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The biotransport of the intravascular nanoparticle (NP) is influenced by both the complex cellular flow environment and the NP characteristics. Being able to computationally simulate such intricate transport phenomenon with high efficiency is of far-reaching significance to the development of nanotherapeutics, yet challenging due to large length-scale discrepancies between NP and red blood cell (RBC) as well as the complexity of NP dynamics. Recently, a lattice-Boltzmann (LB) based multiscale simulation method has been developed to capture both NP scale and cellular level transport phenomenon at high computational efficiency. The basic components of this method include the LB treatment for the fluid phase, a spectrin-link method for RBCs, and a Langevin dynamics (LD) approach to capturing the motion of the suspended NPs. Comprehensive two-way coupling schemes are established to capture accurate interactions between each component. The accuracy and robustness of the LB-LD coupling method are demonstrated through the relaxation of a single NP with initial momentum and self-diffusion of NPs. This approach is then applied to study the migration of NPs in a capillary vessel under physiological conditions. It is shown that Brownian motion is most significant for the NP distribution in capillary vessels. For 1~100 nm particles, the Brownian diffusion is the dominant radial diffusive mechanism compared to the RBC-enhanced diffusion. For ~500 nm particles, the Brownian diffusion and RBC-enhanced diffusion are comparable drivers for the particle radial diffusion process.
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Using a multiscale blood flow solver, the complete diffusion tensor of nanoparticle (NP) in sheared cellular blood flow is calculated over a wide range of shear rate and haematocrit. In the short-time regime, NPs exhibit anomalous dispersive behaviors under high shear and high haematocrit due to the transient elongation and alignment of the red blood cells (RBCs). In the long-time regime, the NP diffusion tensor features high anisotropy. Particularly, there exists a critical shear rate ($sim$100 $s^{-1}$) around which the shear-rate dependence of the diffusivity tensor changes from linear to nonlinear scale. Above the critical shear rate, the cross-stream diffusivity terms vary sublinearly with shear rate, while the longitudinal term varies superlinearly. The dependence on haematocrit is linear in general except at high shear rates, where a sublinear scale is found for the vorticity term and a quadratic scale for the longitudinal term. Through analysis of the suspension microstructure and numerical experiments, the nonlinear hemorheological dependence of the NP diffusion tensor is attributed to the streamwise elongation and cross-stream contraction of RBCs under high shear, quantified by a Capillary number. The RBC size is shown to be the characteristic length scale affecting the RBC-enhanced shear-induced diffusion (RESID), while the NP size at submicron exhibits negligible influence on the RESID. Based on the observed scaling behaviors, empirical correlations are proposed to bridge the NP diffusion tensor to specific shear rate and haematocrit. The characterized NP diffusion tensor provides a constitutive relation that can lead to more effective continuum models to tackle large-scale NP biotransport applications.
Various biological processes such as transport of oxygen and nutrients, thrombus formation, vascular angiogenesis and remodeling are related to cellular/subcellular level biological processes, where mesoscopic simulations resolving detailed cell dynamics provide a key to understanding and identifying the cellular basis of disease. To break this bottleneck and achieve a biologically meaningful timescale, we propose a multiscale parareal algorithm in which a continuum-based solver supervises a mesoscopic simulation in the time-domain. Using an iterative prediction-correction strategy, the parallel-in-time mesoscopic simulation supervised by its continuum-based counterpart can converge fast. The effectiveness of the proposed method is first verified in a time-dependent flow with a sinusoidal flowrate through a Y-shaped bifurcation channel. Physical quantities of interest including velocity, wall shear stress and flowrate are computed to compare against those of reference solutions, showing a less than 1% relative error on flowrate in the Newtonian flow and a less than 3% relative error in the non-Newtonian blood flow. The proposed method is then applied to a large-scale mesoscopic simulation of microvessel blood flow in a zebrafish hindbrain for temporal acceleration. The time-dependent blood flow from heartbeats in this realistic vascular network of zebrafish hindbrain is simulated using dissipative particle dynamics as the mesoscopic model, which is supervised by a one-dimensional blood flow model (continuum-based model) in multiple temporal sub-domains. The computational analysis shows that the resulting microvessel blood flow converges to the reference solution after only two iterations. The proposed method is suitable for long-time mesoscopic simulations with complex fluids and geometries.
Cardiovascular diseases, specifically cerebral aneurysms, represent a major cause of morbidity and mortality, having a significant impact on the cost and overall status of health care. In the present work, we employ a haemorheological blood model originally proposed by Owens to investigate the haemodynamics of blood flow through an aneurytic channel. This constitutive equation for whole human blood is derived using ideas drawn from temporary polymer network theory to model the aggregation and disaggregation of erythrocytes in normal human blood at different shear rates. To better understand the effect of rheological models on the haemodynamics of blood flow in cerebral aneurysms we compare our numerical results with those obtained with other rheological models such as the Carreau-Yasuda (C-Y) model. The results show that the velocity profiles for the Newtonian and the Owens models are approximately similar but differ from those of the C-Y model. In order to stabilize our numerical simulations, we propose two new stabilization techniques, the so-called N-Owens and I-Owens methods. Employing the N-Owens stabilization method enables us to capture the effect of erythrocyte aggregation in blood flow through a cerebral aneurysm at higher Weissenberg (We) and Reynolds (Re) numbers than would otherwise be possible.
Transport of solid particles in blood flow exhibits qualitative differences in the transport mechanism when the particle varies from nanoscale to microscale size comparable to the red blood cell (RBC). The effect of microscale particle margination has been investigated by several groups. Also, the transport of nanoscale particles (NPs) in blood has received considerable attention in the past. This study attempts to bridge the gap by quantitatively showing how the transport mechanism varies with particle size from nano- to microscale. Using a three-dimensional (3D) multiscale method, the dispersion of particles in microscale tubular flows is investigated for various hematocrits, vessel diameters and particle sizes. NPs exhibit a nonuniform, smoothly-dispersed distribution across the tube radius due to severe Brownian motion. The near-wall concentration of NPs can be moderately enhanced by increasing hematocrit and confinement. Moreover, there exists a critical particle size ($sim$1 $mu$m) that leads to excessive retention of particles in the cell-free region near the wall, i.e., margination. Above this threshold, the margination propensity increases with the particle size. The dominance of RBC-enhanced shear-induced diffusivity (RESID) over Brownian diffusivity (BD) results in 10 times higher radial diffusion rates in the RBC-laden region compared to that in the cell-free layer, correlated with the high margination propensity of microscale particles. This work captures the particle size-dependent transition from Brownian-motion dominant dispersion to margination using a unified 3D multiscale computational approach, and highlights the linkage between the radial distribution of RESID and the margination of particles in confined blood flows.
Driven or active suspensions can display fascinating collective behavior, where coherent motions or structures arise on a scale much larger than that of the constituent particles. Here, we report experiments and numerical simulations revealing that red blood cells (RBCs) assemble into regular patterns in a confined shear flow. The order is of pure hydrodynamic and inertialess origin, and emerges from a subtle interplay between (i) hydrodynamic repulsion by the bounding walls which drives deformable cells towards the channel mid-plane and (ii) intercellular hydrodynamic interactions which can be attractive or repulsive depending on cell-cell separation. Various crystal-like structures arise depending on RBC concentration and confinement. Hardened RBCs in experiments and rigid particles in simulations remain disordered under the same conditions where deformable RBCs form regular patterns, highlighting the intimate link between particle deformability and the emergence of order. The difference in structuring ability of healthy (deformable) and diseased (stiff) RBCs creates a flow signature potentially exploitable for diagnosis of blood pathologies.
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