Hemodynamics in the microcirculation and in microfluidics

Advances in Microfluidics for Single Red Blood Cell Analysis

The utilizations of microfluidic chips for single RBC (red blood cell) studies have attracted great interests in recent years to filter, trap, analyze, and release single erythrocytes for various applications. Researchers in this field have highlighted the vast potential in developing micro devices for industrial and academia usages, including lab-on-a-chip and organ-on-a-chip systems. This article critically reviews the current state-of-the-art and recent advances of microfluidics for single RBC analyses, including integrated sensors and microfluidic platforms for microscopic/tomographic/spectroscopic single RBC analyses, trapping arrays (including bifurcating channels), dielectrophoretic and agglutination/aggregation studies, as well as clinical implications covering cancer, sepsis, prenatal, and Sickle Cell diseases. Microfluidics based RBC microarrays, sorting/counting and trapping techniques (including acoustic, dielectrophoretic, hydrodynamic, magnetic, and optical techniques) are also reviewed. Lastly, organs on chips, multi-organ chips, and drug discovery involving single RBC are described. The limitations and drawbacks of each technology are addressed and future prospects are discussed.

Efficacy of molecular and nano-therapies on brain tumor models in microfluidic devices

The three-dimensional (3D) organization of cells affects their mobility, proliferation, and overall response to treatment. Spheroids, organoids, and microfluidic chips are used in cancer research to reproduce in vitro the complex and dynamic malignant microenvironment. Herein, single- and double-channel microfluidic devices are used to mimic the spatial organization of brain tumors and investigate the therapeutic efficacy of molecular and nano anti-cancer agents. Human glioblastoma multiforme (U87-MG) cells were cultured into a Matrigel matrix embedded within the microfluidic devices and exposed to different doses of free docetaxel (DTXL), docetaxel-loaded spherical polymeric nanoparticles (DTXL-SPN), and the aromatic N-glucoside N-(fluorenylmethoxycarbonyl)-glucosamine-6-phosphate (Fmoc-Glc6P). We observed that in the single-channel microfluidic device, brain tumor cells are more susceptible to DTXL treatment as compared to conventional cell monolayers (50-fold lower IC₅₀ values). In the double-channel device, the cytotoxicity of free DTXL and DTXL-SPN is comparable, but significantly lowered as compared to the single-channel configuration. Finally, the administration of 500 μM Fmoc-Glc6P in the double-channel microfluidic device shows a 50 % U87-MG cell survival after only 24 h, and no deleterious effect on human astrocytes over 72 h. Concluding, the proposed microfluidic chips can be used to reproduce the 3D complex spatial arrangement of solid tumors and to assess the anti-cancer efficacy of therapeutic compounds administrated in situ or systemically.

A general numerical model of leukocyte adhesion in microchannels

Leukocyte adhesion on the vascular endothelium plays an important role in human immune system and reflects the physiological condition of a human body. In this paper, a generally implementable dynamic adhesion model based on the length limit of microvilli was developed to explore the behavior of a suspended leukocyte's adhesion process under microchannel shear flow. Simulations showed that the whole adhesion process can be divided into cell sedimentation, preliminary adhesion and stable dynamic adhesion stages. The cell tumbling kinetics, cell deformation, cell adhesion area and adhesion force were studied under the conditions of various bond strength, cell membrane surface tension, inlet flow velocity and cytoplasmic viscosity. Results showed that the bond strength affects the cell tumbling behaviors differently by changing the adhesion force. The cell with lower membrane surface tension induces a larger adhesion area, and eventually results in a greater adhesion and a lower cell tumbling velocity. The flow velocity changes cell velocity through the flow viscous force during the whole adhesion process. The cytoplasmic viscosity affects adhesion mainly in the preliminary adhesion stage by changing the cell deformation rate but has slight effect on the stabilized dynamic adhesion on cells. This study provides a simple theoretical basis to further clarify the mechanism of cell behaviors under stress and adhesion and becomes one of the prerequisites for study of tissue inflammation, wound healing, and disease treatments.

