  Purpose: The impact of microscopic diffusional kurtosis ($\mu K$) - arising
from restricted diffusion and/or structural disorder - remains a controversial
issue in contemporary diffusion MRI (dMRI). Recently, Correlation Tensor MRI
(CTI) was introduced to disentangle the sources contributing to diffusional
kurtosis, without relying on a-priori assumptions. Here, we aimed to
investigate $\mu K$ in in vivo rat brains and assess its impact on
state-of-the-art methods ignoring $\mu K$. Methods: CTI harnesses double
diffusion encoding (DDE) experiments, which were here improved for speed and
minimal bias using four different sets of acquisition parameters. The
robustness of CTI estimates from the improved protocol is assessed in
simulations. The in vivo CTI acquisitions were performed in healthy rat brains
using a 9.4T pre-clinical scanner equipped with a cryogenic coil, and targeted
the estimation of $\mu K$, anisotropic kurtosis, and isotropic kurtosis.
Results: The improved CTI acquisition scheme substantially reduces scan time
and importantly, also minimizes higher-order-term biases, thus enabling robust
$\mu K$ estimation, alongside Kaniso and Kiso metrics. Our CTI experiments
revealed positive $\mu K$ both in white and grey matter of the rat brain in
vivo; $\mu K$ is the dominant kurtosis source in healthy grey matter tissue.
The non-negligible $\mu K$ substantially biases prior state-of-the-art analyses
of Kiso and Kaniso. Conclusion: Correlation Tensor MRI offers a more accurate
and robust characterization of kurtosis sources than its predecessors. $\mu K$
is non-negligible in vivo in healthy white and grey matter tissues and could be
an important biomarker for future studies. Our findings thus have both
theoretical and practical implications for future experiments.
