A wavelet method for modeling and despiking motion artifacts from resting-state fMRI time series

Abstract

The impact of in-scanner head movement on functional magnetic resonance imaging (fMRI) signals has long been established as undesirable. These effects have been traditionally corrected by methods such as linear regression of head movement parameters. However, a number of recent independent studies have demonstrated that these techniques are insufficient to remove motion confounds, and that even small movements can spuriously bias estimates of functional connectivity. Here we propose a new data-driven, spatially-adaptive, wavelet-based method for identifying, modeling, and removing non-stationary events in fMRI time series, caused by head movement, without the need for data scrubbing. This method involves the addition of just one extra step, the Wavelet Despike, in standard pre-processing pipelines. With this method, we demonstrate robust removal of a range of different motion artifacts and motion-related biases including distance-dependent connectivity artifacts, at a group and single-subject level, using a range of previously published and new diagnostic measures. The Wavelet Despike is able to accommodate the substantial spatial and temporal heterogeneity of motion artifacts and can consequently remove a range of high and low frequency artifacts from fMRI time series, that may be linearly or non-linearly related to physical movements. Our methods are demonstrated by the analysis of three cohorts of resting-state fMRI data, including two high-motion datasets: a previously published dataset on children (N=22) and a new dataset on adults with stimulant drug dependence (N=40). We conclude that there is a real risk of motion-related bias in connectivity analysis of fMRI data, but that this risk is generally manageable, by effective time series denoising strategies designed to attenuate synchronized signal transients induced by abrupt head movements. The Wavelet Despiking software described in this article is freely available for download at www.brainwavelet.org.

Keywords: Artifact; Connectivity; Despike; Motion; Non-stationary; Resting-state; Spike; Wavelet; fMRI.

Graphical abstract

Fig. S1

Effects of different regression models on distance-dependent connectivity artifacts. (A) The effect of different regression models (x-axis) on estimates of distance-dependent connectivity bias in cohort 1. For each regression model, the coefficient of determination, r², was computed for the relationship between inter-region distance and ∆R, from the ∆R plot (see the Distance-dependent movement artifact diagnostics section) [where Mot = 6 motion parameters; Motd = first order derivatives of Mot; CSF = ventricular cerebrospinal fluid signal; WM = white matter signal; GS = global signal]. Each of the three regression models was applied in two different pre-processing scenarios, represented as two lines: band-pass filtering followed by linear regression (upper); Time Despike, regression, then band-pass filtering (lower). (B) Group-level ∆R plots for the two pre-processing/regression model combinations highlighted in (A): the first, where 12 motion parameters, CSF signal, white matter signal, and global signal were regressed after Fourier filtering of time series; and the second, where 12 motion parameters plus CSF signal were regressed after Fourier filtering. The former produced a stronger relationship between distance and connectivity compared to where white matter signal and global signal were not regressed.

Fig. S2

Full image and time series processing pipeline. This figure highlights the key pre-processing steps, in the order they were implemented. Pre-processing was divided into two sections: core image processing, and denoising. *Fourier filtering was restricted to a high-pass filter (0.009 Hz < f), except for the analyses presented in Inline Supplementary Figs. S1, S5, S6 and S7, where a band-pass filter (0.009 < f < 0.08 Hz) was used. Results in Figs. 3, 5, 6, and Inline Supplementary Fig. S4, which show outputs immediately after despiking, do not include any frequency filtering. Full image and time series processing pipeline. This figure highlights the key pre-processing steps, in the order they were implemented. Pre-processing was divided into two sections: core image processing, and denoising. *Fourier filtering was restricted to a high-pass filter (0.009 Hz < f), except for the analyses presented in Inline Supplementary Figs. S1, S5, S6 and S7, where a band-pass filter (0.009 < f < 0.08 Hz) was used. Results in Figs. 3, 5, 6, and Inline Supplementary Fig. S4, which show outputs immediately after despiking, do not include any frequency filtering.

