Numerical investigation of heterogeneous soft particle pairs in inertial microfluidics.

The formation of pairs of particles or cells of different types in microfluidic channels can be desired or detrimental in healthcare applications. It is still unclear what role softness heterogeneity plays in the formation of these particle pairs. We use an in-house lattice-Boltzmann-immersed-boundary-finite-element solver to simulate a pair of particles with different softness flowing through a straight channel with a rectangular cross-section under initial conditions representative of a dilute suspension. We find that softness heterogeneity significantly affects the pair dynamics, determining whether a pair will form or not, and determining the lateral and inter-particle equilibrium behaviour in the pair. We also observe close matches between the transient deformation of particles in a linear pair and single particles in isolation. These results further our understanding of pair behaviour, providing a foundation for understanding particle train formation, and open up the potential to develop reduced-order models for particle pair formation based upon the behaviour of single particles.

Survival of P. falciparum infected red blood cell aggregates in elongational shear flow.

Rosetting, the formation of red blood cell aggregates, is a life-threatening condition in malaria tropica and not yet fully understood. We study rosette stability using a set of microfluidic stenotic channels, with varied narrowing angle and erythrocytes of blood groups O and A. We find reduced ability of a rosette to pass a stenosis without disruption, the longer the tapered part of the constriction and the narrower the stenosis is. In general, this ability increases with rosette size and is 5-15% higher in blood group A. The experimental results are substantiated by equivalent experiments using lectin-induced red blood cell aggregates and a simulation of the underlying protein binding kinetics.

Numerical investigation of the dynamics of a rigid spherical particle in a vortical cross-slot flow at moderate inertia.

The study of flow and particle dynamics in microfluidic cross-slot channels is of high relevance for lab-on-a-chip applications. In this work, we investigate the dynamics of a rigid spherical particle in a cross-slot junction for a channel height-to-width ratio of 0.6 and at a Reynolds number of 120 for which a steady vortex exists in the junction area. Using an in-house immersed-boundary-lattice-Boltzmann code, we analyse the effect of the entry position of the particle in the junction and the particle size on the dynamics and trajectory shape of the particle. We find that the dynamics of the particle depend strongly on its lateral entry position in the junction and weakly on its vertical entry position; particles that enter close to the centre show trajectory oscillations. Larger particles have longer residence times in the junction and tend to oscillate less due to their confinement. Our work contributes to the understanding of particle dynamics in intersecting flows and enables the design of optimised geometries for cytometry and particle manipulation.

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).

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.

Numerical investigation of the formation and stability of homogeneous pairs of soft particles in inertial microfluidics.

We investigate the formation and stability of a pair of identical soft capsules in channel flow under mild inertia. We employ a combination of the lattice Boltzmann, finite element and immersed boundary methods to simulate the elastic particles in flow. Validation tests show excellent agreement with numerical results obtained by other research groups. Our results reveal new trajectory types that have not been observed for pairs of rigid particles. While particle softness increases the likelihood of a stable pair forming, the pair stability is determined by the lateral position of the particles. A key finding is that stabilisation of the axial distance occurs after lateral migration of the particles. During the later phase of pair formation, particles undergo damped oscillations that are independent of initial conditions. These damped oscillations are driven by a strong hydrodynamic coupling of the particle dynamics, particle inertia and viscous dissipation. While the frequency and damping coefficient of the oscillations depend on particle softness, the pair formation time is largely determined by the initial particle positions: the time to form a stable pair grows exponentially with the initial axial distance. Our results demonstrate that particle softness has a strong impact on the behaviour of particle pairs. The findings could have significant ramifications for microfluidic applications where a constant and reliable axial distance between particles is required, such as flow cytometry.

Compressed vessels bias red blood cell partitioning at bifurcations in a hematocrit-dependent manner: Implications in tumor blood flow.

