Saskia Bollmann^{1}, Alexander Puckett^{2}, Ross Cunnington^{2}, and Markus Barth^{1}

We investigated the influence of physiological noise on statistical inference in fMRI at the single-subject level. By comparing two SMS sequences with a short and a long TR, we explored the interaction between repetition time, physiological noise modelling and the autoregressive model used to characterize serial correlations in fMRI data. Using variational Bayesian inference, we found that fMRI acquisitions with a short TR require accurate modelling of cardiac and respiratory processes to successfully remove serial correlations from the fMRI time series. For the SMS sequence with a longer TR, the standard AR model of order 1 proved sufficient.

We would like to thank Will Penny for helpful advice on the interpretation of the variational Bayesian inference results.

MB acknowledges funding from ARC Future Fellowship grant FT140100865. The authors acknowledge the facilities of the National Imaging Facility at the Centre for Advanced Imaging, University of Queensland and the scientific support of Siemens Ltd, Bowen Hills, Australia.

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Table 1: Overview of
acquisition parameters.

Figure
1:
Optimal AR model order for the short-TR sequence exemplarily depicted on 4
equidistant, axial slices across the brain from subject 01 without
physiological noise modelling (left), including RETROICOR regressors (centre), and
including RETROICOR and respiratory and cardiac response function regressors
(right). A considerable reduction in the required AR model order from up to 10
to around 4 can be observed when including RETROICOR regressors in the model
estimation. Including RRF and CRF regressors reduced the required model order
more locally, as indicated by the white arrows.

Figure
2:
Optimal AR model order for the long-TR sequence exemplary depicted on 4
equidistant, axial slices across the brain from subject 01 without
physiological noise modelling (left), including RETROICOR regressors (centre),
and including RETROICOR and respiratory and cardiac response function
regressors (right). In general, the optimal AR model order is lower compared to
the short-TR sequence. However, higher optimal model orders mainly in CSF
bearing regions can be reduced when including RETROICOR regressors, as
indicated by the white arrows.

Log
Bayes factor comparing the model evidence exemplary depicted on 4 equidistant,
axial slices across the brain from subject 01 for an AR model of order 4 to an
AR model of order 1 when including RETROICOR, RRF and CRF regressors. Positive
up to strong evidence for an AR(4)-model was found in large areas of the brain
for the short-TR sequence (left). In some white matter voxel, positive evidence
for AR(1) was observed. In contrast, no evidence for an AR(4)-model, but
positive evidence for an AR(1)-model was found in large areas for the long-TR
sequence (right).

Figure
4:
Distribution of optimal AR model orders in three different tissue classes for
the short-TR (top) and the long-TR (bottom) sequence. Mean and standard
deviation across subjects are depicted in solid and dotted lines, respectively.
Without physiological noise modelling, white matter showed the lowest
optimal AR model, CSF the highest and grey matter voxel range in-between.
For the short-TR sequence, physiological noise modelling successfully reduced
the required model order such that the majority of grey matter voxel lie
between order 2 to 4. For the long-TR sequence, the majority of voxel had an
optimal AR model order of 1.