Modeling particle shape-dependent dynamics in nanomedicine

Abstract

One of the major challenges in nanomedicine is to improve nanoparticle cell selectivity and adhesion efficiency through designing functionalized nanoparticles of controlled sizes, shapes, and material compositions. Recent data on cylindrically shaped filomicelles are beginning to show that non-spherical particles remarkably improved the biological properties over spherical counterpart. Despite these exciting advances, non-spherical particles have not been widely used in nanomedicine applications due to the lack of fundamental understanding of shape effect on targeting efficiency. This paper intends to investigate the shape-dependent adhesion kinetics of non-spherical nanoparticles through computational modeling. The ligand-receptor binding kinetics is coupled with Brownian dynamics to study the dynamic delivery process of nanorods under various vascular flow conditions. The influences of nanoparticle shape, ligand density, and shear rate on adhesion probability are studied. Nanorods are observed to contact and adhere to the wall much easier than their spherical counterparts under the same configuration due to their tumbling motion. The binding probability of a nanorod under a shear rate of 8 s(-1) is found to be three times higher than that of a nanosphere with the same volume. The particle binding probability decreases with increased flow shear rate and channel height. The Brownian motion is found to largely enhance nanoparticle binding. Results from this study contribute to the fundamental understanding and knowledge on how particle shape affects the transport and targeting efficiency of nanocarriers, which will provide mechanistic insights on the design of shape-specific nanomedicine for targeted drug delivery applications.

Keywords: Adhesion kinetics; Brownian dynamics; Immersed finite element method; nanomedicine; nanorod.

Fig. 1

Model of ligand-receptor binding kinetics between ligand-coated nanoparticle surface and receptor coated vascular wall surface.

Fig. 2

Illustration of friction coefficient measurement of arbitrarily orientated nanorod

Fig. 3

Shape dependent adhesion dynamics. The left column shows a spherical particle washed away without contact with surface; the right column shows a nanorod tumbles and gets deposited. A, B, C, D are at times t=0 s, 0.25 s, 0.5s, and 0.75 s, respectively. The line labeled on the spherical particle indicates its rotation. The vectors in fluid domain indicate flow field and arrows indicate magnitude and direction of bonding forces.

Fig. 4

Influence of ligand density on adhesion. The left column and right column has a nanorod with low and high ligand coating densities respectively; A, B, C, D are at t=0 s, 0.25 s, 0.5s, and 0.75 s. The vectors in fluid domain indicate flow field and arrows indicate magnitude and direction of bonding forces.

Fig. 5

Illustration of particle trajectory calculation. The nanorod trajectory is defined as the minimum distance between the nanorod surface and the wall surface at any given time. Center of mass of the nanorod is not used in calculation because it doesn’t reflect true minimum distance which actually dictates the binding event.

Fig. 6

Trajectories of a nanorod and a nanosphere. (a) Trajectories of 20 trials of nanorod and nanosphere, where red spots indicate adhesion of nanorods and blue spots indicate adhesion of nanospheres at that location; (b) Mean trajectory of 20 trials of nanorod and nanosphere with standard deviation shown as vertical bar.

Fig. 7

Multiscale model of the nanoparticle targeted delivery process.

Fig. 8

Binding probabilities of a nanorod and a nanospheres at various cell-free layer thicknesses. (A–B) Binding probability of nanorod and nanosphere at shear rates of 10s⁻¹ and 2s⁻¹, respectively.

Fig. 9

Binding probabilities of nanosphere and nanorods of two different aspect ratios for CFL thickness of 5 μm.

Fig. A1

Meshes used in the simulation (a) Nanorod (b) Nanosphere (c) fluid channel.