Predicting different adhesive regimens of circulating particles at blood capillary walls

Abstract

A fundamental step in the rational design of vascular targeted particles is the firm adhesion at the blood vessel walls. Here, a combined lattice Boltzmann-immersed boundary model is presented for predicting the near-wall dynamics of circulating particles. A moving least squares algorithm is used to reconstruct the forcing term accounting for the immersed particle, whereas ligand-receptor binding at the particle-wall interface is described via forward and reverse probability distributions. First, it is demonstrated that the model predicts with good accuracy the rolling velocity of tumor cells over an endothelial layer in a microfluidic channel. Then, particle-wall interactions are systematically analyzed in terms of particle geometries (circular, elliptical with aspect ratios 2 and 3), surface ligand densities (0.3, 0.5, 0.7 and 0.9), ligand-receptor bond strengths (1 and 2) and Reynolds numbers (Re = 0.01, 0.1 and 1.0). Depending on these conditions, four different particle-wall interaction regimens are identified, namely not adhering, rolling, sliding and firmly adhering particles. The proposed computational strategy can be efficiently used for predicting the near-wall dynamics of particles with arbitrary geometries and surface properties and represents a fundamental tool in the rational design of particles for the specific delivery of therapeutic and imaging agents.

Keywords: Computational modeling; Computational nanomedicine; Drug delivery; Immersed boundary; Lattice Boltzmann.

Fig. 1

HCT-15 cells rolling on an HUVEC monolayer into a single-channel microfluidic chip. a Schematic representation of the single-channel microfluidic chip with definition of the main geometric quantities. From top to bottom: bright field epi-fluorescent microscope image of the region of interests (scale bar 250 μm); side and top views of the chip (L = 2.7 cm, H = 42 μm, W = 210 μm). b Representative images of HCT-15 cells rolling over a confluent monolayer of HUVECs (×10 magnification, scale bar 250 μm). c Rolling velocity of HCT-15 under four different flow conditions (50, 100, 150 and 200 nL/min) estimated via numerical and theoretical analyses

Fig. 2

Particle transport in a linear laminar flow. a Schematic representation of the computational domain. b Ligand distributed over the particle perimeter interacting with receptors distributed over the vessel wall. c Ligand-receptor bond modeled as a spring with characteristic forward $k_f$ and reverse $k_{r0}$ strengths

Fig. 3

Vascular adhesion of circular particles ($\mathit{\sigma }=2$). a Schematic representation of the problem. b, f Particle separation distance from the wall versus time. The dashed line corresponds to $y_{\text{cr}}$. c, g Active over total number of ligands versus time. d, h Angular rotation, $\mathit{\theta },$ versus time where the inset presents a magnified view within the interval $25\le t{u}_{max}\le 30$. e, i Normalized rolling velocity versus time

Fig. 4

Vascular adhesion of elliptical particles ($\mathit{\sigma }=2$). a Schematic representation of the problem. b, f Particle separation distance from the wall versus time. The dashed line corresponds to $y_{\text{cr}}$. c, g Active over total number of ligands versus time. d, h Angular rotation, $\mathit{\theta },$ versus time where the inset presents a magnified view within the interval $0\le t{u}_{max}\le 5$. e, i Normalized rolling velocity versus time

Fig. 5

Contour plots for the rolling velocity. a Circular particle transport with soft ($\mathit{\sigma }=1$) and rigid ($\mathit{\sigma }=2$) ligand-receptor bonds. b Elliptical particle, with aspect ratio 2, transport with soft ($\mathit{\sigma }=1$) and rigid ($\mathit{\sigma }=2$) ligand-receptor bonds. c. Elliptical particle, with aspect ratio 3, transport with soft ($\mathit{\sigma }=1$) and rigid ($\mathit{\sigma }=2$) ligand-receptor bonds

Fig. 6

Contour plots for the probability of adhesion. a Circular particle transport with soft ($\mathit{\sigma }=1$) and rigid ($\mathit{\sigma }=2$) ligand-receptor bonds. b Elliptical particle, with aspect ratio 2, transport with soft ($\mathit{\sigma }=1$) and rigid ($\mathit{\sigma }=2$) ligand-receptor bonds. c Elliptical particle, with aspect ratio 3, transport with soft ($\mathit{\sigma }=1$) and rigid ($\mathit{\sigma }=2$) ligand-receptor bonds

Fig. 7

Vascular transport of elliptical particles with different critical bond length. a Schematic representation of the problem. b Active over total number of ligands versus time. c Particle separation distance from the wall versus time. d Centroid lateral position versus time