Tobias Streubel^{1,2}, Leonie Klock^{3}, Martina Callaghan^{4}, Simone Kühn^{3,5}, Antoine Lutti^{6}, Karsten Tabelow^{7}, Nikolaus Weiskopf^{2}, Gabriel Ziegler^{8,9}, and Siawoosh Mohammadi^{1,2}

^{1}Institute for Systems Neuroscience, University Medical Center Hamburg-Eppendorf, Hamburg, Germany, ^{2}Department of Neurophysics, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany, ^{3}Department of Psychiatry and Psychotherapy, University Medical Center Hamburg-Eppendorf, Hamburg, Germany, ^{4}Wellcome Trust Centre for Neuroimaging, UCL Institute of Neurology, UCL, London, United Kingdom, ^{5}Center for Lifespan Psychology, Max Planck Institute for Human Development, Berlin, Germany, ^{6}Laboratory for Research in Neuroimaging, Department of Clinical Neuroscience, Lausanne, Switzerland, ^{7}Stochastic Algorithms and Nonparametric Statistics, Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany, ^{8}Institute of Cognitive Neurology and Dementia Research, Otto-von-Guericke-University, Magdeburg, Germany, ^{9}German Center for Neurodegenerative Diseases, Magdeburg, Germany

We introduced novel error maps for proton density, longitudinal relaxation and magnetization transfer saturation rates that are more sensitive to artifacts than previously used error measures. We showed that they can be used to identify and down weigh local errors in the quantitative parameter maps for an experiment consisting of two successive multi-parameter mapping (MPM) measurements in a group of 10 healthy subjects.

In this study, we introduce a method to calculate error maps that are sensitive to erroneous regions in the quantiatiave MPM maps (Fig.1). For correction of errors, we introduce a method to calculate a weighted average over repeated MPMs using voxel-based weights reflecting local parameter error.

1. Helms, G., Dathe, H. & Dechent, P. Quantitative FLASH
MRI at 3T using a rational approximation of the Ernst equation. Magn Reson
Med **59**, 667–672 (2008).

2. Weiskopf, N. et al. Quantitative
multi-parameter mapping of R1, PD*, MT and R2* at 3T: a multi-center
validation. Front. Neurosci. **7**:, 95 (2013).

3. Callaghan, M. F., Helms, G., Lutti, A.,
Mohammadi, S. & Weiskopf, N. A general linear relaxometry model of R1 using
imaging data. Magn Reson Med **73**, 1309–1314 (2015).

4. Ackenheil, M., Stotz-Ingenlath, G., Dietz-Bauer, R. & Vossen, A. MINI Mini International Neuropsychiatric Interview, German Version 5.0.0, DSM IV. Psychiatrische Universit{ä}tsklinik M{ü}nchen, Germany (1999) doi:10.1016/0968-0004(94)90058-2.

5. Lutti, A. et al. Robust and fast whole brain
mapping of the RF transmit field B1 at 7T. PLoS ONE **7**, e32379
(2012).

6. Frahm, J., Haase, A. & Matthaei, D.
Rapid three-dimensional MR imaging using the FLASH technique. J Comput
Assist Tomogr **10**, 363–368 (1986).

7. Tabelow, K. et al. hMRI – A
toolbox for quantitative MRI in neuroscience and clinical research. NeuroImage
**194**, 191–210 (2019).

8. Weiskopf, N., Callaghan, M. F.,
Josephs, O., Lutti, A. & Mohammadi, S. Estimating the apparent transverse
relaxation time (R2*) from images with different contrasts (ESTATICS) reduces
motion artifacts. Front. Neurosci **8**, 278 (2014).

Fig.1: Illustration of the
error maps (middle column), their dependence on the parameters from the gradient-recall
echo signal (first column, colored lines), and their sensitivity to artifacts
in MPM maps (third column, circles). The MT-error
map (top row) depends on S_{T1w}, S_{PDw},
and S_{MTw} at TE = 0,
as well as on the residuals $$$\epsilon_{T1w},\epsilon_{PDw}\,and\, \epsilon_{MTw}$$$.
In contrast, the
R_{1}-
(bottom row) and PD-
(middle row) error maps (dR_{1} and dPD),
depend on S_{T1w} and S_{PDw} at TE=0,
as well as on the residuals $$$\epsilon_{T1w}, \epsilon_{PDw}$$$ (blue and yellow lines)

Fig.2: Illustration
of the sensitivity of proposed error maps of MT on
artifacts due to subject motion and physiological variation. Depicted are: two
successive runs with superscript S1
and S2 (top row), the associated
error maps for each run (middle row), and their arithmetic mean and weighted
average with superscript am and wm (bottom row). An area is magnified
(red box, left column), where the error maps were sensitive to artifacts and
the weighted average contained less artificially increased values than the
arithmetic mean (circle).

Fig.3: Same
as Fig. 2 for PD maps.

Fig.4: Same
as Fig. 2 for R_{1} maps.

Fig.5: Variability
across subjects assessed by the standard-error-of-the-mean (*SEM*) for the quantitative MPM maps MT (top
row), PD (middle row) and R_{1} (bottom
row) illustrated for white matter. Depicted are (a, left to right): *SEM* maps for the arithmetic mean (AM) of 1^{st}
run (S_{1}) and 2^{nd} run (S_{2}); (b): the relative change of *SEM *(*rSEM*) with
respect to AM for S_{1},S_{2} and their weighted combination (WA); (c): *rSEM* across
white matter; (d): the group-averaged MPM maps. Regions showing improvement when
combining 1^{st} and 2^{nd} run were highlighted (blue: AM was
better, red: AM was worse).