Signal Fluctuations Induced by non-T₁-related Confounds in Variable TR fMRI Experiments

Abstract

Purpose

To assess and model signal fluctuations induced by non-T₁-related confounds in variable repetition time fMRI and to develop a compensation procedure to correct for the non-T₁- related artifacts.

Materials and Methods

Radio-frequency disabled volume gradient sequences were effected at variable offsets between actual image acquisitions, enabling perturbation of the measurement system without perturbing longitudinal magnetization, allowing the study of non-T₁-related confounds that may arise in variable TR experiments. Three imaging sessions utilizing a daily quality assurance (DQA) phantom were conducted to assess the signal fluctuations, which were then modeled as a second order system. A modified projection procedure was implemented to correct for signal fluctuations arising from non-T₁-related confounds, and statistical analysis was performed to assess the significance of the artifacts with and without compensation.

Results

Assessment using phantom data reveals that the signal fluctuations induced by non-T₁- related confounds was consistent in shape across the phantom and well-modeled by a second order system. The phantom exhibited significant spurious detections (at p < 0.01) almost uniformly across the central slices of the phantom. Second-order system modeling and compensation of non-T₁-related confounds achieves significant reduction of spurious detection of fMRI activity in a phantom.

INTRODUCTION

Variable repetition time (TR) acquisition and associated intensity correction have long been utilized to alleviate physiologic and environmental confounds during fMRI acquisition. One of the earliest fMRI applications of variable TR acquisitions was cardiac gating, in which the linkage of acquisition to the cardiac cycle reduces the effect of pulsatile motion, particularly in the brain-stem (1). Variable TR acquisition has been used more recently to mitigate acoustic masking of a desired auditory stimulus (2) and to study the interactions between acoustic imaging noise-induced responses and auditory stimulus-induced responses (3).

Associated with a variable TR acquisition is the need for an intensity correction, necessitated by the differences in T₁ contrast brought about by variable excitation delays between successive image acquisitions. In the studies noted above, and in general, signal variations due to a variable TR are modeled as being solely due to T₁ relaxation, and compensation is effected by scaling using a T₁ saturation model:

$$S(TR)=M_0\left[1-e^{-TR/T_1}\right]$$ [1]

Variable TR correction effected using the T₁ saturation model may not be sufficient for other, non-T₁-related confounds that may arise in variable TR fMRI experiments. Birn et al. (4) investigated the efficacy of the T₁ saturation model for variable TR correction in cardiac gating. In order to assess its efficacy, Birn et al. (4) acquired spiral images of a phantom without and then with gating, and observed that the noise variance increased by a factor of three with gating (from 0.4% to 1.3%). Langers et al. (3) observed oscillatory behavior of signal intensities with respect to TR utilizing a variable TR paradigm (TR = 2, 4, 6, 8, 10 s), and initially attributed the observed behavior to partial volume effects. Therefore, in addition to the T₁-related signal fluctuation, a higher order process appears to be involved, likely due to reproducible non-idealities in the measurement system such as eddy currents and gradient coil heating.

This study exploited a novel acquisition scheme to characterize, mathematically model, and improve compensation for non-T₁-related confounds in variable TR experiments. Radio-frequency disabled volume gradient sequences were effected at variable offsets between actual image acquisitions, enabling perturbation of the measurement system without perturbing longitudinal magnetization, allowing the study of non-T₁-related confounds that may arise in variable TR experiments. Assessment using phantom data reveals that second-order system compensation results in significant reduction of spurious detection of fMRI activity in a phantom, arising from non-T₁-related confounds.

MATERIALS AND METHODS

Paradigm

Radio-frequency (RF) disabled volume gradient sequences were applied at variable post-offset sample times between actual volume acquisitions, occurring at a fixed TR (Figure 1). These RF-disabled volume gradient sequences were generated using a normal blipped EPI slice acquisition with a zero-amplitude RF pulse. Variation of the temporal position of the RF-disabled volume gradient sequence between actual image acquisitions simulates a variable TR without perturbing longitudinal magnetization, enabling study of non-T₁-related confounds.

