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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
Magn Reson Med. Author manuscript; available in PMC 2010 September 1.
Published in final edited form as:
PMCID: PMC2763441

Interleaved Spiral-In/Out with Application to fMRI


The conventional spiral-in/out trajectory samples k-space sufficiently in the spiral-in path and sufficiently in the spiral-out path to enable creation of separate images. We propose an interleaved spiral-in/out trajectory comprising a spiral-in path that gathers half of the k-space data, and a complimentary spiral-out path that gathers the other half. The readout duration is thereby reduced by approximately half, offering two distinct advantages: reduction of signal dropout due to susceptibility-induced field gradients (at the expense of signal-to-noise ratio), and the ability to achieve higher spatial resolution when the readout duration is identical to the conventional method. Two reconstruction methods are described; both involve temporal filtering to remove aliasing artifacts. Empirically, interleaved spiral-in/out images are free from false activation resulting from signal pileup around the air/tissue interface, which is common in the conventional spiral-out method. Comparisons with conventional methods using a hyperoxia stimulus reveal greater frontal-orbital activation volumes but a slight reduction of overall activation in other brain regions.

Keywords: Functional magnetic resonance imaging, spiral-in/out methods, susceptibility artifacts


The gradient-recalled echo (GRE) method is the most common technique for Blood Oxygen Level Dependent (BOLD) functional Magnetic Resonance Imaging (fMRI). fMRI requires rapid imaging-sequences and long echo time (TE) to capture the haemodynamic response due to neural activity in brain. Usually a single-shot trajectory is employed to cover a desired k-space volume with each radio frequency (RF) excitation. A single-shot trajectory is used because it can generate an image much faster than conventional imaging techniques (e.g. spin warp), thereby helping to mitigate motion effects. But the readout duration of a single-shot trajectory can be long compared to T2* decay (e.g. with a typical commercial scanner, acquiring a 64×64 image with 20cm field of view (FOV) takes at least 25ms with an echo planar imaging trajectory.) Long readout duration increases image susceptibility to pulsatile motion and to off-resonance. Long echo time worsens the effect of field inhomogeneities, caused by susceptibility effects, which results in signal loss in regions near air/tissue interfaces (e.g. TE is usually set to T2*, which is 30-40ms at 3T) (1). These disadvantages lead to artifacts in images and hamper study of memory and attention involving regions near the ventral frontal, medial temporal, and inferior temporal lobes.

Several techniques have been proposed in the past, to reduce susceptibility-induced signal dropout. They fall into two main categories:

  1. Inhomogeneity minimization (e.g. localized resistive shim coils (2) or diamagnetic passive shims (3), tailored radio frequency (RF) excitation pulses (4)(5), and z-shim techniques (6)-(8)). Localized resistive shim coils and local passive shims are effective only in small areas and may cause discomfort. Tailored RF pulses require individualized design per subject and may be too long, reducing signal-to-noise ratio (SNR) in uniform brain areas and reducing the scan efficiency. The Z-shim technique generally lengthens scan duration by sampling with several shim values.
  2. Modification of readout trajectories to minimize signal loss (9)-(11). The conventional spiral-in/out technique (9) falls into this category and motivates the present work. A brief review of conventional spiral-in/out will be given, followed by the focus of this paper: interleaved spiral-in/out trajectory.

Conventional spiral-out trajectory has been shown to have excellent motion and distortion immunity (12). A single-shot spiral trajectory can cover k-space in a very short time (e.g. 20ms for FOV=20cm, 64×64 resolution with commercial scanners). For fMRI applications, however, this readout duration is still too long and causes susceptibility-induced signal loss at air/tissue interfaces. In fact, activation maps made from conventional spiral-out often have false activation appearing as circular rings around the frontal region. Signal in the frontal lobe region experiences rapid phase change from the air/tissue interface, resulting in displacement of activated pixels (signal pileup). The spiral-in/out sequence was introduced in part to reduce this signal loss (9).

