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