Figure 1.

Acquisition paradigm used to examine non-T₁-related confounds in variable TR experiments. Radio-frequency (RF) disabled volume gradient sequences were generated at variable times during the quiescent period between clustered volume acquisitions to permit measurement at a series of post-volume-offset delays. Variation of the temporal position of the RF-disabled volume gradient sequence between actual acquisitions simulates a variable TR without perturbing longitudinal magnetization.

Three experiments were conducted, in each of which a RF-disabled volume gradient sequence, comprising of a 1, 10 or 15-slice gradient sequence, was effected. The RF-disabled volume gradient sequence was grouped as per a clustered volume acquisition (CVA) (5) and generated in the quiescent period between actual CVAs. For all three cases, the delay between a RF-disabled volume gradient sequence and the subsequent actual volume acquisition was varied over a set of post-offset (relative to the RF-disabled volume gradient sequence) sampling times (Table 1) using a stroboscopic paradigm (6), including a null condition in which no RF-disabled volume gradient sequence was generated.

Table 1.

Post-offset sample times for 15, 10, and 1-slice radio-frequency (RF) disabled volume gradient sequence experiments. Note that times are measured relative to offset of the the radio-frequency (RF) disabled volume gradient sequence. Thirty-six trials of each post-offset sample time and the null condition (in which no RF-disabled volume gradient sequence was generated) were acquired over the course of three imaging sessions for each of the experiments. The long TR values were used to permit the gradient coil assemblies to approach thermal and mechanical equilibrium prior to each RF-disabled volume gradient sequence. All functional scans utilized the following parameters: TE = 40 ms, flip angle = 90°, FOV = 24 cm, in-plane resolution = 3.75 mm × 3.75 mm.

RF-Disabled Volume Gradient Sequence	TR (s)	# Sample Times	Variable Post-Offset Sample Times (s)
15-slice	33	18	0.1, 0.2, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 5, 7, 9, 10, 11, 12.5, 14, 15
10-slice	33	7	2, 2.5, 3, 4, 5.5, 7.5, 11.5
1-slice	29	9	1.5, 3, 3.5, 4, 5, 6.5, 7.5, 8.5, 12.5

Imaging Protocol

Three scanning sessions were conducted in which a daily quality assurance (DQA) phantom (11.5cm diameter) was imaged using a GE 1.5 T Signa CVi. These sessions were conducted at intervals of approximately one month. Each imaging session consisted of six experimental runs using a centric slice acquisition order. Imaging was conducted using bilateral surface coils.

ROI Selection and Percent Signal Change Calculation

To estimate signal change induced by variable TR in the absence of T₁ perturbation, a volumetric region of interest (ROI) was constructed comprising 54 voxels in each of the left and right halves of the central three slices (108 voxels per slice; 324 voxels total), where the coils yielded maximum sensitivity. Signal changes for each voxel within the ROI were estimated by calculating the percent signal change, with respect to the null acquisition, induced by the RF-disabled volume gradient sequence at each offset sample time. Average ROI percent signal change time-series were computed, on both a slice- and volumetric-basis, for each of the 1-, 10-, and 15-slice experiments by averaging estimated percent signal changes across voxels, runs, and sessions.

Modeling of Non-T₁-Related Artifact

The non-T₁-related artifact was modeled as the general solution of a second order differential equation, modified by the presence of an offset:

$$F(t)=(Acos(\omega t)+Bsin(\omega t))e^{\lambda t}+C$$ [2]

The second order decay function is commonly used to model physical systems because this tends to be characteristic of natural system (7). The model as defined in Eq. [2] is an exponentially damped oscillatory function with parameters controlling the amplitude of oscillation (A, B), the frequency of oscillation (ω), constant offset (C), and the decay rate (λ), representing the natural thermal decay or damping rate for the coils. Constrained non-linear regression was performed to obtain a least squares fit to this second order model. The frequency ω was constrained to be positive; the decay rate λ was constrained to be negative to model the exponential decay; and the offset C is constrained to be negative due to the observed negative offset of the non-T₁-related signal fluctuations.