The conventional spiral-in/out sequence has been shown to improve T2* sensitivity and reduce susceptibility-induced signal dropout in BOLD contrast fMRI. This sequence consists of a trajectory that starts at the edge of k-space and spirals inward to the origin, followed by an outward spiral (Figure 1) traversing the same path. Each of the two spirals fully samples the same k-space at or above the critical rate so that two independent images are formed. While this sequence recovers substantial signal in regions of magnetic heterogeneity, images can still suffer from signal dropout especially when higher resolution (requiring longer readout) is desired.

Figure 1
Real parts of gradients and k-space trajectories of (a): conventional spiral-in/out, (b): proposed interleaved spiral-in/out with same maximum gradient-magnitude and slew rate constraints. In (a), conventional spiral-in/out consists of two paths: spiral-in ...

Interleaved spiral-in/out

Here, a sequence is proposed comprising two interleaves, spiral-in and spiral-out, but each samples only half the desired k-space. Both interleaves are required to meet the Nyquist sampling rate in k-space. This sequence will be denoted interleaved spiral-in/out to distinguish it from the conventional spiral-in/out acquisition method (9). These two trajectories are illustrated in Figure 1. The interleaved spiral-in/out sequence is approximately half as long in readout-duration as the conventional spiral-in/out; thereby, it is advantageous in recovering signal in susceptibility-induced dropout regions. Compaction of the readout time near TE is also useful for increasing spatial or temporal resolution.

With reference to Figure 1b, the first interleaf is acquired from a spiral-in trajectory while the second from a spiral-out trajectory. These two trajectories coincide at the origin of k-space. The entire sequence fully samples the desired k-space, so its readout duration is half that of the conventional spiral-in/out method illustrated in Figure 1a. The trajectory direction is reversed in every other time frame by negating polarity of the gradient waveforms. (If spiral-in and spiral-out trajectories respectively sample interleaf 1 and interleaf 2 in time frame n, for example, then their roles become reversed in time frame n+1.)

Reconstruction Methods

Data gathered with the interleaved spiral-in/out trajectory are reconstructed with two methods. The first method includes the entire set of readout data, i.e. both the spiral-in and spiral-out halves; together they sample k-space critically, and images are reconstructed by gridding and FFT. Due to off-resonance and trajectory imperfections, images made from this method often have residual artifacts. T2* decay also causes adjacent interleaves in the composite spiral trajectory to have signal magnitude differences, most prominently at the outer k-space edge. This in turn could lead to azimuthal artifacts. However, there is little signal energy at high spatial frequencies, and simulations confirm that these T2* decay effects are negligible in comparison to off-resonance and trajectory imperfections. This is the motivation for reversing trajectory direction in every other frame: residual artifacts are modulated to the temporal Nyquist frequency and then removed by filtering using UNFOLD. (13)(14) Reconstruction is completed by Fourier transforming each pixel's time-series to obtain its frequency spectrum, multiplying the spectrum by a window that eliminates a small region around the Nyquist frequency, and inverse Fourier transforming back to the time domain. Figure 2 shows the images before and after temporal filtering, as well as their frequency spectra averaged over all brain pixels. Response of the temporal lowpass filter is also shown. The bandwidth, at half maximum, of the lowpass filter is about 83% of the spectral bandwidth, found empirically to be a minimum bandwidth to sufficiently remove artifacts.

Figure 2
Signal spectra from pixel time series averaged over entire image gathered with interleaved spiral-in/out trajectory and reconstructed with method 1. Dashed blue line shows magnitude response of lowpass filter used in temporal filtering. Full width at ...

The second reconstruction method applies the UNFOLD technique (13) to each half of the readout data. Since the trajectory direction is reversed in every other frame, UNFOLD can be used to generate two sets of images: one from the spiral-in half of the trajectory and the other from the spiral-out half. These two sets of images can be combined with various methods (15). Lowpass filtering in the UNFOLD step uses the same window as for the first method.

If the spiral-out (or spiral-in) part of the trajectory is ignored, data acquisition is identical to that of the conventional 2-shot spiral-in (or spiral-out) using two time-adjacent shots.


