Phase stability in fMRI time series: Effect of noise regression, off-resonance correction and spatial filtering techniques
Highlights
► Noise of the phase signal in EPI time series has specific spatiotemporal characteristics. ► Phase noise is mainly caused by respiration, heart-beat and scanner instabilities. ► Prior knowledge of physiology reduces noise but to a limited extent. ► Spatial high-pass filters efficiently remove low-spatial frequency phase noise. ► Results may improve phase based fMRI, ncMRI and thermography.
Introduction
Functional MRI studies are based on repeated acquisitions of Gradient Echo (GE) Echo-Planar-Imaging (EPI) image volumes in order to follow signal changes related to neuronal activity in time. Although the majority of fMRI studies exploit magnitude changes only, there is an increasing interest regarding the potential added information conveyed by the phase signal.
In general, there is a qualitatively important difference between phase and magnitude MRI signal changes. While phase changes will depend on the voxel-averaged magnetic field shift, the magnitude changes are dictated by the root-mean-square of the magnetic field variations. This means that if the voxel covers a single structure or if all structures inside the voxel have the same orientation, phase changes will build up while for voxels covering several structures with random orientations the phase effect will tend to cancel out. Magnitude changes on the other hand, will occur for both situations in GE-EPI. This principle is the basis for using fMRI phase changes to separate voxels dominated by large draining veins from voxels located in the parenchyma (Menon, 2002). More recently, Zhao et al., 2007, Feng et al., 2009 used the concept of the sphere of Lorentz to demonstrate that phase changes related to the bulk magnetic field variations of the BOLD effect may also occur. Statistical methods for the combined analysis of the two datasets have been proposed (Rowe, 2005, Rowe and Logan, 2004) and such effects may potentially aid to increase signal detection sensitivity in fMRI studies (Arja et al., 2010, Tomasi and Caparelli, 2007).
In neuronal current MRI (ncMRI) direct effects of neuronal activity is targeted by measurements of ultra-weak magnetic field changes that the neuronal currents evoke (Bodurka et al., 1999, Kamei et al., 1999). For evoked potentials, ncMRI phase changes are expected to outsize magnitude changes (Blagoev et al., 2007, Cassarà et al., 2008, Konn et al., 2003). Such changes have been reported in vitro (Petridou et al., 2006). Despite of this characteristic, experimental in vivo studies targeting evoked potentials mainly report on magnitude changes (Chow et al., 2006, Parkes et al., 2007, Xiong et al., 2003, Xue et al., 2009). Only in a few works that investigate spontaneous activity in the EEG alpha band by GE-EPI (Konn et al., 2004, Mandelkow et al., 2007) or evoked activity by spin echo EPI (Bianciardi et al., 2004) phase changes were investigated.
Methods for acquiring accurate phase measurements over time by GE-EPI sequences may also be of value for thermography (Cernicanu et al., 2008), and acquisition of single-shot GE-EPI time series has been proposed as a suitable method (Kickhefel et al., 2010). The success of such measurements will depend on the available temporal stability of the phase signal, since the temperature related magnetic field changes are limited and amount to 0.01 ppm/°C (Yablonskiy et al., 2000).
A shortcoming associated with the signal phase is its high sensitivity to unwanted signal fluctuations linked with physiology and scanner-related noise. These are generally more manifest in the phase than in the magnitude images and scale with the external magnetic field strength (Hagberg et al., 2008). In order to improve phase stability, several retrospective correction schemes have been proposed. In a study by Tomasi and Caparelli (2007), phase correction was performed by referencing the data to the first time-point in the time series. Similar results were obtained by simply unwrapping the phase in space and in time, followed by linear detrending of the data (Hagberg et al., 2008). Other techniques specifically aim to compensate the scan-to-scan off-resonance effects and use different ways of getting an estimate of the fluctuations. These techniques encompass the dynamic off-resonance in k-space (DORK) and the temporal off-resonance alignment of single-echo time series techniques (TOAST). In DORK, the global field-changes are estimated by the phase evolution of the central k-space point between subsequent TRs and then each read-out line is corrected in k-space assuming a linear phase accrual in time (Pfeuffer et al., 2002). In TOAST, phase rewinding is performed based on a voxel wise estimate of the B0 changes from the smoothed difference between the phase at each single time point and the average phase in the entire fMRI time series (Hahn et al., 2009). As an alternative, unwanted variations of physiologic origin can be removed by regression. Petridou et al. (2009) showed that targeted removal of breathing and heart beat related instabilities could be achieved by RETROICOR (Glover et al., 2000), however the efficiency of physiological noise removal varied with the voxel size and was still 20–50% higher than expected from the magnitude data.
