Complex and magnitude-only preprocessing of 2D and 3D BOLD fMRI data at 7 Tesla

Abstract

A challenge to ultra high field functional magnetic resonance imaging (fMRI) is the predominance of noise associated with physiological processes unrelated to tasks of interest. This degradation in data quality may be partially reversed using a series of preprocessing algorithms designed to retrospectively estimate and remove the effects of these noise sources. However, such algorithms are routinely validated only in isolation, and thus consideration of their efficacies within realistic preprocessing pipelines and on different data sets is often overlooked. We investigate the application of eight possible combinations of three pseudo-complementary preprocessing algorithms – phase regression, Stockwell transform filtering, and retrospective image correction (RETROICOR) – to suppress physiological noise in 2D and 3D functional data at 7 Tesla. The performance of each preprocessing pipeline was evaluated using data-driven metrics of reproducibility and prediction. The optimal preprocessing pipeline for both 2D and 3D functional data included phase regression, Stockwell transform filtering, and RETROICOR. This result supports the hypothesis that a complex preprocessing pipeline is preferable to a magnitude-only pipeline, and suggests that fMRI studies should retain complex images and externally monitor subjects’ respiratory and cardiac cycles so that these supplementary data may be used to retrospectively reduce noise and enhance overall data quality.

INTRODUCTION

Numerous preprocessing pipelines have been developed to improve the quality of data from blood oxygenation level dependent (BOLD) functional magnetic resonance imaging (fMRI) studies. Algorithms within these pipelines share the same broad goal: to identify and remove one or more sources of extraneous temporal variance (i.e., “noise”) while preserving genuine BOLD contrast related to the functional paradigm (i.e., “signal”) so that subsequent statistical analyses can reliably detect BOLD signal changes (1). Preprocessing steps commonly include k-space corrections and unaliased image reconstruction, slice timing correction, geometric unwarping, physiological noise correction, rigid-body motion correction, temporal filtering, spatial smoothing, and group alignment (1,2), and may also include de-noising based upon independent or principal component analysis (3–5). The ultimate task of optimizing the entire fMRI pipeline (data acquisition, processing, and analysis) is daunting and currently impossible due to the increase in required resources (scanner availability, storage space and/or computation time) for each variable permutation. Thus, current endeavors focus on one or a few steps with an implicit understanding that optimizing a subset of the pipeline is unlikely to result in a globally optimal fMRI pipeline. Furthermore, considering multiple steps simultaneously (e.g., 6–8,5,9–15) is methodologically preferable to evaluating algorithms individually and in isolation because the former approach permits investigations of interactions between sequential steps, thereby better characterizing the complexities of real pipelines.

It is well known that MRI data are inherently complex: each datum has a real and an imaginary part, and thus a magnitude and phase (16). Although many applications of anatomical imaging use only the magnitude component of reconstructed images, phase images contain unique and useful information that has been exploited for applications such as very low signal-to-noise ratio image detection (17), water/fat imaging (18), susceptometry (19), susceptibility weighted imaging (20), and tissue segmentation (21). Furthermore, phase image time courses have been characterized (22,23) and used to measure changes in venous blood oxygenation (24), detect activation from phase-only images (25), suppress BOLD signal contributions from large vessels (26,27), and improve the detection of genuine BOLD signal changes (28–30,12,31). It is therefore surprising that the use of magnitude-only images is still virtually ubiquitous in BOLD fMRI, and we hypothesize that a complex preprocessing pipeline that exploits magnitude and phase information is preferable to a conventional pipeline that uses only magnitude information.

As physiological noise has been shown to be the dominant noise source in high field fMRI (32–36), we elected to focus this study on three pseudo-complementary algorithms designed to mitigate the unwanted effects of physiological noise: retrospective image correction (“RETROICOR”) (37), Stockwell transform filtering (38), and phase regression (26,12). A brief description of each algorithm is provided below, and complete details may be found in the original references. Firstly, Glover et al. (37) proposed RETROICOR to reduce components of physiological noise attributed to respiration and cardiac pulsatility in data acquired with single-shot echo-planar imaging (EPI) (39,40). External monitors are used to detect the cardiac and respiratory cycles, and low order Fourier series are fit to the monitored waveforms and regressed from time series of magnitude data. Secondly, the Stockwell (S) transform of a one-dimensional time series provides an informative time-frequency representation that permits identification of higher frequency signal components (41). Goodyear et al. (38) proposed selective filtering in the S transform domain to suppress sporadic high frequency noise. Thirdly, since MR data are complex, Menon (26) proposed phase regression on a per-voxel basis to suppress BOLD signal changes from larger vessels and draining veins that can be several millimeters or more away from the site of neural activation (42). Barry et al. (12) investigated an alternative use of this algorithm to mitigate temporal variance from noise sources exhibiting correlated changes in magnitude and phase.

