Optimized EPI for fMRI studies of the orbitofrontal cortex: compensation of susceptibility-induced gradients in the readout direction

In fMRI experiments based on the BOLDeffect as measured by GE EPI, the local BOLD sensitivity (BS) can be theoretically estimated from where I is the local intensity in the T*₂-weighted image [14]. TE is the effective echo time including echo time shifts due to gradients in the PE direction [14]. Note that this simple relationship is only strictly correct for a monoexponential decay of the MR signal. From Eq. (1) it is obvious that losses in the BOLD sensitivity due to susceptibility-induced gradients can be caused by a reduction of the image intensity or shortening of the effective echo time.

Since it has been previously described how susceptibility-induced gradients in the through-plane [11,13] and PE direction [14] cause signal loss, we focus here on signal loss caused by susceptibility-induced gradients (G _x ^susc ) in the RO direction. We consider the case of EPI with cartesian sampling (Fig. 1a, cyan solid line) and assume that the field of view L _x,L _y in the RO and PE directions, respectively, is scanned with a resolution of Δx and Δy. The gradient G _x ^susc causes a shift of the echo in the k _x/RO direction in k-space. The shift increases linearly with the duration between the RF pulse and each echo in the EPI echo train, resulting in a shifted and sheared k-space trajectory (Fig. 1a, red dotted line). If an additional compensation gradient G _x ^comp in the RO direction is switched on for the duration τ before the data acquisition, the total k-space shift ΔK _susc at the local echo time TE is with the compensation gradientmoment M _x ^comp x =G _x ^comp · τ, and γ being the gyromagnetic ratio. In the presence of a susceptibility-induced gradient in the PE direction (G _y ^susc ) the effective echo time is given by \({\rm{TE}} = {\rm{T}}{{\rm{E}}_0}/{Q_{{\rm{pos/neg}}}}\) with \({Q_{{\rm{pos/neg}}}} = 1 \mp {(2\pi )^{ - 1}} \cdot \gamma \cdot \Delta t \cdot {L_y} \cdot G_y^{{\rm{susc}}}\) for a positive or negative PE prewinder moment [14, 15], where TE₀ is the nominal echo time as entered on the scanner interface and Δt is the echo spacing

Severe signal loss occurs if the echo is shifted outside the acquisition window (Fig. 1b, cyan solid line), i.e., if the k-space shift ΔKsusc at TE exceeds the sampled k-space window in the RO direction .

As can be seen from Eqs. (2) and (3), the maximal susceptibility-induced gradient which can be tolerated before dropouts occur depends on the RO resolution Δx and the effective local echo time TE. The echo time may be modified locally by susceptibility-induced gradients in the PE direction, resulting in an interaction of the in-plane gradients in the RO and PE direction on signal dropouts. In contrast to the susceptibility-induced gradients in the PE direction, the gradients in the RO direction do not shift the echo time significantly (maximally by Δt/2), so the local TE and thus the BOLD sensitivity are minimally affected. However, the signal is abruptly lost when the central echo falls outside the acquisition window (when the shift exceeds Δt/2). Even before the echo is completely shifted outside the acquisition window, the point-spread-function (PSF) may be altered, leading to intensity fluctuations and a reduction in spatial resolution (for simulations of susceptibility-induced distortions of spiral trajectories and PSF, see [19]).

We can use Eqs. (2) and (3) to calculate the spatial resolution and TE required to avoid dropouts due to susceptibility-induced gradients in the RO direction. At 3T, susceptibility gradients are limited to approximately 300 µT/m in most brain areas (e.g., for the most severely affected OFC see [20]). The minimal TE providing adequate BOLD sensitivity is in the range of 25 ms-30 ms [2, 21]. Thus, using a TE = 25 ms at 3T and assuming a maximal |G _x ^susc | ≈ 300 µ T/m the lowest RO resolution not causing dropouts is Δx = 1.5 mm. At 1.5T with a maximal |G _x ^susc | ≈ 150 µ T/m (estimated from the values at 3 T) and aminimal TE of about 35–40 ms [21], the respective resolution is approximately Δx = 2mm at TE= 37ms. Note that we have neglected any local echo time shifts for this simplified calculation. However, if significant echo time shifts occur and can be predicted, the maximal local TE should be used instead of the nominal TE₀ in Eq. (2).