These previous studies imply that fluctuations in the phase data will tend to outsize magnitude fluctuations. In order to elaborate on these findings, we investigated spatial patterns of frequency specific fluctuations and explored scanner and subject related effects. The efficiency for suppressing unwanted fluctuations was investigated for existing retrospective processing methods and compared with alternative approaches on a common set of data. In a first alternative approach (termed k-space nuisance variable regression, NVRk) we regressed the fMRI time series data with the phase evolution of the central k-space point. This value reflects the magnetic field offsets averaged across the image slice and is mainly affected by respiration-induced changes although cardiac pulsation also may contribute (Le and Hu, 1996, Van de Moortele et al., 2002, Wowk et al., 1997). The second approach is based on spatial high-pass filtering methods, of wide-spread use for anatomic phase imaging. Considering the low spatial frequency of most unwanted effects in the phase time series, we hypothesized that this kind of filters may prove beneficial for fMRI.
In practice, the phase and magnitude signal evolution were measured during resting-state conditions in healthy volunteers at 3 T using different voxel sizes and two temporal sampling frequencies (TR) in order to vary the magnitude signal-to-noise ratio (SNR) and to investigate temporal and spatial patterns of the phase noise. The physiologic noise model by Krüger and Glover (2001) that evaluates the relationship between the magnitude signal stability and the SNR0 at a single time point has been adapted to the phase signal as described in Hagberg et al. (2008). These models were used for fitting the experimental data for each retrospective processing method. We found that neither regression techniques nor off-resonance correction methods were able to reduce the signal fluctuations in the phase data to levels expected based on the magnitude stability. We also observed that the suppression efficiency depended not only on the spatial but also on the temporal sampling frequency. From the results it emerged that the dominating noise component in phase images had large-scale variations (estimated to exceed > 20 mm), and could be reduced by Gaussian high-pass filters as well as by an alternative, dynamically updated k-space spline filter technique.
Section snippets
Data acquisition
Magnitude and phase fMRI time series were acquired by a gradient echo single-shot 2D sequence with EPI read-out at 3 T (Allegra, Siemens Medical Systems) in 8 healthy subjects (26 ± 7y) that volunteered to participate in the study, approved by the local ethics review board. The subjects were scanned under resting conditions using a set of different fMRI protocols while placed in the standard birdcage transmit/receive coil at the center of the magnet bore, with dim lighting inside the RF-shielded
Results
Frequency specific fluctuations and their spatial patterns were explored on phantoms to evaluate scanner related effects on the phase time series. For the subjects, the frequencies for the respiration and cardiac beat cycles were identified by Fourier analysis of the physiological recordings. Voxel-wise Fourier analysis of the time series was performed to explore the spatial patterns in the corresponding frequency bands (Frequency specific noise sources section). Likewise, spatial patterns of
Discussion
There is an increasing interest in exploiting the phase information available in GE-EPI time series for fMRI studies, ncMRI and phase-based thermography. A general difficulty in these studies is the many unwanted effects that come with the phase signal and their temporal evolution. In the present study we investigated scanner-related and physiologic factors that influence the phase signal obtained by different temporal and spatial sampling schemes and evaluated several retrospective processing
Conclusion
We investigated the effect of scanner and physiological noise on the phase signal in fMRI time-series, acquired with varying voxel sizes and temporal sampling (TR). We found that B0 related effects with large length-scales have different effects on the phase and the magnitude data and we proposed methods for improving data stability. Although phase unwinding and noise regression based on the phase evolution in the central point of the k-space, combined with information from simultaneously
Acknowledgment
We would like to thank Fabio Cannata for assisting us with the data acquisition, Oliver Speck for the mosaic EPI sequence and Jesper L Andersson for valuable discussions.
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