Artifact Correction and Performance Assessment

The modeled second order signal change can be utilized to compensate for the observed non-T₁-related artifact. First, a modeled fit to each slice-based estimated percent signal change time-series is generated. Voxel-based correction is effected on each voxel in a slice by a modified projection procedure in which the modeled fit for the given slice is scaled to the average signal level obtained for the voxel during the null acquisition condition (i.e., no RF-disabled volume gradient sequence), and subsequently subtracted.

To assess the effectiveness of this compensation procedure, the contribution from the non-T₁-related signal to the DQA phantom images was assessed prior to and after compensation using a K-fold cross-validation methodology (8). For the K=18 acquired runs, 17 runs were used as training data to estimate and model the non-T₁-related artifact while the remaining run served as the testing dataset to assess effectiveness of compensation. All 18 possible testing/training dataset combinations were evaluated.

Group-level activation maps were generated via AFNI (http://afni.nimh.nih.gov) both for the uncorrected and corrected datasets, using standard fMRI analysis procedures with the percent signal change time-series estimated over the entire ROI serving as the reference waveform. First, all datasets in a given group were realigned to a reference image to maintain consistent spatial location across datasets and then spatially smoothed with a Gaussian kernel (FWHM=8 mm). Multiple linear regression was performed to generate t-statistic maps for the 15-slice phantom data. One factor random effects analysis was performed to generate a t-statistic map from which activations at different p-value thresholds could be obtained.

RESULTS

Non-T₁-Related Artifact Estimates

Figure 2a depicts estimated percent signal changes induced within the volumetric ROI in the DQA phantom by the 1-, 10- and 15-slice RF-disabled volume gradient sequence, at the indicated post-offset sample times. The estimated signal changes for all three experiments exhibited a peak at 3 s post-offset, and a local minimum near 4 s post-offset. The shape/phase of the estimated percent signal waveform remained consistent across slices with the amplitude and offset value varying across slices. The amplitude of the artifact is largest in the central slices (acquired first under the centric slice acquisition order) and decreases with acquisition order, in agreement with findings described by Talavage et al. (9). The percent signal change waveforms for all three experiments exhibit both exponential and oscillatory behavior, consistent with a second-order system. All pair-wise cross-correlations of the non-T₁-related artifact associated with the 15-slice experiment (estimated individually for each session) were statistically significant at the p < 0.05 level, signifying that the non-T₁-related signal fluctuations remained consistent over an extended period of time.

Figure 2.

(a) Non-T₁-related artifactual signal changes induced in central three slices of a daily quality assurance (DQA) phantom by 1-, 10- and 15-slice RF-disabled volume gradient sequences. Error bars indicate standard error assessed for 18 runs acquired over three imaging sessions. (b) Estimated (repeated from first subplot) and modeled signal change induced in DQA phantom by the 15-slice RF-disabled volume gradient sequence. Constrained non-linear regression yielded the following fitting parameters to the second order model for the estimated signal change: A=-0.36, B=-0.01, ω=3.07, λ=-0.87, and C=-0.23.

Model of Non-T₁-Related Artifact

Figure 2b depicts the second order solution fit obtained for constrained non-linear regression with the 15-slice experiment (for which the most post-offset sample times were acquired). Signal changes induced in the phantom by the gradient readouts during the 15-slice RF-disabled volume gradient sequence are well-modeled by the second order process for offset sample times less than 5 s, resulting in a mean squared error of 0.0061. Whereas the oscillations of the modeled signal change cease by 5 s, the oscillatory and decay behaviors persist in the estimated signal change, resulting in a mean squared error of 0.0703 for offset sample times greater than 5 s. This suggests that the signal change induced by the RF-disabled volume gradient sequence is dominated by a second order process at earlier post-offset sample times and later becomes a higher order process. Note that typical variable TR experiments employ TRs of 0.5–6 s, for which the confound is well-modeled by the second order process.