The signal-to-noise ratio (SNR) of a single image is:


where c is a constant, v is voxel size, Tad is readout duration, and the normalized spectral filter factor (13) is


where F (ω) is the filter spectrum, with 0 < F (ω) < 1.

To simplify the calculations, we assume no noise correlation between spiral-in and spiral-out images when choosing weights to calculate their average signal magnitude. For in vivo data, there exists some correlation between the two images (due to presence of physiological noise), and the SNR calculations are thus slightly over-estimated. (9)


Comparison with conventional spiral-in/out

To demonstrate advantages of the interleaved spiral-in/out trajectory, fMRI activation volumes were compared with those obtained by conventional spiral-in/out acquisition at high resolution. Readout durations were 60ms (interleaved) and 120ms (conventional) for an image matrix size of 128×128. Minimum echo times was used for both trajectories (36ms and 66ms respectively). All experiments were carried out at 3T (GE Signa, Milwaukee, WI) with a FOV of 20cm. When reconstructing the conventional spiral-in/out trajectory, we employed the same temporal lowpass filtering (filter bandwidth/spectral bandwidth=83%) to remove part of the temporal spectrum in the vicinity of the Nyquist frequency. In this way, a comparison of the interleaved spiral-in/out with conventional spiral-in/out method could be achieved using the same temporal resolution and noise characteristics.

Task and Data Acquisition

Oxygen inhalation modulates blood T2* based on changes in oxygen saturation level, during which signal intensity is expected to increase. (16) The oxygen inhalation task consists of two on/off blocks of 200 seconds each, alternating between pure oxygen and room air. Oxygen is delivered through a nasal cannula at 10L/min during on-blocks, but no gas is administrated (i.e., volunteers breathed room air) during off-blocks. The bore fan in the scanner is on at all times to minimize oxygen buildup. Each volunteer was scanned with conventional spiral-in/out and interleaved spiral-in/out trajectories. The order of trajectory used was counterbalanced across volunteers to reduce bias. T1-weighted fast spin-echo (FSE) scans were obtained for anatomic reference (TR/TE/ETL=68ms/4000ms/12). Eight volunteers were scanned with a single-channel head coil. Five oblique slices were gathered for fMRI experiments (TR/α/TH/gap/FOV/matrix = 1s/70°/5mm/1mm/20cm/128×128). Volunteers provided informed consent in accordance with a protocol approved by the Stanford Institutional Review Board.

Images were reconstructed with an off-line computer (Dell PC, Pentium 4). Linear shim corrections for each slice were applied during reconstruction by modifying the k-space mapping using individual field maps obtained during the scan. (17) Concomitant field effects and navigator corrections were performed. (18)

Data Analysis

Interleaved spiral-in/out data were reconstructed using several methods to yield four time-series:

(1) using reconstruction method 1,

(2) and (3) spiral-in and spiral-out using UNFOLD technique in reconstruction method 2,

(4) signal magnitude-weighted combination of 2 and 3.

Conventional spiral-in/out data reconstruction generated the following time series:

(5) signal magnitude-weighted combination of spiral-in and spiral-out images (temporally filtered before summing).

The method for calculating t-score was adapted from Lee et al. (17). Each fMRI time series was detrended with a second order polynomial. It was then correlated with a reference function consisting of the convolution of a standard haemodynamic response function (HRF) (18) with task on/off paradigm. Because the response for a gas challenge is slower, a gamma variate HRF with a 30-s lag, determined empirically to account for the slow response to inspired gas stimuli, was also applied to one volunteer's data. Although the number of activated pixels from each reconstruction technique was slightly changed, the relative activation volumes remained consistent. This was expected, given the long task blocks employed here, and therefore the conventional HRF was used for convenience with no loss in accuracy. A Fisher transform converted the correlation coefficient to t-score according to each voxel's degrees of freedom, based on Worsley et al. (19) and Kruggel et al. (20). Finally, a sigma filter (21)(22) was applied to these maps to cluster pixels in a 3×3 region, thereby reducing single-voxel false positives.

