Phase stability in fMRI time series: Effect of noise regression, off-resonance correction and spatial filtering techniques

Abstract

Although the majority of fMRI studies exploit magnitude changes only, there is an increasing interest regarding the potential additive information conveyed by the phase signal. This integrated part of the complex number furnished by the MR scanners can also be used for exploring direct detection of neuronal activity and for thermography. Few studies have explicitly addressed the issue of the available signal stability in the context of phase time-series, and therefore we explored the spatial pattern of frequency specific phase fluctuations, and evaluated the effect of physiological noise components (heart beat and respiration) on the phase signal. Three categories of retrospective noise reduction techniques were explored and the temporal signal stability was evaluated in terms of a physiologic noise model, for seven fMRI measurement protocols in eight healthy subjects at 3 T, for segmented CSF, gray and white matter voxels. We confirmed that for most processing methods, an efficient use of the phase information is hampered by the fact that noise from physiological and instrumental sources contributes significantly more to the phase than to the magnitude instability. Noise regression based on the phase evolution of the central k-space point, RETROICOR, or an orthonormalized combination of these were able to reduce their impact, but without bringing phase stability down to levels expected from the magnitude signal. Similar results were obtained after targeted removal of scan-to-scan variations in the bulk magnetic field by the dynamic off-resonance in k-space (DORK) method and by the temporal off-resonance alignment of single-echo time series technique (TOAST). We found that spatial high-pass filtering was necessary, and in vivo a Gaussian filter width of 20 mm was sufficient to suppress physiological noise and bring the phase fluctuations to magnitude levels. Stronger filters brought the fluctuations down to levels dictated by thermal noise contributions, and for 62.5 mm³ voxels the phase stability was as low as 5 mrad (0.27°). In conditions of low SNR_o and high temporal sampling rate (short TR); we achieved an upper bound for the phase instabilities at 0.0017 ppm, which is close to the dHb contribution to the GM/WM phase contrast.

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.