For all experiments, unless otherwise noted in the individual experimental sections, the following procedures, techniques, and parameters were used. For each experiment one volunteer was scanned in a 1.5 T whole-body scanner (Magnetom Sonata, Siemens Medical,Erlangen, Germany) or a 3T head scanner (Magnetom Allegra, Siemens Medical). The whole-body scanner was operated with a body transmit and a head receive coil, the head scanner with a head transmit-receive coil. The volunteers (2 females, 1 male, age 32–37 year) gave written informed consent according to the guidelines of the local ethics committee.

The manufacturer’s standard automatic 3D-shim procedure was performed at the beginning of each experiment, correcting for first and second order distortions in the static magnetic field within the imaged volume. We implemented single-shot EPI sequences which allowed us to freely choose the moment M _x ^comp of the compensation gradient prepulse in the RO direction, the moment of the z-shimming gradient prepulse, and the PE gradient polarity. The details of the imaging parameters for each experiment are given separately. EPI magnitude images, echo time (TE) maps, and BOLD sensitivity (BS) maps were reconstructed from the complex measurement data using a generalized reconstruction method based on the measured EPI k-space trajectory to minimize ghosting [22]. The TE maps and BS maps were estimated according to the procedures in Deichmann et al. [14], i.e., the local TE was determined from the local phase evolution during the acquisition and the BS was then determined by Eq. (1).

A field map was recorded for distortion correction, anatomical reference, and simulating EPI dropouts. The parameterswere at 1.5 T/3T: double echo FLASH, 64/48 oblique transverse slices, slice thickness = 2 mm, gap between slices = 1 mm, repetition time TR = 1,170/761 ms, flip angle α = 90°, short TE = 10 ms, long TE = 14.76/12.46 ms, BW = 260 Hz/pixel, PE direction anterior-posterior, field of view FOV = 192 × 192 mm², matrix size 64 × 64, flow compensation. Using the FieldMap toolbox [4, 23], fieldmaps were estimated from the phase difference between the images acquired at the short and long TE and unwrapped [24]. After spatial smoothing (Gaussian kernel, FWHM = 6mm) of each field map and applying a brain mask created by the Brain Extraction Tool [25], voxel displacements for the EPI images were determined from the field map and imaging parameters. Distortion correction was performed by applying the inverse displacement to the EPI magnitude images (displacement maps were resliced in the EPI space by trilinear interpolation), TE maps, and BS maps without a correction for the intensity distortions.

The gradients of the field inhomogeneities were estimated by numerical differentiation from the field maps. We used 8th order sinc interpolation and smoothed the field maps with FWHM = 3mm (trading signal-to-noise ratio (SNR) for higher resolution; [4]). The field maps, gradient maps, and all images derived from EPI (magnitude, TE, BS) were coregistered and resliced [26]. The field inhomogeneity gradient maps were used to calculate maps of predicted signal dropout in the measured EPI images on the basis of our theory given the chosen imaging parameters, i.e., TE, spatial resolution, echo spacing Δt, slice tilt, and compensation gradient prepulse moment M _x ^comp . We simulated the effects of both in-plane and through-plane field gradients. Since the effects of through-plane gradients had been described previously [14, 15], results were only reported for the dropouts due to the in-plane gradients. All data analyses and simulations were performed using SPM2 ([26]; WellcomeTrust Centre forNeuroimaging,London,UK) and custom-made scripts in Matlab7 (The MathWorks, Natick, MA).