ROI definition and activation volumes calculation

To evaluate activation detection with the proposed trajectory and reconstruction methods, the numbers of activated pixels were recorded within a region of interest (ROI) near the prefrontal cortex and from the whole brain for each slice. The ROI near the prefrontal cortex was drawn by hand from the central slice, for each volunteer, and chosen where signal is lost but avoiding areas of signal pileup. This ROI was applied to all reconstructions for that volunteer. The number of activated pixels from each time-series was normalized to that obtained from signal magnitude-weighted conventional spiral-in/out data (time-series 5). This normalization was performed separately for the ROI region and the whole brain for each volunteer.

Comparison with Conventional Spiral-Out at optimal echo time

Volunteers 5-8 also underwent an extra functional scan that employs a conventional spiral-out trajectory at echo time of 30ms to maximize BOLD contrast. The motivation behind this extra scan is: Spiral-out images from the conventional spiral-in/out acquisition are gathered at TE=66ms because of the long spiral-in readout (Figure 1). Choosing TE=30ms is a better representative of typical results, had only a conventional spiral-out trajectory been used. This acquisition yielded the time-series:

(6) conventional spiral-out at TE=30ms, with temporal filtering,

SNR verification with phantom

The theoretical SNR was verified with phantom measurements. A uniform-sphere phantom (T2=46ms) was imaged under identical conditions as human functional scans except only 100 time-frames were collected. The same reconstruction procedures as with in vivo data were employed. For each time-series, an identical rectangular ROI was drawn inside the phantom. Temporal mean and standard deviation of the detrended pixel time-series were calculated to form a temporal SNR map. (23) After all SNR maps were calculated, they were normalized by the map from time series 6 (conventional spiral-out without temporal filtering at TE=30ms). Finally, the spatial mean and standard deviation of the normalized SNR were calculated and listed in Table 1.

Table 1
Theoretical SNR compared with measurement. Interleaved spiral-in/out trajectory generates time series 1-4, conventional spiral-in/out trajectory generates time series 5, and conventional spiral-out at TE=30ms generates time series 6. Experiments were ...


Table 1 shows the theoretical SNR and phantom measurement of SNR. Most of the measurements agree well with theoretical SNR. For time series (2/3) (interleaved spiral-in/out plus UNFOLD), residual aliasing artifacts from UNFOLD have probably contributed to the loss in SNR.

Figure 3a shows activation maps from volunteer 2 (p<0.001). The temporally averaged T2*-weighted images from the same volunteer are shown in Figure 3b. The interleaved spiral-in/out method reduces signal loss in prefrontal cortex region and decreases the amount of artifact around brain boundaries. Time series 1 and 4 from the proposed method compare well with conventional technique (time series 5) in homogeneous brain regions, and reveal higher activation volumes in prefrontal cortex.

Figure 3
(a) Activation maps (t-score, p<0.001) and (b) temporally averaged magnitude images from volunteer 2 gathered with (1-4) interleaved spiral-in/out, (5) conventional spiral-in/out trajectories, and (6) conventional spiral-out at optimal TE. Only ...

The normalized number of activated pixels within the prefrontal cortex ROI for all volunteers is shown in Figure 4(a), and those counted using the entire brain area are plotted in Figure 4(b). Boxes have a red line at the median quartile and are bounded by lower and upper quartile values. Results from each time series are normalized to that using signal-magnitude weighted conventional spiral-in/out trajectory (time series 5). Volunteers 1-8 contribute to all results, while only volunteers 5-8 contribute to the results for the conventional spiral-out method at TE=30ms. Note the scale difference in ROI and whole-brain columns.

Figure 4
Normalized activation volumes in ROI from different time series (a) near frontal area and (b) in entire brain. Interleaved spiral-in/out (time-series 1 and 4) outperforms others in detecting activation in frontal ROI while offering results comparable ...

The interleaved spiral-in/out trajectory (time series 1 and 4) yields the highest number of activated pixels in susceptibility-induced signal dropout regions, while results for the whole brain reveal slightly fewer activated pixels than the conventional spiral-in/out (time series 5).