The tumor microenvironment is abnormal and associated with tumor tissue hypoxia, immunosuppression, and poor response to treatment. One important abnormality present in tumors is vessel compression. Vessel decompression has been shown to increase survival rates in animal models via enhanced and more homogeneous oxygenation. However, our knowledge of the biophysical mechanisms linking tumor decompression to improved tumor oxygenation is limited. In this study, we propose a computational model to investigate the impact of vessel compression on red blood cell (RBC) dynamics in tumor vascular networks. Our results demonstrate that vessel compression can alter RBC partitioning at bifurcations in a hematocrit-dependent and flow rate-independent manner. We identify RBC focusing due to cross-streamline migration as the mechanism responsible and characterize the spatiotemporal recovery dynamics controlling downstream partitioning. Based on this knowledge, we formulate a reduced-order model that will help future research to elucidate how these effects propagate at a whole vascular network level. These findings contribute to the mechanistic understanding of hemodilution in tumor vascular networks and oxygen homogenization following pharmacological solid tumor decompression.

Association between erythrocyte dynamics and vessel remodelling in developmental vascular networks.

Sprouting angiogenesis is an essential vascularization mechanism consisting of sprouting and remodelling. The remodelling phase is driven by rearrangements of endothelial cells (ECs) within the post-sprouting vascular plexus. Prior work has uncovered how ECs polarize and migrate in response to flow-induced wall shear stress (WSS). However, the question of how the presence of erythrocytes (widely known as red blood cells (RBCs)) and their impact on haemodynamics affect vascular remodelling remains unanswered. Here, we devise a computational framework to model cellular blood flow in developmental mouse retina. We demonstrate a previously unreported highly heterogeneous distribution of RBCs in primitive vasculature. Furthermore, we report a strong association between vessel regression and RBC hypoperfusion, and identify plasma skimming as the driving mechanism. Live imaging in a developmental zebrafish model confirms this association. Taken together, our results indicate that RBC dynamics are fundamental to establishing the regional WSS differences driving vascular remodelling via their ability to modulate effective viscosity.

Label-Free Biophysical Markers from Whole Blood Microfluidic Immune Profiling Reveal Severe Immune Response Signatures.

Disease manifestation and severity from acute infections are often due to hyper-aggressive host immune responses which change within minutes. Current methods for early diagnosis of infections focus on detecting low abundance pathogens, which are time-consuming, of low sensitivity, and do not reflect the severity of the pathophysiology appropriately. The approach here focuses on profiling the rapidly changing host inflammatory response, which in its over-exuberant state, leads to sepsis and death. A 15-min label-free immune profiling assay from 20 µL of unprocessed blood using unconventional L and Inverse-L shaped pillars of deterministic lateral displacement microfluidic technology is developed. The hydrodynamic interactions of deformable immune cells enable simultaneous sorting and immune response profiling in whole blood. Preliminary clinical study of 85 donors in emergency department with a spectrum of immune response states from healthy to severe inflammatory response shows correlation with biophysical markers of immune cell size, deformability, distribution, and cell counts. The speed of patient stratification demonstrated here has promising impact in deployable point-of-care systems for acute infections triage, risk management, and resource allocation at emergency departments, where clinical manifestation of infection severity may not be clinically evident as compared to inpatients in the wards or intensive care units.

Emergent cell-free layer asymmetry and biased haematocrit partition in a biomimetic vascular network of successive bifurcations.

