics within a module and between modules. There was no correlation between capillary RBC velocity and lineal density. A passive inverse relationship between module length and haemodynamics was remarkably absent, providing direct evidence for microvascular flow regulation at the level of the CM. In summary, the CF is an updated paradigm for characterizing RBC distribution in skeletal muscle, and strengthens the theory of capillary networks as major contributors to the signal that regulates capillary perfusion.

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.

Voxelized simulation of cerebral oxygen perfusion elucidates hypoxia in aged mouse cortex

Departures of normal blood flow and metabolite distribution from the cerebral microvasculature into neuronal tissue have been implicated with age-related neurodegeneration. Mathematical models informed by spatially and temporally distributed neuroimage data are becoming instrumental for reconstructing a coherent picture of normal and pathological oxygen delivery throughout the brain. Unfortunately, current mathematical models of cerebral blood flow and oxygen exchange become excessively large in size. They further suffer from boundary effects due to incomplete or physiologically inaccurate computational domains, numerical instabilities due to enormous length scale differences, and convergence problems associated with condition number deterioration at fine mesh resolutions. Our proposed simple finite volume discretization scheme for blood and oxygen microperfusion simulations does not require expensive mesh generation leading to the critical benefit that it drastically reduces matrix size and bandwidth of the coupled oxygen transfer problem. The compact problem formulation yields rapid and stable convergence. Moreover, boundary effects can effectively be suppressed by generating very large replica of the cortical microcirculation in silico using an image-based cerebrovascular network synthesis algorithm, so that boundaries of the perfusion simulations are far removed from the regions of interest. Massive simulations over sizeable portions of the cortex with feature resolution down to the micron scale become tractable with even modest computer resources. The feasibility and accuracy of the novel method is demonstrated and validated with in vivo oxygen perfusion data in cohorts of young and aged mice. Our oxygen exchange simulations quantify steep gradients near penetrating blood vessels and point towards pathological changes that might cause neurodegeneration in aged brains. This research aims to explain mechanistic interactions between anatomical structures and how they might change in diseases or with age. Rigorous quantification of age-related changes is of significant interest because it might aide in the search for imaging biomarkers for dementia and Alzheimer’s disease.

Brain function critically depends on the maintenance of physiological blood supply and metabolism in the cortex. Disturbances to adequate perfusion have been linked to age-related neurodegeneration. However, the precise correlation between age-related hemodynamic changes and the resulting decline in oxygen delivery is not well understood and has not been quantified. Therefore, we introduce a new compact, and therefore highly scalable, computational method for predicting the physiological relationship between hemodynamics and cortical oxygen perfusion for large sections of the cortical microcirculation. We demonstrate the novel mesh generation-free (MGF), multi-scale simulation approach through realistic in vivo case studies of cortical microperfusion in the mouse brain. We further validate mechanistic correlations and a quantitative relationship between blood flow and brain oxygenation using experimental data from cohorts of young, middle aged and old mouse brains. Our computational approach overcomes size and performance limitations of previous unstructured meshing techniques to enable the prediction of oxygen tension with a spatial resolution of least two orders of magnitude higher than previously possible. Our simulation results support the hypothesis that structural changes in the microvasculature induce hypoxic pockets in the aged brain that are absent in the healthy, young mouse.

Lingering Dynamics in Microvascular Blood Flow

The microvascular networks in the body of vertebrates consist of the smallest vessels such as arterioles, capillaries, and venules. The flow of red blood cells (RBCs) through these networks ensures the gas exchange in as well as the transport of nutrients to the tissues. Any alterations in this blood flow may have severe implications on the health state. Because the vessels in these networks obey dimensions similar to the diameter of RBCs, dynamic effects on the cellular scale play a key role. The steady progression in the numerical modeling of RBCs, even in complex networks, has led to novel findings in the field of hemodynamics, especially concerning the impact and the dynamics of lingering events when a cell meets a branch of the network. However, these results are yet to be matched by a detailed analysis of the lingering experiments in vivo. To quantify this lingering effect in in vivo experiments, this study analyzes branching vessels in the microvasculature of Syrian golden hamsters via intravital microscopy and the use of an implanted dorsal skinfold chamber. It also presents a detailed analysis of these lingering effects of cells at the apex of bifurcating vessels, affecting the temporal distribution of plasmatic zones of blood flow in the branches and even causing a partial blockage in severe cases.

