A cell-and-plasma numerical model reveals hemodynamic stress and flow adaptation in zebrafish microvessels after morphological alteration.

The development of a functional cardiovascular system ensures a sustainable oxygen, nutrient and hormone delivery system for successful embryonic development and homeostasis in adulthood. While early vessels are formed by biochemical signaling and genetic programming, the onset of blood flow provides mechanical cues that participate in vascular remodeling of the embryonic vascular system. The zebrafish is a prolific animal model for studying the quantitative relationship between blood flow and vascular morphogenesis due to a combination of favorable factors including blood flow visualization in optically transparent larvae. In this study, we have developed a cell-and-plasma blood transport model using computational fluid dynamics (CFD) to understand how red blood cell (RBC) partitioning affect lumen wall shear stress (WSS) and blood pressure in zebrafish trunk blood vascular networks with altered rheology and morphology. By performing live imaging of embryos with reduced hematocrit, we discovered that cardiac output and caudal artery flow rates were maintained. These adaptation trends were recapitulated in our CFD models, which showed reduction in network WSS via viscosity reduction in the caudal artery/vein and via pressure gradient weakening in the intersegmental vessels (ISVs). Embryos with experimentally reduced lumen diameter showed reduced cardiac output and caudal artery flow rate. Factoring in this trend into our CFD models, simulations highlighted that lumen diameter reduction increased vessel WSS but this increase was mitigated by flow reduction due to the adaptive network pressure gradient weakening. Additionally, hypothetical network CFD models with different vessel lumen diameter distribution characteristics indicated the significance of axial variation in lumen diameter and cross-sectional shape for establishing physiological WSS gradients along ISVs. In summary, our work demonstrates how both experiment-driven and hypothetical CFD modeling can be employed for the study of blood flow physiology during vascular remodeling.

A mechanistic model of cross-bridge migration in RBC aggregation and disaggregation.

Red blood cells (RBCs) clump together under low flow conditions in a process called RBC aggregation, which can alter RBC perfusion in a microvascular network. As elevated RBC aggregation is commonly associated with cardiovascular and inflammatory diseases, a better understanding of aggregation is essential. Unlike RBC aggregation in polymer solutions which can be well explained by polymer depletion theory, plasma-mediated RBC aggregation has features that best match explanations with cross-bridging mechanisms. Previous studies have demonstrated the dominant role of fibrinogen (Fg) in promoting aggregate formation and recent cell-force spectroscopy (CFS) experiments on interacting RBC doublets in plasma have reported an inverse relationship between disaggregation force and the adhesive contact area between RBCs. This has led investigators to revisit the hypothesis of inter-RBC cross-bridging which involves cross-bridge migration under interfacial tension during the forced disaggregation of RBC aggregates. In this study, we developed the cross-bridge migration model (CBMM) in plasma that mechanistically represents the migrating cross-bridge hypothesis. Transport of mobile Fg cross-bridges (mFg) was calculated using a convection-diffusion transport equation with our novel introduction of convective cross-bridge drift that arises due to intercellular friction. By parametrically transforming the diffusivity of mFg in the CBMM, we were able to match experimental observations of both RBC doublet formation kinematics and RBC doublet disaggregation forces under optical tweezers tension. We found that non-specific cross-bridging promotes spontaneous growth of adhesion area between RBC doublets whereas specific cross-bridging tends to prevent adhesion area growth. Our CBMM was also able to correlate Fg concentration shifts from healthy population blood plasma to SLE (lupus) condition blood plasma with the observed increase in doublet disaggregation forces for the RBC doublets in SLE plasma.

High-Throughput Imaging of Blood Flow Reveals Developmental Changes in Distribution Patterns of Hemodynamic Quantities in Developing Zebrafish.

Mechanical forces from blood flow and pressure (hemodynamic forces) contribute to the formation and shaping of the blood vascular network during embryonic development. Previous studies have demonstrated that hemodynamic forces regulate signaling and gene expression in endothelial cells that line the inner surface of vascular tubes, thereby modifying their cellular state and behavior. Given its important role in vascular development, we still know very little about the quantitative aspects of hemodynamics that endothelial cells experience due to the difficulty in measuring forces in vivo. In this study, we sought to determine the magnitude of wall shear stress (WSS) exerted on ECs by blood flow in different vessel types and how it evolves during development. Utilizing the zebrafish as a vertebrate model system, we have established a semi-automated high-throughput fluorescent imaging system to capture the flow of red blood cells in an entire zebrafish between 2- and 6-day post-fertilization (dpf). This system is capable of imaging up to 50 zebrafish at a time. A semi-automated analysis method was developed to calculate WSS in zebrafish trunk vessels. This was achieved by measuring red blood cell flow using particle tracking velocimetry analysis, generating a custom-made script to measure lumen diameter, and measuring local tube hematocrit levels to calculate the effective blood viscosity at each developmental stage. With this methodology, we were able to determine WSS magnitude in different vessels at different stages of embryonic and larvae growth and identified developmental changes in WSS, with absolute levels of peak WSS in all vessel types falling to levels below 0.3 Pa at 6 dpf. Additionally, we discovered that zebrafish display an anterior-to-posterior trend in WSS at each developmental stage.

