Diffusion MRI is a non-invasive method that potentially gives insight into the brain's white matter structure regarding the pathway of connections and properties of the axons. Here, we propose a novel global tractography method named Plausibility Tracking that provides the most plausible pathway, modeled as a smooth spline curve, between two locations in the brain. Compared to other tractography methods, Plausibility Tracking combines the more complete connectivity pattern of probabilistic tractography with smooth tracks that are globally optimized using the fiber orientation density function and hence is relatively robust against local noise and error propagation. It has been tested on phantom and biological data and compared to other methods of tractography. Plausibility Tracking provides reliable local directions all along the fiber pathways which makes it especially interesting for tract-based analysis in combination with direction dependent indices of diffusion MRI. In order to demonstrate this potential of Plausibility Tracking, we propose a framework for the assessment and comparison of diffusion derived tissue properties. This framework comprises atlas-guided parameterization of tract representation and advanced bundle-specific indices describing fiber density, fiber spread and white matter complexity. We explore the new method using real data and show that it allows for a more specific interpretation of the white matter's microstructure compared to rotationally invariant indices derived from the diffusion tensor.