It would be prudent to also consider the limitations of the methods by which preprocessing algorithms are validated, and investigate plausible circumstances that may challenge their efficacies. For example, since the majority of fMRI data are acquired using 2D EPI, it follows that most algorithms have been validated using only 2D single-shot EPI data. Recent renewed interest in 3D multi-shot acquisition strategies (e.g., 43–46) to obviate challenges with EPI at higher fields suggests we reconsider whether algorithms validated using 2D EPI data at 1.5 or 3 Tesla will work just as well on 3D data and/or at ultra high (7+ Tesla) fields. Therefore, the goals of this paper are to use established data-driven metrics to (1) validate the efficacy of RETROICOR on highly multi-shot 3D functional data; (2) confirm the efficacies of S transform filtering and phase regression on ultra high field (7 Tesla) data; (3) investigate interactions between phase regression, S transform filtering, RETROICOR, and isotropic spatial smoothing; and (4) compare complex and magnitude-only preprocessing pipelines to determine if standard practices for acquiring 2D and/or 3D BOLD functional data should be updated to retain phase information whenever possible.

METHODS

Data Acquisition

Experiments were performed on a Philips Achieva 7T scanner with a quadrature transmit coil and 16-channel receive-only head coil. A complete description of the experimental setup and data acquisition may be found in Barry et al. (46), and a brief description is as follows. Twelve volunteers were studied under a protocol approved by the Vanderbilt University Institutional Review Board. The visual paradigm was a block design with four segments of 24 sec baseline (central fixation) and 24 sec activation (stationary 8 Hz flashing checkerboard wedge). Twelve slices (2 mm thick) were planned parallel to the calcarine sulcus with the shim volume situated to cover only the occipital lobe. Four functional runs were acquired alternating between 2D EPI and 3D PRESTO (Principles of Echo-Shifting with a Train of Observations) (47,48) with the following acquisition parameters: 2D EPI: voxel size = 2.19 × 2.19 × 2 mm³, TE = 28 ms, TR = volume acquisition time (VAT) = 2000 ms, θ = 87°, SENSE factor = 3.2, 96 volumes; 3D PRESTO: voxel size = 2.19 × 2.19 × 2 mm³, TE = 28 ms, TR = 22.22 ms, VAT = 1000 ms, θ = 12°, SENSE factor = 3.2, 192 volumes. Respiratory and cardiac cycles were monitored at a sampling frequency of 500 Hz using respiratory bellows (secured to the torso at the position of maximal deflection between inhalation and exhalation) and a pulse oximeter (placed on an index finger).

Preprocessing Steps

Matlab (MathWorks, Natick, MA) and AFNI (Analysis of Functional NeuroImages) (49) were used for all preprocessing steps. Stockwell transform filtering (ST) and phase regression (PR) were implemented in Matlab as described in the original papers, and RETROICOR (RI) was implemented using AFNI as described in the original paper. PR requires complex data as an input (and outputs magnitude-only data) whereas ST and RI are applied to magnitude-only data, so the two orders in which these three steps may be applied are: PR+ST+RI and PR+RI+ST. We hypothesized that ST and RI are approximately commutable operations (since ST removes aperiodic high-frequency noise and RI removes quasi-periodic low-frequency noise), and therefore excluded the latter permutation from further consideration to help control the overall computation time of the analyses. These three steps were either applied or not applied, resulting in 2³ = 8 preprocessing configurations before spatial smoothing: ‘none’, PR, ST, RI, PR+ST, PR+RI, ST+RI, and PR+ST+RI.

Data Processing

The workflow for data processing and analysis was automated using software written in Matlab. Binary masks were created for each functional run, and voxels included only in both masks (for each pair of runs) that were also within the shim volume were retained for subsequent analyses. In preparation for group analyses, data from each preprocessing configuration were spatially smoothed to compensate for anatomical and functional heterogeneities (50) and group alignment issues (51). Since maximal between-subject spatial variation along the posterior calcarine sulcus is ~2 cm in group space (52,53), we considered three full-width-at-half-maximum Gaussian spatial smoothing (SS) kernel widths for this study: (1) low=8 mm, as ~6–8 mm is typically used for group analyses; (2) high=16 mm, as this is close to the upper limit of expected between-subject spatial variation; and (3) medium=12 mm, as an intermediate value between 8 and 16 mm, which resulted in 8×3=24 preprocessing pipelines (12 magnitude-only and 12 using phase information).

