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-fig-04-02-0.jpg FMRI – Week 3 – Image Formation Scott Huettel, Duke University

T2 Decay fmri-fig-04-03-0.jpg 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

I fmri-fig-02-07-1.jpg FMRI – Week 3 – Image Formation Scott Huettel, Duke University

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-fig-04-09-0.jpg 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-fig-04-10-0.jpg FMRI – Week 3 – Image Formation Scott Huettel, Duke University

Choosing a Slice fmri-fig-04-11-1.jpg FMRI – Week 3 – Image Formation Scott Huettel, Duke University

Changing Slice Thickness fmri-fig-04-11-2.jpg FMRI – Week 3 – Image Formation Scott Huettel, Duke University

Changing Slice Location fmri-fig-04-11-3.jpg (Note: manipulating gradient is simpler than changing slice bandwidth.) FMRI – Week 3 – Image Formation Scott Huettel, Duke University

Interleaved Slice Acquisition … 12 13 … 3 2 1 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-fig-04-05-1.jpg FMRI – Week 3 – Image Formation Scott Huettel, Duke University

Effects of Gradients on Phase fmri-fig-04-12-0.jpg FMRI – Week 3 – Image Formation Scott Huettel, Duke University

Core Concept: k-space coordinate = Integral of Gradient Waveform fmri-fig-04-04-0.jpg FMRI – Week 3 – Image Formation Scott Huettel, Duke University

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

Spatial Image = Combination of Spatial Frequencies fmri-fig-04-05-2.jpg FMRI – Week 3 – Image Formation Scott Huettel, Duke University

k Space fmri-fig-04-08-0.jpg FMRI – Week 3 – Image Formation Scott Huettel, Duke University

Image space and k space fmri-fig-04-06-0.jpg FMRI – Week 3 – Image Formation Scott Huettel, Duke University

Parts of k space fmri-fig-04-07-0.jpg FMRI – Week 3 – Image Formation Scott Huettel, Duke University

What would happen if we turned on both gradients simultaneously? 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-fig-04-13-2.jpg FMRI – Week 3 – Image Formation 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-fig-04-13-2.jpg FMRI – Week 3 – Image Formation Scott Huettel, Duke University

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

Sampling in k-space Dk K FOV FOV = 1/Dk, Dx = 1/K 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-fig-04-15-0.jpg FMRI – Week 3 – Image Formation Scott Huettel, Duke University

Gradient Problems fmri-fig-04-16-0.jpg FMRI – Week 3 – Image Formation Scott Huettel, Duke University