In this 1.5T experiment we investigated those brain areas where signal losses cannot be recovered using the established compensation technique for susceptibility-induced gradients in the through-plane and PE direction [13, 15]. The technique relies on an optimal slice tilt, z-shimming gradient prepulse, and PE gradient polarity to minimize signal losses [18]. To determine the parameter set optimizing the BS for each brain region, EPI were acquired with different z-shim gradient moments from M _z ^comp = −4mT/m×ms to +4 mT/m×ms (in steps of 1mT/m×ms), different slice tilts from −45° to +45° from the transverse plane (in steps of 15°), and different PE gradient polarities. For each parameter set, five EPI volumes were recorded. The first four volumes were discarded to allow for T1-equilibration. The following were the basic EPI imaging parameters: 48 slices, slice thickness = 2 mm, gap between slices = 1 mm, TR = 4.4 s, α = 90°, TE₀ = 50 ms, BW = 2,298 Hz/pixel, bandwidth in PE direction BWPE = 31.2Hz/pixel, PE direction anterior-posterior, FOV = 192 × 192mm², matrix size 64 × 64. A maximal BS map was calculated from all BS maps acquired with different parameters. The maximal BS map displayed the highest BS in each voxel achievable using optimally adjusted parameters. A subset of these data was used previously to construct a BS atlas [18] where further details on the data analysis and BS maps can be found. The maximal BS map was qualitatively assessed for residual signal losses by comparison with the anatomical FLASH image. It was further assessed whether the residual BS losses coincided with high amplitudes in the susceptibility-induced gradients.

In this 1.5T experiment, we assessed how the signal dropouts vary when compensation gradient prepulses are applied in the RO direction before the k-space acquisition. The moment was varied from M _x ^comp = −3m T/m×ms to +3 mT/m×ms in steps of 1mT/m×ms. For each moment, five EPI volumes were recorded. The first four volumes were discarded to allow for T1-equilibration. The EPI imaging parameters were the same as in Experiment 1. Since the OFC was a main target region of this study, dropouts due to field gradients in the PE direction in this area were minimized by tilting the oblique transverse slices by 30° towards the coronal plane (with the anterior edge being more superior than the posterior edge) while using a positive PE gradient polarity according to Deichmann et al. [13]. The measured EPI images were assessed qualitatively to identify signal losses dependent on the compensation gradient prepulse moment M _x ^comp . We then compared the dropouts in the image recorded with zero prepulse to our theoretical prediction.

In this experiment, we investigated the dependence of the signal loss on the effective TE at 1.5 T. The effective local echo time TE depends not only on the nominal echo time TE₀ but also on the field gradients in the PE direction and the polarity of the PE imaging gradient. When the PE imaging gradient polarity is inverted, the shift in TE is reversed. To assess how the signal dropouts in EPI vary due to the local echo time shifting, EPI images with different gradient prepulse moments in the RO direction and different PE gradient polarities were recorded. For each of the two PE polarities, the prepulse moment was varied from M _x ^comp = t=4mT/m×ms to +4 mT/m×ms in steps of 1mT/m×ms. For each prepulse moment and PE polarity, ten EPI volumes were recorded (same EPI parameters as in Experiment 1, except for TE₀ = 70ms, TR= 5.4s, z-shim gradient prepulse moment = −1.5mT/m×ms). The first four volumes were discarded to allow for T1-equilibration and the remaining six volumes were averaged to increase the SNR. The calculated TE maps were assessed for echo time shifts due to susceptibility-induced gradients in the PE direction. Based on this information, the theoretically predicted dropouts, and the measured EPI images were assessed qualitatively for local TE dependent signal losses.

In this experiment at 3T, we determined whether an increase of resolution can recover the BOLD contrast-to-noise ratio (CNR) in the OFC areas affected by susceptibility-induced gradients in the RO direction. Although the BOLD sensitivity (BS) may be estimated from a single EPI image [14], we additionally conducted an fMRI breath hold experiment [27] to exclude the possibility that an increase in the estimated BS is masked by an increased temporal noise. Breath holding as a hypercapnic challenge reliably increases the cerebral blood flow and the BOLD signal, and is comparable to CO₂ inhalation, as shown in previous studies [27].