Phantom Artifact Correction

Figure 3 shows the number of voxels exhibiting spurious phantom “activation” (i.e., signal changes similar to the variable TR artifact) with and without correction, illustrating that this simple compensation procedure is effective for removal of the non-T₁-related artifactual fluctuations in fMRI time-series. Without correction, 896 voxels exhibited significant artifact-related fluctuations (p < 0.01, uncorrected, t-test), producing a false alarm rate of 0.098. Correction led to a 78% decrease in these detections, with a resultant false alarm rate of 0.022. Figure 4 graphically illustrates the effectiveness of this compensation procedure. The map of statistically significant (p < 0.01, uncorrected, t-test) “activation” for the uncompensated phantom data (Figure 4a) reveals that the non-T₁-related artifact produces false alarms at a consistent rate across the central slices of the phantom. The corrected phantom data (Figure 4b) exhibits a major reduction in detections, and a decrease in significance for those false alarms that remain. It is notable that the false detections remaining in the corrected data are clustered along the midline of the phantom where the signal-to-noise ratio (SNR) is the lowest due to the decreased sensitivity along the midline of the bilateral surface coils. fMRI studies utilizing similar surface coils (5,9), voxels in the acquired data with low SNR have been discarded from subsequent analysis, due to limited confidence in these regions. In such cases, a threshold of at least half the maximum SNR was used. Note that the remaining spurious detections in the corrected dataset are almost exclusively in regions with SNR < 25.5 (Figure 4c), falling below one-half the maximum SNR (SNR_max = 51) observed in this study.

Figure 3.

Number of voxels in which signals corresponding to the variable TR artifact were detected, with respect to p-value threshold, with and without compensation. The phantom imaging volume comprises 9133 voxels. Included dash-dot line represents the theoretical expected number of false detections at each p-value, computed by treating each p-value as an α-level threshold and multiplying by the number of voxels within the phantom.

Figure 4.

Statistical maps of non-T₁-related artifact-induced false alarms at the p < 0.01 level (uncorrected, t-test), shown for the first three slices acquired by the centric acquisition (slice 8 being the central slice of the 15-slice volume). Maps depict (a) uncorrected and (b) corrected phantom data, complemented by (c) signal-to-noise ratio (SNR; defined as the mean signal level divided by the variance) map. Significance level of the detection is indicative of the strength of the non-T₁-related signal components in the imaging time-series of each voxel while the SNR may be interpreted as an indication of the (relative) confidence in a detection being related to external stimuli as opposed to artifactual sources.

DISCUSSION

Based on this demonstration, the modeling of the non-T₁-related artifact as a second order system and the subsequent correction method can be said to be effective in eliminating signal contributions associated with such confounds and can be applied to variable TR experiments.

The modified projection procedure is likely to offer advantages over the traditional least-mean-square (LMS) projection method when applied to variable TR experiments in which the experimental paradigm is correlated with the non-T₁-related artifact, as in the case of some previous studies (2,3). The LMS projection procedure is dependent on the shape of each individual voxel’s time-series, which is affected by the stimulus paradigm. Therefore, when correlation exists between the non-T₁-related artifact and the experimental paradigm, it is probable that LMS projection would remove both the non-T₁-related artifact and the desired stimulus-induced components of the fMRI signal. In contrast, the use of an external model for the artifact in this modified projection procedure permits dependence only on the mean of the voxel time-series, which is expected to be independent of the stimulus paradigm. While normalization of the mean signal level over a time-series is a feasible alternative, it may not generalize across all fMRI experiments. The critical limitation is the identification of an appropriate reference signal (i.e., definitively non-activated tissue), requiring strong a priori hypotheses regarding involvement of cortical or sub-cortical structures. If such hypotheses do not exist for a given experiment, selection of a reference signal becomes an iterative process or may become subject to investigator bias. Therefore, the artifact characterization and modified projection procedures used in this study should enable effective removal of the artifact without distorting desired fMRI signal components.