Fig. S3

Guided example of the Time Despike method. For each time point in time series X_t, the local median was first calculated from a local region (4 × 4 window) of values in the neighborhood of that time point (A). The local Median Absolute Deviation (MAD) was then calculated for each time point across this same window (B). Any time point that had a larger value than the MAD multiplied by a threshold value of 6.8, was despiked to the level of the local median (C). Please see the Time Despike section for more details.

Fig. S4

Time series denoising capabilities of the Time and Wavelet Despike in high-motion subjects. This figure shows the effects of the Time and Wavelet Despike algorithms, on voxel time series from two high-movement cohort 1 subjects. The upper row shows the Framewise Displacement for each subject. This figure is analogous to Fig. 3. Original time series (central, black), were taken from voxels after core image processing (see Fig. 1). These voxels were then independently entered into the two despiking algorithms, and the despiked outputs are shown, along with the spikes (or noise signals) removed. The diagrams underneath the Wavelet Despiked outputs represent the temporally aligned MODWTs for the original time series (upper panel), and the maxima and minima chains detected for removal by the algorithm (lower panel). More details on the wavelet algorithm can be found in the Wavelet Despike section.

Fig. S5

Effects of despiking on distance-dependent connectivity bias, as measured by the ‘∆R plot’. This figure shows group-level ∆R plots (see the Distance-dependent movement artifact diagnostics section) across all subjects in the three cohorts analyzed. Column 1 represents the pre-processing scenario where the Time Despike was applied prior to 13-parameter confound regression, and column 2 represents the scenario where the Wavelet Despike was applied prior to 13-parameter confound regression (see Fig. 1). In each case, the ∆R plots were computed after fully pre-processing the time series, including band-pass filtering (0.009 < f < 0.08 Hz) in the last step.

Fig. S6

Effects of despiking on distance-dependent connectivity bias, as measured by the ‘motion-correlation plot’. This figure shows group-level motion-correlation plots (see the Distance-dependent movement artifact diagnostics section) across all subjects in the three cohorts analyzed. Column 1 represents the pre-processing scenario where the Time Despike was applied prior to 13-parameter confound regression, and column 2 represents the scenario where the Wavelet Despike was applied prior to 13-parameter confound regression (see Fig. 1). In each case, the motion-correlation plots were computed after fully pre-processing the time series, including band-pass filtering at 0.009 < f < 0.08 Hz. Histograms adjacent to the respective motion-correlation plots represent the null distribution of mean correlation between connectivity and motion (the mean y axis value averaged across all distances for the adjacent motion-correlation plot) that could arise by chance. This distribution was calculated by randomly permuting the movement estimate for each subject 1000 times, each time calculating the mean correlation of the resultant random motion-correlation plot. The mean values above each histogram represent the mean correlation with movement across all distances, from the true motion correlation plots (pictured to the left of the histograms). Starred means represent those significantly different from the null distribution at p = 0.05.

Fig. S7

Ordering of pre-processing steps can affect the magnitude of distance-dependent connectivity bias. Left panels show ∆R plots (see the Distance-dependent movement artifact diagnostics section) for different pre-processing scenarios: (A) where 13-parameter confound regression was implemented after band-pass filtering (at 0.009 < f < 0.08 Hz) and regressors were not frequency filtered beforehand; and (B) where 13-parameter regression was implemented before band-pass filtering. In both cases, the despiking step (see Fig. 1) was omitted. For both (A) and (B), right upper panels show the effects of differently ordered pre-processing steps on an example voxel time series. Right lower panels show the Fourier transform for the fully pre-processed time series (lowest time series in the upper panels).