NPAIRS

The quality of fMRI data was evaluated via metrics of prediction and reproducibility using NPAIRS^† (Non-parametric Prediction, Activation, Influence and Reproducibility re-Sampling) (54,55). Reproducibility (r ∈ [0,1]) measures the similarity (Pearson correlation coefficient) of activation maps generated from two independent data sets, and prediction (p ∈ [0,1]) evaluates the degree (e.g., posterior probability) to which a trained model can assign correct class labels to an independent test set. The current study implemented NPAIRS as described in Barry et al. (46) except that the split-half resampling procedure considered all possible splits (¹²C₆/2 = 462) for each PC range to generate the most accurate results possible for each analysis. Reported values for prediction and reproducibility are the medians across split-half samples for the range of inclusive PCs selected to jointly maximize prediction and reproducibility for each pipeline.

RESULTS

Figure 1 plots prediction vs. reproducibility for NPAIRS analyses of data acquired using (A) 2D EPI and (B) 3D PRESTO. Equal weight is given to prediction and reproducibility, so the Euclidean distance d from (p,r) to the ideal point at (p=1, r=1) is used as a scalar metric to quantify the overall performance of a given pipeline. Increasingly preferable pipelines are identified by decreasing d, and minimizing d is synonymous with identifying the optimal preprocessing steps for a given acquisition strategy. For 2D EPI data (Fig. 1A), comparisons of magnitude-only pipelines show that ST and RI in isolation (‘ST only’ or ‘RI only’) are preferable to (i.e., decreasing d) no physiological noise correction (‘none’) for all SS kernels, which confirms the original works (37,38) and is attributed primarily to increasing reproducibility. Low smoothing: ST, RI, and ST+RI demonstrate tradeoffs between small changes in p and r and all exhibit approximately the same d. Medium/high smoothing: RI is preferable to ST and ST+RI. The implementation of PR before other steps transforms pipelines from magnitude-only to complex, and decreases d in 11 of these 12 pipelines. The only pipeline exhibiting a slight increase in d after the inclusion of PR (caused by a slight decrease in r) is ‘none’ with SS=12 mm, which is presumably due to the predominance of suppression of BOLD activation from larger vessels. It should also be noted that pipelines without any physiological noise correction are included here for the sake of comparison, but are arguably less realistic because the use of at least one algorithm to reduce physiological noise is commonplace in fMRI analyses. Low smoothing: The preferable pipeline is PR+RI (d=0.252). Medium smoothing: The preferable pipeline is also PR+RI (d=0.229), although PR+ST is noteworthy in that it produces the highest overall prediction (p=0.846). High smoothing: The preferable pipeline is PR+ST+RI, which also has the highest reproducibility (r=0.899) and is the optimal 2D pipeline (d=0.220).

FIG. 1.

Plots of prediction vs. reproducibility (p,r) for NPAIRS analyses of images acquired using (A) 2D EPI and (B) 3D PRESTO. In theory, an analysis of noiseless fMRI data with a perfect model would map to the point (1,1). Concentric dotted curves mark points that are equidistant to (1,1), and the dashed line marks equal prediction and reproducibility (p = r). As defined in the legend [none = no preprocessing, PR = phase regression, ST = Stockwell transform filtering, RI = RETROICOR], each ‘x’ represents a magnitude-only pipeline, and the ‘o’ of the same color and size represents that pipeline with PR. The size of each symbol represents the degree of spatial smoothing (SS) that was applied in preparation for group analyses (small → SS = 8 mm FWHM; medium → SS = 12 mm FWHM; and large → SS = 16 mm FWHM).

Analyses of magnitude-only 3D PRESTO data (‘x’s in Fig. 1B) demonstrate similar benefits of physiological noise correction across SS kernels, with 8 of 9 magnitude-only pipelines demonstrating a decrease in d compared to no physiological noise correction (the sole exception being ST with SS=8mm). Low/medium/high smoothing: ST+RI is identified as the most preferable magnitude-only pipeline across SS kernels. As before, the implementation of PR before other steps transforms pipelines from magnitude-only to complex (‘o’s in Fig. 1B). The three pipelines without physiological noise correction exhibit increasing d after the inclusion of PR, which is, as previously stated, most likely due to the predominance of suppression of BOLD activation from larger vessels. Of the remaining 9 pipelines (ST, RI, and ST+RI for each SS kernel), the inclusion of PR decreases d in 4 pipelines, is unchanged in 2 pipelines, and increases d in 3 pipelines (PR+ST across SS kernels). Low smoothing: The preferable pipeline is PR+ST+RI (d=0.363). Medium smoothing: The ST+RI and PR+ST+RI pipelines are equivalently preferable (d=0.326). High smoothing: The preferable pipeline is PR+ST+RI, which also has the highest reproducibility (r=0.864) and is the optimal 3D pipeline (d=0.318).

