1. Numerical Simulations of Interleaved kY MRI Techniques John A. Roberts, Dennis L. Parker The 14th Annual Research Symposium Sundance Resort, September 13, 2002 Medical Imaging Research Laboratory Department of Radiology, University of Utah

2. Outline Of Talk Background –ky-Interleaving Methods –Experimental Measurements Simulations –RF Excitation Model –Interleaving Model –Noise Studies Results Conclusions

3. ky-Interleaving Methods Motivation: Overcome Slab Boundary Artifact (SBA) due to slab profile Approach: Transform SBA from Z to ky-Direction Challenge: Address ky-artifact Possible Solution: Remove with navigators

4. ky-Interleaving Methods Navigator Correction –Acquire Navigator Sample plane at (k x,0,k z ) OR Sample line at (0,0,k z ) –Extract Slab Profile From Navigator –Remove Slab Profile From Data (k x,k y,k z ) Phase profile only Phase and magnitude

5. ky-Interleaving Methods Drawbacks –Requires Time To Acquire Navigator –Assumes Spatial Invariance of Profile In (x,y) Measure signal S(k x,k y,k z ) Transform along k z, S(k x,k y,z) If the slab profile is invariant in (x,y) The slab profile is removed by simple complex division –What If The Slab Profile Varies With Position (x,y)?

6. Experimental Measurements Highly Overlapped MOTSA –Multiple Thin Slabs –Overlap By All But One Slice –Fully Sample Each (x,y) At Each Possible Position Within The Slab Profile

7. Brain Slab Profile Magnitudes

8. Brain Slab Profile Phase

9. Neck Slab Profile Magnitudes

11. Fourth-order Runge-Kutta (Press et al., Numerical Recipes in C, 2 nd Edition, 1992) k 1 = hf(x n, y n )k 2 = hf(x n +h/2, y n +k 1 /2) k 3 = hf(x n +h/2,y n +k 2 /2)k 4 = hf(x n +h, y n +k 3 ) y n+1 = y n + k 1 /6 + k 2 /3 + k 3 /3 + k 4 /6 + O(h 5 ) RK4, IDL ® Routine based on above NR xt: time (s) yM(z): Magnetization vector at position z (T) hΔt: numerical time step (s) RF-Excitation Model

12. Input –Slab: slab thickness, model extent in Z, number of samples (N z ) –RF: number of RF zeros, pulse width in Hertz –Material properties: Chemical shift, T 1, T 2, M 0 –Other: tip angle θ tip, time step Δt, main field B 0 Output Magnetization as a function of z following excitation by an asymmetric RF-pulse in the presence of slice- select and rephasing gradients G z.

13. M x / M 0 M y / M 0 M z / M 0 Field Due To G z M T =sqrt(M x 2 + M y 2 ) Φ=arctan(M y /M x ) Legend B 1 RF Envelope GzGz

14. Interleaving Model Repetitive Excitation Slice Encoding –From high resolution (Δz) excitation model –To lower resolution (Δz s ) of simulated acquisition

15. Interleaving Model Multiple RF-Excitation Profiles 3D Slabs Simulated –Properties invariant along z –Properties change along xy-direction –Create slab s(x,y,z s ) –Fourier transform, S(k x,k y,z s ) Create Interleaved Dataset –Interleave multiple S(k x,k y,z s ) –Reconstruct z y x

16. Varied T 1 Study

17. Noise Study: SNR MOTSA HOTSA, Phase Correction SLINKY, Phase Correction SLINKY, Full Correction

18. Results & Conclusions Results –Navigator correction sensitive to slab profile variations –Tradeoff exists between ghosting and SNR Conclusions –Numerical model simplifies analysis –HOTSA reduces ghosting of large objects –Interleaving studies difficult in the neck