The objective of this work is to develop numerical tools useful for the understanding of fundamental phenomena in Blood Flow, including some biochemistry and cellular dynamics. An open problem that may benefit from multi-scale numerical tools is for example the understanding of the relation ship between inflammation and cholesterol plaque. The corresponding topics we address in this paper are (1) Heterogeneous Domain Decomposition for Multi-Scale Problem (2) Fluid-Structure Interaction in the Boundary Layer and (3) Immersed Boundary Method for the dynamic of cells (ref. C.Peskin et Al). In this present paper we concentrate on (1) and give preliminary results on (2) and (3) in the framework of heterogeneous domain decomposition.