Digitally Fabricated and Naturally Augmented In Vitro Tissues

Human in vitro tissues are extracorporeal 3D cultures of human cells embedded in biomaterials, commonly hydrogels, which recapitulate the heterogeneous, multiscale, and architectural environment of the human body. Contemporary strategies used in 3D tissue and organ engineering integrate the use of automated digital manufacturing methods, such as 3D printing, bioprinting, and biofabrication. Human tissues and organs, and their intra- and interphysiological interplay, are particularly intricate. For this reason, attentiveness is rising to intersect materials science, medicine, and biology with arts and informatics. This report presents advances in computational modeling of bioink polymerization and its compatibility with bioprinting, the use of digital design and fabrication in the development of fluidic culture devices, and the employment of generative algorithms for modeling the natural and biological augmentation of in vitro tissues. As a future direction, the use of serially linked in vitro tissues as human body-mimicking systems and their application in drug pharmacokinetics and metabolism, disease modeling, and diagnostics are discussed.

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.

Biofabrication Strategies and Engineered In Vitro Systems for Vascular Mechanobiology

The vascular system is integral for maintaining organ-specific functions and homeostasis. Dysregulation in vascular architecture and function can lead to various chronic or acute disorders. Investigation of the role of the vascular system in health and disease has been accelerated through the development of tissue-engineered constructs and microphysiological on-chip platforms. These in vitro systems permit studies of biochemical regulation of vascular networks and parenchymal tissue and provide mechanistic insights into the biophysical and hemodynamic forces acting in organ-specific niches. Detailed understanding of these forces and the mechanotransductory pathways involved is necessary to develop preventative and therapeutic strategies targeting the vascular system. This review describes vascular structure and function, the role of hemodynamic forces in maintaining vascular homeostasis, and measurement approaches for cell and tissue level mechanical properties influencing vascular phenomena. State-of-the-art techniques for fabricating in vitro microvascular systems, with varying degrees of biological and engineering complexity, are summarized. Finally, the role of vascular mechanobiology in organ-specific niches and pathophysiological states, and efforts to recapitulate these events using in vitro microphysiological systems, are explored. It is hoped that this review will help readers appreciate the important, but understudied, role of vascular-parenchymal mechanotransduction in health and disease toward developing mechanotherapeutics for treatment strategies.

In vitro investigations of red blood cell phase separation in a complex microchannel network

Microvascular networks feature a complex topology with multiple bifurcating vessels. Nonuniform partitioning (phase separation) of red blood cells (RBCs) occurs at diverging bifurcations, leading to a heterogeneous RBC distribution that ultimately affects the oxygen delivery to living tissues. Our understanding of the mechanisms governing RBC heterogeneity is still limited, especially in large networks where the RBC dynamics can be nonintuitive. In this study, our quantitative data for phase separation were obtained in a complex in vitro network with symmetric bifurcations and 176 microchannels. Our experiments showed that the hematocrit is heterogeneously distributed and confirmed the classical result that the branch with a higher blood fraction received an even higher RBC fraction (classical partitioning). An inversion of this classical phase separation (reverse partitioning) was observed in the case of a skewed hematocrit profile in the parent vessels of bifurcations. In agreement with a recent computational study [P. Balogh and P. Bagchi, Phys. Fluids 30,051902 (2018)], a correlation between the RBC reverse partitioning and the skewness of the hematocrit profile due to sequential converging and diverging bifurcations was reported. A flow threshold below which no RBCs enter a branch was identified. These results highlight the importance of considering the RBC flow history and the local RBC distribution to correctly describe the RBC phase separation in complex networks.