Blood is a vital soft matter, and its normal circulation in the human body relies on the distribution of red blood cells (RBCs) at successive bifurcations. Understanding how RBCs are partitioned at bifurcations is key for the optimisation of microfluidic devices as well as for devising novel strategies for diagnosis and treatment of blood-related diseases. We report the dynamics of RBC suspensions flowing through a biomimetic vascular network incorporating three generations of microchannels and two classical types of bifurcations at the arteriole level. Our microfluidic experiments with dilute and semidilute RBC suspensions demonstrate the emergence of excessive heterogeneity of RBC concentration in downstream generations upon altering the network's outflow rates. Through parallel simulations using the immersed-boundary-lattice-Boltzmann method, we reveal that the heterogeneity is attributed to upstream perturbations in the cell-free layer (CFL) and lack of its recovery between consecutive bifurcations owing to suppressed hydrodynamic lift under reduced flow conditions. In the dilute/semidilute regime, this perturbation dominates over the effect of local fractional flow at the bifurcation and can lead to inherently unfavourable child branches that are deprived of RBCs even for equal flow split. Our work highlights the importance of CFL asymmetry cascading down a vascular network, which leads to biased phase separation that deviates from established empirical predictions.

Abnormal morphology biases hematocrit distribution in tumor vasculature and contributes to heterogeneity in tissue oxygenation.

Oxygen heterogeneity in solid tumors is recognized as a limiting factor for therapeutic efficacy. This heterogeneity arises from the abnormal vascular structure of the tumor, but the precise mechanisms linking abnormal structure and compromised oxygen transport are only partially understood. In this paper, we investigate the role that red blood cell (RBC) transport plays in establishing oxygen heterogeneity in tumor tissue. We focus on heterogeneity driven by network effects, which are challenging to observe experimentally due to the reduced fields of view typically considered. Motivated by our findings of abnormal vascular patterns linked to deviations from current RBC transport theory, we calculated average vessel lengths [Formula: see text] and diameters [Formula: see text] from tumor allografts of three cancer cell lines and observed a substantial reduction in the ratio [Formula: see text] compared to physiological conditions. Mathematical modeling reveals that small values of the ratio λ (i.e., [Formula: see text]) can bias hematocrit distribution in tumor vascular networks and drive heterogeneous oxygenation of tumor tissue. Finally, we show an increase in the value of λ in tumor vascular networks following treatment with the antiangiogenic cancer agent DC101. Based on our findings, we propose λ as an effective way of monitoring the efficacy of antiangiogenic agents and as a proxy measure of perfusion and oxygenation in tumor tissue undergoing antiangiogenic treatment.

Deterministic Lateral Displacement: Challenges and Perspectives.

The advent of microfluidics in the 1990s promised a revolution in multiple industries from healthcare to chemical processing. Deterministic lateral displacement (DLD) is a continuous-flow microfluidic particle separation method discovered in 2004 that has been applied successfully and widely to the separation of blood cells, yeast, spores, bacteria, viruses, DNA, droplets, and more. Deterministic lateral displacement is conceptually simple and can deliver consistent performance over a wide range of flow rates and particle concentrations. Despite wide use and in-depth study, DLD has not yet been fully elucidated or optimized, with different approaches to the same problem yielding varying results. We endeavor here to provide up-to-date expert opinion on the state-of-art and current fundamental, practical, and commercial challenges with DLD as well as describe experimental and modeling opportunities. Because these challenges and opportunities arise from constraints on hydrodynamics, fabrication, and operation at the micro- and nanoscale, we expect this Perspective to serve as a guide for the broader micro- and nanofluidic community to identify and to address open questions in the field.

Limitation of spiral microchannels for particle separation in heterogeneous mixtures: Impact of particles' size and deformability.

Spiral microchannels have shown promising results for separation applications. Hydrodynamic particle-particle interactions are a known factor strongly influencing focusing behaviors in inertial devices, with recent work highlighting how the performance of bidisperse mixtures is altered when compared with pure components in square channels. This phenomenon has not been previously investigated in detail for spiral channels. Here, we demonstrate that, in spiral channels, both the proportion and deformability of larger particles (13 µm diameter) impact upon the recovery (up to 47% decrease) of small rigid particles (4 µm). The effect, observed at low concentrations (volume fraction <0.0012), is attributed to the hydrodynamic capture of beads by larger cells. These changes in particles focusing behavior directly impede the efficiency of the separation-diverting beads from locations expected from measurements with pure populations to co-collection with larger cells-and could hamper deployment of technology for certain applications. Similar focusing behavior alterations were noted when working with purification of stem cell end products.

