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Numerical Simulations of Numerical Simulations of Interleaved kY MRI Interleaved kY MRI
TechniquesTechniques
John A. Roberts, Dennis L. ParkerJohn A. Roberts, Dennis L. Parker
The 14th Annual Research SymposiumThe 14th Annual Research SymposiumSundance Resort, September 13, 2002
Medical Imaging Research LaboratoryDepartment of Radiology, University of Utah
Outline Of TalkOutline Of Talk
• Background– ky-Interleaving Methods– Experimental Measurements
• Simulations– RF Excitation Model– Interleaving Model– Noise Studies
• Results
• Conclusions
ky-Interleaving Methodsky-Interleaving MethodsMotivation: 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
ky-Interleaving Methodsky-Interleaving Methods• Drawbacks
– Requires Time To Acquire Navigator– Assumes Spatial Invariance of Profile In (x,y)
• Measure signal S(kx,ky,kz)
• Transform along kz, S(kx,ky,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)?What If The Slab Profile Varies With Position (x,y)?
)(),,(),,(
)(),,(),,(
zfzkkMzkkS
zfzyxmzyxs
slabyxyx
slab
Brain Slab Profile MagnitudesBrain Slab Profile Magnitudes
Brain Slab Profile PhaseBrain Slab Profile Phase
• Fourth-order Runge-Kutta (Press et al., Numerical Recipes in C, 2nd Edition, 1992)
k1 = hf(xn, yn) k2 = hf(xn+h/2, yn+k1/2)
k3 = hf(xn+h/2,yn+k2/2) k4 = hf(xn+h, yn+k3)
yn+1 = yn + k1/6 + k2/3 + k3/3 + k4/6 + O(h5)
• RK4, IDL® Routine based on above NR
x t : time (s)
y M(z) : Magnetization vector at position z (T)
h Δt : numerical time step (s)
RF-Excitation ModelRF-Excitation Model
1
0
2
ˆ)(ˆˆ
T
kMM
T
jMiMHM
dt
Md zyx
RF-Excitation ModelRF-Excitation Model• Input
– Slab: slab thickness, model extent in Z, number of samples (Nz)
– RF: number of RF zeros, pulse width in Hertz
– Material properties: Chemical shift, T1, T2, M0
– Other: tip angle θtip, time step Δt, main field B0
• Output Magnetization as a function of z following excitation by
an asymmetric RF-pulse in the presence of slice-select and rephasing gradients Gz.
Mx / M0
My / M0
Mz / M0
Field Due To Gz
MT=sqrt(Mx2 + My
2)
Φ=arctan(My/Mx)
Legend
B1 RF Envelope
Gz
Interleaving ModelInterleaving Model• Repetitive Excitation
• Slice Encoding– From high resolution (Δz) excitation model
– To lower resolution (Δzs) of simulated acquisition
)exp()/exp(sin)/exp(cos1
)(exp1)( 2
1
10
iTTE
TTR
TR/TMTEtM tip
tipT
hi
lo
Z
Zzszs zkTEzMkS )exp(),()(
zszss Nkz
1
z
T
tip M
M
arctan
x
y
M
Marctan
Interleaving ModelInterleaving Model• Multiple RF-Excitation
Profiles• 3D Slabs Simulated
– Properties invariant along z– Properties change along
xy-direction
– Create slab s(x,y,zs)
– Fourier transform, S(kx,ky,zs)
• Create Interleaved Dataset– Interleave multiple S(kx,ky,zs)
– Reconstruct
z
y
x
Varied TVaried T11 Study Study
Noise Study: SNRNoise Study: SNR
MOTSA HOTSA, Phase Correction
SLINKY, Phase Correction SLINKY, Full Correction
Results & ConclusionsResults & 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