Session J14: Biofluids: Small Vessels and Microcirculation I

Margination Behavior of a Circulating Cell in a Tortuous Microvessel

In the microcirculation, hydrodynamic interactions between red blood cells (RBCs) and a circulating cell (e.g. leukocyte, cancer cell) can drive the latter to flow next to the vessel wall. This behavior, known as margination, is an essential step in physiology as it precedes cell extravasation from the blood stream and into surrounding tissue. Current understanding of the fluid mechanics influencing margination is based on flow in straight tubes, where a circulating cell will not marginate in absence of RBCs. Recent work has shown a cross-stream wall-directed movement of a deformable cell at low Reynolds number due to vessel curvature. This suggests margination behavior can occur even in absence of RBCs in tortuous microvessels such as that which occurs in vivo. Using high-fidelity 3D cell-resolved simulations, we present a computational study on the margination behavior of a circulating cell flowing through a tortuous microvessel based on in vivo images of the rat mesentery. A long length (1mm) of a 20μm diameter vessel is modeled to capture a wide spectrum of curvature variations, and we simulate transport both with and without RBCs. Hematocrit and shear rate are varied to cover a range of conditions. We quantify mechanistic contributions which influence lateral movement and show how margination can occur either in or out of the curvature plane. We further identify margination under conditions not reported for straight tubes, where RBCs and tortuosity work together to lock the circulating cell near the wall.   

Development and Feasibility Analysis of an Idealized Benchtop Model to Characterize Cerebral Flow Pathways

Understanding the hemodynamics and flow paths in the cerebral vascular network can provide insights into neurovascular diseases and inform therapeutics. The key component of this network is a ring-like anastomosis pf arteries named Circle of Willis that connects the six major cerebral arteries at the base of the brain. This ring-like network forms a proximal pathway for collateral flow across the cerebral artery territories. These pathways are further augmented by collateral contributions from distal leptomeningeal routes. Systematic understanding of this combined collateral flow remains a challenge, and insights on coupling between distal flow pathways and proximal collateral flow remain limited. In prior in silico analysis we have demonstrated features of proximal collateral flow in the Circle of Willis. Here, we discuss the proof-of-concept development, and feasibility analysis, of a benchtop flow network model to study brain collateral flow. The study involves: development of an idealized planar model of the Circle of Willis derived from patient images; integration of model distal collateral routes; distribution of controlled pulsatile flow through the cervical vessel entry points; and dynamic dye injection and washout analysis. The quantitative trends obtained from dye intensity distributions were used to assess the combined proximal and distal collateral flow status; and evaluate feasibility of this model system for parametric investigations of various collateral configurations.   

Microfluidic model of micro-haemodynamics in porous media

Quantifying the flow of red blood cells (RBCs) within complex biological porous tissues, such as the heterogeneous intervillous space (IVS) in the human placenta, remains an open problem. Due to comparable dimensions between RBCs and IVS structures, it is essential to model blood flow as a suspension rather than a continuum. The rheology of this soft suspension remains unexplored in disordered porous media. We design a suspension of ultra-soft, deflated polydimethylsiloxane (PDMS) microcapsules, which can mimic the large deformation of RBCs when propagated at a constant flow rate in confined capillary tubes, to serve as a valuable tool to investigate microhaemodynamics. We aim to relate the global resistance of our porous medium to the local distribution of particles and their velocity as a function of the disorder of the medium, volume fraction and capillary number Ca. In contrast to a hexagonal array, where the lateral dispersion of capsules is approximately linear with downstream distance, a uniformly random array provides preferential paths that are weakly influenced by clogs and lead to anomalous dispersion. The interaction between suspension and geometry results in a non-linear variation of the relative resistance as a function of both volume fraction and Ca.   

Cell Distributions and Segregation During Blood Flow within Curved and Bifurcated Vascular Geometries in Blood Disorders

The spatial distribution of blood cellular components is nontrivial. Red blood cells (RBCs) migrate toward vessel center leaving an RBC-depleted cell-free layer (CFL) near walls, while white blood cells and platelets reside in CFL, a flow-induced segregation termed margination. Margination is significant in blood disorders like sickle cell disease (SCD). A complication of SCD is that endothelial cells are dysfunctional and pro-inflammatory in circulation. One might hypothesize diseased cells strongly marginate, residing primarily in CFL, and generating physical interactions that damage endothelium.

We characterize cell distributions for mixtures of normal and aberrant RBC in various vascular geometries using an immersed boundary method. We test the hypothesis with a range of blood disorders, such as SCD, iron deficiency anemia, COVID-19, and spherocytosis. Smaller and stiffer aberrant RBCs strongly marginate due to contrasts in physical properties relative to normal cells. Marginated aberrant cells near walls causing large stresses fluctuation, potentially leading to increased vascular inflammation. In curved vessels, distribution of marginated cells is very heterogeneous, indicating importance of geometry. In addition, we examine modified Zweifach-Fung (Z-F) effect at vessel bifurcations in blood disorders. Cell segregation results in a thinner CFL, reducing Z-F effect and leads to higher-than-normal hematocrits in low-flow branches, an observation of clinical importance for SCD.   

