Lecture 14Magnetic Resonance Imaging

Functional MRI SCAN of Physics 290 Student (Winter 2000)

Magnetic Resonance Detection

Pick-up Coil Detects Changing M by FARADAY INDUCTION

Amplifier

1.00.50.0

-0.5-1.0si

gnal

(vo

lts)

2.01.51.00.50.0time (msec)

T = 1/fL

Superconductivity• Near Absolute Zero• Metals and Alloys loose all electrical resistance

(electrical current is conducted by ELECTRONS)

Liquid HELIUM Bath

• Hi-TC Superconductivity: Ceramics• Liquid Nitrogen

• Not Practical for Magnets(superconductivity depends on magnetic field/current)

• But Do Nice Tricks Meisner Effect - Magnetic Levitation

1.5 Tesla: Energy Stored

Solenoid Magnet

DC Current

1000 Amps

Inductor Stores Electric Energy (E=1/2 L I2)

Megawatt hours

Encoding Position

Position

Frequency(log2) 440

22011055

8801760

Encoding Position

Magnetic Field(Tesla)

Frequency(MHz)

64.0

63.8

64.2

1.50

63.6

1.51

1.49POSITION

MAGNETIC FIELD GRADIENT

Imaging: Mapping M(x,y,x)• GRADIENTS of B: B=B(x,y,z) make f(x,y,z)

x

Bx

x

Bx

x

Bx

1.00.50.0

-0.5-1.0

43210

-1.0-0.50.00.5

43210

1.00.50.0

-0.5

1612840

Gradient Time Domain Frequency Domain

Constant M

f(x)=2πgxGx +f0

f0

B0

B=B0+xGx

Fourier TransformMoving from Time to Frequency

F(f) = ∫ S(t) ei2π f t dt

= ∫ S(t) cos(2π f t)dt

+i ∫ S(t) sin (2π f t)dt

1.00.50.0

-0.5

1612840

Time Domain Frequency Domain

FT

f=gxGx

Image Reconstruction• The frequency domain encodes M(x):

x

f(x)

frequency Time Domaint (kx)x

Mx

Magnetization

f(x)=gxGx

S(t) = ∫ M(x) ei2π f t dx

S(kx) = ∫ M(x) ei x*kx dx (kx= gGxt)

S(kx) is the Fourier Transform of M(x)M(x) is the INVERSE Fourier Transform of S(kx)

M(x) = ∫ S(kx) e-i x*kx dkx

4

3

2

1

0

120100806040200

S(t)4

2

0

-2

-4

120100806040200

Each Step in Time -- Step in kx

4

3

2

1

0

120100806040200

Gx FT

Tomography:Step 1. Slice SelectionExcitiation

• Pulse with Gradient to select slice

z

Bz

Gradient

Selects this slice in z

ONLY SPINS WITHIN A (SMALL) RANGE ALONG z are RESONANT

Frequencyf

0.3

0.2

0.1

0.0

120100806040200

Tomography: 2. Steps in k-space

• 2-D: Encode along y axis

x

By

Gradientx

Mx

Magnetization

Timet (kx)

S(t)4

2

0

-2

-4

120100806040200

x

Bx

Gradient

4

3

2

1

0

120100806040200

4

3

2

1

0

120100806040200

y1

y44

3

2

1

0

120100806040200

4

3

2

1

0

120100806040200

4

2

0

-2

-4

120100806040200

0.10

0.05

0.00

-0.05

120100806040200

-40

-20

0

20

x10-3

120100806040200

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

120100806040200

(ky= gGyt)ky

1

kx

2

3

4

Tomography: 2 D Imaging Sequence

Gradient Echo Sequence

p/2 pulseSlice select gradient Gz

readout gradient Gx

Signal S(t) time (ms)

Phase enconde gradient Gy

Resolution and k-spaceSteps are discrete (digital sampling)

kix= gGxti

Dx= 1/NDkx

FOV = ± N Dx /2

-FOV +FOV

Dx

number of steps

Image Formation• Image is Gray Scale Map of M(x,y,z)

• M(x) = ∫ S(kx) sin(-2πkxx) dkx

Contrast in MRI• Frequency Shifts:

– Magnetic Field at the Nucleus is SHIELDED diamagnetic shielding

25 ppm for Hydrogen, 24,000 ppm for U(2.4%)

• T1 Multiple pulse sequences/INVERSION - π pulse

• T2

• Contrast Agents: Gadolinium - T1; Iron compounds - T2 ; deoxy-hemoglobin - T2)

1.0

0.8

0.6

0.4

0.2

0.0

302520151050

M

Faster Pulses: Less Signal (Saturation Recovrery)

Bz out of page

Be into page

Shorter T1:MORE Signal1.0

0.8

0.6

0.4

0.2

0.0

302520151050

1.0

0.8

0.6

0.4

0.2

0.0

302520151050

0.5

0.0

-0.5

120100806040200

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

120100806040200

More Signal longer T2) Less Signal (shorter T2)

T1 and T2 Weighting

Contrast in MRI

T1 T1 Gadolinium

Functional Brain ImagingBOLD

• Blood Oxygenation Affects Contrast• Metabolism uses oxygen• Contrast Reveals regions of oxygen

consumption

Speech CenterBOLD - fMRI