Simona Schiavi^{1}, Marco Pizzolato^{2}, Mario Ocampo-Pineda^{1}, Erick Canales-Rodriguez^{3,4}, Jean-Philippe Thiran^{2,3}, and Alessandro Daducci^{1}

Diffusion MRI connectometry is a widely used tool to investigate features of structural connectomes that reflect differences in white matter tracks integrity. It consists in averaging microstructural tissues properties (obtained from any voxel-wise map) along streamlines recovered with diffusion tractography. Nevertheless, the average of a microstructural measure is a weak information about an entire bundle. Using microstructure-informed tractography (COMMIT), we were able to simultaneously estimate fiber’s specific myelin water fraction, intra-axonal volume fraction, and g-ratio. We also computed new connectomes with bundles’ specific measures instead of the commonly used averages.

**Proposed approach.** The *Convex Optimization Modeling for Microstructure Informed Tractography* (COMMIT)^{2-4}
is a framework to complement tractography with additional microstructural
information about the neuronal tissue. Its originality lies in
the possibility to express tractography and tissue microstructure in a unified
formulation using convex optimization. The observation model is $$$\mathbf{y}=\mathbf{Ax}+\eta$$$, where the matrix $$$\mathbf{A}$$$ implements the specific multi-compartments model
adopted to characterize the neuronal tissue, $$$\mathbf{x}$$$ are the contributions that are needed to explain the input data $$$\mathbf{y}$$$ and $$$\eta$$$ represents noise. In this work, we implemented a simple forward-model that assigns a signal contribution to every streamline proportionally to its length inside each voxel. Our input data $$$\mathbf{y}$$$ includes both AVF and MWF maps, so the total amount of streamlines traversing a voxel must sum up to, simultaneously, the AVF and MWF values estimated in it. To estimate the individual AVF and MWF contributions of each streamline, while coupling their values, non-negative least-squares with *group
lasso regularization* can be used as in ^{4}: $$$\text{argmin}_{\mathbf{x}\geq 0}||\mathbf{Ax}-\mathbf{y}||_2^2+λ\sum_{g\in G}||\mathbf{x}^g||_2$$$.

**Experimental settings.** For illustrative purposes, we tested our proposed approach on a
synthetic phantom with two crossing bundles having different MWF and AVF intrinsic contributions (Figure 1). We also tested it on in-vivo data acquired on a healthy volunteer with a Philips 3T scanner.
We computed the connectivity matrices from the estimated MWF and AVF contributions of each bundle and compared them with the corresponding averaged values obtained with
connectometry.

This work was supported by the Rita Levi Montalcini Programme of the Italian Ministry of Education, University and Research (MIUR), as well as the Instituto de Salud Carlos III (Research project grant: PI15/00277 to ECR). Marco Pizzolato is supported by the Swiss National Science Foundation under grant number CRSII5_170873 (Sinergia project).

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Figure 1. Synthetic phantom used to illustrate and validate the proposed method. a) ground-truth configuration of bundles passing through five voxels and crossing in the middle
one; b) bundles’ specific values of myelin water fraction (MWF) and axonal
volume fraction (AVF); c) corresponding ground-truth voxel-wise maps of MWF and AVF.

Figure 2. Comparisons
of the results obtained with state-of-the-art connectometry, computing the
average of microstructural properties along the streamlines, and COMMIT, which instead decomposes each property in individual components associated to each streamline. As shown
in the bottom corner, the proposed method allows to correctly estimate the intra-axonal signal fraction and myelin fraction of each bundle, instead of assigning them an average value which may likely be biased.

Figure 3. In-vivo results obtained for one healthy subject. On the top row we show the
connectometry matrices for intra-axonal volume fraction (AVF), myelin volume
fraction (MWF) and g-ratio, on the bottom row the results of bundle’s specific
quantities of AVF, MWF and g-ratio estimated with COMMIT. We notice that the top
row appears to be flat over the bundles while in the bottom row we find
different values. The intra-hemispheric bundles result more myelinated. The
more myelinated inter-hemispheric bundle appears to be the anterior frontal
(zoom).

Figure 4. Histograms relative to the connectivity matrices of Figure 3. In the top row are shown the results obtained with diffusion MRI connectometry whereas in the bottom those of COMMIT.