These results may be summarized in three succinct points: (1) if only one of these three algorithms could be implemented to reduce physiological noise, then RETROICOR would be the best choice; (2) enhanced suppression of physiological noise is consistently achieved when phase regression precedes RETROICOR; and (3) further reduction in physiological noise may also be possible by implementing S transform filtering between phase regression and RETROICOR.

DISCUSSION

This brief report explores the dependence of physiological noise suppression on a priori decisions that pertain to data acquisition and monitoring. If MR data are magnitude-only and physiological monitoring equipment is not used (or not available), then only 2 (‘none’, ST) of the 8 configurations may be considered; if MR data are magnitude-only but physiological processes are monitored, then 4 configurations are possible (‘none’, ST, RI, ST+RI); if complex data are retained but physiological processes are not monitored, then 4 configurations are also possible (‘none’, PR, ST, PR+ST); and only if both complex data are retained and physiological processes are monitored are all 8 configurations possible. Our finding that every preferable configuration (for each spatial scale) included phase regression and RETROICOR highlights the importance of retaining complex data and externally monitoring subjects’ respiratory and cardiac cycles to improve overall data quality. Furthermore, the fact that the optimal configuration for both 2D and 3D functional data was PR+ST+RI also reinforces the importance of investigating possible synergistic interactions between algorithms when designing a preprocessing pipeline.

Each preprocessing pipeline was evaluated using data-driven metrics of reproducibility and prediction, and the Euclidean distance d from coordinates (p,r) (generated from an NPAIRS analysis) to the ideal point at (1,1) succinctly quantified the overall pipeline performance. This framework was used to both validate the application of RETROICOR on highly multi-shot 3D PRESTO data and confirm the efficacies of S transform filtering and phase regression for use on ultra high field data. However, systematic differences in the relative shifts of (p,r) points are observed between Figs. 1A (2D EPI) and 1B (3D PRESTO), suggesting a divergence in the efficacies of PR and ST that is logically attributed to the chosen acquisition sequence. For example, EPI data processed with only PR and/or ST (i.e., ST, PR, and PR+ST for each SS kernel) decreased d in 8 of these 9 pipelines relative to ‘none’ (with the exception being PR with SS=12 mm). In comparison, PRESTO data processed with only PR and/or ST decreased d in 3 (ST with SS=12 mm and SS=16 mm, and PR+ST with SS=16 mm) of these 9 pipelines relative to ‘none’; however, the addition of RI to the remaining 6 pipelines decreased d in all cases relative to the respective pipelines without RI (e.g., ST+RI vs. ST with SS=8mm), and also to beyond what was possible with ‘RI only’ in 5 of 6 instances (whilst the sixth comparison, PR+RI vs. RI only with SS=12 mm, had equivalent d=0.332). As previously mentioned, PR and ST were applied to 2D EPI and 3D PRESTO data in identical fashions exactly as described in the original papers. However, these algorithms were developed and validated using EPI data, and 2D EPI data is known to have markedly different signal and noise characteristics compared to 3D PRESTO data (43), so it is plausible that such divergent efficacies may be attributed to suboptimal implementations on 3D functional data. Thus, avenues for future work include further investigations of how the optimal application of such algorithms may differ between 2D and 3D functional data sets.

In conclusion, we have investigated the implementation of eight preprocessing configurations using three pseudo-complementary algorithms – phase regression, S transform filtering, and RETROICOR – to retrospectively suppress physiological noise in 2D and 3D functional data at 7T. Whereas S transform filtering may be applied to any fMRI data set, phase regression may only be applied if complex images are retained and RETROICOR may only be applied if subjects’ cardiac and respiratory cycles are externally monitored. The performance of each preprocessing pipeline was evaluated using data-driven NPAIRS metrics of prediction and reproducibility, which facilitated an unbiased comparison between competing preprocessing strategies. The preferable configuration for each spatial scale always included phase regression and RETROICOR, and the optimal preprocessing pipeline for both 2D EPI and 3D PRESTO data included phase regression, S transform filtering, and RETROICOR. These results support the hypothesis that a complex preprocessing pipeline is preferable to a magnitude-only pipeline, and suggest that fMRI studies should routinely retain complex images and externally monitor subjects’ physiological cycles so that these supplementary data are available to retrospectively reduce noise and enhance overall data quality. Future work will extend the application of various preprocessing algorithms to other 2D and 3D functional data sets, as well as investigate the dual role of phase regression in suppressing macrovascular BOLD signals and extraneous noise sources in single-subject fMRI analyses.