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Particle deposition in the small bronchial tubes (generations six through twelve) is strongly influenced by the vortex-dominated secondary flows that are induced by axial curvature of the tubes. In this paper, we employ particle destination maps in conjunction with two-dimensional, finite-time Lyapunov exponent maps to illustrate how the trajectories of finite-mass particles are influenced by the presence of vortices. We consider two three-generation bronchial tube models: a planar, asymmetric geometry and a non-planar, asymmetric geometry. Our visualizations demonstrate that these techniques, coupled with judiciously seeded particle trajectories, are effective tools for studying particle/flow structure interactions.