Seul Lee^{1} and Gary Glover^{2}

Three-dimensional (3D) acquisition is beneficial for functional MRI (fMRI) compared to two-dimensional (2D) acquisition since it can provide higher spatial resolution, resulting from potentially higher temporal signal-to-noise ratio (tSNR) and thinner slices. However, 3D has higher physiological noise due to higher signal at the center of k-space, which results in lower tSNR. The number of slices can be decreased to reduce physiological noise. However, a small number of slices in Fourier encoding results in Gibbs ringing. In this study, we show that 3D Hadamard acquisition avoids Gibbs artifacts while increasing SNR compared with conventional 2D and 3D methods.

**Data
acquisition: **With
IRB approval, we scanned a human brain using a 2D, 3D Fourier encoded and 3D
Hadamard encoded spiral GRE sequences. All the data were obtained using a 3T GE
whole-body MRI scanner equipped with a single-channel RF receive coil and
single-shot GRE sequence with TE/TR=29/2000ms, 3.4mm × 3.4mm × 4mm voxels, FOV=22cm × 22cm, 32 slices, 128 timeframes and scan time=4min. Flip angles of
80, 20 and 70 and 45 degrees are used for 2D, 3D with Fourier, 3D with Hadamard
2 and 3D with Hadamard 4, respectively. **Data
analysis:** Let *Hn* be a Hadamard
matrix of order *n* (power of 2) containing ±1 in the *n
× n* matrix (Eqn.1).

$$ H_{2}=\begin{bmatrix}1 & 1 \\1 & -1 \end{bmatrix},\ H_{4}=\begin{bmatrix}1 & 1 & 1 & 1 \\1 & -1 & 1 & -1 \\ 1 & 1 & -1 & -1 \\ 1 & -1 & -1 & 1 \end{bmatrix} \ \ \ \ \cdot\cdot\cdot \ (1) $$

Let *S*
be a column matrix containing the RF pulse waveforms for each slice to be
simultaneously encoded, *S _{i}*.
For Hadamard 2 (for 2 slices), for example, sinc pulses for each slice

$$ H_{2}\cdot S=\begin{bmatrix}1 & 1 \\1 & -1 \end{bmatrix} \begin{bmatrix} S_{1} \\S_{2}\end{bmatrix}=\begin{bmatrix} S_{1}+S_{2} \\S_{1}-S_{2}\end{bmatrix}=A \ (Let\ this\ matrix\ be\ A) \cdot\cdot\cdot \ (2) $$

$$ S = (H_{2})^{-1}\cdot A = \frac{1}{2}H_{2}\cdot A =\frac{1}{2}\begin{bmatrix}1 & 1 \\1 & -1 \end{bmatrix}\begin{bmatrix}S_{1}+S_{2} \\S_{1}-S_{2} \end{bmatrix}=\begin{bmatrix}S_{1} \\S_{2} \end{bmatrix} \ \ \ \ \cdot\cdot\cdot (3) $$

We compared the reconstructed images and tSNR
maps with 2D, 3D Fourier encoding, Hadamard 2 and 4. We also compared the
activation maps from a combined sensory-motor, visual and auditory task fMRI.
Activation maps are created by correlating the reconstructed timeseries with
sine and cosine timeseries model functions. In the activation maps, t-scores
are calculated and thresholded by *p<0.01*.

1. “Physiological noise in oxygenation-sensitive magnetic resonance imaging”. Kruger G, Glover GH. Magnetic Resonance in Medicine, 46(4): 631-637, 2001

2. “Neuroimaging at 1.5 T and 3.0 T: comparison of oxygenation-sensitive magnetic resonance imaging”. Kruger G, Kastrup A, Glover GH. Magnetic Resonance in Medicine, 45(4): 595-604, 2001

3. “Hadamard matrices and their applications”. Hedayat A., Wallis WD, Annals of Statistics. 6(6): 1184–1238, 1978

4. “Simultaneous multislice acquisition of MR images”. Weaver JB, Magn Res Med 1988; 8:275–284