Spatiotemporal Dynamics of Dilute Red Blood Cell Suspensions in Low-Inertia Microchannel Flow.

Microfluidic technologies are commonly used for the manipulation of red blood cell (RBC) suspensions and analyses of flow-mediated biomechanics. To enhance the performance of microfluidic devices, understanding the dynamics of the suspensions processed within is crucial. We report novel, to our knowledge, aspects of the spatiotemporal dynamics of RBC suspensions flowing through a typical microchannel at low Reynolds number. Through experiments with dilute RBC suspensions, we find an off-center two-peak (OCTP) profile of cells contrary to the centralized distribution commonly reported for low-inertia flows. This is reminiscent of the well-known "tubular pinch effect," which arises from inertial effects. However, given the conditions of negligible inertia in our experiments, an alternative explanation is needed for this OCTP profile. Our massively parallel simulations of RBC flow in real-size microfluidic dimensions using the immersed-boundary-lattice-Boltzmann method confirm the experimental findings and elucidate the underlying mechanism for the counterintuitive RBC pattern. By analyzing the RBC migration and cell-free layer development within a high-aspect-ratio channel, we show that such a distribution is co-determined by the spatial decay of hydrodynamic lift and the global deficiency of cell dispersion in dilute suspensions. We find a cell-free layer development length greater than 46 and 28 hydraulic diameters in the experiment and simulation, respectively, exceeding typical lengths of microfluidic designs. Our work highlights the key role of transient cell distribution in dilute suspensions, which may negatively affect the reliability of experimental results if not taken into account.

Computational inertial microfluidics: a review.

Since the discovery of inertial focusing in 1961, numerous theories have been put forward to explain the migration of particles in inertial flows, but a complete understanding is still lacking. Recently, computational approaches have been utilized to obtain better insights into the underlying physics. In particular, fundamental aspects of particle focusing inside straight and curved microchannels have been explored in detail to determine the dependence of focusing behavior on particle size, channel shape, and flow Reynolds number. In this review, we differentiate between the models developed for inertial particle motion on the basis of whether they are semi-analytical, Navier-Stokes-based, or built on the lattice Boltzmann method. This review provides a blueprint for the consideration of numerical solutions for modeling of inertial particle motion, whether deformable or rigid, spherical or non-spherical, and whether suspended in Newtonian or non-Newtonian fluids. In each section, we provide the general equations used to solve particle motion, followed by a tutorial appendix and specified sections to engage the reader with details of the numerical studies. Finally, we address the challenges ahead in the modeling of inertial particle microfluidics for future investigators.

Effects of size and elasticity on the relation between flow velocity and wall shear stress in side-wall aneurysms: A lattice Boltzmann-based computer simulation study.

Blood flow in an artery is a fluid-structure interaction problem. It is widely accepted that aneurysm formation, enlargement and failure are associated with wall shear stress (WSS) which is exerted by flowing blood on the aneurysmal wall. To date, the combined effect of aneurysm size and wall elasticity on intra-aneurysm (IA) flow characteristics, particularly in the case of side-wall aneurysms, is poorly understood. Here we propose a model of three-dimensional viscous flow in a compliant artery containing an aneurysm by employing the immersed boundary-lattice Boltzmann-finite element method. This model allows to adequately account for the elastic deformation of both the blood vessel and aneurysm walls. Using this model, we perform a detailed investigation of the flow through aneurysm under different conditions with a focus on the parameters which may influence the wall shear stress. Most importantly, it is shown in this work that the use of flow velocity as a proxy for wall shear stress is well justified only in those sections of the vessel which are close to the ideal cylindrical geometry. Within the aneurysm domain, however, the correlation between wall shear stress and flow velocity is largely lost due to the complexity of the geometry and the resulting flow pattern. Moreover, the correlations weaken further with the phase shift between flow velocity and transmural pressure. These findings have important implications for medical applications since wall shear stress is believed to play a crucial role in aneurysm rupture.

