A Retrospective Physiological Noise Correction Method for Oscillating Steady-State Imaging (OSSCOR)

Abstract

Purpose:

Oscillating Steady-State Imaging (OSSI) is an SNR-efficient steady-state sequence with T2* sensitivity suitable for fMRI. Due to the frequency sensitivity of the signal, respiration and drift induced field changes can create unwanted signal fluctuations. This study aims to address this issue by developing retrospective signal correction methods which utilize OSSI signal properties to denoise task-based OSSI fMRI experiments.

Methods:

A retrospective denoising approach was developed which leverages the unique signal properties of OSSI to perform denoising without a manually specified noise ROI and works with both voxel timecourses (OSSCOR) or FID timecourses (F-OSSCOR). Simulations were performed to estimate the number of principal components (PCs) optimal for denoising. In vivo experiments at 3T field strength were conducted to compare the performance of proposed methods against a standard PCA-based method (CompCor), measured using mean t-score within an ROI, number of activations, and mean tSNR.

Results:

Correction using OSSCOR was significantly better than the standard method in all metrics. Correction using F-OSSCOR was not significantly different from the standard method using an equal number of principal components. Increasing the number of OSSCOR PCs decreased activation strength and increased the number of suspected false positives. However, increasing the number of PCs in F-OSSCOR increased activation strength without additional false positives.

Conclusion:

Both OSSCOR and F-OSSCOR substantially reduce physiological noise components and increase tSNR, improving the functional results of task-based OSSI functional experiments. F-OSSCOR demonstrates a proof of concept utilization of coil-localized FID signal information for physiological noise correction.

1. Introduction

Oscillating Steady-State Imaging (OSSI) is a sequence that combines balanced gradients with a quadratic RF phase increment to produce a large, oscillating signal [1]. This signal has been shown to exhibit frequency sensitivity which leads to a T2* weighting that is similar to GRE, creating the potential for high SNR fMRI acquisitions. While OSSI’s frequency sensitivity results in desirable T2* weighting, it also increases sensitivity to any temporally varying changes to B₀. Two primary causes of B₀ changes over an fMRI experiment are respiration and scanner drift, which are known to vary throughout the brain spatially [2][3][4][5]. The resulting physiological noise is commonly addressed in fMRI using a retrospective method as a post-processing step. However, OSSI exhibits a complex non-linear response to frequency changes, making model-based correction methods that use external physiological recordings such as RETROICOR [6] poorly suited to correct the OSSI signal. Instead, these non-linear changes to the OSSI steady-state may be addressed using previous data-driven approaches that differentiate physiological noise from functional changes through a spatial or temporal model [7][8][9][10].

To this end, we present a novel data-driven method for retrospective correction method titled Oscillating Steady-State CORrection (OSSCOR). OSSCOR uses principal components as nuisance regressors, similar to CompCor [8]. However, OSSCOR does not rely on specifying a noise ROI, and instead utilizes a unique property of OSSI where multiple images with different contrasts are acquired for each time point. Results from simulation reveal that signal changes caused by frequency changes are low-rank across these images, allowing estimation of physiological noise using principal component analysis. We show that the use of OSSCOR-derived nuisance regressors in a task-based fMRI experiment can significantly reduce physiological noise compared to standard methods, as measured by activated voxels, mean t-score, and tSNR. Finally, we present a variation of our approach deemed F-OSSCOR, where FID timecourses are used to generate nuisance regressors instead of image data. By using FID data instead of image data, physiological noise can be sampled every TR, independently of the slice or volume acquisition rate.

2. Methods

Image-Based Physiological Noise Estimation

During an OSSI fMRI experiment, quadratic phase cycling is used to create a periodically oscillating signal which repeats every n_c TRs, where n_c is a scan parameter. The n_c signals from each period are then combined into one timepoint, resulting in an fMRI image series with an effective temporal resolution of TR_eff = n_c ∗ TR. The OSSI signal combination strategy is an effective way to reduce frequency-dependent signal variance in steady-state. However, temporally varying frequency due to respiration and scanner drift result in transient disturbances to the steady-state, resulting in unwanted signal fluctuations. Herein, we refer to such signal fluctuations caused by both sources as “physiological noise” for simplicity.