Image-Based Experimental Measurement Techniques to Characterize Velocity Fields in Blood Microflows

Predicting blood microflow in both simple and complex geometries is challenging because of the composition and behavior of the blood at microscale. However, characterization of the velocity in microchannels is the key for gaining insights into cellular interactions at the microscale, mechanisms of diseases, and efficacy of therapeutic solutions. Image-based measurement techniques are a subset of methods for measuring the local flow velocity that typically utilize tracer particles for flow visualization. In the most basic form, a high-speed camera and microscope setup are the only requirements for data acquisition; however, the development of image processing algorithms and equipment has made current image-based techniques more sophisticated. This mini review aims to provide a succinct and accessible overview of image-based experimental measurement techniques to characterize the velocity field of blood microflow. The following techniques are introduced: cell tracking velocimetry, kymographs, micro-particle velocimetry, and dual-slit photometry as entry techniques for measuring various velocity fields either in vivo or in vitro.

Microfluidics Approach to the Mechanical Properties of Red Blood Cell Membrane and Their Effect on Blood Rheology

In this article, we describe the general features of red blood cell membranes and their effect on blood flow and blood rheology. We first present a basic description of membranes and move forward to red blood cell membranes’ characteristics and modeling. We later review the specific properties of red blood cells, presenting recent numerical and experimental microfluidics studies that elucidate the effect of the elastic properties of the red blood cell membrane on blood flow and hemorheology. Finally, we describe specific hemorheological pathologies directly related to the mechanical properties of red blood cells and their effect on microcirculation, reviewing microfluidic applications for the diagnosis and treatment of these diseases.

Computational simulations of the 4D micro-circulatory network in zebrafish tail amputation and regeneration

Wall shear stress (WSS) contributes to the mechanotransduction underlying microvascular development and regeneration. Using computational fluid dynamics, we elucidated the interplay between WSS and vascular remodelling in a zebrafish model of tail amputation and regeneration. The transgenic Tg (fli1:eGFP; Gata1:ds-red) zebrafish line was used to track the three-dimensional fluorescently labelled vascular endothelium for post-image segmentation and reconstruction of the fluid domain. Particle image velocimetry was used to validate the blood flow. Following amputation to the dorsal aorta and posterior cardinal vein (PCV), vasoconstriction developed in the dorsal longitudinal anastomotic vessel (DLAV) along with increased WSS in the proximal segmental vessels (SVs) from amputation. Angiogenesis ensued at the tips of the amputated DLAV and PCV where WSS was minimal. At 2 days post amputation (dpa), vasodilation occurred in a pair of SVs proximal to amputation, followed by increased blood flow and WSS; however, in the SVs distal to amputation, WSS normalized to the baseline. At 3 dpa, the blood flow increased in the arterial SV proximal to amputation and through anastomosis with DLAV formed a loop with PCV. Thus, our in silico modelling revealed the interplay between WSS and microvascular adaptation to changes in WSS and blood flow to restore microcirculation following tail amputation.

Computational simulations of the 4D micro-circulatory network in zebrafish tail amputation and regeneration

Wall shear stress (WSS) contributes to the mechanotransduction underlying microvascular development and regeneration. Using computational fluid dynamics, we elucidated the interplay between WSS and vascular remodelling in a zebrafish model of tail amputation and regeneration. The transgenic Tg (fli1:eGFP; Gata1:ds-red) zebrafish line was used to track the three-dimensional fluorescently labelled vascular endothelium for post-image segmentation and reconstruction of the fluid domain. Particle image velocimetry was used to validate the blood flow. Following amputation to the dorsal aorta and posterior cardinal vein (PCV), vasoconstriction developed in the dorsal longitudinal anastomotic vessel (DLAV) along with increased WSS in the proximal segmental vessels (SVs) from amputation. Angiogenesis ensued at the tips of the amputated DLAV and PCV where WSS was minimal. At 2 days post amputation (dpa), vasodilation occurred in a pair of SVs proximal to amputation, followed by increased blood flow and WSS; however, in the SVs distal to amputation, WSS normalized to the baseline. At 3 dpa, the blood flow increased in the arterial SV proximal to amputation and through anastomosis with DLAV formed a loop with PCV. Thus, our in silico modelling revealed the interplay between WSS and microvascular adaptation to changes in WSS and blood flow to restore microcirculation following tail amputation.

