Partial k-space acquisition method for improved SNR efficiency and temporal resolution in 3D fMRI
Y. Hu1,2, G. H. Glover2
1Department of Physics, Stanford University, Stanford, CA, United States, 2Department of Radiology, Stanford University, Stanford, CA, United States
Introduction: Previous studies have shown the relative importance of physiological noise and thermal noise in 2D MR images (1). Since physiological noise is
proportional to the signal, it is the dominant component at the center of k-space. In partial k-space methods (2), the high spatial frequency components are doubled,
resulting in twice as much noise from those components. However in sum these contributions are relatively small compared to those at the low spatial frequencies
where physiological noise is dominant. Therefore, an improved SNR efficiency and temporal resolution can be achieved since the SNR benefit from increased time
frames overcomes the SNR decrease from the partial k-space method itself.
Theory: Let (kl, km, kn) denote the position of a
sampling point. Then the k-space noise at that point is
where λ is a proportional constant. The noise in the
image space is given as
where w(n) is the filter used to smooth the transition
and generate the corresponding weighting for the
partial-k method. Nz is the reconstruction matrix size in
the slab-select direction. Given the same scan time, the
SNR efficiency ratio of the partial-k method over the
full-k method is given as
pkz pk im
fkz fk im
where Nz, fk and Nz, pk are numbers of k-space planes collected for full-k and partial-k methods respectively. Simulations were performed based on the thermal SNR in the
reconstructed images (~80) and the measured constant λ (~0.03). The object is assumed to have a rectangular shape which fills 0.6 of the field of view (FOV) in all three
dimensions. The results are shown in Fig. 2. Although reducing the k-space coverage will result in higher SNR efficiency, a minimum number of k-space lines (40 of 64)
is needed to produce reasonable images.
Methods: Experiments were performed on a 1.5T scanner equipped with the manufacturer’s head coil (Signa, GE Medical Systems, Milwaukee, WI). A 3D stack-of-
spirals trajectory (3,4) was used to cover k-space. In the slab-select direction, the excited slab thickness was 93mm with a FOV of 96mm and slice thickness of 1.5mm.
Two end slices were discarded to reduce aliasing artifacts. TR was 100ms and the scan time per time frame was 6.4s. Flip angle was set to be Ernst angle (27˚) to
maximize the signal. The in-plane trajectory is a single shot, uniform density spiral with an echo time of 40 ms, in-plane FOV of 22 cm and in-plane effective matrix
size of 64 by 64. 50 time frames were collected for rest state scans and 80 time frames were collected for functional scans with a block design of 20s-on/20s-off and a
task of a contrast-reversing checkerboard visual stimulus and bilateral sequential finger apposition paced by auditory cueing tones at 3Hz supplied through earphones.
The same set of data was used in the comparison to remove the behavioral difference in different scans. To make the effective scan time the same, only 5/8 of time
frames with full-k coverage and all time frames but with only 5/8 of the k-space coverage were used for full-k and partial-k methods respectively for functional studies.
Results: Rest state studies showed that the average SNR increase is 8.8% among 6 volunteers.
The comparisons of functional results in the motor, auditory and visual area from a
representative volunteer are shown in Fig. 3. In each comparison, the top row depicts the
activation maps using the full k-space method and the bottom row is the activation maps using
the partial k-space method. The scale of p-values, which is from 0.01 to 0.0005, is the same for
all figures. The total activated voxels and the corresponding average t scores are 983, 3.51 for
the full k-space method and 1452, 3.84 for the partial k-space method respectively. Paired 2-
tails Student T tests were calculated using functional data from all 7 volunteers, showing
significant differences in the number of activations (p = 0.004, 0.0005 and 0.014 for motor,
auditory and visual activations respectively) between full-k and partial-k methods.
Discussion: Experiments have shown advantages of the partial-k method over the full-k
method in detecting neuronal activation. Although the technique was tested using a 3D stack-
of-spirals trajectory, it is also applicable to fMRI studies using EPI trajectories as long as
reduced number of k-space lines collected can result in a reduced number of RF excitations
(scan time). In the simulation, special care was needed and the values of parameters should be
determined based on the raw data. Behavioral difference in different scans could be large even
for the same volunteer. Therefore the comparison should be the fairest if we use the same set
of data but keep the effective scan time the same. Low SNR and low temporal resolution are
the problematic issues in the high resolution fMRI studies. The 3D method has the benefit of
increased SNR compared to the multi-slices 2D method especially when the number of slices
is large. Partial k-space method can further increase the SNR efficiency and the temporal
resolution. Thus, the combination of two techniques may provide a possible way of doing high
resolution fMRI studies over the whole brain within a reasonable amount of scan time.
Supported by NIH P41-09784
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method (bottom row) are shown in a, b and c respectively.
Figure 1. The filters for image reconstructions use
Fermi function for transitions. In the partial-k
method, 40 out of 64 k-space lines are collected.
Figure 2. The effect of physiological noise and the
number of k-space lines collected on the SNR
Figure 3. The comparisons of motor, auditory and visual activations
between the full k-space method (top row) and the partial k-space
Proc. Intl. Soc. Mag. Reson. Med. 14 (2006)2819