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Physiological noise removal in fast fMRI without separate physiological signal acquisition
Uday Agrawal1, Emery Brown1,2,3,4, and Laura Lewis5,6,7

1Harvard-MIT Division of Health Sciences and Technology (HST), Cambridge, MA, United States, 2Department of Anesthesia, Critical Care and Pain Medicine, Massachusetts General Hospital, Harvard Medical School, Boston, MA, United States, 3Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, MA, United States, 4Institute for Medical Engineering and Science, Massachusetts Institute of Technology, Cambridge, MA, United States, 5Department of Biomedical Engineering, Boston University, Boston, MA, United States, 6Department of Radiology, Harvard Medical School, Boston, MA, United States, 7Athinoula A. Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital, Boston, MA, United States

Synopsis

Recent work has shown that commonly used methods to account for physiological noise and serial correlations in conventional fMRI are inadequate for fast (TR<500 ms) fMRI and may lead to incorrect inferences1. We created a model of physiological noise based on harmonic regression with autoregressive noise that utilizes the enhanced sampling of fast fMRI to estimate physiological noise directly from the fMRI data; therefore, it does not require physiological reference signals such as respiration. We found that our model performs as well as gold standard reference-based approaches in removing physiological noise and improves the detection of task-driven fMRI activity.

Introduction

Technological advances in acquisition protocols have enabled an order of magnitude increase in the speed of fMRI measurements2–7. While this new, “fast” fMRI has enormous potential for neuroscientists, the scaling of physiological noise with the improved resolution of fast fMRI limits its applicability8,9. Commonly used pre-whitening and physiological noise regression techniques in conventional fMRI are insufficient to account for serial correlations in fast fMRI, which may lead to errors in interpretation of the fMRI signal1,10. Here we propose a statistical framework that can accurately detect physiological noise sources and separate them from the neurally-driven hemodynamic signal in fast fMRI. Importantly, our approach leverages the enhanced temporal resolution to sample physiological noise directly from the fMRI data, and obviates the need for physiological reference signals (e.g. respiratory belt), which can be technically challenging to collect.

Methods

Prior literature and visual inspection of fast fMRI time-series suggest that physiological noise is associated with periodic cardiac and respiratory activity (Figure 1)11. In contrast to conventional fMRI, the temporal resolution of fast fMRI allows direct observation of typical cardiac and respiratory frequencies. Based on these observations and similar models12,13, we designed a model of Harmonic Regression with Autoregressive Noise (HRAN) and an efficient algorithm to compute the maximum likelihood parameter estimates (Figure 2). We first evaluated HRAN performance in a simulated fast fMRI response to a 0.1 Hz stimulus with added cardiac noise (simulated as a 1 Hz sinusoid) and respiratory noise (simulated as a 0.3 Hz sinusoid with one harmonic). Next, we examined HRAN performance in fast resting-state fMRI data collected with physiological reference signals (TR = .367s, 2.5 x 2.5 x 2.5 mm3, 5mm FWHM Gaussian smoothing). Physiological frequency estimates were derived from the mean time series of the 4th ventricle and compared to those obtained from the physiological reference signals. Optimal parameter orders were obtained using the Bayesian Information Criterion (BIC). In the same dataset, the lowest required AR order to remove autocorrelation in each voxel was determined in models with a) no physiological regression, b) physiological regression derived from the fast fMRI data directly using HRAN, and c) physiological regression derived from reference signals using RETROICOR11. Autocorrelations were assessed using the Ljung-Box-Q test. Finally, we evaluated the impact of HRAN on signal detection in a fast fMRI experiment with a 0.1 Hz oscillating visual stimulus for 24s where no reference data was collected (TR = .227s, 2 x 2 x 2 mm3, 5mm FWHM Gaussian smoothing). We derived physiological regressors using HRAN on the left lateral ventricle. We then utilized FSL (fsl.fmrib.ox.ac.uk/fsl/fslwiki/) to obtain activation maps with and without physiological noise removal.

Results

In a simulated fast fMRI signal driven by a 0.1 Hz stimulus, HRAN was able to estimate and remove the added physiological noise (Fig 3A,B) and reduce the root mean squared error. In resting-state fast fMRI data, we found that the estimated physiological frequencies derived from the 4th ventricle accurately tracked the average heart rate and respiration rate obtained from the EKG and respiratory belt (Figure 3C,D). HRAN also satisfied goodness of fit criteria with model parameters determined using BIC (Figure 3E). At the single-voxel level, HRAN reduced autocorrelations in the residuals as effectively as RETROICOR (Figure 4A), with greatest impact in gray matter (Figure 4B,C). In a fast fMRI experiment with a 0.1 Hz visual stimulus, HRAN was able to estimate physiological frequencies from the lateral ventricle and improve detection of visually-driven voxels, as compared to standard FSL analysis (Figure 5A-C). For example, in one exemplar voxel, physiological noise modelling with HRAN reduced the residual variance by 56%, enabling detection with a voxel-wise corrected threshold of p < .05 (Figure 5D-F).