The OSSCOR method is a data-driven method like CompCor, adapted to the unique acquisition strategy and features of the OSSI signal. First, OSSCOR seeks to remove physiological noise from the OSSI signal prior to the signal combination step, in order to exploit shared information between the magnetization states. This information sharing is accomplished by treating each of the n_c phases in an OSSI cycle are treated as separate image timecourses. We refer to each of these separate timecourses as a “phase timecourse,” such that each voxel will have n_c phase time courses prior to combination.

Formally, we can represent the magnitude of an original OSSI voxel timecourse $m\in {ℝ}_{+}^t$ with t timepoints as the following matrix:

$$\text{M}=\left[\begin{array}{cccc}m(1)& m\text{(2)}& \cdots & m(n_c)\\ m(n_c+1)& m(n_c+2)& \cdots & m(2n_c)\\ ⋮& ⋮& \ddots & ⋮\\ m(t-n_c+1)& m(t-n_c+2)& \cdots & m\text{(}t\text{)}\end{array}\right],$$ (1)

where each column of M $\in {ℝ}_{+}^{t/n_c\times n_c}$ is a phase timecourse. Although the n_c timepoints in each row are acquired sequentially, for purposes of the noise analysis we assume that are acquired simultaneously since the time to acquire each row (∼100ms) is considerably faster than respiration or scanner drift induced signal changes. The signals from each row of M form one timepoint in the combined timecourse $c\in {\text{R}}_{+}^{t/n_c}$

$$c(i)=\sqrt{\sum _{j=1}^{n_c}{\text{M}}_{ij}{}^2}$$ (2)

Each phase timecourse will then exhibit different frequency-dependent physiological artifacts. An example of this can be seen in Figure 1a, where simulated respiration and drift results in different physiological artifacts for each phase timecourse. Figure 1b shows how combining phase timecourses can cause constructive or destructive interference of these physiological artifacts, resulting in signal fluctuations which change in amplitude and shape through time.

Figure 1.

Simulated gray matter signals with respiration and scanner drift effects. Plot a) shows phase timecourses (3 of 6 plotted for clarity). Plot b) shows the associated combined timecourse. c) shows simulated B0 changes, modeled using two terms: a respiration waveform at 12 breaths/min and pk-pk amplitude of 1 Hz, and a linear scanner drift term of 1 Hz/min.

We can use the matrix representation of the OSSI signal in Eq. 1 to estimate the physiological noise components which are common between phase time courses and between voxels. We achieve this by forming a block matrix S for all r voxels:

$$\mathbf{S}=\left[{\text{M}}_1{\text{M}}_2\cdots {\text{M}}_r\right],$$ (3)

where the columns of S are the phase timecourses of all r voxels. Through simulation (as described below), we show that the physiological noise components are low-rank across the columns of S and can be represented using principal component analysis (PCA). This is the central concept of OSSCOR, where the signal properties of OSSI allow for a small number of principal components to sufficiently describe the physiological noise in any phase timecourse at any spatial location.

Once the principal components of S are determined, we can remove physiological noise components using the following signal model commonly used for BOLD fMRI:

$${\mathbf{S}}_i=\mathbf{X}{\beta }_1+\mathbf{T}{\beta }_2+\mathbf{P}{\beta }_3+ϵ,$$ (4)

where S_i is the ith column of S, X is a matrix of experimental design variables, T is a matrix of polynomial detrending terms, and P is a matrix containing principal components of S which act as nuisance regressors for physiological noise. β₁, β₂, and β₃, contain weights for each respective matrix, and ε is random error. The use of polynomial terms T was not found to improve the performance of OSSCOR but were included to maintain consistent degrees of freedom with CompCor in the later comparison.

