Mathematical framework for simulating diffusion tensor MR neural fiber bundles

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Abstract
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. Magn Reson Med 53:944–953, 2005.