Recovery of cell-free layer and wall shear stress profile symmetry downstream of an arteriolar bifurcation.

Unequal RBC partitioning at arteriolar bifurcations contributes to dissimilar flow developments between daughter vessels in a bifurcation. Due to the importance of the cell-free layer (CFL) and the wall shear stress (WSS) to physiological processes such as vasoregulation and gas diffusion, we investigated the effects of a bifurcation disturbance on the development of the CFL width and WSS in bifurcation daughter branches. The analysis was performed on a two-dimensional (2-D) computational model of a transverse arteriole at three different flow rates corresponding to parent branch (PB) pseudoshear rates of 60, 170 and 470s(-1), while maintaining a 2-D hematocrit of about 55% in the PB. Flow symmetry was defined using the statistical similarity of the CFL and WSS distributions between the two walls of the vessel branch. In terms of the flow symmetry recovery, higher flow rates caused larger reductions in the flow symmetry indices in the MB and subsequently required longer vessel lengths for complete recovery. Lower tube hematocrits in the SB led to complete symmetry recovery for all flow rates despite the higher initial asymmetry in the SB than in the MB. Arteriolar bifurcations produce unavoidable local CFL asymmetry and the persistence of the asymmetry downstream may increase effective blood viscosity which is especially significant at higher physiological flow rates.

A review of numerical methods for red blood cell flow simulation.

In this review, we provide an overview of the simulation techniques employed for modelling the flow of red blood cells (RBCs) in blood plasma. The scope of this review omits the fluid modelling aspect while focusing on other key components in the RBC-plasma model such as (1) describing the RBC deformation with shell-based and spring-based RBC models, (2) constitutive models for RBC aggregation based on bridging theory and depletion theory and (3) additional strategies required for completing the RBC-plasma flow model. These include topics such as modelling fluid-structure interaction with the immersed boundary method and boundary integral method, and updating the variations in multiphase fluid property through the employment of index field methods. Lastly, we summarily discuss the current state and aims of RBC modelling and suggest some research directions for the further development of this field of modelling.

Two-dimensional strain-hardening membrane model for large deformation behavior of multiple red blood cells in high shear conditions.

BACKGROUND: Computational modeling of Red Blood Cell (RBC) flow contributes to the fundamental understanding of microhemodynamics and microcirculation. In order to construct theoretical RBC models, experimental studies on single RBC mechanics have presented a material description for RBC membranes based on their membrane shear, bending and area moduli. These properties have been directly employed in 3D continuum models of RBCs but practical flow analysis with 3D models have been limited by their computationally expensive nature. As such, various researchers have employed 2D models to efficiently and qualitatively study microvessel flows. Currently, the representation of RBC dynamics using 2D models is a limited methodology that breaks down at high shear rates due to excessive and unrealistic stretching. METHODS: We propose a localized scaling of the 2D elastic moduli such that it increases with RBC local membrane strain, thereby accounting for effects such as the Poisson effect and membrane local area incompressibility lost in the 2D simplification. Validation of our 2D Large Deformation (2D-LD) RBC model was achieved by comparing the predicted RBC deformation against the 3D model from literature for the case of a single RBC in simple shear flow under various shear rates (dimensionless shear rate G = 0.05, 0.1, 0.2, 0.5). The multi-cell flow of RBCs (38% Hematocrit) in a 20 µm width microchannel under varying shear rates (50, 150, 150 s-1) was then simulated with our proposed model and the popularly-employed 2D neo-Hookean model in order to evaluate the efficacy of our proposed 2D-LD model. RESULTS: The validation set indicated similar RBC deformation for both the 2D-LD and the 3D models across the studied shear rates, highlighting the robustness of our model. The multi-cell simulation indicated that the 2D neo-Hookean model predicts noodle-like RBC shapes at high shear rates (G = 0.5) whereas our 2D-LD model maintains sensible RBC deformations. CONCLUSION: The ability of the 2D-LD model to limit RBC strain even at high shear rates enables this proposed model to be employed in practical simulations of high shear rate microfluidic flows such as blood separation channels.

Effect of deformability difference between two erythrocytes on their aggregation.

In this study, we investigated the rheology of a doublet that is an aggregate of two red blood cells (RBCs). According to previous studies, most aggregates in blood flow consist of RBC doublet-pairs and thus the understanding of doublet dynamics has scientific importance in describing its hemodynamics. The RBC aggregation tendency can be significantly affected by the cell's deformability which can vary under both physiological and pathological conditions. Hence, we conducted a two-dimensional simulation of doublet dynamics under a simple shear flow condition with different deformability between RBCs. To study the dissociation process of the doublet, we employed the aggregation model described by the Morse-type potential function, which is based on the depletion theory. In addition, we developed a new method of updating fluid property to consider viscosity difference between RBC cytoplasm and plasma. Our results showed that deformability difference between the two RBCs could significantly reduce their aggregating tendency under a shear condition of 50 s(-1), resulting in disaggregation. Since even under physiological conditions, the cell deformability may be significantly different, consideration of the difference in deformability amongst RBCs in blood flow would be needed for the hemodynamic studies based on a numerical approach.