Fig. 1

Overview of image and time series processing methods. This figure summarizes the key pre-processing steps used to process the resting-state fMRI data. Pre-processing was divided into core image processing, and denoising. *Fourier filtering was restricted to a high-pass filter (0.009 Hz < f), except for the analyses presented in Inline Supplementary Figs. S1, S5, S6 and S7, where a band-pass filter (0.009 < f < 0.08 Hz) was used. Results in Figs. 3, 5, and 6, and Inline Supplementary Fig. S4, which show outputs immediately after despiking, do not include any frequency filtering. A more detailed diagram of our pre-processing methods can be found in Inline Supplementary Fig. S2. Overview of image and time series processing methods. This figure summarizes the key pre-processing steps used to process the resting-state fMRI data. Pre-processing was divided into core image processing, and denoising. *Fourier filtering was restricted to a high-pass filter (0.009 Hz < f), except for the analyses presented in Inline Supplementary Figs. S1, S5, S6 and S7, where a band-pass filter (0.009 < f < 0.08 Hz) was used. Results in Figs. 3, 5, and 6, and Inline Supplementary Fig. S4, which show outputs immediately after despiking, do not include any frequency filtering. A more detailed diagram of our pre-processing methods can be found in Inline Supplementary Fig. S2.

Fig. 2

Guided example of the Wavelet Despike method. Each numbered step in the figure refers to the correspondingly numbered step in the Wavelet Despike section. Wavelet Despiking was performed for each voxel time series separately. In step (1), each time series was decomposed using the Maximal Overlap Discrete Wavelet Transform (MODWT) to add an extra dimension of information, the scale (or frequency band). The wavelet decomposition is represented as a number matrix of time vs. scale (or frequency band). In (2), local maxima and minima were defined from this matrix by searching through coefficients in the scale plane. For each coefficient, maxima and minima were defined within a local 2 × 2 window of coefficients, and boundaries were circularized. A coefficient was defined as maximal (or minimal) if its value was at least half the size of the local (within a 2 × 2 window) maximum (or minimum) and its modulus was greater than a threshold value of 10. This produced a relatively dense set of maxima and minima; the diagram only shows a few of these for clarity. In step (3), maxima and minima were chained across scales. For each maximum, a sliding window function searched across scales for any adjacent maxima (denoted in pink), and for each minimum, searched for adjacent minima (denoted in blue). The window size was fixed at 2 × 2 in the scale plane, 1 × 1 in the time plane, and was circularized in the scale plane. Only maxima that had at least one other accompanying maximum within this window were kept (denoted by ticks), others were removed from the set (denoted by crosses); the same applied for the set of minima. This resulted in a final set of maximal and minimal wavelet coefficients that were part of maxima or minima chains. In the final step (4), the signals were recomposed using the inverse Maximal Overlap Discrete Wavelet Transform (iMODWT). Two time series were recomposed at this stage. First, the set of maximal and minimal wavelet coefficients were removed from the time vs scale plane, and the remaining coefficients recomposed to create a denoised ‘Wavelet Despiked’ time series. Secondly, the maximal and minimal wavelet coefficients themselves were recomposed to create a ‘noise signal’. The noise signals were used for a variety of analyses to look at the nature of the signals being removed by the algorithm.

Fig. 3

Time series denoising capabilities of the Time and Wavelet Despike. This figure shows the effects of the two despiking algorithms, the Time Despike, and the Wavelet Despike, on voxel time series from a moderately high, and two low movement cohort 1 subjects. Original time series (central, black), were taken from voxels after core image processing (see Fig. 1). These voxel time series were then independently entered into the two despiking algorithms, and the despiked outputs are shown, along with the spikes (or noise signals) removed. The diagrams underneath the Wavelet Despiked outputs represent the temporally aligned MODWTs for the original time series, used by the wavelet algorithm. Further examples from two high-movement cohort 1 subjects can be found in Inline Supplementary Fig. S4. More details on the wavelet algorithm can be found in the Wavelet Despike section. Time series denoising capabilities of the Time and Wavelet Despike. This figure shows the effects of the two despiking algorithms, the Time Despike, and the Wavelet Despike, on voxel time series from a moderately high, and two low movement cohort 1 subjects. Original time series (central, black), were taken from voxels after core image processing (see Fig. 1). These voxel time series were then independently entered into the two despiking algorithms, and the despiked outputs are shown, along with the spikes (or noise signals) removed. The diagrams underneath the Wavelet Despiked outputs represent the temporally aligned MODWTs for the original time series, used by the wavelet algorithm. Further examples from two high-movement cohort 1 subjects can be found in Inline Supplementary Fig. S4. More details on the wavelet algorithm can be found in the Wavelet Despike section.

