The design of components for inertial microfluidic focusing and separation is primarily designed from basic geometric primitives. This paper presents a topology optimization methodology to the design synthesis of microfluidic particle manipulators. The flow is modeled by the Navier-Stokes equations in an Eulerian frame while the particle transport is modeled as a Lagrangian particle model. The model assumes that the particles are small and the suspension is dilute such that both the particle influence on the fluid motion and collisions between particles can be neglected. Two manipulator design problems are studied—one that makes particles follow a predefined trajectory, and another where particles are focused at the outlet utilizing the inertia of the particles. The latter is extracted and post-analyzed using a commercial software COMSOL verifying the method’s ability to synthesize inertial microfluidic components.