As the magnetic field is increased, in principle, blood-oxygen-level-dependence (BOLD) imaging can have improved spatial specificity in functional magnetic resonance imaging (fMRI) because more signal originates from tissue and small capillaries rather than from large veins. (1
) The fundamental tradeoffs, between spatial and temporal resolution, present many challenges for high resolution and high field fMRI. Higher spatial resolution requires longer readout duration and postponed echo time (TE) that respectively result in increased sensitivity to off-resonance and non-optimum BOLD contrast. Readout duration and TE can be shortened by multi-shot acquisition, but temporal resolution will consequently decrease. Despite reduction of signal-to-noise ratio (SNR), parallel imaging (PI) methods in fMRI are known to be advantageous for reducing signal loss in susceptibility-induced signal dropout regions of the brain. (2
) Parallel imaging allows increase in spatial and temporal resolution with shorter TE and is particularly advantageous at higher-field.
Weiger et al.
first demonstrated use of a spiral sequence together with parallel imaging. (3
) They applied parallel imaging to reduce readout duration in the spiral trajectory, which lessens signal dropout in frontal regions. Consequently, they successfully detected activation in a tasting task stimulating the orbito-frontal cortex. To calibrate coil sensitivity, required by the sensitivity encoding (SENSE) reconstruction algorithm, they gathered an extra fully-sampled image prior to their fMRI experiment. We refer to their technique for calculating sensitivity maps as the reference frame
An alternative method for deriving coil sensitivity, from a time-series without a separate image acquisition, was presented by Kellman et al.
) There, the UNFOLD method, “Unaliasing by Fourier-Encoding the Overlaps Using the Temporal Dimension,” together with SENSE reconstruction was employed to remove spatial and temporal aliasing. This Adaptive Sensitivity Encoding Incorporating Temporal Filtering method (TSENSE) was demonstrated for real-time nonbreath-held cardiac imaging with an acceleration factor
R = 2. (Acceleration is a measure of undersampling in k
-space.) They acquire odd and even k
-space lines in sequential images. Sensitivity profiles are calculated by temporally filtering the aliased images of the same undersampled data. Kellman shows that, with TSENSE, sensitivity profiles can be calculated adaptively to track signal changes due to breathing or motion. In order to obtain accurate sensitivity profiles, images used to generate them must be alias-free. The amount of residual artifact after temporal filtering is related to a subject’s dynamic nature, number of temporal frames used for filtering, and filter bandwidth. Depending upon the application and subjects (e.g.
, task design in fMRI and children vs.
adults), filtering parameters may require monitoring and adjustment.
Preibisch et al
) used an EPI-SENSE sequence to investigate SNR vs.
fMRI sensitivity at two spatial resolutions. At low spatial resolution, parallel imaging was used to reduce readout duration; surprisingly, SNR and fMRI sensitivity were hardly reduced. At high spatial resolution, parallel imaging was used to increase spatial resolution. Physiological noise was reduced and fMRI sensitivity was similar to that of the regular low-resolution single-shot acquisition. They concluded that parallel imaging has negligible effect on fMRI sensitivity despite decrease in SNR.
The lack of reduction in fMRI sensitivity with decreasing SNR in parallel imaging has been observed and explained by several authors. (5
) fMRI sensitivity is inversely related to temporal signal instability originating from physiological and thermal noise. Parallel imaging increases thermal noise but not physiological noise. Thus, when physiological noise dominates, fMRI sensitivity is hardly affected. Therefore, as long as physiological noise is much greater than thermal noise, PI fMRI sensitivity is comparable to non-PI techniques. Nevertheless, a major incentive to use parallel imaging at high field is high spatial resolution; i.e.
, small voxel size. As voxel size decreases, thermal noise dominates. At present, the limiting factor in achieving high spatial resolution with parallel imaging (at high field and with sufficient fMRI sensitivity) is the fact that thermal noise leads to temporal signal instability, thereby degrading fMRI sensitivity.
Herein we present a PI technique for improving fMRI sensitivity at high spatial resolution when thermal noise predominates. We propose measurement of coil sensitivity by combining fully sampled data from a number of adjacent frames in an interleaved acquisition. In a two-shot interleaved acquisition, for example, k-space is fully sampled at every two repetition times (TR). Sensitivity profiles are then calculated from these full-resolution alias-free images and updated synchronously with image acquisition. This technique provides the convenience of self-calibrating sensitivity maps. In addition, we demonstrate that the technique provides inherent noise filtering and significantly enhances fMRI activation measurement. Improvement is especially significant at higher resolution and thinner slices where thermal noise exceeds physiological noise. For example, the technique detects activation at high spatial-resolutions (e.g. slice thickness of 2mm) better than previous methods. The technique results in higher temporal resolution and slightly more or comparable activated volumes compared to a standard two-shot reconstruction in fMRI experiments.
