Terry M. Button, Ph.D.

Principals of Magnetic Resonance Image Formation

General Signal Localization

• Region of interest is excited with fL.

• Magnetic field is modified in a planned way using gradients.

• Emitted frequency is now dependent on location.

• Signal vs. time is collected, FT provides signal vs. f which is also signal vs. location!

2D FT

• Initial approach will be descriptive and non-mathematical.

• The second approach will be semi-mathematical.

Overview of 2D FT

• Slice selection

• Phase encoding

• Frequency encoding

Slice selection

• Apply a gradient along z• Excite with RF which covers (Bo- ) to (Bo+ )

Bo+

Bo+

Z

RF profile

I

Slice Thickness is Determined by Bandwidth and Gradient Strength

x

B

fl = (Bo - )

fh = (Bo + )

x2t

T

Slice Selection

• Excite bandwidth (kHz) is usually fixed and gradient strength used to change slice thickness.

• Slice orientation is controlled using the gradients; oblique is one gradient tilted by a second gradient.

• Slice position is moved by changing reference frequency.

Frequency Encode

• Frequency encoding is accomplished during signal acquisition (read) by application of a gradient.

Bo - BoBo +

fl = (Bo - ) fo = Bo fh = (Bo + )

Frequency Encoding Gradient Provides a Simple Projection

Bo

S

t

I

f

FFT

Sample Collection

• Signal is sampled N times (128, 256, 512, 1024)

• Sample collection time is t (1-100 sec)– SNR t

• Total collection time T = N t– T< TE

• Bandwidth = 1/ t t = 50 sec, BW = 20 kHz

S

t

FOV

• Field of view (FOV) is controlled by:– Gradient strength– Bandwidth

• From the last slide; BW = 20 kHz– Nyquist criteria; max freq 10 kHz– If the read gradient is 1mT/m then the FOV is:

42 MHz/T x 0.001T/m = 42 kHz/m

– The FOV is:(10 kHz)/(42 kHz/m) = 24 cm

Phase Encode

• Phase encoding is accomplished by applying a gradient for a time .

Bo - Bo Bo +

t = 0

t =

Slice Image formation

Frequency encode

Phase encode

fn,n

f1,1

Must Satisfy Nyquist Sampling: Phase Encode

• Suppose a 60o phase difference at each voxel:– 60o,120o,180o, 240o, 300o, 360o, 60o

– Phase encode is not unique; must repeat with incremented phase encoding gradient strength.

Basic Spin Echo

N phase encodes

Image Acquisition Time

• Suppose TE = 20 msec, TR = 500 msec, N = 256 and only one average is required.

• T = TR x N x Avg

• T = 0.5 sec x 256 x 1 = 128 sec = 2 min 8 sec

• This is the time to make one slice!!

Multi-slice

• In the previous example, collected data for slice in 20 msec but had to wait 480 msec before re-excite.

• Acquire additional slices during this time.

• Max slices = TR/(TE+).

480 ms20 ms

Image Reconstruction

• After demodulation, the frequency for any column along the frequency encoded axis is:

f(x) = Gx x

And the phase along any row in the phase encoded axis is:

(y) = Gy y

• The sinusoidal signal detected from any element is:

S(x,y) = M (x,y) e [2i (f(x)+ (y))] t

Image Reconstruction• The total signal collected as a function of time is then:

S(t1, t2) = M (x,y) e 2i [f(x)t1+ (y) t2] dx dy

• Substituting:

S(t1, t2) = M (x,y) e 2i [ Gx x t1+ Gy y t2] dx dy

• Let:

kx = Gx t1

ky = Gy t2

• Substituting:

S(k1, k2) = M (x,y) e 2i [kx x+ ky y] dx dy

• Recognized as a 2D FT! Therefore:

M(x,y) = s(kx, ky) = S(kx, ky) e -2i [kx x+ ky y] dkx dky

Importance of k-space

FT

http://www.leedscmr.org/images/mritoy.jpg

S(kx ,ky ) s(x,y) = M (x,y)

FT

Filling k-space

Frequency encode

Phase encode

N phase encodes

k-space Contribution to Image Properties

Center of k-spacecontrols contrast

Periphery of k-spacecontrols resolution

http://www.radinfonet.com/cme/mistretta/traveler1.htm#part1

k-space Contribution to Image Properties

Center - contrast

Periphery - resolution

k-space Applications

• Conjugate symmetry– Acquire only half of k-space and employ symmetry.

– Cuts acquisition time in half.

– Reduces SNR by 40%.

• Centric ordering– Acquire center of k-space as contrast arrives to ensure

maximum contrast enhancement.

Spin Echo Contrast

• SE image contrast can be weighted to provide T1, T2 and dependence

• Weighting is adjusted by modifying TE and TR.

Spin Echo T1 Weighting

Long T1

Short T1

t

t

For T1 weighting short* TR is required.

Low signal

High signal

T1 Contrast

TR

Mz short T1

long T1

Spin Echo T2 Weighting

Long T1

Short T1

For T2 weighting long* TE is required.

High signal

Low signal

T2 Contrast

TE

Mz

short T2

long T2

Spin Echo Contrast

• T1 - short TR and short TE – TR = 500 ms, TE = 10 ms

• T2 - long TR and long TE– TR = 2500 ms, TE = 100 ms

• Proton density (H) – not T1 or T2– longTR and short TE– TR = 2500 ms, TE = 10 ms

• Long TR and long TR are never used– T1 and T2 contrast conflicts

Proton

T1

T2

T1

Proton

T2

Introduction to Contrast Agents

Magnetic Properties of Materials

Weakly repel:water and tissue

Weakly attract:Gd T1 and T2 Reducing agents

Interact strongly:Fe susceptibilityagents (T2*).

Contrast Agents

• Contrast agents can function by altering:– T1 – Paramagnetic agents– T2 – Paramagnetic and Susceptibility agents– T2* – Susceptibility agents– proton density – hormones and diuretics

Paramagnetic

• Molecular tumbling results in reduced T1 and T2.– Shorten T2 => reduced signal– Shorten T1 => increased signal

• Gd chelate– Used as an enhancing agent (T1 weighted

sequence).

Gd Enhanced Brain Malignancy

Superparamagnetic

• Susceptibility agents– Cause local field inhomogeneity and very short

T2*.

– Used to remove signal on T2 or T2* weighted images.

Negative Contrast From Iron Oxide

Factors controlling SNR

• Basic factors– Field strength– Coil tune and match– Magnet shim

• Setup factors:– Coil selection (Filling factor)– Sequence selection (longer TR/shorten TE)

• Sequence variables:– Voxel volume– Averages– Bandwidth– Gap