The number of principal components was determined by simulating OSSI timecourses (TR = 15 ms, FA = 10°, n_c = 6) with temporally varying B₀. An example of how B₀ was varied can be seen in Figure 1c. The effects of respiration on B₀ were varied by changing the amplitude from 0–2 Hz peak-to-peak, with a step size of 0.1 Hz (21 steps). A center frequency offset was then added to each respiration waveform, where each respiration waveform was initialized over ± 50 Hz with a step size of 0.1 Hz (1001 steps). The respiration rate was kept constant at 12 breaths/minute. A linear drift component of 1 Hz/min was added to the respiration component for all frequency amplitude values. T1 and T2 were not found to affect the results of the simulation and were held constant at 1286 ms and 110 ms, respectively. Each of the 21,021 parameter combinations was initialized at steady-state and simulated for 90 seconds, then reshaped into a matrix of 126,126 phase timecourses per Eq. 1. PCA was then applied to the simulated timecourses. A subsequent scree test was used to select a rank of k = 6 for denoising. Supporting Information Figure S2a shows associated scree plots of the simulated physiological noise.

2.1. FID Based Physiological Noise Estimation

In addition to image data, principal components can be determined from acquiring extra samples of the signal FID prior to readout. We refer to this as “F-OSSCOR”, an FID-based variation of the previously described method. While this signal source is not spatially encoded using gradients, the individual coils in a receive-array provide spatially varying sensitivity to different regions of the brain, which in turn have varying distributions of off-resonant spins. Similar to a blind source separation problem, PCA can then be used to estimate the independent signals that comprise the low-rank physiological noise subspace.

We implement this method by acquiring multiple samples at k_xy = 0 before readout, which are then averaged into a single magnitude value. This is performed coil-wise, resulting in n_coil measurements per TR. Considering these to be n_coil separate timecourses, the same methods previously described for image data are then applied. The number of FID samples was varied to determine its effect on the quality of estimates produced, which showed negligible improvement past 16 samples.

2.2. Experimental Setup

All studies (n = 6 subjects) were performed on a 3T GE MR750 scanner (GE Healthcare, Waukesha, WI) with a 32-channel head coil (Nova Medical, Wilmington, MA). All experiments were conducted in accordance with the local Institutional Review Board (IRB), and all subjects were provided written informed consent. We implemented the OSSI pulse sequence using the vendor’s pulse programming language, EPIC, as well as our own in-house pulse sequence development framework, TOPPE [11]. Single slice imaging with was performed using a single shot constant-density spiral out trajectory (n_c = 6, TR = 17.5 ms, FA = 10^◦, FOV=19 × 19 cm², matrix = 45 × 45 reconstructed at 64 × 64, slice thickness = 2.5 mm, sampling BW = 250 kHz), with 16 extra k-space center samples prior to readout. Spatial distortions due to B₀ field inhomogeneity were corrected using a separately acquired field map.

Subjects were presented with a visual stimulus composed of right- and left-hemifield counter-phased 10Hz flickering checkerboards in 40-second blocks, repeated 6 times (240 seconds). The subject was instructed to gaze at a fixation cross in the center of their visual field during the experiment.

2.3. Data Analysis

Analysis of functional data was performed using MATLAB (The Mathworks, Inc., Natick, MA). A block diagram illustrating the following analysis workflow is shown in Figure 2. The OSSCOR and F-OSSCOR analysis methods were applied by removing physiological noise components to phase timecourses S using least-squares fitting of the signal model (Eq. 4), which included the task waveform and linear/quadratic detrending terms. 6 principal components were used in the OSSCOR and F-OSSCOR analyses. The denoised phase timecourses were then combined using Eq. 2, resulting in one denoised combined timecourse per voxel. For comparison, CompCor was implemented on combined timecourses with linear/quadratic detrending. Temporal standard deviation (tSTD) was used to select the top 2% of noisy voxels, discarding any timecourse with task correlation higher than 0.2 (tCompCor variation). In all methods, the resulting denoised combined timecourses were then evaluated for activation using a simple correlation threshold of r > 0.5. No high-pass filtering or spatial smoothing was performed.

Figure 2.