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.

Evolution of Water-in-Oil Droplets in T-Junction Microchannel by Micro-PIV

Water-in-oil droplets have huge importance in chemical and biotechnology applications, despite their difficulty being produced in microfluidics. Moreover, existing studies focus more on the different shape of microchannels instead of their size, which is one of the critical factors that can influence flow characteristics of the droplets. Therefore, the present work aims to study the behaviours of water-in-oil droplets at the interfacial surface in an offset T-junction microchannel, having different radiuses, using micro-PIV software. Food-grade palm olein and distilled water seeded with polystyrene microspheres particles were used as working fluids, and their captured images showing their generated droplets’ behaviours focused on the junction of the respective microfluidic channel, i.e., radiuses of 400 µm, 500 µm, 750 µm and 1000 µm, were analysed via PIVlab. The increasing in the radius of the offset T-junction microchannel leads to the increase in the cross-sectional area and the decrease in the distilled water phase’s velocity. The experimental velocity of the water droplet is in agreement with theoretical values, having a minimal difference as low as 0.004 mm/s for the case of the microchannel with a radius of 750 µm. In summary, a small increase in the channel’s size yields a significant increase in the overall flow of a liquid.

Artificial intelligence velocimetry and microaneurysm-on-a-chip for three-dimensional analysis of blood flow in physiology and disease

Understanding the mechanics of blood flow is necessary for developing insights into mechanisms of physiology and vascular diseases in microcirculation. Given the limitations of technologies available for assessing in vivo flow fields, in vitro methods based on traditional microfluidic platforms have been developed to mimic physiological conditions. However, existing methods lack the capability to provide accurate assessment of these flow fields, particularly in vessels with complex geometries. Conventional approaches to quantify flow fields rely either on analyzing only visual images or on enforcing underlying physics without considering visualization data, which could compromise accuracy of predictions. Here, we present artificial-intelligence velocimetry (AIV) to quantify velocity and stress fields of blood flow by integrating the imaging data with underlying physics using physics-informed neural networks. We demonstrate the capability of AIV by quantifying hemodynamics in microchannels designed to mimic saccular-shaped microaneurysms (microaneurysm-on-a-chip, or MAOAC), which signify common manifestations of diabetic retinopathy, a leading cause of vision loss from blood-vessel damage in the retina in diabetic patients. We show that AIV can, without any a priori knowledge of the inlet and outlet boundary conditions, infer the two-dimensional (2D) flow fields from a sequence of 2D images of blood flow in MAOAC, but also can infer three-dimensional (3D) flow fields using only 2D images, thanks to the encoded physics laws. AIV provides a unique paradigm that seamlessly integrates images, experimental data, and underlying physics using neural networks to automatically analyze experimental data and infer key hemodynamic indicators that assess vascular injury.

Vessel-on-a-chip models for studying microvascular physiology, transport, and function in vitro

To understand how the microvasculature grows and remodels, researchers require reproducible systems that emulate the function of living tissue. Innovative contributions toward fulfilling this important need have been made by engineered microvessels assembled in vitro with microfabrication techniques. Microfabricated vessels, commonly referred to as "vessels-on-a-chip," are from a class of cell culture technologies that uniquely integrate microscale flow phenomena, tissue-level biomolecular transport, cell-cell interactions, and proper three-dimensional (3-D) extracellular matrix environments under well-defined culture conditions. Here, we discuss the enabling attributes of microfabricated vessels that make these models more physiological compared with established cell culture techniques and the potential of these models for advancing microvascular research. This review highlights the key features of microvascular transport and physiology, critically discusses the strengths and limitations of different microfabrication strategies for studying the microvasculature, and provides a perspective on current challenges and future opportunities for vessel-on-a-chip models.

