Numerical Simulation of Arbitrarily Shaped Particle Transport in an Incompressible Flow

Abstract

Passive delivery of arbitrarily shaped particles is one of the main concern for several biomedical applications. Properly designed particles, once administrated at the systemic level and transported by the blood flow along the circulatory system, are expected to improve the efficiency of molecule-based therapy and imaging by increasing the mass fraction of therapeutic molecules and tracers that are able to reach their targets. To this purpose different kinds of particle have been presented in the literature, with different composition and chemico-physical properties. The prediction of the transport dynamics of one or more particles (bolus) in a blood vessel becomes of primary importance, the main parameters involved in the phenomenon being: (a) dimension and shape of the particle; (b) Reynolds number based on the flow rate and diameter of the vessel; (c) density of the particle; (d) number of particles in the bolus. The development of suitable computational techniques able to predict such a complex dynamics could help and speed-up the design process, shedding some light onto the basic mechanism of the phenomena of interest.

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

“…This was also demonstrated experimentally [3,4,8,16]. Indeed, multiple techniques have been proposed for modeling vascular flow and nanoconstruct transport in a variety of vascular districts, including direct numerical simulations (DNS) [17], immersed finite element methods (IFEM) [13,18], immersed boundary methods (IBM) [19], and Isogeometric Analysis (IA) [14,15]. These approaches are all based on the discretization and numerical integration of the Navier-Stokes and continuity equations, and still remains challenging the modelling of vascular transport of multiple particles with complex shapes and mechanical properties.…”

“…After few initial fluctuations the particle finds its equilibrium position and settles in the middle of the channel with an horizontal inclination. Figure 4(c) shows the comparison with the finite difference Navier-Stokes IB method [19,47]. The maximum displacement of the sedimentation velocity with respect to the solution of such a method is found for t × u Max /L re f = 4.7 and the corresponding relative error is equal to ε = 3.07 × 10 −4 .…”

“…, where ν the kinematic viscosity. Lines are for the present LBM formulation results, circles correspond to the benchmark test by Yu& Shao [46], triangles and squares are results obtained with a validated finite-difference approach [19,47].…”

“…For comparison we use also the results obtained with a validated finite-difference method for the solution of the Navier-Stokes equation equipped with a MLS-IBM approach [19,47]. The This test case has also been used to perform a mesh-refinement convergence analysis of the computational method.…”

“…For the LBM modelling, the lattice equation is derived on a rigorous mathematical basis by a Gauss-Hermite projection. The particle dynamics is simulated through a rigid-body-dynamics equations solver [19] weakly coupled with the flow solver.…”