Reliable selection of the number of fascicles in diffusion images by estimation of the generalization error

A number of diffusion models have been proposed to overcome the limitations of diffusion tensor imaging (DTI) which cannot represent multiple fascicles with heterogeneous orientations at each voxel. Among them, generative models such as multi-tensor models, CHARMED or NODDI represent each fascicle with a parametric model and are of great interest to characterize and compare white matter properties. However, the identification of the appropriate model, and particularly the estimation of the number of fascicles, has proven challenging. In this context, different model selection approaches have been proposed to identify the number of fascicles at each voxel. Most approaches attempt to maximize the quality of fit while penalizing complex models to avoid overfitting. However, the choice of a penalization strategy and the trade-off between penalization and quality of fit are rather arbitrary and produce highly variable results. In this paper, we propose for the first time to determine the number of fascicles at each voxel by assessing the generalization error. This criterion naturally prevents overfitting by comparing how the models predict new data not included in the model estimation. Since the generalization error cannot be directly computed, we propose to estimate it by the 632 bootstrap technique which has low bias and low variance. Results on synthetic phantoms and in vivo data show that our approach performs better than existing techniques, and is robust to the choice of decision threshold. Together with generative models of the diffusion signal, this technique will enable accurate identification of the model complexity at each voxel and accurate assessment of the white matter characteristics.