FMRI Graduate Course (NBIO 381, PSY 362)
Dr. Scott Huettel, Course Director
FMRI – Week 3 – Image Formation Scott Huettel, Duke University

Introductory Exercise
• Write down the major steps involved in the generation of MR signal
– Just write an outline, not an essay
– Note what scanner component contributes to each step
FMRI – Week 3 – Image Formation Scott Huettel, Duke University

Generation of MR Signal
FMRI – Week 3 – Image Formation Scott Huettel, Duke University

FMRI – Week 3 – Image Formation
T
1
T
2
Scott Huettel, Duke University

Relaxation Times and Rates
• Net magnetization changes in an exponential fashion
– Constant rate (R) for a given tissue type in a given magnetic field
– R = 1/T, leading to equations like e –Rt
• T
1
(recovery): Relaxation of M back to alignment with B
– Usually 500-1000 ms in the brain (lengthens with bigger B
0
0
)
• T
2
(decay): Loss of transverse magnetization over a microscopic region
(  5-10 micron size)
– Usually 50-100 ms in the brain (shortens with bigger B
0
)
• T
2
*: Overall decay of the observable RF signal over a macroscopic region (millimeter size)
– Usually about half of T
2 in the brain (i.e., faster relaxation)
FMRI – Week 3 – Image Formation Scott Huettel, Duke University

T
1
Recovery
FMRI – Week 3 – Image Formation Scott Huettel, Duke University

T
2
Decay
FMRI – Week 3 – Image Formation Scott Huettel, Duke University

T
1 and T
2 parameters
FMRI – Week 3 – Image Formation
By selecting appropriate pulse sequence parameters (Week 4’s lecture), images can be made sensitive to tissue differences in T
1
, T
2
, or a combination.
Scott Huettel, Duke University

FMRI – Week 3 – Image Formation Scott Huettel, Duke University

FMRI – Week 3 – Image Formation v


2

B
0
Scott Huettel, Duke University

Gradients change the Strength, not
Direction of the Magnetic Field
FMRI – Week 3 – Image Formation Scott Huettel, Duke University

Parts of 2D Image Formation
• Slice selection
– Linear z-gradient
– Tailored excitation pulse
• Spatial encoding within the slice
– Frequency encoding
– Phase encoding
FMRI – Week 3 – Image Formation Scott Huettel, Duke University

FMRI – Week 3 – Image Formation
Scott Huettel, Duke University

FMRI – Week 3 – Image Formation Scott Huettel, Duke University

Linear z-gradient
FMRI – Week 3 – Image Formation Scott Huettel, Duke University

Why can’t we just use an excitation pulse of a single frequency?
FMRI – Week 3 – Image Formation Scott Huettel, Duke University

Selecting a Band of Frequencies
FMRI – Week 3 – Image Formation Scott Huettel, Duke University

Choosing a Slice
FMRI – Week 3 – Image Formation Scott Huettel, Duke University

Changing Slice Thickness
FMRI – Week 3 – Image Formation Scott Huettel, Duke University

Changing Slice Location
FMRI – Week 3 – Image Formation
(Note: manipulating gradient is simpler than changing slice bandwidth.)
Scott Huettel, Duke University

Interleaved Slice Acquisition
…
…
3
13
2
1
12
Scott Huettel, Duke University FMRI – Week 3 – Image Formation

FMRI – Week 3 – Image Formation Scott Huettel, Duke University

FMRI – Week 3 – Image Formation Scott Huettel, Duke University

How not to do spatial encoding…
FMRI – Week 3 – Image Formation Scott Huettel, Duke University

… a better approach
FMRI – Week 3 – Image Formation Scott Huettel, Duke University

Temporal Signal =
Combination of Frequencies
FMRI – Week 3 – Image Formation Scott Huettel, Duke University

Effects of Gradients on Phase
FMRI – Week 3 – Image Formation Scott Huettel, Duke University

Core Concept:
k-space coordinate = Integral of Gradient Waveform
FMRI – Week 3 – Image Formation Scott Huettel, Duke University

Image space y
Fourier Transform x
Inverse Fourier
Transform
Final Image k-space k y
Acquired Data k x
FMRI – Week 3 – Image Formation Scott Huettel, Duke University

Spatial Image =
Combination of Spatial Frequencies
FMRI – Week 3 – Image Formation Scott Huettel, Duke University

k Space
FMRI – Week 3 – Image Formation Scott Huettel, Duke University

Image space and k space
FMRI – Week 3 – Image Formation Scott Huettel, Duke University

Parts of k space
FMRI – Week 3 – Image Formation Scott Huettel, Duke University

FMRI – Week 3 – Image Formation
So, we know that two gradients are necessary for encoding information in a two-dimensional image?
What would happen if we turned on both gradients simultaneously?
Scott Huettel, Duke University

Frequency Encoding
• During readout (or data acquisition, DAQ)
• Uses gradient perpendicular to slice-selection gradient
• Signal is sampled & digitized about once every few microseconds
– Readout window ranges from 5–100 milliseconds
– Why not longer than this?
• Fourier transform converts signal S(t) into frequency components S(f )
FMRI – Week 3 – Image Formation Scott Huettel, Duke University

Phase Encoding
• Apply a gradient perpendicular to both slice and frequency gradients
• The phase of Mxy (its angle in the xy-plane) signal depends on that gradient
• Fourier transform measures phase  of each S(f) component of S(t)
• By collecting data with many different amounts of phase encoding strength, we can assign each S(f) to spatial locations in 3D
FMRI – Week 3 – Image Formation Scott Huettel, Duke University

FMRI – Week 3 – Image Formation Scott Huettel, Duke University

Echo-Planar Imaging (EPI)
FMRI – Week 3 – Image Formation Scott Huettel, Duke University

D k
Sampling in k-space
. . . . . . . . . .
. . . . . . . . . .
. . . . . . . . . .
. . . . . . . . . .
. . . . . . . . . .
K
. . . . .
. . . . .
FOV
FMRI – Week 3 – Image Formation
FOV = 1/
D k,
D x = 1/K
Scott Huettel, Duke University

FMRI – Week 3 – Image Formation Scott Huettel, Duke University

Magnetic Field Inhomogeneity
FMRI – Week 3 – Image Formation Scott Huettel, Duke University

Gradient Problems
FMRI – Week 3 – Image Formation Scott Huettel, Duke University