Page 1

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

22

T

2

P

2

T

)),,((

nmlk

kkkS

λσσσσ+=+=

,

where λ is a proportional constant. The noise in the

image space is given as

[

∑

=

nml

zyx

NNN

,,

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

σ

=

]

nmlk im

kkknw

2

),,()(

1

σσ

,

pkz pk im

fkz fk im

fk

pk

N

N

SNR

SNR

,,

,,

σ

,

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

References:

1. Kruger G, Glover GH. Physiological noise in oxygenation-sensitive magnetic resonance

imaging. Magn Reson Med 2001;46(4):631-637.

2. Noll DC, Nishimura D, Macovski A. Homodyne detection in magnetic resonance imaging.

IEEE Trans Med Imaging 1991;MI-10(2):154-163.

3. Irarrazabal P, Nishimura DG. Fast three dimensional magnetic resonance imaging. Magn

Reson Med 1995;33(5):656-662.

4. Lai S, Glover GH. Three-dimensional spiral fMRI technique: a comparison with 2D spiral

acquisition. Magn Reson Med 1998;39(1):68-78.

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

efficiency (SNRpk/SNRfk).

a

b

c

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