Self-organization of red blood cell suspensions under confined 2D flows

Assessing a heterogeneous model for accounting for endovascular devices in hemodynamic simulations of cerebral aneurysms

The heterogeneous model developed by Berod et al [Int J Numer Method Biomed Eng 38, 2021] for representing the hemodynamic effects of endovascular prostheses is applied to a series of 10 patient specific cerebral aneurysms, 6 being treated by flow diverters, 4 being equipped with WEBs. Two markers correlated with the medical outcome of the treatment are used to assess the potential of the model, namely the saccular mean velocity and the inflow rate at the neck of the aneurysm. The comparison with the corresponding wire-resolved simulations is very favorable in both cases, and the model-based simulations also retrieve the jetting-type flows generated downstream of the struts. Noteworthy, the very same model was used for representing the flow diverters and the WEBs, showing the versatility and robustness of the heterogeneous modeling of the devices.

Cell-free layer development and spatial organization of healthy and rigid red blood cells in a microfluidic bifurcation

Bifurcations and branches in the microcirculation dramatically affect blood flow as they determine the spatiotemporal organization of red blood cells (RBCs). Such changes in vessel geometries can further influence the formation of a cell-free layer (CFL) close to the vessel walls. Biophysical cell properties, such as their deformability, which is impaired in various diseases, are often thought to impact blood flow and affect the distribution of flowing RBCs. This study investigates the flow behavior of healthy and artificially hardened RBCs in a bifurcating microfluidic T-junction. We determine the RBC distribution across the channel width at multiple positions before and after the bifurcation. Thus, we reveal distinct focusing profiles in the feeding mother channel for rigid and healthy RBCs that dramatically impact the cell organization in the successive daughter channels. Moreover, we experimentally show how the characteristic asymmetric CFLs in the daughter vessels develop along their flow direction. Complimentary numerical simulations indicate that the buildup of the CFL is faster for healthy than for rigid RBCs. Our results provide fundamental knowledge to understand the partitioning of rigid RBC as a model of cells with pathologically impaired deformability in complex in vitro networks.

Rheology and structure of elastic capsule suspensions within rectangular channels

Three-dimensional simulations of the pressure-driven flow dynamics of elastic capsule suspensions within both slit and rectangular cross-section channels are presented. The simulations utilize the Immersed Boundary Method and the Lattice-Boltzmann Method models. The capsule volume fraction is fixed at 0.1 (i.e., a semi-dilute suspension), while the channel Reynolds number (Re), the capillary number (Ca), and the cross-sectional channel dimensions are systematically varied. Comparing results for slit and rectangular channels, it is found that multi-directional confinement hinders inertial focusing due to the capsule-free layers that develop in the two transverse directions. Furthermore, the thicknesses of the capsule-free layers in the two transverse directions differ when the height and width of the channel are not equal. Both the size and aspect ratio of the channel impact the apparent viscosity. It is found that square channels exhibit maximal viscosity and that holding one dimension fixed while increasing or decreasing the other results in a decrease in viscosity. The results therefore represent an expansion of the Fahraeus-Lindqvist effect from 1D cylindrical channels to 2D rectangular channels.

Flow-induced "waltzing" red blood cells: Microstructural reorganization and the corresponding rheological response

We investigate flow-induced structural organization in a dilute suspension of tumbling red blood cells (RBCs) under confined shear flow. For small Reynolds (Re = 0.1) and capillary numbers (Ca), with fully coupled hydrodynamic interaction (HI) and without interparticle adhesion, we find that HI between the biconcave discoid particles prompts the formation of layered RBC chains and synchronized rotating RBC pairs, referred here as "waltzing doublets." As the volume fraction ϕ increases, more waltzing doublets appear in RBC files. Stronger shear stress disrupts structural arrangements at higher Ca. We find that the flow-induced organization of waltzing doublets changes how the suspension viscosity varies with ϕ qualitatively. The intrinsic viscosity is particularly sensitive to microstructural rearrangement, increasing (decreasing) with ϕ at low (high) Ca that correlates with the change in the fraction of doublets. We verified flow-induced collective motion with comparison to two-cell simulations in which the cell volume fraction is controlled by varying the domain volume.