The technique may be incorporated into any interleaved acquisition. We demonstrate an implementation with two-shot interleaved spiral-in/out trajectory using an acceleration factor R = 2. The spiral-in/out trajectory is known to be effective in reducing signal drop-out from susceptibility-induced field gradients. (7
) We compare the proposed sliding window
PI technique with conventional (non-accelerated) two-shot reconstruction, as well as with the conventional PI reference
frame method and an all-frame
method. In the all-frame
method, data acquired over the whole time-series is averaged together to calculate coil sensitivity. In all three comparisons, the proposed technique demonstrates enhanced BOLD activation. The improvement is most significant for high resolution, thin slice, and low SNR cases.
Sliding Window method
In the sliding window method, several adjacent two-shot images are selected for calculation of sensitivity profiles. These profiles are then applied exclusively to reconstruct data under that window. The minimum sliding window width that will provide fully-sampled data, with which to calculate sensitivity maps, is the acceleration factor R ; which is taken to be 2 here for all demonstrations and further discussion. The technique eliminates the temporal filtering step required by TSENSE. Since the sensitivity profiles are calculated from two-shot images, they are fully sampled, unaliased, and free of other post-processing artifacts. Moreover, these two-shot images are reconstructed from functional data itself; so no extra scans are needed. We shall show that our proposed coil sensitivity calculations reduce image noise when compared with all-frame or reference frame methods both in theory and in vivo, especially when thermal noise equals or exceeds physiological noise.
The original TSENSE diagram from Kellman (4
) and a diagram of our proposed sliding window
technique are shown in for comparison. The main difference between our technique and TSENSE is that TSENSE calculates its sensitivity maps by temporally lowpass filtering time frames of undersampled k-space data. Those time frames have alternating k-space undersampling patterns so that aliasing is modulated at the Nyquist frequency and then removed via lowpass filtering. The minimum number of time frames required for lowpass filtering is the number of alternating k-space sampling patterns (same as reduction factor R). In practice, the number of time frames used for lowpass filtering is generally greater than R for better separation of desired and aliasing frequency components. In our sliding window
technique, sensitivity maps are calculated from multi-shot reconstructed images. The number of time frames used in our multi-shot reconstruction is equal to the number of alternating k-space sampling patterns (exactly R), so that the calibration maps are fully sampled, thus distortion free. The impact of averaging more time frames will be discussed later where we will find that reduction in thermal noise is best when R frames are used.
Figure 1 (a) TSENSE diagram adapted from Kellman (4). (b) Proposed sliding window technique (R=2) as comparison.
Effect of noise
We express the acquired k
-space data as
is the object image vector, p
is a physiological noise vector, ε
is a vector of thermal noise, S
is a matrix of coil sensitivities, and E
is the Fourier kernel matrix. A reconstructed image with estimated sensitivity maps Ŝ
We show, in Appendix A
, how an image reconstructed under the sliding window
method can be expressed
is a vector of thermal noise averaged over a number of consecutive temporal frames, and Q−1
is a normalization matrix to the estimate of coil sensitivity.
, the image estimate
is free of thermal noise. But that would occur only when R=1, which is not of interest since no readout acceleration is provided. When sliding window width is minimal (R=2), then
is the closest approximation to thermal noise ε achievable and so
will contain the least amount of noise. As the sliding window width becomes wider,
to a lesser degree which results in
having more thermal noise. When the all-frame
method is used, on the other hand,
is averaged to zero under a Gaussian noise assumption; thermal noise sampled in k
-space is therefore propagated to
. Smoothing sensitivity maps would also result in thermal noise propagation to
The difference of the noise terms in Eq.
leads to a reduction of noise because thermal noise in ε
is correlated with that in
; that is, the case of a sliding window
method with a narrow window width. Otherwise, the subtraction would not necessarily lead to a noise reduction.