Fig. 4

Effects of despiking on time series correlation with movement and percent signal change. (A) For two high-movement cohort 1 subjects, voxel time series were correlated with estimates of subject movement (Framewise Displacement) or the percentage of gray matter voxels containing spikes for each frame of data (Spike Percentage, see the Framewise Displacement, DVARS and Spike Percentage section of the Methods), under various pre-processing scenarios. Row 1 maps were generated immediately after core image processing (see Fig. 1). Row 2–4 map were generated under different pre-processing scenarios immediately after core image processing. In all cases, low-pass filtering was omitted. (B) DVARS traces for the subjects in (A). Upper panels show the effects of Time Despiking + 13-parameter regression (blue), and lower panels show the effects of Wavelet Despiking + 13-parameter regression (green). The DVARS trace for the noise signal removed by the Wavelet Despike algorithm is also shown for each subject (brown). In summary, despiking prior to regression was able to reduce time series correlation with movement better than regression alone, and large fluctuations in frame-to-frame percent signal change were captured and removed much more effectively by the Wavelet Despike than the Time Despike.

Fig. 5

Spatial adaptivity of despiking to areas of high correlation with movement. (A) Spatial correlation maps (as in Fig. 4) of correlations between voxel time series and the Framewise Displacement or Spike Percentage, for a high-motion cohort 1 subject. (B) Standard deviation maps for the same subject in (A). Central panel (shaded gray), shows the standard deviation map of the brain after it had been processed through the core image processing module (see Fig. 1). Upper panel shows the impact and spatial adaptivity of the Time Despike algorithm, with regard to how it was able to accommodate regional variability in time series standard deviation that corresponded to areas affected by subject movement. Lower panel shows the same for the Wavelet Despike algorithm. In summary, the Wavelet Despike was able to effectively remove spatially variable motion-related increases in signal standard deviation, much more robustly than the Time Despike.

Fig. 6

Spatial adaptivity of despiking in further example subjects. This figure highlights the spatial adaptivity of despiking (using the Time and Wavelet Despike algorithms), by means of standard deviation maps, in a range of high-, medium-, and low-motion cohort 1 subjects. The amount of motion in these subject was characterized by the mean Spike Percentage $\left(\overline{\mathit{SP}}\right)$ denoted in the far left column. This figure is analogous to Fig. 5. The central column shows the spatial variability in standard deviation after the subjects had been processed through the core image processing module (see Fig. 1). The two columns to the left of this show the impact, and spatial adaptivity, of the Time Despike algorithm, with regard to how it was able to accommodate regional variability in time series standard deviation; and the two columns to the right show the same for the Wavelet Despike algorithm. In summary, the Wavelet Despike was able to deal with spatial variability in signal standard deviation much more effectively that the Time Despike, for all subjects.

Fig. 7

Scrubbing methods do not always correctly identify spike-containing frames. (A) Framewise Displacement, DVARS and Spike Percentage vectors for a single subject in cohort 1 (see the Framewise Displacement, DVARS and Spike Percentage section of the Methods for information on how these vectors were computed). This demonstrates that frames containing spikes in small areas of the brain (identified by the Spike Percentage, shaded in gray) may not always be picked up by the global measures of Framewise Displacement and DVARS. The Spike Percentage was calculated after core image processing, and DVARS after 13-parameter regression and high-pass filtering at 0.009 Hz (as in Power et al., 2012). The low-pass filter was omitted here, to prevent bias from temporal smoothing. (B) The relationship between Spike Percentage and both Framewise Displacement and DVARS, across all subjects in cohort 1. Lines represent the linear best fit when the two vectors presented in the x and y axes were plotted against each other. Lines were extrapolated for some subjects in order to allow better visual comparison between subjects. While there is good correspondence for some subjects, this is not always the case, as highlighted by the group average correlation $\left({\displaystyle {\overline{\mathit{r}}}_{\mathit{group}}}\right)$. (C) Left panel shows the percentage of spike-containing frames captured by the different scrubbing criteria described in previous papers, across all subjects in cohort 1. Spike-containing frames were defined as any frame with a Spike Percentage > 0.25%. This corresponded to, on average, 125 voxels, which was the maximum size of any region defined by our 230 region parcellation. Outlier points marked by crosses are subjects with values > q₃ + 1.5(q₃ − q₁) or < q₁ − 1.5(q₃ − q₁), where q_n refers to the relevant quartile. Right panel shows the percentage of data left across all subjects in cohort 1 for the top three box plots in the left panel, compared to the percentage of spike-containing frames successfully identified.

