EE 591 Project 2 D spatially selective excitation pulse design and the artifact evaluation 12 / 08 / 2004

Two-dimensional spatially selective excitation is used to excite a volume such as pencil beam or cylinder-like shape (1). It can also be used to obtain reduced FOV in slice selective excitation, which corresponds to a rectangular stick in the object domain (2). This study is to explore how to design RF and gradient pulses in order to excite a desired volume given gradient limitations, and to see how off-resonance and gradient delay affect the excitation profile. In the present work, echo-planar RF pulse with forward-backward design scheme is adopted (3). PULSE DESIGN As Pauly et al. developed (4), the relationship between the spatial weighting deposited by RF pulse and the 2D excitation volume is Fourier transform formula. M xy (x,y) = i γ M o integral ∫ kx ∫ ky P(k x, k y) e ixkx e iyky dk x dk y [1] where P(k x, k y) = W(k x, k y) S(k x, k y). S(k x, k y) is a sampling structure that is determined by the k-space trajectory, and W(k x, k y) is a spatial weighting function defined by W(k x, k y) = B1(t)/| γG(t)|. Also, k x (t) =-γ ∫ t T G x (s)ds [2] k y (t) =-γ ∫ t T G y (s)ds [3] More exactly, P(k x , k y)=1/(2πγ) FT{ M xy (x,y) } [4] The desired excitation shape in the object domain is set to rect(ax)cos 2 (by) as shown in Fig.1 so that the spatial weighting function in the excitation k-space is 1/a sinc(1/a k/(2π)) π 2 (δ (k y +2b) + 2δ(k y) + δ(k y-2b), i.e., !(ax)cos 2 (by) ↔ 1/a sinc(1/a k/(2π)) π 2 (δ (k y +2b) + 2δ(k y) + δ(k y-2b) [ 5 ] which leads to 1-2-1 binomial weighting (5) with sub-pulses, as shown in Fig.1. The sub-pulses used here are only the main-lobe of sinc pulse which covers the k-space from –2π to 2π in k x-axis, and –2b from to 2b in k y-axis as visualized in Fig.2. The truncation in the coverage of k x-axis will cause blurring in x-axis in the object domain. Fig.3 shows the forward-backward design trajectory also known as non-flyback. Since Fourier relationship holds true mostly for a small tip-angle, the RF pulse amplitude should not be chosen too large. In this experiment, the parameter a and b are both set to …