Mesoscale simulation of soft particles with tunable contact angle in multicomponent fluids.

Soft particles at fluid interfaces play an important role in many aspects of our daily life, such as the food industry, paints and coatings, and medical applications. Analytical methods are not capable of describing the emergent effects of the complex dynamics of suspensions of many soft particles, whereas experiments typically either only capture bulk properties or require invasive methods. Computational methods are therefore a great tool to complement experimental work. However, an efficient and versatile numerical method is needed to model dense suspensions of many soft particles. In this article we propose a method to simulate soft particles in a multicomponent fluid, both at and near fluid-fluid interfaces, based on the lattice Boltzmann method, and characterize the error stemming from the fluid-structure coupling for the particle equilibrium shape when adsorbed onto a fluid-fluid interface. Furthermore, we characterize the influence of the preferential contact angle of the particle surface and the particle softness on the vertical displacement of the center of mass relative to the fluid interface. Finally, we demonstrate the capability of our model by simulating a soft capsule adsorbing onto a fluid-fluid interface with a shear flow parallel to the interface, and the covering of a droplet suspended in another fluid by soft particles with different wettability.

Mesoscopic modelling and simulation of soft matter.

The deformability of soft condensed matter often requires modelling of hydrodynamical aspects to gain quantitative understanding. This, however, requires specialised methods that can resolve the multiscale nature of soft matter systems. We review a number of the most popular simulation methods that have emerged, such as Langevin dynamics, dissipative particle dynamics, multi-particle collision dynamics, sometimes also referred to as stochastic rotation dynamics, and the lattice-Boltzmann method. We conclude this review with a short glance at current compute architectures for high-performance computing and community codes for soft matter simulation.

Anisotropic permeability in deterministic lateral displacement arrays.

We uncover anisotropic permeability in microfluidic deterministic lateral displacement (DLD) arrays. A DLD array can achieve high-resolution bimodal size-based separation of microparticles, including bioparticles, such as cells. For an application with a given separation size, correct device operation requires that the flow remains at a fixed angle to the obstacle array. We demonstrate via experiments and lattice-Boltzmann simulations that subtle array design features cause anisotropic permeability. Anisotropic permeability indicates the microfluidic array's intrinsic tendency to induce an undesired lateral pressure gradient. This can cause an inclined flow and therefore local changes in the critical separation size. Thus, particle trajectories can become unpredictable and the device useless for the desired separation task. Anisotropy becomes severe for arrays with unequal axial and lateral gaps between obstacle posts and highly asymmetric post shapes. Furthermore, of the two equivalent array layouts employed with the DLD, the rotated-square layout does not display intrinsic anisotropy. We therefore recommend this layout over the easier-to-implement parallelogram layout. We provide additional guidelines for avoiding adverse effects of anisotropy on the DLD.

Effect of body deformability on microswimming.

In this work we consider the following question: given a mechanical microswimming mechanism, does increased deformability of the swimmer body hinder or promote the motility of the swimmer? To answer this we run immersed-boundary-lattice-Boltzmann simulations of a microswimmer composed of deformable beads connected with springs. We find that the same deformations in the beads can result in different effects on the swimming velocity, namely an enhancement or a reduction, depending on the other parameters. To understand this we determine analytically the velocity of the swimmer, starting from the forces driving the motion and assuming that the deformations in the beads are known as functions of time and are much smaller than the beads themselves. We find that to the lowest order, only the driving frequency mode of the surface deformations contributes to the swimming velocity, and comparison to the simulations shows that both the velocity-promoting and velocity-hindering effects of bead deformability are reproduced correctly by the theory in the limit of small bead deformations. For the case of active deformations we show that there are critical values of the spring constant - which for a general swimmer corresponds to its main elastic degree of freedom - which decide whether the body deformability is beneficial for motion or not.