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.

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.

A heterogeneous model of endovascular devices for the treatment of intracranial aneurysms

Numerical computations of hemodynamics inside intracranial aneurysms treated by endovascular braided devices such as flow-diverters contribute to understanding and improving such treatment procedures. Nevertheless, these simulations yield high computational and meshing costs due to the heterogeneity of length scales between the dense weave of the fine struts of the device and the arterial volume. Homogeneous strategies developed over the last decade to circumvent this issue substitute local dissipations due to the wires with a global effect in the form of a pressure-drop across the device surface. However, these methods cannot accurately reproduce the flow-patterns encountered near the struts, the latter strongly dictating the intra-saccular flow environment. In this work, a versatile theoretical framework which aims at correctly reproducing the local flow heterogeneities due to the wires while keeping memory consumption, meshing and computational times as low as possible is introduced. This model reproduces the drag forces exerted by the device struts onto the fluid, thus producing local and heterogeneous effects on the flow. Extensive validation for various flow and geometric configurations using an idealized device is performed. To further illustrate the method capabilities, a real patient-specific aneurysm endovascularly treated with a flow-diverter is used, enabling quantitative comparisons with classical approaches for both intra-saccular velocities and computational costs reduction. The proposed heterogeneous model endeavors to bridge the gap between computational fluid dynamics and clinical applications and ushers in a new era of numerical treatment planning with minimally costing computational tools.

Optimizing pressure-driven pulsatile flows in microfluidic devices

Unsteady and pulsatile flows receive increasing attention due to their potential to enhance various microscale processes. Further, they possess significant relevance for microfluidic studies under physiological flow conditions. However, generating a precise time-dependent flow field with commercial, pneumatically operated pressure controllers remains challenging and can lead to significant deviations from the desired waveform. In this study, we present a method to correct such deviations and thus optimize pulsatile flows in microfluidic experiments using two commercial pressure pumps. Therefore, we first analyze the linear response of the systems to a sinusoidal pressure input, which allows us to predict the time-dependent pressure output for arbitrary pulsatile input signals. Second, we explain how to derive an adapted input signal, which significantly reduces deviations between the desired and actual output pressure signals of various waveforms. We demonstrate that this adapted pressure input leads to an enhancement of the time-dependent flow of red blood cells in microchannels. The presented method does not rely on any hardware modifications and can be easily implemented in standard pressure-driven microfluidic setups to generate accurate pulsatile flows with arbitrary waveforms.

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.

The influence of red blood cell deformability on hematocrit profiles and platelet margination

The influence of red blood cell (RBC) deformability in whole blood on platelet margination is investigated using confocal microscopy measurements of flowing human blood and cell resolved blood flow simulations. Fluorescent platelet concentrations at the wall of a glass chamber are measured using confocal microscopy with flowing human blood containing varying healthy-to-stiff RBC fractions. A decrease is observed in the fluorescent platelet signal at the wall due to the increase of stiffened RBCs in flow, suggesting a decrease of platelet margination due to an increased fraction of stiffened RBCs present in the flow. In order to resolve the influence of stiffened RBCs on platelet concentration at the channel wall, cell-pair and bulk flow simulations are performed. For homogeneous collisions between RBC pairs, a decrease in final displacement after a collision with increasing membrane stiffness is observed. In heterogeneous collisions between healthy and stiff RBC pairs, it is found that the stiffened RBC is displaced most. The influence of RBC deformability on collisions between RBCs and platelets was found to be negligible due to their size and mass difference. For a straight vessel geometry with varying healthy-to-stiff RBC ratios, a decrease was observed in the red blood cell-free layer and platelet margination due to an increase in stiffened RBCs present in flow.