Fig. 8

A comparison between voxel-specific despiking and different regression approaches. (A) A comparison of previously published regression-based methods, with the Time and Wavelet Despike methods. Upper panel shows violin plots of frame-to-frame percent signal change (DVARS), across all subjects in cohort 1, for different pre-processing methods. Lower panel shows the analogous plots for the Spike Percentage (SP). The Spike Percentage for the Wavelet Despike is by definition zero. (B) A comparison of DVARS and Spike Percentage vectors for a single high-motion subject from cohort 1 for different pre-processing methods. Spike Percentage and DVARS were computed at various stages of pre-processing, and under different regression scenarios after core image processing, as indicated by the key. For visual clarity, only the first 5.5 min of data for the run is shown. In each case, time series were high-pass filtered at 0.009 Hz in the last step (see Fig. 1). Low-pass filtering was omitted to prevent bias from temporal smoothing. (C) Scatter plots of mean variance across the entire brain for each subject, against the mean Framewise Displacement $\left(\overline{\mathit{FD}}\right)$ or mean Spike Percentage $\left(\overline{\mathit{SP}}\right)$ for that subject. Superimposed on the scatter plots are linear regression lines representing the strength of association between whole brain variance and movement across subjects. Adjacent numbers represent the gradient of the line ± 95% confidence intervals. In summary, Wavelet Despiking outperformed all other methods at reducing frame-to-frame percent signal change, and was quantifiably superior at ameliorating the effects of head movement on fMRI time series variance.

Fig. 9

Percentage of temporal variance removed by pre-processing. This figure highlights the amount of variance remaining after pre-processing with traditional regression, compared to Wavelet Despike + regression, for cohort 1. No low-pass filtering was conducted to enable comparison with all other analyses shown in the main figures. (A) A scatter plot representing the percentage of variance remaining after pre-processing, for each gray matter voxel in each cohort 1 subject, after conventional 13-parameter regression only, compared to Wavelet Despiking + regression. In 31% of voxels (green points), Wavelet Despiking + regression conserved more variance than conventional regression alone. (B) Box plots of the variance left after pre-processing (shown in A) across the gray matter of cohort 1 subjects. The mean for conventional regression only denoising (gray) is 39%, and for Wavelet Despike + regression (green) is 35%. Outlier points marked by crosses are values > q₃ + 1.5(q₃ − q₁) or < q₁ − 1.5(q₃ − q₁), where q_n refers to the relevant quartile.

Fig. 10

Group seed correlation analysis. This figure compares resting-state networks obtained from seeds (3 mm radii) located in three brain regions (right primary visual cortex, right primary motor cortex, and right posterior cingulate cortex) for two pre-processing strategies: denoising with conventional 13-parameter regression analysis only, and denoising with Wavelet Despiking + regression. Resulting pair-wise correlations with all other voxels in the maps were consistently threshold at a p-value equivalent to FDR q < 1 × 10^- 6. Arrows indicate areas of anatomically predictable connectivity (ipsilateral thalamus and contralateral cerebellum) that were observed after Wavelet Despiking, but not after conventional regression analysis. No low-pass frequency filtering was conducted in order to preserve components of networks that may have been present in higher frequencies.