White matter (WM) fiber tractography (i.e., the reconstruction of the 3D architecture of WM fiber pathways) is known to be an important application of diffusion tensor magnetic resonance imaging (DT-MRI). For the quantitative evaluation of several fiber-tracking properties, such as accuracy, noise sensitivity, and robustness, synthetic ground-truth DT-MRI data are required. Moreover, an accurate simulated phantom is also required for optimization of the user-defined tractography parameters, and objective comparisons between fiber-tracking algorithms. Therefore, in this study a mathematical framework for simulating DT-MRI data, based on the physical properties of WM fiber bundles, is presented. We obtained a model of a WM fiber bundle by parameterizing the various features that characterize this bundle. We then evaluated three different synthetic DT-MRI models using experimental data in order to test the proposed methodology, and to determine the optimum model and parameter settings for constructing a realistic simulated DT-MRI phantom. Several examples of how the mathematical framework can be applied to compare fiber-tracking algorithms are presented.
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