Antimargination of Microparticles and Platelets in the Vicinity of Branching Vessels

We investigate the margination of microparticles/platelets in blood flow through complex geometries typical for in vivo vessel networks: a vessel confluence and a bifurcation. Using three-dimensional lattice Boltzmann simulations, we confirm that behind the confluence of two vessels, a cell-free layer devoid of red blood cells develops in the channel center. Despite its small size of roughly 1 μm, this central cell-free layer persists for up to 100 μm after the confluence. Most importantly, we show from simulations that this layer also contains a significant amount of microparticles/platelets and validate this result by in vivo microscopy in mouse venules. At bifurcations, however, a similar effect does not appear, and margination is largely unaffected by the geometry. This antimargination toward the vessel center after a confluence may explain earlier in vivo observations, which found that platelet concentrations near the vessel wall are seen to be much higher on the arteriolar side (containing bifurcations) than on the venular side (containing confluences) of the vascular system.

Red blood cells stabilize flow in brain microvascular networks

Capillaries are the prime location for oxygen and nutrient exchange in all tissues. Despite their fundamental role, our knowledge of perfusion and flow regulation in cortical capillary beds is still limited. Here, we use in vivo measurements and blood flow simulations in anatomically accurate microvascular network to investigate the impact of red blood cells (RBCs) on microvascular flow. Based on these in vivo and in silico experiments, we show that the impact of RBCs leads to a bias toward equating the values of the outflow velocities at divergent capillary bifurcations, for which we coin the term “well-balanced bifurcations”. Our simulation results further reveal that hematocrit heterogeneity is directly caused by the RBC dynamics, i.e. by their unequal partitioning at bifurcations and their effect on vessel resistance. These results provide the first in vivo evidence of the impact of RBC dynamics on the flow field in the cortical microvasculature. By structural and functional analyses of our blood flow simulations we show that capillary diameter changes locally alter flow and RBC distribution. A dilation of 10% along a vessel length of 100 μm increases the flow on average by 21% in the dilated vessel downstream a well-balanced bifurcation. The number of RBCs rises on average by 27%. Importantly, RBC up-regulation proves to be more effective the more balanced the outflow velocities at the upstream bifurcation are. Taken together, we conclude that diameter changes at capillary level bear potential to locally change the flow field and the RBC distribution. Moreover, our results suggest that the balancing of outflow velocities contributes to the robustness of perfusion. Based on our in silico results, we anticipate that the bi-phasic nature of blood and small-scale regulations are essential for a well-adjusted oxygen and energy substrate supply.

Glucose and oxygen are key energy sources of the brain. As energy storage capabilities are limited in the brain, a continuous supply of oxygen and glucose via the bloodstream is crucial for the brain’s functioning. The bulk of discharge occurs at the level of capillaries, which are the smallest and most frequent vessels of the cortical vasculature. Nonetheless, our understanding of perfusion and topology of the capillary bed is still limited. Here, we use in vivo two-photon based blood flow measurements and numerical simulations in large realistic microvascular networks to study the flow in the cortical microvasculature. Our results reveal that the impact of red blood cells enhances the robustness of microvascular perfusion and increases the heterogeneity in red blood cell distribution. It is well established that higher neuronal activity leads to an increase in blood flow. However, the precise regulation mechanisms and their spatial extent remain largely unknown. We show that small-scale regulations locally alter flow and red blood cell distribution. We suggest that these mechanisms are key for an efficient and flexible circulatory system. Moreover, our results reveal a novel role of the bi-phasic nature of blood.