The non-T₁-related oscillatory signal fluctuation is likely due to eddy currents and vibrations of the gradient coil assemblies, brought about by interaction of rapidly switched gradient field-producing currents with the static magnetic field. Eddy currents cause intensity and phase distortions in the image and in the spectra (11). The vibrations of the gradient coil assemblies produce temperature fluctuations in the gradient coils (12) that along with the presence of eddy currents may result in a second or higher order signal change unrelated to T₁ fluctuations in variable TR experiments. In addition to eddy currents and vibration, gradient coil heating is another non-T₁-related confound in variable TR experiments. Chu et al. (13) investigated temperature responses of gradient coils induced by a constant current and discovered an inverse exponential relationship. With a variable TR, the temperature state of the gradient coils differs depending on the variable time interval between successive activations of the gradient coils.

It is important to note that the precise characteristics of the non-T₁-related artifact are likely to differ depending on various system and acquisition factors. The particular MRI system and associated gradient coil design will affect the nature and contribution from eddy currents and mechanical vibration. Since the observed artifact in this study remained consistent over several months, it cannot be attributed to short-term scanner instability or scanner signal fluctuation. Some acquisition parameters that could affect the transient behavior of the gradient system include TR, gradient slew rate, and readout duration. Additionally, receive coil design could affect the importance of the non-T₁-related artifacts, depending upon the shape and extent of the coil sensitivity. For example, surface coils, such as used in this study, have an inherent intensity gradient along an axis normal to the plane of the coil (14). Consequently, the use of a surface coil could exacerbate the observed artifact if physical displacement of the coil from the imaging target were to occur. Note, however, that the results of this investigation cannot be attributed to such an artifact, as the artifact is almost uniformly distributed in the x and y directions across the central slices of the phantom. In fact, no appreciable spatial dependence is observed for the non-T₁-related artifact, suggesting that a global noise signal of roughly fixed (though varying for each voxel) amplitude is introduced to the imaging data. This behavior is most consistent with a slice-select (z-gradient, in this case) error, because variations in the readout gradients would be expected to expand/shrink the spatial extent of the object, resulting in observation of maximal error near signal intensity gradients (such as at edges) – findings which are not observed in these data.

Non-T₁-related artifacts can degrade the precision of fMRI detection. It is key to note that the phenomenon emerges from the acquired signal over a series of averages, making it more likely to be observed when the experimenter seeks to improve the contrast-to-noise ratio. For blocked-paradigm fMRI designs, the percent signal changes induced by a stimulus typically reach 2–5% at 1.5T. Given that the observed artifacts produced (for typical variable TR values) signal changes limited to approximately 0.3%, such experiments are not likely to be critically affected. However, for event-related fMRI designs in which, at 1.5T, induced percent signal changes are often close to 1%, neglecting to account for these non-T₁-related confounds may critically affect the accuracy of localization and amplitude estimation from studies using a variable TR, particularly if the variable TR is correlated with stimulus presentation. Therefore it is important to specifically characterize and compensate for the non-T₁-related artifacts associated with the particular hardware and imaging parameters used to conduct variable TR experiments.

In conclusion, the non-T₁-related signal fluctuations induced by eddy currents and gradient or body coil heating in variable TR experiments represent an observable and potentially deleterious confound. This confound can be modeled by a second order solution and effectively corrected with the modified projection procedure examined in this work. Variable TR experiments should incorporate modeling and compensation of non-T₁-related confounds to improve accuracy in localization and amplitude estimation of fMRI responses.