Medical Imaging Systems:MRI Image Formation

Instructor: Walter F. Block, PhD 1-3

Notes: Walter Block and Frank R Korosec, PhD 2-3

Departments of Biomedical Engineering 1,Radiology 2 and Medical Physics 3

University of Wisconsin - Madison

MRI Physics: So far...

What we can do so far:

1) Excite spins using RF field at o2) Record time signal (Known as FID)3) Mxy decays, Mz grows4) Repeat.

But so far RF coils only integrate signal from entire body. We have no way of forming an image. That brings us to the last of the three magnetic fields in MRI.

Image Formation Overview

• Gradient fundamentals• Slice Selection

• Limit excitation to a slice or slab• Can be in any orientation

• Gradient echo in-plane spatial encoding• Radial imaging ( like CT)• Frequency encoding• Phase encoding

3nd Magnetic Field • Static High Field

• Termed B0

• Creates or polarizes signal• 1000 Gauss to 100,000 Gauss

• Earth’s field is 0.5 G

• Radiofrequency Field (RF)• Termed B1

• Excites or perturbs signal into a measurable form• O.1 G but in resonant with signal

• Gradient Fields • 1 -4 G/cm• Used to determine spatial position of signal• MR signal not based directly on geometry

Gradient Coils

Fig. Nishimura, MRI Principles

X Gradient Example: Gx

Magnetic field all along z, but magnetic strength can varies spatially with x. Stronger at right, no change in middle, weaker at left.

Gradient Coil Fundamentals

• Gradient strength directly proportional to current in coil• On the order of 100 amps peak

• Performance• Power needed proportional to radius5

• Tight bore for patient• Strength – G/cm or mT/m

• 4 G/cm is near peak now for clinical scanners• Higher strength with localized gradients (research only)

• Slew rate• Need high voltages to change current quickly• 100- 200 T/m/s is high performance

• Rise to 1 G in .1 ms at 100 T/m/s• Limited by peripheral nerve stimulation

Magnetic Field Gradient Timing Diagrams

B0

Larmor Equation

PrecessionalFrequency

Static Magnetic Field

tB0 + Gx(t)x)

Before, only B0

Now with Gx

Gx, Gy, Gz: One for each spatial dimension

Magnetic field all along z, but magnetic strength can vary spatially with x, y, and/or z.

Two Object Example of Spatial Encoding

x

m(x)

t

sr(t)

Receiver Signal: No gradient

Gx On: Beat Frequency Demodulated Signal

Water

Gz Gradient Example

The effects of the main magnetic field and the applied slice gradient. In this example, the local magnetic field changes in one-Gauss increments accompanied by a change in the precessional frequency from chin to the top of the head.

Image, caption: copyright Proruk & Sawyer, GE Medical Systems Applications Guide, Fig. 11

Selective RF Excitation

Build RF pulse from sum of narrow frequency range

Recall frequency of RF excitation has to be equal

or in resonance with spins

Slice Selection- Consider a pulse B1(t) that is multiplied by cos(ot). This is called

modulation .

B1(t) is called the RF excitation.

o is the carrier frequency = B0. Mixer

cos(ot)

B1(t) cos(ot)

A(t)

o f

Frequency profile of modulated RF pulse

o = 2fo

Frequency Encoding

Spin Frequency (x)

Image each voxel along x as a piano key that has a different pitch. MR coil sums the “keys” like your ear.

Frequency Encoding

GRE Pulse Sequence Timing Diagram

SliceSelect

Freq.Encode

rf

Signal

°

TE

Frequency Encoding & Data Sampling

FrequencyEncoding

GeneratedSignal

DAQ

SampledSignal

In-plane Encoding

• MR signal in frequency encoding (x) is Fourier transform of projection of object

• Line integrals along y

• Encoding in other direction • Vary angle of frequency encoding direction

• 1D FT along each angle and Reconstruct similar to CT

• Apply sinusoidal weightings along y direction• Spin-warp imaging or phase-encoding

• By far the most popular

2D Projection Reconstruction MRI

kx

Gx

Gy

DAQ

Reconstruction: convolution back projection or filtered back projection

ky

Central Section Theorem in MRI

In MR, echo gives a radial line in spatial frequency space (k-space).

x’

x’

y’

x

y

Interesting - Time signal gives spatial frequency information of m(x,y)

ky

kx

F.T.

θ

θ

Object

CT Projection

MR Signal (t)

k-Space Acquisition (Radial Sampling)

ky

kx

Y readout

X readout

kx

ky

In-plane Encoding

• MR signal in frequency encoding (x) is Fourier transform of projection of object

• Line integrals along y

• Encoding in other direction • Vary angle of frequency encoding direction

• 1D FT along each angle and Reconstruct similar to CT

• Apply sinusoidal weightings along y direction• Apply prior to frequency encoding• Repeat several times with different sinusoidal weightings• Spin-warp imaging or phase-encoding• By far the most popular

Phase Encoding: Apply Gy before Freq. encoding

GRE Pulse Sequence Timing Diagram

SliceSelect

PhaseEncode

Freq.Encode

rf

Signal

°

TE

PhaseDirection

Frequency DirectionOne line of k-space

acquired per TR

k-Space Acquisition

PhaseEncode

DAQ

SampledSignal

kx

ky

kx

ky

k-Space Signal

8 x 8512 x 512

16 x 16512 x 512

32 x 32512 x 512

64 x 64512 x 512

128 x 128

512 x 512

256 x 256

512 x 512

512 x 32512 x 512

Scan Duration

Scan Time = TR PE NEX

TR = Repetition TimePE = Number of phase encoding valuesNEX = Number of excitations (averages)

GRE Pulse Sequence Timing Diagram

SliceSelect

PhaseEncode

Freq.Encode

rf

Signal

°

TE

Images of the Knee

-weighted T2-weightedNeeds longer TE

T2 & T2* Relaxation: Sources of Image Contrast

Mxy

Time

T2*

T2

T2*

1 =T2

1 + B0

t

Gx(t)

6GRADECH.AVI

Effects of Local Magnetic Inhomogeneity

Perils of Gradient Echo Imaging and T2*

TE = 8 ms TE = 24 ms

0.17 T GE Orthopedic Scanner

Image Formation Overview

• Gradient fundamentals• Slice Selection

• Limit excitation to a slice or slab• Can be in any orientation

• Gradient echo in-plane spatial encoding• Radial imaging• Frequency encoding• Phase encoding

T1-, T2-, and Density-Weighted Images

T1-weighted T2-weighted -weighted

T2-Weighted Image of the Spine

Images of the Knee

-weighted T2-weighted

T1-, T2-, and Density-Weighted Images

T1-weighted T2-weighted -weighted

Spin Echo Parameters

TR TE

T1-weighting short (400 msec) short (20 msec)

T2-weighting long (3000 msec) long (100 msec)

-weighting long (3000 msec) short (20 msec)

Signal vs Weighting

T1-weighting long T1, small signal short T1, large signalT2-weighting long T2, large signal short T2, small signal-weighting high , large signal low , small signal

T1-weighted T2-weighted -weighted