A diagram outlining the steps implemented for each analysis method. OSSCOR and F-OSSCOR both calculate principal components and perform denoising before phase timecourse combination, while CompCor was applied on the final combined timecourse.

Method performance was evaluated using average t-score, number of activated voxels, and average tSNR. Average t-score was calculated within a per-subject-ROI defined by the union of the activated voxels found in all correction methods, with df = 2079 for each voxel. In counting the total number of activations, only voxels from the bottom-third of the brain could be considered true active, approximately corresponding to the visual cortex. Additionally, because the visual stimulus was counter-phased, only negative correlations were considered from the left hemisphere and positive correlations from the right hemisphere. For comparison, an additional non-parametric analysis was conducted using a random blockwise permutation approach with randomized circular shifting, 50,000 permutations, and 10 blocks [12].

3. Results

Detailed results from one subject (#4) is described here, with results for other subjects summarized in Table 1. Figure 3a shows activation and tSNR maps for the proposed methods, with CompCor for comparison. Using a paired t-test, OSSCOR, F-OSSCOR, and CompCor all significantly improved the number of activated voxels (all P < .03, d > 1.26), average t-score (all P < .001, d > 4.44), and tSNR (all P < .001, d > 6.36) compared to only polynomial detrending (Table 1). OSSCOR performed significantly better than CompCor in all three metrics (P = .025, P = .042, P = 0.0025, and d =1.29, d = 1.11, d = 2.29, respectively). F-OSSCOR results were not found to be significantly different compared to CompCor. An example uncorrected and OSSCOR corrected phase timecourse is shown in Figure 4, illustrating successful reduction of high-frequency respiratory noise as well as drift induced low frequency components. The OSSCOR nuisance regressors for subject #4 are shown in Supporting Information Figure S1.

Table 1:

Summary of Functional Experimental Results

	Subject 1	Subject 2	Subject 3	Subject 4	Subject 5	Subject 6
Average t-score with detrending	15.1	26.4	38.3	19.0	19.2	27.5
Average t-score with CompCor	31.6	43.4	47.0	33.5	31.1	41.7
Average t-score with OSSCOR	34.5	44.3	49.4	38.6	41.5	43.2
Average t-score with F-OSSCOR	32.8	43.9	48.1	35.7	36.6	41.4
# activated voxels with detrending	0	16	53	27	10	39
# activated voxels with CompCor	22	32	66	91	19	67
# activated voxels with OSSCOR	30	31	71	109	34	75
# activated voxels with F-OSSCOR	28	28	70	87	27	63
Average tSNR with detrending	47.9	41.4	83.9	60.2	46.1	67.2
Average tSNR with CompCor	88.1	72.0	125.6	94.0	74.1	106.4
Average tSNR with OSSCOR	94.9	94.3	135.9	106.1	83.5	119.2
Average tSNR with F-OSSCOR	87.3	75.9	132.6	95.1	80.4	106.7

Figure 3.

a) Activation and tSNR map for each respective correction methods: polynomial detrending only, and CompCor, OSSCOR, and F-OSSCOR with six principal components each. OSSCOR outperformed both CompCor and F-OSSCOR, but all three correction methods significantly increased the number of activated voxels and mean tSNR. Voxels with a significant vascular component were observed to have lower tSNR than their surroundings, which is thought to be the effect of through-plane flow unable to reach steady-state due to the single-slice acquisition. b) Activation maps for OSSCOR and F-OSSCOR with varying number of principal components. Increasing the number of OSSCOR PCs reduced activation sensitivity and increased the number of false positives, while increasing the number of F-OSSCOR PCs increased sensitivity without increasing false positives.

Figure 4.

An example of uncorrected and OSSCOR corrected phase timecourses, with the visual task indicated by black bars on the x-axis. While the uncorrected timecourse shows high sensitivity to respiration changes in the first minute of the scan, the OSSCOR method is able to regress out these physiological effects.

