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

MR Image Formation

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

T1 T2

FMRI – Week 3 – Image Formation 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

• T1 (recovery): Relaxation of M back to alignment with B0

– Usually 500-1000 ms in the brain (lengthens with bigger B0)

• T2 (decay): Loss of transverse magnetization over a microscopic region ( 5-10 micron size)– Usually 50-100 ms in the brain (shortens with bigger B0)

• T2*: Overall decay of the observable RF signal over a macroscopic region (millimeter size)– Usually about half of T2 in the brain (i.e., faster relaxation)

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

T1 Recovery

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

T2 Decay

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

T1 and T2 parameters

By selecting appropriate pulse sequence parameters (Week 4’s

lecture), images can be made sensitive to tissue differences in

T1, T2, or a combination.

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

II

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

02Bv

FMRI – Week 3 – Image Formation 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

Slice Selection

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

(Note: manipulating gradient is simpler than changing slice

bandwidth.)

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

Interleaved Slice Acquisition

1

2

3

…

12

13

…

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

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

Spatial Encoding

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

Fourier TransformFourier Transform

k-spacek-space

kkxx

kkyy

Acquired DataAcquired Data

Image spaceImage space

xx

yy

Final ImageFinal Image

Inverse Fourier Inverse Fourier TransformTransform

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

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?

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

• 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 )

Frequency Encoding

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

• 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

Phase Encoding

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

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FOV = 1/k, x = 1/K

FOV

k

K

Sampling in k-space

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

Problems in Image Formation

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

Magnetic Field Inhomogeneity

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

Gradient Problems