  Recovering the T2 distribution from multi-echo T2 magnetic resonance (MR)
signals is challenging but has high potential as it provides biomarkers
characterizing the tissue micro-structure, such as the myelin water fraction
(MWF). In this work, we propose to combine machine learning and aspects of
parametric (fitting from the MRI signal using biophysical models) and
non-parametric (model-free fitting of the T2 distribution from the signal)
approaches to T2 relaxometry in brain tissue by using a multi-layer perceptron
(MLP) for the distribution reconstruction. For training our network, we
construct an extensive synthetic dataset derived from biophysical models in
order to constrain the outputs with \textit{a priori} knowledge of \textit{in
vivo} distributions. The proposed approach, called Model-Informed Machine
Learning (MIML), takes as input the MR signal and directly outputs the
associated T2 distribution. We evaluate MIML in comparison to non-parametric
and parametric approaches on synthetic data, an ex vivo scan, and
high-resolution scans of healthy subjects and a subject with Multiple
Sclerosis. In synthetic data, MIML provides more accurate and noise-robust
distributions. In real data, MWF maps derived from MIML exhibit the greatest
conformity to anatomical scans, have the highest correlation to a histological
map of myelin volume, and the best unambiguous lesion visualization and
localization, with superior contrast between lesions and normal appearing
tissue. In whole-brain analysis, MIML is 22 to 4980 times faster than
non-parametric and parametric methods, respectively.
