Predicting the vascular adhesion of deformable drug carriers in narrow capillaries traversed by blood cell

In vascular targeted therapies, blood-borne carriers should realize sustained drug release from the luminal side towards the diseased tissue. In this context, such carriers are required to firmly adhere to the vessel walls for a sufficient period of time while resisting force perturbations induced by the blood flow and circulating cells. Here, a hybrid computational model, combining a Lattice Boltzmann (LBM) and Immersed Boundary Methods (IBM), is proposed for predicting the strength of adhesion of particles in narrow capillaries (7.5 $\mu \mathrm{m})$ traversed by blood cells. While flowing down the capillary, globular and biconcave deformable cells ( $7 \mu \mathrm{m}$ ) encounter $2 \mu \mathrm{m}$ discoidal particles, adhering to the vessel walls. Particles present aspect ratios ranging from $0.25$ to $1.0$ and a mechanical stiffness varying from rigid $(\mathrm{Ca}=0)$ to soft $\left(\mathrm{Ca}=10^{-3}\right)$. Cell-particle interactions are quantitatively predicted over time via three independent parameters: the cell membrane stretching $\delta p$; the cell-to-particle distance $r$, and the number of engaged ligand-receptor bonds $N_{\mathrm{L}}$.