Model-based Analysis of Multishell Diffusion MR Data for Tractography: How to Get over Fitting Problems

In this article, we highlight an issue that arises when using multiple b-values in a model-based analysis of diffusion MR data for tractography. The non-monoexponential decay, commonly observed in experimental data, is shown to induce overfitting in the distribution of fiber orientations when not considered in the model. Extra fiber orientations perpendicular to the main orientation arise to compensate for the slower apparent signal decay at higher b-values. We propose a simple extension to the ball and stick model based on a continuous gamma distribution of diffusivities, which significantly improves the fitting and reduces the overfitting. Using in vivo experimental data, we show that this model outperforms a simpler, noise floor model, especially at the interfaces between brain tissues, suggesting that partial volume effects are a major cause of the observed non-monoexponential decay. This model may be helpful for future data acquisition strategies that may attempt to combine multiple shells to improve estimates of fiber orientations in white matter and near the cortex.