We demonstrate the technique with a two-shot spiral-in/out trajectory providing an acceleration factor of R=2. For all even time frames, the trajectory is rotated by 180 degrees so that k-space is fully sampled every two TRs. Experiments were performed with four slice thicknesses (2mm, 3mm, 4mm, and 5mm) in order to alter the relative contributions of thermal and physiological noise, and the number of slices gathered was 9, 7, 7, and 5 respectively to cover approximately the same volume of brain tissue. Slices were separated with a gap of 1mm. All experiments were performed on a GE 3T whole-body scanner (GE Signa, GE Healthcare, Waukesha, WI) equipped with a maximum gradient amplitude of 40 mT/m and a slew rate of 150 mT/m/ms. An 8-channel head coil (MRI Devices Corporation, Pewaukee, WI) was used for all image acquisitions. The TE was set to be minimal allowed by the spiral-in trajectory (35.4 ms), TR/α/matrix size/FOV = 2s/70°/128×128/20cm. The scan time was 248 seconds (data from the first 8 seconds discarded). T2-weighted fast spin-echo (FSE) scans were obtained for anatomic reference (TR/TE/ETL=4000ms/68ms/12). Six healthy subjects participated after giving informed consent in accordance with a protocol approved by the Stanford Institutional Review Board.
The fMRI task consisted of 6 cycles of an on/off block design having a period of 40s. During the on-block, subjects saw a checker board flashing at 8Hz. Subjects were told to stare at a fixation-cross to reduce eye movement during the off-block. To keep subjects’ attention throughout scans, a red cross appeared at random times; twice for 0.5s during each on-block. Subjects were instructed to press a button as soon as they saw the cross. This experiment was performed once for each slice thickness; the order of the slice thickness scans was randomized among subjects.
Subjects 1–3 also participated in noise measurement scans in separate sessions. Noise measurement scans are similar to functional scans above except that the flip angle is set to 0 so that only thermal noise is gathered. Only 3 slices and 64 time frames were collected. Two scans were performed: flip-angle = 70° and 0°. A fast T1 mapping scan (8
) was utilized to obtain images for later gray matter segmentation; one for each slice thickness. Subjects were instructed to relax while no stimulation or task was given.
Sensitivity profiles are calculated using the functional data itself. No extra calibration scans are needed; this reduces inconsistency between a reference frame and the functional data to be reconstructed. Standard spiral trajectory gridded-reconstruction is used to make two-shot images from each coil's data. (9
) For every two TRs, in other words, two fully-sampled two-shot images (one spiral-in and one spiral-out) are reconstructed for each coil. The sensitivity profile of each coil is the ratio of a fully sampled two-shot image from that coil to the square root of pixel-wise sum of squares of all coil images. Separate sensitivity profiles are generated for spiral-in and spiral-out data. For the all-frame
method, all fully sampled two-shot images of each coil over the entire time series are first averaged for sensitivity profile calculation. The resulting sensitivity profiles are used for conjugate gradient (CG-)SENSE reconstruction (10
) of the entire time series. The number of iterations in CG-SENSE reconstruction is 7 regardless of sensitivity map calculation method. For the sliding window
method (window width = 2 TRs), a new fully sampled two-shot image from each coil is formed after every TR. The sensitivity profile for each coil is then updated at every TR and used for CG-SENSE image reconstruction at that TR. The window width (number of TRs included in the average for SENSE map calculation) is assumed to be 2 TRs for the sliding window
method unless otherwise noted. Concomitant field effects correction and navigator correction are first performed on the raw data. (12
) The same CG-SENSE program (written in MATLAB, Mathworks R13, Natick, MA) is used for reconstruction regardless of sensitivity profile calculation methods; it generates one spiral-in image and one spiral-out image for every TR.
Data gathered for noise measurement (flip angle 70° and 0° with no task performed) is reconstructed with all-frame
and sliding window
methods described above. A gray matter mask is segmented manually from a T1 map for each slice and each slice thickness. This mask is used to extract gray matter pixel time-series from data at flip-angle=70°. The temporal standard deviation of each gray matter pixel is recorded and then averaged over three slices; this gives the total noise σ. The thermal noise σ0
is calculated by the same procedure using images with flip-angle = 0°, and the resulting standard deviation is multiplied by 1.527 to correct for the Rayleigh distribution of Gaussian noise in magnitude images. (13
) Physiological noise σp
is then calculated from (15
The method for calculating t-score is adapted from Lee et al.
) (also see 17
). The steps involved are summarized here: each fMRI time series is first fitted to a second order polynomial for detrending. It is then correlated with sine and cosine functions at the fundamental task frequency (higher harmonics are negligible because the task blocks are short). The temporal phase of those voxels, with correlation coefficients exceeding a threshold of 0.2, is computed from the arctangent of sine and cosine correlations and averaged across each slice. The correlation is then projected onto this phase, per voxel, to provide a maximally in-phase correlation map. This model-free (Fourier) method eliminates bias from inaccuracy in assumed hemodynamic response function. Finally, a Fisher transform converts the correlation coefficient to t-score according to each voxel’s degrees of freedom. A sigma filter (12
) is applied to these maps to cluster pixels in a 3×3 region, thereby reducing single-voxel false positives.