Deformation of Red Blood Cells, Air Bubbles, and Droplets in Microfluidic Devices: Flow Visualizations and Measurements

Techniques, such as micropipette aspiration and optical tweezers, are widely used to measure cell mechanical properties, but are generally labor-intensive and time-consuming, typically involving a difficult process of manipulation. In the past two decades, a large number of microfluidic devices have been developed due to the advantages they offer over other techniques, including transparency for direct optical access, lower cost, reduced space and labor, precise control, and easy manipulation of a small volume of blood samples. This review presents recent advances in the development of microfluidic devices to evaluate the mechanical response of individual red blood cells (RBCs) and microbubbles flowing in constriction microchannels. Visualizations and measurements of the deformation of RBCs flowing through hyperbolic, smooth, and sudden-contraction microchannels were evaluated and compared. In particular, we show the potential of using hyperbolic-shaped microchannels to precisely control and assess small changes in RBC deformability in both physiological and pathological situations. Moreover, deformations of air microbubbles and droplets flowing through a microfluidic constriction were also compared with RBCs deformability.

Tailored environments to study motile cells and pathogens

Motile cells and pathogens migrate in complex environments and yet are mostly studied on simple 2D substrates. In order to mimic the diverse environments of motile cells, a set of assays including substrates of defined elasticity, microfluidics, micropatterns, organotypic cultures, and 3D gels have been developed. We briefly introduce these and then focus on the use of micropatterned pillar arrays, which help to bridge the gap between 2D and 3D. These structures are made from polydimethylsiloxane, a moldable plastic, and their use has revealed new insights into mechanoperception in Caenorhabditis elegans, gliding motility of Plasmodium, swimming of trypanosomes, and nuclear stability in cancer cells. These studies contributed to our understanding of how the environment influences the respective cell and inform on how the cells adapt to their natural surroundings on a cellular and molecular level.

Collective spreading of red blood cells flowing in a microchannel

Due to recent advances in micro total analysis system technologies, microfluidics provides increased opportunities to manipulate, stimulate, and diagnose blood cells. Controlling the concentration of cells at a given position across the width of a channel is an important aspect in the design of microfluidic devices. Despite its biomedical importance, the collective spreading of red blood cells (RBCs) in a microchannel has not yet been fully clarified. In this study, we experimentally investigated the collective spreading of RBCs in a straight microchannel, and found that RBCs initially distributed in one side of the microchannel spread to the spanwise direction during downstream flow. Spreading increased considerably as the hematocrit increased, though the flow rate had a small effect. We proposed a scaling argument to show that this spreading phenomenon was diffusive and mainly induced by cell-cell interactions. The dispersion coefficient was approximately proportional to the flow rate and the hematocrit. These results are useful in understanding collective behaviors of RBCs in a microchannel and in microcirculation.

A physical approach to model occlusions in the retinal microvasculature

Blood occlusions in the retinal microvasculature contribute to the pathology of many disease states within the eye. These events can cause haemorrhaging and retinal detachment, leading to a loss of vision in the affected patient. Here, we present a physical approach to characterising the collective cell dynamics leading to plug formation, through the use of a bespoke microfluidic device, and through the derivation of a probabilistic model. Our microfluidic device is based on a filtration design that can tune the particle volume fraction of a flowing suspension within a conduit, with sizes similar to arterioles. This allows us to control and reproduce an occlusive event. The formation of the occlusion can be examined through the extracted motion of particles within the channel, which enables the assessment of individual and collective particle dynamics in the time leading to the clogging event. In particular, we observe that at the onset of the occlusion, particles form an arch bridging the channel walls. The data presented here inform the development of our mathematical model, which captures the essential factors promoting occlusions, and notably highlights the central role of adhesion in these processes. Both the physical and probabilistic models rely on significant approximations, and future investigation will seek to assess these approximations, including the deformability and complex flow profiles of the blood constituents. However, we anticipate that the general mechanisms of occlusion may be elucidated from these simple models. As microvascular flows in the eye can now be measured in vivo and non-invasively with single cell resolution, our model will also be compared to the pathophysiological characteristics of the human microcirculation.