Organization and dynamics of red blood cells in a stenosed microchannel under time-dependent flow

The circulatory system is a complex vessel network that distributes blood to body tissues and organs. In the microcirculation, red blood cells (RBCs) tend to migrate away from the vessel walls, thus forming a core RBC flow and a cell-free layer (CFL) that determines the unique flow properties of blood. Constricted vessels, such as stenosed arteries, can dramatically affect RBC distribution and CFL development.

This study investigates RBC organization and CFL dynamics under time-dependent flow. We use a high-precision pressure device to pump RBC suspensions with concentrations ranging from 1% to 20% in volume through a microfluidic constriction. We employ a sinusoidal pressure modulation to examine the time-dependent CFL and perform high-speed optical microscopy at various positions before and after the constriction. The resulting image sequences are synchronized with the phase of the driving and post-processed with a customized routine that allows us to determine the RBC core flow even at low concentrations and under time-dependent flow conditions. Our results highlight the dominant effects of the RBC concentration and the amplitude of the applied pressure signal on the CFL dynamics. Complementary numerical simulations reveal how the time-dependent CFL is coupled with the dynamically changing flow field at the constriction. Our study provides crucial insight into the flow behavior of complex fluids in unsteady microscale flows.   

Dynamics and Rheology of Immersed Elastic Capsules in A Simple Shear Flow

Biological fluids like blood serve as nutrient transport and immune response in the human body. These fluids consist of a viscous phase with suspended deformable membranes that enclose an inner fluid, commonly known as capsules. Understanding these fluids provides insights into diseases like aneurysms and aid in developing microfluidic diagnostic devices. The recent development of inertial migration techniques holds promise to facilitate non-invasive blood plasma extraction and improve size-dependent cell segregation. In this work, we investigate the dynamics and rheology behavior of an elastic capsule suspension in a simple inertial shear flow. Governing physical parameters are capsule volume fraction, imposed shear rate, flow inertia and capsule deformability. Computations are performed with our open-source front-tracking solver implemented in Basilisk on octree adaptive grids for local mesh refinement of areas of interest. The capsule stresses are resolved with a linear finite element method and a paraboloid fitting technique to accurately compute the elastic and bending force. While non-inertial capsules have been studied extensively, to our knowledge, this is the first systematic study of the capsule suspensions at finite Re. Our numerical findings highlight the influence of capsule volume fraction on suspension rheology. We analyze quantitatively the deformation and dynamics of the capsule suspensions and their impact on the system.   

Hemodynamic Fluctuations in Patient-Specific Intracranial Aneurysms: An In-Vitro and In-Silico Study

Intracranial aneurysms (IAs) are permanent dilatations of brain vessels, posing a rupture risk that leads to subarachnoid hemorrhage. This study focuses on understanding how hemodynamic fluctuations—which are known to exist in IAs—affect risk of rupture of patient-specific IA geometris. We employ in-vitro 4D particle image velocimetry (PIV) and in-silico computational fluid dynamics (CFD) modalities to identify and analyze flow structures in ten IA cases from the University hospital of Magdeburg, Germany. The IA cases maintained varying size, shape, and location along the Circle of Willis; the inflow pulsatile waveform for each geometry was assumed from literature. To minimize errors across modalities, CT scans were performed for all manufactured in vitro models and the measured shape was used for the CFD simulations. Flow structures, hemodynamic metrics of interest such as wall shear stress (WSS) and oscillatory shear index (OSI), as well as fluctuation levels in velocity, WSS, and OSI were evaluated for both modalities. Results were analyzed to qualitatively and quantitatively consider the magnitude of hemodynamic fluctuations across the IA cohort and improve clinical understanding for patient-specific pathological data applications.   

A computational study of flow of deformable capsules through inflating microvessels

Flow of deformable particles through compliant microvessels is encountered in biological and synthetic applications. Examples include flow of deformable blood cells, vesicles and capsules through small blood vessels and flexible microfluidic passages. Here we present a computational approach for modeling the flow of deformable capsules through inflating microtubes. The capsules are viscous drops surrounded by thin hyperelastic membranes. The tube wall is also taken to be thin and modeled as a hyperelastic membrane. A finite-element method is used for membrane mechanics, and a finite-volume/spectral method is used for the fluid motion. A diffuse-interface immersed-boundary method is used for the capsule/flow coupling while a hybrid of the sharp-interface (ghost-node) and diffuse-interface immersed-boundary methods for vessel/flow coupling. We find that a capsule can go through different phases of shape transition as it travels through the inflating tube, from bullet to parachute to complex multilobe shapes, unlike in a tube of constant cross-section. We further find that an initially single-file train of capsules becomes unstable and transforms into random capsule distribution as the tube inflates. A quantitative comparison of capsule dynamics in inflating versus rigid-walled tubes is presented.