Nanoparticle deposition to a cell transiting through a soft tissue: three-dimensional simulation and Lagrangian coherent structure dynamics.

We elucidate the role of time-invariant spatial attractors-repellers in segregating nano-suspensions around a tumour cell. A major challenge for targeted therapeutic drug delivery is the inadequate understanding of active nano-bio-separatrices at the delivery site. Using the lattice-Boltzmann-immersed-boundary method, first, we simulate the kinematics of a compound cell in a micro-vessel partly blocked by an invasive tissue and examine the stretching of its plasma membrane (PM) and nuclear envelope (NE) for varied nucleus size, capillary number and blockage hole. Second, we compute the trajectories of the suspended large number of inertial nanoparticles (NPs) in the vessel using a dynamical system approach. Third, we compute the particle Lagrangian coherent structures (pLCS) for the advecting NPs and identify the time-invariant geometric separatrices. The dominant attractive-repulsive pLCS effectually demarcates fluid regions from where NPs move closer/attach to the cell and from where NPs move away. Our study explains that delivering nanomedicine to a cell is feasible only through its stretched PM's high-tension rear side. The created repulsive pLCS barricades NPs from moving closer to a cell's PM's low-tension lateral/front sides. We thus unfold a universal separation behaviour of NPs around a cell. NP delivery rate increased for a larger capillary number and cell nucleus size. It decreased for heavier NPs and a cell stiffer nucleus/NE.