Theory and algorithms to compute Helfrich bending forces: a review

Cell membranes are vital to shield a cell's interior from the environment. At the same time they determine to a large extent the cell's mechanical resistance to external forces. In recent years there has been considerable interest in the accurate computational modeling of such membranes, driven mainly by the amazing variety of shapes that red blood cells and model systems such as vesicles can assume in external flows. Given that the typical height of a membrane is only a few nanometers while the surface of the cell extends over many micrometers, physical modeling approaches mostly consider the interface as a two-dimensional elastic continuum. Here we review recent modeling efforts focusing on one of the computationally most intricate components, namely the membrane's bending resistance. We start with a short background on the most widely used bending model due to Helfrich. While the Helfrich bending energy by itself is an extremely simple model equation, the computation of the resulting forces is far from trivial. At the heart of these difficulties lies the fact that the forces involve second order derivatives of the local surface curvature which by itself is the second derivative of the membrane geometry. We systematically derive and compare the different routes to obtain bending forces from the Helfrich energy, namely the variational approach and the thin-shell theory. While both routes lead to mathematically identical expressions, so-called linear bending models are shown to reproduce only the leading order term while higher orders differ. The main part of the review contains a description of various computational strategies which we classify into three categories: the force, the strong and the weak formulation. We finally give some examples for the application of these strategies in actual simulations.

Microfluidic viscometers for shear rheology of complex fluids and biofluids

The rich diversity of man-made complex fluids and naturally occurring biofluids is opening up new opportunities for investigating their flow behavior and characterizing their rheological properties. Steady shear viscosity is undoubtedly the most widely characterized material property of these fluids. Although widely adopted, macroscale rheometers are limited by sample volumes, access to high shear rates, hydrodynamic instabilities, and interfacial artifacts. Currently, microfluidic devices are capable of handling low sample volumes, providing precision control of flow and channel geometry, enabling a high degree of multiplexing and automation, and integrating flow visualization and optical techniques. These intrinsic advantages of microfluidics have made it especially suitable for the steady shear rheology of complex fluids. In this paper, we review the use of microfluidics for conducting shear viscometry of complex fluids and biofluids with a focus on viscosity curves as a function of shear rate. We discuss the physical principles underlying different microfluidic viscometers, their unique features and limits of operation. This compilation of technological options will potentially serve in promoting the benefits of microfluidic viscometry along with evincing further interest and research in this area. We intend that this review will aid researchers handling and studying complex fluids in selecting and adopting microfluidic viscometers based on their needs. We conclude with challenges and future directions in microfluidic rheometry of complex fluids and biofluids.

Computational fluid dynamics in the microcirculation and microfluidics: what role can the lattice Boltzmann method play?

Patient-specific simulations, efficient parametric analyses, and the study of complex processes that are otherwise experimentally intractable are facilitated through the use of Computational Fluid Dynamics (CFD) to study biological flows. This review discusses various CFD methodologies that have been applied across different biological scales, from cell to organ level. Through this discussion the lattice Boltzmann method (LBM) is highlighted as an emerging technique capable of efficiently simulating fluid problems across the midrange of scales; providing a practical analytical tool compared to methods more attuned to the extremities of scale. Furthermore, the merits of the LBM are highlighted through examples of previous applications and suggestions for future research are made. The review focusses on applications in the midrange bracket, such as cell-cell interactions, the microcirculation, and microfluidic devices; wherein the inherent mesoscale nature of the LBM renders it well suited to the incorporation of fluid-structure interaction effects, molecular/particle interactions and interfacial dynamics. The review demonstrates that the LBM has the potential to become a valuable tool across a range of emerging areas in bio-CFD, such as understanding and predicting disease, designing lab-on-a-chip devices, and elucidating complex biological processes.