The fMRI experiment comprised three sessions. Each session consisted of four blocks of breath holding (30 s duration) alternating with blocks of free breathing (45 s duration), beginning and ending with free breathing. The subject was cued at the beginning of each block via head phones. Relatively long breath holding/free breathing periods were chosen to maximize the BOLD signal changes and to allow a steady breathing state to be reached.

To reduce the residual dropouts in the OFC, EPI images were acquired with the optimal parameters as given in the Theory section: resolution of 1.5mm in the RO direction and 3mm in the PE direction, and TE₀ = 25 ms. The other EPI parameters were: 46 oblique transverse slices tilted by 30°, slice thickness = 2 mm, gap between slices = 1 mm, TR = 2.99 s, α = 90°, TE₀ = 25 ms, BW = 1,953 Hz/pixel, BWPE = 27.9Hz/pixel, PE direction anterior-posterior, FOV = 192 × 192mm², matrix size 128 × 64 (ROx PE), z-shim gradient prepulse moment = −1mT/m×ms. For anatomical reference, a high-resolution T₁-weighted 3D image was used that was previously acquired at 1.5 T (3D MDEFT [28]; FOV = 256×224, matrix size 256×224, 176 partitions, slab thickness 176 mm, τ ₁ = 222.6ms, τ ₂ = 307.4ms, TR = 12.24 ms, TE = 3.56 ms, α = 23°, BW = 106 Hz/pixel).

In order to determine the impact of spatial resolution on signal dropouts, images were reconstructed from the k-space data at the full resolution of 1.5mm (high resolution) and the reduced resolutions of 3mm (intermediate resolution) and 4mm (low resolution) in the RO direction. The lower resolution images were calculated by limiting the image reconstruction to the central portion of data in regridded k-space, taking into account ramp sampling. By using the identical k-space raw data and resampling, any bias in the comparison of the different resolutions due to different physiological noise, head motion, or scanner instabilities is avoided.

The low, intermediate and high resolution EPI time series were identically preprocessed and statistically analyzed using SPM2. The EPI images were corrected for motion, distortions, and for interactions of motion and distortions using the FieldMap toolbox [5,23] and the variance weighted smoothed field map. All images were coregistered, resliced, and smoothed with a Gaussian kernel of FWHM = 5 mm. The time series of each voxel was high-pass filtered with a cut-off period of 150 s.

A general linear model (GLM) was applied to the time series of each voxel [29]. Breath holding blocks were modeled as a boxcar reference function which was convolved with a Gaussian function (σ =7.48 s) to account for the delayed and dispersed blood flow response. In order to reduce artifacts caused by head motion, covariates derived from the head motion parameters (six per scanned volume) were included in the GLM [30] as effects of no interest. Temporal autocorrelations were modeled by a first order autoregressive model. Activated voxels were determined by testing for significant positive correlation of the measured signal with the modeled response, i.e., significant signal increase due to the breath holding. T statistics were estimated for each voxel and activations passing a fixed voxel-wise threshold of t > 3.12 were considered significant (corresponds to P < 0.001).

For a direct comparison of the BOLD CNR of the lower and high resolution images, the image intensity of each time point and voxel of the preprocessed lower resolution time series was subtracted from the image intensity of the corresponding time point and voxel of the high resolution time series. This differential time series reflected the signal difference between the two resolutions and therefore also the BOLD signal difference. The differential time series was statistically analyzed the same way as the individual time series, however, the motion parameters of both individual time series were included as regressors in the GLM. All voxels that showed a higher activation for the higher spatial resolution were determined by testing for significant positive correlation of the differential signal with the modeled breath holding BOLD response. Activations passing a fixed voxel-wise threshold of t > 3.12 and a cluster size of 0.12 ml were considered significant. The statistical maps were masked with a brain mask generated from the T₁-weighted anatomical MDEFT image [25].