While activation in the heterogeneous brain regions is expected to be high using conventional spiral-out (TE=30ms) acquisition, normalized activation volumes within frontal ROI (Figure 4(a)) are falsely high. Activation maps reveal that signal pileup around the frontal lobe is easily distinguished (Figure 5). This displaced activation is common when imaging near the frontal area using the conventional spiral-out trajectory.

Figure 5
Two slices near temporal lobe; activation maps are overlaid on anatomic images from volunteer 5. (Top) Interleaved spiral-in/out trajectory reconstructed with method 1 (time-series 1). (Bottom) Conventional spiral-out with temporal filtering (time-series ...

Absence of signal pileup with interleaved spiral-in/out

Signal pileup should be considered with caution because the signal's origin is not clear; such false activations are obviously displaced when compared to anatomic structure. There should be no signal present unless grey matter exists there; for example, the boxes in Figure 5 call out such false activation. Results of conventional spiral-out (TE=30ms) acquisitions within the frontal ROI in Figure 4(a) are therefore erroneous since the majority of activated voxels came from these signal pileup regions. Although the fraction of false activation from frontal region compared to the whole brain is smaller, activation volumes for the whole brain (Figure 4(b)) are likely inflated for the same reason.

In comparison, interleaved spiral-in/out images are free from signal pileup near air/tissue interface and detect activation in that area.


We present a new imaging trajectory utilizing spiral-in and spiral-out interleaves efficiently. When compared with conventional spiral-in/out methods having the same resolution, the proposed interleaved spiral-in/out trajectory is half as long in readout duration so that susceptibility-induced signal dropout is reduced. As a result, activation within susceptibility-compromised regions is better detected using the proposed trajectory, and/or higher spatial or temporal resolution can be achieved.

When comparing the number of activated pixels within Figure 4, keep in mind that conventional spiral-in/out has a readout duration of 120ms (60ms for spiral-in and spiral-out interleaves) while interleaved spiral-in/out has a total readout-duration of 60ms. Thus, the combined spiral-in and spiral-out images from conventional spiral-in/out trajectory (time series 5), in theory, have an SNR advantage due to longest readout duration (120ms). On the other hand, spiral-in and spiral-out images reconstructed with the UNFOLD technique from the interleaved spiral-in/out trajectory (time series 2 and 3) have SNR disadvantage in uniform brain since their readout durations are only 30ms.

Activation maps (Figure 3) alone cannot be used to decide on the best trajectory. When the imaging region is homogeneous, the readout duration can be relatively long to achieve high SNR. Then use of conventional spiral-out is a good choice. When the imaging region is heterogeneous, on the other hand, reducing readout duration can minimize signal loss. In that case, use of interleaved spiral-in/out is recommended. Interleaved spiral-in/out offers the advantage of using a two-shot trajectory (improved spatial resolution and reduced signal loss), but without the disadvantage of losing temporal resolution.

The interleaved spiral-in/out trajectory is effective in reducing susceptibility-induced signal dropout and detecting activation in the affected regions (as shown in Table 1 and Figures 3, ,4).4). With the compact readout-duration of the interleaved spiral-in/out trajectory, repetition time can be reduced such that more time frames are gathered in a fixed scan-time so as to increase SNR efficiency and temporal resolution. On the other hand, interleaved spiral-in/out can provide higher spatial resolution than conventional spiral-in/out if readout-duration is fixed.

What motivated our choice of spiral sampling, instead of Cartesian, is motion insensitivity, low distortion (12)(24), and the potential for high speed of acquisition when used in conjunction with acceleration techniques like parallel imaging. The proposed method is easy to incorporate into parallel imaging techniques such as spiral SENSE (25)(26), for example. Combining parallel imaging with interleaved spiral-in/out can further reduce readout duration (and signal dropout), certainly a direction for continuing research.


The authors would like to thank Drs. Elfar Adalsteinsson, Daniel Ennis, Gunnar Krueger, and Angel Pineda for helpful comments and Dr. Greg Zaharchuk for help in the oxygen experiments.

Supported by NIH RR 09784, the Lucas Foundation, and GE Health Care.


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