Modeling microcirculatory blood flow: current state and future perspectives

Microvascular blood flow determines a number of important physiological processes of an organism in health and disease. Therefore, a detailed understanding of microvascular blood flow would significantly advance biophysical and biomedical research and its applications. Current developments in modeling of microcirculatory blood flow already allow to go beyond available experimental measurements and have a large potential to elucidate blood flow behavior in normal and diseased microvascular networks. There exist detailed models of blood flow on a single cell level as well as simplified models of the flow through microcirculatory networks, which are reviewed and discussed here. The combination of these models provides promising prospects for better understanding of blood flow behavior and transport properties locally as well as globally within large microvascular networks.

Flow structures and red blood cell dynamics in arteriole of dilated or constricted cross section

Vessel with 'circular' or 'star-shaped' cross sections are studied, representing respectively dilated or constricted cases where endothelial cells smoothly line or bulge into the lumen. Computational haemodynamics simulations are carried out on idealised periodic arteriole-sized vessels, with red blood cell 'tube' hematocrit value=24%. A further simulation of a single red blood cell serves for comparison purposes. The bulk motion of the red blood cells reproduces well-known effects, including the presence of a cell-free layer and the apparent shear-thinning non-Newtonian rheology. The velocity flow field is analysed in a Lagrangian reference frame, relative to any given red blood cell, hence removing the bulk coaxial motion and highlighting instead the complex secondary flow patterns. An aggregate formation becomes apparent, continuously rearranging and dynamic, brought about by the inter-cellular fluid mechanics interactions and the deformability properties of the cells. The secondary flow field induces a vacillating radial migration of the red blood cells. At different radial locations, the red blood cells express different residence times, orientation and shape. The shear stresses exerted by the flow on the vessel wall are influenced by the motion of red blood cells, despite the presence of the cell-free layer. Spatial (and temporal) variations of wall shear stress patters are observed, especially for the 'circular' vessel. The 'star-shaped' vessel bears considerable stress at the protruding endothelial cell crests, where the stress vectors are coaxially aligned. The bulging endothelial cells hence regularise the transmission of stresses on the vessel wall.

Understanding particle margination in blood flow - A step toward optimized drug delivery systems

Targeted delivery of drugs and imaging agents is very promising to develop new strategies for the treatment of various diseases such as cancer. For an efficient targeted adhesion, the particles have to migrate toward the walls in blood flow - a process referred to as margination. Due to a huge diversity of available carriers, a good understanding of their margination properties in blood flow depending on various flow conditions and particle properties is required. We employ a particle-based mesoscopic hydrodynamic simulation approach to investigate the margination of different carriers for a wide range of hematocrits (volume fraction of red blood cells) and flow rates. Our results show that margination strongly depends on the thickness of the available free space close to the wall, the so-called red blood cell-free layer (RBC-FL), in comparison to the carrier size. The carriers with a few micrometers in size are comparable with the RBC-FL thickness and marginate better than their sub-micrometer counterparts. Deformable carriers, in general, show worse margination properties than rigid particles. Particle margination is also found to be most pronounced in small channels with a characteristic size comparable to blood capillaries. Finally, different margination mechanisms are discussed.

Microscale flow propulsion through bioinspired and magnetically actuated artificial cilia

Recent advances in microscale flow propulsion through bioinspired artificial cilia provide a promising alternative for lab-on-a-chip applications. However, the ability of actuating artificial cilia to achieve a time-dependent local flow control with high accuracy together with the elegance of full integration into the biocompatible microfluidic platforms remains remote. Driven by this motive, the current work has constructed a series of artificial cilia inside a microchannel to facilitate the time-dependent flow propulsion through artificial cilia actuation with high-speed (>40 Hz) circular beating behavior. The generated flow was quantified using micro-particle image velocimetry and particle tracking with instantaneous net flow velocity of up to 10(1 ) μm/s. Induced flow patterns caused by the tilted conical motion of artificial cilia constitutes efficient fluid propulsion at microscale. This flow phenomenon was further measured and illustrated by examining the induced flow behavior across the depth of the microchannel to provide a global view of the underlying flow propulsion mechanism. The presented analytic paradigms and substantial flow evidence present novel insights into the area of flow manipulation at microscale.