A combined Lattice Boltzmann and Immersed boundary approach for predicting the vascular transport of differently shaped particles

Abstract

Highlights• Systematic analysis of a LB-IB model for arbitrarily shaped particle.• The model is validated towards benchmark numerical results.• The near wall dynamics of a single particle in linear laminar flow is analysed.• The effect of particle shape on the angular velocity distribution is analysed. AbstractModelling the vascular transport and adhesion of man-made particles is crucial for optimizing their efficacy in the detection and treatment of diseases. Here, a Lattice Boltzmann and Immersed Boundary methods are combined together for predicting the near wall dynamics of particles with different shapes in a laminar flow. For the lattice Boltzmann modelling, a Gauss-Hermite projection is used to derive the lattice equation; wall boundary conditions are imposed through the Zou-He framework; and a moving least squares algorithm accurately reconstructs the forcing term accounting for the immersed boundary. First, the computational code is validated against two well-known test cases: the sedimentation of circular and elliptical cylinders in a quiescent fluid. A very good agreement is observed between the present results and those available in the literature. Then, the transport of circular, elliptical, rectangular, square and triangular particles is analyzed in a Couette flow, at Re=20. All particles drifted laterally across the stream lines reaching an equilibrium position, independently of the initial conditions. For this large Reynolds number, the particle shape has no significant effect on the final equilibrium position but it does affect the absolute value and periodicity of the angular velocity. Specifically, elongated particles show longer oscillation periods and, most interestingly, larger variations in angular velocity. The longest particles exhibit a zero angular velocity for almost the whole rotational period. Collectively, this data demonstrates that the proposed approach can be efficiently used for predicting complex particle dynamics in biologically relevant flows. This computational strategy could have significant impact in the field of computational nanomedicine for optimizing the specific delivery of therapeutic and imaging agents.

Predicting different adhesive regimens of circulating particles at blood capillary walls

“…The mathematical method used to model the fluid evolution and the fluid-structure interaction, proposed and validated by Coclite et al (2016), is briefly described in the following.…”

“…The pressure and velocity derivatives in Eqs. (7) and (8) are evaluated considering a probe in the normal positive direction of each element, the probe length being 1.2Δx, and using the moving least squares formulation cited (Coclite et al 2016). In this framework, the velocity derivatives evaluated at the probe are considered equal to the ones on the linear element centroid as previously done by the authors (Coclite et al 2016;de Tullio and Pascazio 2016).…”

“…where f ib is the body force term evaluated through the formulation by Favier et al (2014), combined with the moving least squares reconstruction (Vanella and Balaras 2009) in the immersed boundary technique by Coclite et al (2016). Due to the presence of the forcing term  i , the macroscopic quantities, given by the moments of the distribution functions, are obtained as:…”

“…For instance, at the macrovascular scale, the isogeometric analysis (IA) was fruitfully exploited to predict the vascular deposition of microparticles, directly infused via a catheter positioned within the left coronary artery, as a function of the endothelial receptor densities (Hossain et al 2013(Hossain et al , 2014. Similarly, direct numerical simulations (DNS) and the immersed boundary (IB) were employed to predict the fluid-structure interaction of bodies with arbitrary shapes immersed in an incompressible fluid (Coclite et al 2016;de Tullio and Pascazio 2016). At the microscopic scale, the immersed finite element method (IFEM) was also used to study the transport of micro-and nanoparticles within whole blood and demonstrate that sub-micro-and micron-sized particles would tend to be pushed laterally toward the vessel walls by the fast-moving and more abundant red blood cells (Lee et al 2013(Lee et al , 2014.…”

“…This computational tool was efficiently applied to follow the dynamics of rigid particles and deformable capsules, such us red blood cells (RBCs) and leukocytes, in whole blood capillary flow. Specifically, it was applied to finely tune the geometry and viscoelastic properties of RBCs in order to accurately replicate the rheological response of whole blood as well as to reduce computing burden (Fedosov et al 2010;Sun and Munn 2005;Kruger et al 2011), predict the clustering of RBCs and microcapsules in narrow capillaries (McWhirter et al 2009), explain the role of RBCs on the vascular rolling of leukocytes (Sun et al 2003), determine numerically the size of the cell-free layer developing next to the vessel walls (Fedosov et al 2010) and model the vascular transport of micro-/nanoparticles (Coclite et al 2016;Gekle 2016;Tan et al 2016;Basagaoglu et al 2013).…”