Increasing the number of principal components used in OSSCOR resulted in decreased activation area and mean t-score, and an increase in false positives as defined by activations outside of the visual task ROI. This reduction of performance was observed across all subjects. However, increasing the rank of the F-OSSCOR analysis improved the number of activations and mean t-score across all subjects with little to no increase false activation. Activation maps for representative principal component numbers are shown in Figure 3b. Scree plots for OSSCOR and F-OSSCOR are shown in the Supporting Information Figure S2b and S2c. The results of the random blockwise permutation analysis are shown in Supporting Information Figure S3 and Supporting Information Table S1, showing general agreement with the performance results from the correlation analysis.

4. Discussion

The “phase timecourse” analysis of OSSCOR assumes that the time to acquire each period of n_c TRs is much shorter than the timescales at which respiration and drift occur. Therefore, temporally varying frequency and resulting transient effects can be treated as quasi-static over the duration of a full n_c OSSI period. This assumption does not imply that transient effects are negligible, but rather are slowly varying compared to the speed to acquire a period, TR_eff. This assumption performs well at the chosen parameters (n_c = 6, TR_eff = 105 ms), though we found in initial tests that longer readouts or higher n_c values reduced the effectiveness of OSSCOR. Furthermore, higher values of n_c result in reduced amplitude of respiration and drift artifacts due to a more stable combined frequency response, reducing the need for retrospective correction. For example, a period of n_c = 10 was shown to have a combined frequency response variation of less than 5% compared to the 17% variation of n_c = 6, though at the cost of a 66% longer TR_eff.

F-OSSCOR extends the OSSCOR method by using FID timecourses instead of voxel timecourses. Though not spatially encoded, the FID time series data can be used to estimate spatially varying physiological noise due to two sources of signal diversity: coil sensitivity and B₀ inhomogeneity. Since the FID signal is detected independently per coil, each coil will only be sensitive to a spatially localized distribution of off-resonant spins with certain physiological noise structure. Furthermore, OSSI effectively acquires a sequence of n_c different images with different center frequencies, resulting in each coil receiving FID signals from n_c different regions of the frequency response. In our experimental setup using a 32-channel head array and n_c = 6, the 192 separate FID timecourses produced for the F-OSSCOR analysis were sufficient for correcting the data. An additional benefit of the F-OSSCOR approach is that the requisite FID signals are measured every TR regardless of the encoding strategy, and is therefore compatible with any multi-shot, 3D, or undersampling scheme.

The concept of using FID-based nuisance regressors assumes that FID signal variance is dominated by respiration or drift artifacts that are of lower-rank than functional signal changes. This is supported by the comparison shown in Figure 3b, which shows OSSCOR and F-OSSCOR activation maps denoised using different numbers of principal components. As the number of principal components was increased passed the theorized rank of the physiological noise, OSSCOR functional sensitivity and specificity decreased in all subjects. In contrast, increasing the number of principal components in F-OSSCOR increased activation strength with minimal reduction in specificity across subjects, while maintaining similar activation areas. We conclude that OSSCOR is more sensitive to the number of PCs used and begins to capture functional activity in its regressors when the selected rank is too high. Conversely, F-OSSCOR performance is relatively insensitive to exceeding the rank of the physiological noise.

Both OSSCOR and F-OSSCOR use PCA to produce nuisance regressors for subsequent functional analysis, similar to the CompCor denoising approach. However, a fundamental difference is that CompCor seeks to target noisy voxels and exclude activated voxels from the PCA by specifying a noise ROI, while OSSCOR and F-OSSCOR include all data. Despite including activated voxels in the PCA analysis, OSSCOR performed significantly better than CompCor in all three metrics, and F-OSSCOR performed comparably to CompCor. In fact, our testing showed that including all voxels as inputs was found to be critical for OSSCOR, as excluding voxels via a tSTD threshold resulted in a loss of denoising performance. This implies that a sufficient range of off-resonant signals needs to be included in the analysis and that only selecting timecourses with high tSTD results in a limited range of off-resonant behaviors represented in the nuisance regressors.