An experimental erythrocyte rigidity index (Ri) and its correlations with Transcranial Doppler velocities (TAMMV), Gosling Pulsatility Index PI, hematocrit, hemoglobin concentration and red cell distribution width (RDW)

Brain artery velocities (Time-Averaged Maximum Mean Velocity, TAMMV) by Transcranial Doppler (TCD), hematocrit, hemoglobin, Red blood cell (RBC) Distribution Width (RDW) and RBC rigidity index (Ri), when reported together with their correlations, provide a accurate and useful diagnostic picture than blood viscosity measurements alone. Additionally, our study included a sixth parameter provided by TCD, the Gosling Pulsatility Index PI, which is an indicator of CBF (Cerebral Blood Flow) resistance. All these parameters are routine in Hematology except for values of Ri. The rigidity (Ri) of the RBC is the main rheological characteristic of the blood of Sickle Cell Anemia (SCA) patients and several pathologies. However, its quantification depends on many commercial and experimental techniques, none disseminated and predominant around the World. The difference in absorbance values of the blood, during the process of sedimentation in a microwell of a Microplate Reader, is a straightforward way of semi-quantifying the RBC rigidity Ri, since the fraction of irreversibly sickled red blood cells does not form rouleaux. Erythrocyte Rigidity Index (Ri) was calculated using initial absorbance A_initial (6 s) and final A_final (540 s), Ri = 1 / (Ai-Af). The Ri of 119 patients (2–17 y / o, M & F) SCA, SCC (Sickle Cell/hemoglobin C), SCD (Sickle Cell/hemoglobin D), Sβ0thal (Sickle Cell/hemoglobin Beta Zero Thalassemia) and 71 blood donors (20–65 y / o, M & F) were measured in our laboratory while the five parameters (TAMMV and PI by TCD, Hct, Hb and RDW) were obtained from medical records. The in vitro addition of hydroxyurea (HU, 50mg /dl, n = 51 patients, and n = 8 healthy donors) in the samples decreased the rouleaux adhesion strength of both donor and patients’ blood samples, leading to extraordinarily high Ri values. The correlation between the studied parameters was especially significant for the direct relationships between Ri, TAMMV, and PI.

Cross-sectional focusing of red blood cells in a constricted microfluidic channel

Constrictions in blood vessels and microfluidic devices can dramatically change the spatial distribution of passing cells or particles and are commonly used in biomedical cell sorting applications. However, the three-dimensional nature of cell focusing in the channel cross-section remains poorly investigated. Here, we explore the cross-sectional distribution of living and rigid red blood cells passing a constricted microfluidic channel by tracking individual cells in multiple layers across the channel depth and across the channel width. While cells are homogeneously distributed in the channel cross-section pre-contraction, we observe a strong geometry-induced focusing towards the four channel faces post-contraction. The magnitude of this cross-sectional focusing effect increases with increasing Reynolds number for both living and rigid red blood cells. We discuss how this non-uniform cell distribution downstream of the contraction results in an apparent double-peaked velocity profile in particle image velocimetry analysis and show that trapping of red blood cells in the recirculation zones of the abrupt construction depends on cell deformability.

Numerical simulation of deformable particles in a Coulter counter

In Coulter counters, cells counting and volumetry are achieved by monitoring their electrical print when they flow through a sensing zone. However, the volume measurement may be impaired by the cell dynamics, which may be difficult to control. In this paper, numerical simulations of the dynamics and electrical signature of red blood cells in a Coulter counter are presented, accounting for the deformability of the cells. In particular, a specific numerical pipeline is developed to overcome the challenge of the multi-scale nature of the problem. It consists in segmenting the whole computation of the cell dynamics and electrical response in a series of dedicated computations, with a saving of one order of magnitude in computational time. This numerical pipeline is used with rigid spheres and deformable red blood cells in an industrial Coulter counter geometry, and compared with experimental measurements. The simulations not only reproduce electrical signatures typical of those measured experimentally, but also allow an analysis of the electrical signature in terms of the heterogeneity of the electrical field and dynamics of the particles in the measurement zone. This study provides a methodology for computing the sizing of rigid or deformable particles by Coulter counters, opening the way to a better understanding of cells signatures in such devices.