Red blood cell distribution in a microvascular network with successive bifurcations

Nonproportional RBC distribution is an important characteristic in microvascular networks, which can result in heterogeneity of oxygen supply that may cause ischemic death in severe cases. In this paper, we perform three-dimensional numerical simulations of a large number of RBCs in a microvascular network, by using a hybrid method of smoothed dissipative particle dynamic and immersed boundary method. The distribution of multiple RBCs in a T-bifurcation is first simulated as a validation study, and a reasonable agreement is observed both qualitatively and quantitatively on the RBC flux between our results and the previously published numerical and empirical results. Next, the distribution of a large number of RBCs in a microvascular network is investigated, including the effects of cell deformability, aggregation and tube hematocrit. The simulation results indicate that decreased deformability and increased aggregation strength have a similar effect on the RBC distribution: the large RBC flux becomes larger, but the small becomes smaller. A high hematocrit also causes a similar phenomenon that the RBCs are more apt to flow into a high RBC-flux branch, because they are arranged compactly into a rouleaux and difficultly broken up at a high hematocrit. These results imply that lower cell deformability, stronger aggregation or higher tube hematocrit would be conducive to the phase separation of hematocrit and plasma skimming processes in microcirculation.

Three-dimensional distribution of wall shear stress and its gradient in red cell-resolved computational modeling of blood flow in in vivo-like microvascular networks

Using a high-fidelity, 3D computational model of blood flow in microvascular networks, we provide the full 3D distribution of wall shear stress (WSS), and its gradient (WSSG), and quantify the influence of red blood cells (RBCs) on WSS and WSSG. The deformation and flow dynamics of the individual RBCs are accurately resolved in the model, while physiologically realistic microvascular networks comprised of multiple bifurcations, convergences, and tortuous vessels are considered. A strong heterogeneity in WSS and WSSG is predicted across the networks, with the highest WSS occurring in precapillary bifurcations and capillary vessels. 3D variations of WSS and WSSG are shown to occur due to both network morphology and the influence of RBCs. The RBCs increase the WSS by as much as three times compared to that when no RBCs are present, and the highest increase is observed in venules. WSSG also increases significantly, and high WSSGs occur over wider regions in the presence of RBCs. In most vessels, the circumferential component of WSSG is observed to be greater than the axial component in the presence of RBCs, while the opposite trend is observed when RBCs are not considered. These results underscore the important role of RBCs on WSS and WSSG that cannot be predicted by widely used 1D models of network blood flow. Furthermore, the subendothelium-scale variations of WSS and WSSG predicted by the present model have implications in terms of endothelial cell functions in the microvasculature.

Physical and geometric determinants of transport in fetoplacental microvascular networks

Across mammalian species, solute exchange takes place in complex microvascular networks. In the human placenta, the primary exchange units are terminal villi that contain disordered networks of fetal capillaries and are surrounded externally by maternal blood. We show how the irregular internal structure of a terminal villus determines its exchange capacity for diverse solutes. Distilling geometric features into three parameters, obtained from image analysis and computational fluid dynamics, we capture archetypal features of the structure-function relationship of terminal villi using a simple algebraic approximation, revealing transitions between flow- and diffusion-limited transport at vessel and network levels. Our theory accommodates countercurrent effects, incorporates nonlinear blood rheology, and offers an efficient method for testing network robustness. Our results show how physical estimates of solute transport, based on carefully defined geometrical statistics, provide a viable method for linking placental structure and function and offer a framework for assessing transport in other microvascular systems.

In vitro analysis of blood flow in a microvascular network with realistic geometry

In vitro blood flow was measured in a polydimethysiloxane micro channel to reflect the complex geometry of a microvascular network. Flow rates were determined from the velocities of tracer particles moving along the center line of the flow channel, and the flow rates of two working fluids were then compared: water and blood. In some bifurcating channels, the measured flow rate showed that the effects of bifurcation in the apparent viscosity depend on the hematocrit, such that the flow rate in the daughter channel with the higher (lower) flow rate was lower (higher) for blood than for water. The measured flow rates in other bifurcating channels reflected effects from the surrounding flow channels acting as bypasses, which tended to balance out the effects of bifurcation.