Our implementation of CompCor excluded timecourses that were correlated with the task above a threshold, though this pre-processing step was found to be unimportant for analyzing OSSI data. This result was confirmed by manually inspecting the unmodified tSTD-derived ROI, which did not include voxels near the activated regions of the visual cortex. This pre-processing step was tested with OSSCOR to exclude phase timecourses potentially containing functional signal but was also found to have a negligible impact. Preprocessing the data using second-order polynomial detrending was effective at removing slowly varying noise components attributed to drift. This detrending step was found to be essential for defining the CompCor noise ROI based on tSTD, since respiration-induced noise magnitude is small compared to drift. However, the detrending step had a negligible effect on OSSCOR since no ROI is used and low-frequency components are captured in the principal components. Though not necessary, polynomial detrending terms were included in OSSCOR and F-OSSCOR in order to match the degrees of freedom in method comparisons.

While OSSCOR and F-OSSCOR demonstrate the ability to mitigate the effects of respiratory and scanner drift induced frequency changes in OSSI, both methods inherit limitations of data-driven correction approaches. The first is the selection of how many principal components should be included in the analysis. Here we have shown a rank can be selected through simulation, however, this does not account for subject-specific B₀ distributions or temporally varying respiration rates. This can lead to a deterioration of performance for some frequencies, as shown in the last two stimulus blocks in Figure 4 where no respiration artifacts are removed. Furthermore, flow-related artifacts in OSSI result in complex frequency-dependent signal evolutions, which were not well corrected by either proposed methods or CompCor. This effect can be seen in Fig. 2, where tSNR did not improve in areas with significant vascular components.

Including all timecourses in OSSCOR creates the possibility of the nuisance regressors representing functional signal instead of noise, which would result in decreased functional sensitivity. This is of concern in the event of widespread activation or for cases where there is no pre-defined task activity, such as in resting-state fMRI. For OSSCOR, such an issue may potentially be addressed through a CompCor-like strategy where only white matter and CSF voxels are used as inputs. It is possible that F-OSSCOR would be less sensitive to the loss of resting-state activity in due to using FID timecourses instead of voxel timecourses. This notion is supported by Figure 3b, where increasing the number of F-OSSCOR PCs did not appear to increase the number of false positives at the threshold used. Either of these modifications could be combined with common pre-processing steps such as band-pass filtering to exclude resting-state frequencies prior to applying PCA.

5. Conclusion

We have shown that the application of OSSCOR and F-OSSCOR can significantly reduce physiological noise due to temporally varying off-resonance during an OSSI-based fMRI acquisition. Unlike the previous PCA based methods such as CompCor, OSSCOR does not require the selection of a designated noise ROI and instead uses OSSI-specific signal properties to determine correlated physiological noise components. Similarly, we show through F-OSSCOR that FID samples can be used to produce nuisance regressors independent of the image encoding strategy.

Supplementary Material

supp info

Supporting Information Figure S1 Individual OSSCOR nuisance regressors plotted for k = 6. Each principal component can be seen to contain low frequency components due to drift effects, as well as high frequency components due to respiration. Note that while each of the 6 regressors contains fluctuations due to respiration, the phase of the fluctuations varies between regressors.

Supporting Information Figure S2 Scree plots for simulated physiological noise (a), as well as OSSCOR (b) and F-OSSCOR (c) applied to n = 6 subject scans. In the experimental data, the plots show that energy of the PCs is reduced by slightly reduced amount for OSSCOR and a similar amount for F-OSSCOR, in comparison to the simulated physiological noise.

Supporting Information Figure S3 Activation maps for all n = 6 subjects computed for each denoising approach using a random blockwise permutation analysis, thresholded at P = 0.001. Each analysis used 1,000,000 permutations of 10 timecourse blocks, with random circular shifts added before block randomization. Masks for each subject are shown, indicating voxel regions that were counted as true activation. See “Data Analysis” for a description of how true and false activation regions were estimated.

Supporting Information Table S1 Summary of permutation test results, showing the number of true and false activated voxels from the activation maps and masks shown in Supporting Information Figure S3.