Discussion

We found that HRAN is able to accurately estimate physiological frequencies using the fast fMRI data directly and satisfies model goodness of fit criteria. HRAN is as effective as removing autocorrelation as commonly employed techniques such as RETROICOR, while estimating these noise patterns directly from the data itself. These findings suggest that HRAN is able to successfully remove physiological noise from fast fMRI and account for autocorrelation, increasing the accuracy of subsequent statistical analyses.

Conclusion

Our model is able to estimate and remove physiological noise from fast fMRI data without the need for physiologic reference signals. Capturing serial correlations using the HRAN framework will not only help to improve interpretations of future fast fMRI experiments, but also help to guide researchers in prospective experimental design. Future work includes implementing time-varying parameter estimates, either by extending our model using state space approaches or incorporating dynamic models such as DRIFTER14.

Acknowledgements

This work was funded by NIH grants K99-MH111748, S10-RR023401, and S10-RR023403. Uday Agrawal is a Howard Hughes Medical Institute Medical Research Fellow.

References

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9. Triantafyllou, C. et al. Comparison of physiological noise at 1.5 T, 3 T and 7 T and optimization of fMRI acquisition parameters. Neuroimage26,243–250 (2005).

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11. Glover, G. H., Li, T. Q. & Ress, D. Image-based method for retrospective correction of physiological motion effects in fMRI: RETROICOR. Magn. Reson. Med.44,162–167 (2000).

12. Krishnaswamy, P. et al. Reference-free removal of EEG-fMRI ballistocardiogram artifacts with harmonic regression. Neuroimage128,398–412 (2016).

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14. Särkkä, S. et al. Dynamic retrospective filtering of physiological noise in BOLD fMRI: DRIFTER. Neuroimage60,1517–1527 (2012).

Figures

Physiological noise is sampled directly in fast fMRI. (A) Spectrogram of mean time series in 4th ventricle (TR = .367s) shows high power in both low-frequency respiratory (0 - 0.4 Hz) and high-frequency cardiac (0.8 – 1.2 Hz) bands. Rectangle indicates 15s of data plotted as time series on the right. (B) fMRI time series from the ventricle (black) has low frequency oscillations with same period as respiratory reference signal (respiratory belt, blue) and high frequency oscillations with same period as cardiac reference signal (electrocardiogram, red). Shaded regions indicate one period of respiratory and cardiac oscillations in respective colors.

Model Structure. (Top) We modeled the fMRI signal as the sum of respiratory and cardiac signals represented by a harmonic regression model, a neurally-driven signal represented by a baseline term plus the convolution of the neural stimulus with an appropriate hemodynamic response function, and autoregressive noise of order P. (Bottom) Maximum likelihood parameter estimates are obtained efficiently using a cyclic descent algorithm, as in12,13. In brief, autoregression parameters are iteratively updated with harmonic regression estimates, and vice versa, for given physiologic frequencies. The process is then optimized across a range of plausible cardiac and respiratory frequencies.

HRAN accurately estimates physiological frequencies. (A) Simulated fMRI data as described in Methods. (B) HRAN removed simulated physiological noise and reduced the root mean squared error (RMSE). (C) Spectrogram of mean time series in 4th ventricle (TR = .367s). (D) Physiological frequency estimates obtained from the 4th ventricle with HRAN tracked the heart rate and respiration rate obtained from reference signals. (E) HRAN separated the data into AR noise, physiological noise, and residual components. The residual remained within the 95% CI of ideal white noise (with 1 cardiac harmonic, 1 respiratory harmonic, and 2 AR terms), demonstrating goodness of fit.

HRAN removes autocorrelation as well as RETROICOR without the need for physiological reference signals. (A) For each voxel, 24 seconds of data were fit to a model with either i) no physiological regression, ii) HRAN, or iii) RETROICOR. Autocorrelations were assessed using the Ljung-Box-Q test. (B,C) The cumulative proportions of required AR model orders were plotted in gray matter and white matter across the three conditions. As expected, gray matter contains the largest autocorrelations, and our method successfully removes them. The shaded region indicates the standard deviation across 6 consecutive time segments.

Physiological noise regression using HRAN alters activation maps. Activation maps for a fast fMRI experiment with a .1 Hz neural stimulus (TR = .227 Hz) were obtained using standard FSL settings (including pre-whitening) with (A) no physiological noise modelling and (B) physiological noise modelling using HRAN. (C) The difference between methods shows that HRAN increases z-scores for the visual activation specifically in visual cortex. (D-F) Removing physiological noise reduces the residual variance in an exemplar voxel (voxel with dark border) by 56%, enabling voxel-wise corrected detection with p < .05.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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