Abstract-Tractography is a class of algorithms aiming at invivo mapping the major neuronal pathways in the white matter from diffusion MRI data. These techniques offer a powerful tool to noninvasively investigate at the macroscopic scale the architecture of the neuronal connections of the brain. However, unfortunately, the reconstructions recovered with existing tractography algorithms are not really quantitative even though diffusion MRI is a quantitative modality by nature. As a matter of fact, several techniques have been proposed in recent years to estimate, at the voxel level, intrinsic microstructural features of the tissue, such as axonal density and diameter, by using multicompartment models. In this article, we present a novel framework to reestablish the link between tractography and tissue microstructure. Starting from an input set of candidate fiber-tracts, which are estimated from the data using standard fiber-tracking techniques, we model the diffusion MRI signal in each voxel of the image as a linear combination of the restricted and hindered contributions generated in every location of the brain by these candidate tracts. Then, we seek for the global weight of each of them, i.e. the effective contribution or volume, such that they globally fit the measured signal at best. We demonstrate that these weights can be easily recovered by solving a global convex optimization problem and using efficient algorithms. The effectiveness of our approach has been evaluated both on a realistic phantom with known ground-truth and in-vivo brain data. Results clearly demonstrate the benefits of the proposed formulation, opening new perspectives for a more quantitative and biologically-plausible assessment of the structural connectivity of the brain.

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One of the major limitations of diffusion MRI tractography is that the fiber tracts recovered by existing algorithms are not truly quantitative. Local techniques for estimating more quantitative features of the tissue microstructure exist, but their combination with tractography has always been considered intractable. Recent advances in local and global modeling made it possible to fill this gap and a number of promising techniques for microstructure informed tractography have been suggested, opening new and exciting perspectives for the quantification of brain connectivity. The ease-of-use of the proposed solutions made it very attractive for researchers to include such advanced methods in their analyses; however, this apparent simplicity should not hide some critical open questions raised by the complexity of these very high-dimensional problems, otherwise some fundamental issues may be pushed into the background. The aim of this article is to raise awareness in the diffusion MRI community, notably researchers working on brain connectivity, about some potential pitfalls and modeling choices that make the interpretation of the outcomes from these novel techniques rather cumbersome. Through a series of experiments on synthetic and real data, we illustrate practical situations where erroneous and severely biased conclusions may be drawn about the connectivity if these pitfalls are overlooked, like the presence of partial/missing/duplicate fibers or the critical importance of the diffusion model adopted. Microstructure informed tractography is a young but very promising technology, and by acknowledging its current limitations as done in this paper, we hope our observations will trigger further research in this direction and new ideas for truly quantitative and biologically meaningful analyses of the connectivity.

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