  In this paper, we deploy a Lattice Boltzmann - Particle Dynamics (LBPD)
method to dissect the transport properties within arterioles and venules.
First, the numerical approach is applied to study the transport of Red Blood
Cells (RBC) through plasma and validated by means of comparison with the
experimental data in the seminal work by F{\aa}hr{\ae}us and Lindqvist. Then,
the presence of micro-scale, soft spheres within the blood flow is considered:
the evolution in time of the position of such spheres is studied, in order to
highlight the presence of possible \textit{margination} effects. The results of
the simulations and the evaluation of the computational eff