The related factors for the recovery and maintenance time of sinus rhythm in hospitalized patients with cardiopulmonary resuscitation: A single-center retrospective case-control study

No matter in or outside hospital, the success rate of cardiopulmonary resuscitation (CPR) is very low. The sign of successful CPR is the recovery of spontaneous circulation. The premise of the recovery of spontaneous circulation is the recovery and maintenance of sinus rhythm, but there is still no related research.We aim to study the factors for the recovery and maintenance time of sinus rhythm in patients with CPR.A single-center retrospective case-control study.Ethical review was obtained (ethical approval number: 20180031).The second affiliated hospital of Xi'an Jiaotong University, Xi'an Shaanxi, China.From January 2011 to December 2016, totally 344 cases met the inclusion and exclusion criteria, sinus rhythm recovered group (SR group) (n = 130 cases), sinus rhythm unrecovered group (SUR group) (n = 214 cases).The multivariate logistic regression analysis showed that red blood cell counts (OR = 1.30, 95% CI:1.04-1.63, P = .02), rescue time (OR = 0.95, 95% CI:0.94-0.97, P <.001), the usage of norepinephrine (OR = 2.14, 95% CI:1.06-4.35, P = .04) were important factor for the recovery of sinus rhythm in patients with CPR. Multivariate linear regression analysis showed that the dosage of epinephrine, the usage of naloxone and diagnosis were important factors for maintenance time of sinus rhythm after resuscitation, P <.05. The rescue time had high accuracy to predict the recovery of sinus rhythm, the area under the receiver operator characteristic (ROC) curve (AUC) was 0.84 (0.80, 0.88), sensitivity and specificity are respectively 71.54% and 93.46%.Red blood cell counts, the rescue time and the usage of norepinephrine might be important factors for the recovery of sinus rhythm, and the dosage of epinephrine, the usage of naloxone and the diagnosis might be important factors for the maintenance time of sinus rhythm in patients with CPR.

Blood flow and transport in the human placenta

The placenta is a multi-functional organ that exchanges blood gases and nutrients between a mother and her developing fetus. In humans, fetal blood flows through intricate networks of vessels confined within villous trees, the branches of which are bathed in pools of maternal blood. Fluid mechanics and transport processes play a central role in understanding how these elaborate structures contribute to the function of the placenta, and how their disorganization may lead to disease. Recent advances in imaging and computation have spurred significant advances in simulations of fetal and maternal flows within the placenta, across a range of lengthscales. Models describe jets of maternal blood emerging from spiral arteries into a disordered and deformable porous medium, and solute uptake by fetal blood flowing through elaborate three-dimensional capillary networks. We survey recent developments and emerging challenges in modeling flow and transport in this complex organ.

ATP Release by Red Blood Cells under Flow: Model and Simulations

ATP is a major player as a signaling molecule in blood microcirculation. It is released by red blood cells (RBCs) when they are subjected to shear stresses large enough to induce a sufficient shape deformation. This prominent feature of chemical response to shear stress and RBC deformation constitutes an important link between vessel geometry, flow conditions, and the mechanical properties of RBCs, which are all contributing factors affecting the chemical signals in the process of vasomotor modulation of the precapillary vessel networks. Several in vitro experiments have reported on ATP release by RBCs due to mechanical stress. These studies have considered both intact RBCs as well as cells within which suspected pathways of ATP release have been inhibited. This has provided profound insights to help elucidate the basic governing key elements, yet how the ATP release process takes place in the (intermediate) microcirculation zone is not well understood. We propose here an analytical model of ATP release. The ATP concentration is coupled in a consistent way to RBC dynamics. The release of ATP, or the lack thereof, is assumed to depend on both the local shear stress and the shape change of the membrane. The full chemo-mechanical coupling problem is written in a lattice-Boltzmann formulation and solved numerically in different geometries (straight channels and bifurcations mimicking vessel networks) and under two kinds of imposed flows (shear and Poiseuille flows). Our model remarkably reproduces existing experimental results. It also pinpoints the major contribution of ATP release when cells traverse network bifurcations. This study may aid in further identifying the interplay between mechanical properties and chemical signaling processes involved in blood microcirculation.