MRI basics lecture 9 26

Magnetic Resonance Imaging:
Physical Principles

Lewis Center for
NeuroImaging

,


Physics of MRI, An Overview
 Nuclear Magnetic Resonance
– Nuclear spins
– Spin precession and the

Larmor equation
– Static B0
– RF excitation
– RF detection

 Spatial Encoding
– Slice selective excitation
– Frequency encoding
– Phase encoding
– Image reconstruction

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 Fourier Transforms
– Continuous Fourier

Transform

– Discrete Fourier Transform
– Fourier properties
– k-space representation in
MRI

2


Physics of MRI
 Echo formation
– Vector summation
– Phase dispersion
– Phase refocus

 2D Pulse Sequences
– Spin echo
– Gradient echo
– Echo-Planar Imaging

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 Medical Applications
– Contrast in MRI
– Bloch equation

 Tissue properties
– T1 weighted imaging
– T2 weighted imaging
– Spin density imaging

 Examples
 3D Imaging
 Spectroscopy

3


Many spins in a voxel: vector summation
spins in step

spins not in step

Rotating
frame
Lamor
precession

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4


Phase dispersion due to perturbing B
fields
Spin Phase φ ∝ γ Bt
B = B0 + δB0 + δBcs + δBpp
sampling
Immediately after RF excitation

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sometime after RF excitation

5


Refocus spin phase – echo formation

Echo Time (TE)
• Invert perturbing field:
δB
Phase
0
δBt
(gradient echo, k-space sampling)
• Invert spin state:
Phase
0
(spin echo)
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δBt

-δB
φ-δB(t-TE/2)
φ -φ
-φ+δB(t-TE/2)

time

0

0
6


Spin Echo
 Spins dephase with time
 Rephase spins with a 180° pulse
 Echo time, TE
 Repeat time, TR
 (Running analogy)

1 . E q u ilib riu m

2 . 9 0 P u lse
t= 0
3 . S p in D e p h a s in g

5 . S p in e c h o
t= T E

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4 . 1 8 0 P u lse
t= T E /2

7

Frequency encoding - 1D imaging
Spatial-varying resonance frequency during RF detection

B = B0 + Gxx
S(t) ~ eiγ Βt
S(t) ~ ∫ m(x)eiγ Gxxtdx

m(x)
x
S(t) = ∫ m(x)eikxxdx = S(kx),
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kx = γ Gxt
m(x) = FT{S(kx)}

8


Slice selection
Spatial-varying resonance frequency during RF excitation

ω

ω = ω0 + γ Gzz

B1 freq band

z
Excited location
Slice profile

m+ = mx+imy ~ γ ∫ b1(t)e-iγ Gzztdt = B1(γ Gzz)

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9


Gradient Echo FT imaging
35000

Amplitude (arb)

x Gradient

ky

0

-35000

Amplitude (arb)

35000

Readout

y Gradient

0

-35000

Amplitude (arb)

35000

kx

z Gradient

0

γ
k (t ) =
G (t )dt
∫
2π

-35000

Amplitude (arb)

35000

RF

0

-35000

0

2000

4000

Time (us)

6000

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8000

10000

Repeat with different phase-encoding
amplitudes to fill k-space
10


Pulse sequence design
35000

prewinder
spoiler

Amplitude (arb)

x Gradient

0

rephasor

Amplitude (arb)

35000
-35000

y Gradient

0

Amplitude (arb)

rewinder
spoiler

Amplitude (arb)

35000
-35000

z Gradient

0

35000

-35000

RF

0

-35000

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0

2000

4000

Time (us)

6000

8000

10000

11


X

EPI (echo planar imaging)

ky

Y
Z

kx

RF
time
Quick, but very susceptible to artifacts, particularly B 0 field inhomogeneity.
Can acquire a whole image with one RF pulse – single shot EPI
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Spin Echo FT imaging
Amplitude (arb)

35000

ky

x Gradient

0

-35000

Amplitude (arb)

35000

Readout

y Gradient

0

-35000

Amplitude (arb)

35000

z Gradient

γ
k (t ) =
G (t )dt
∫
2π

0

-35000

Amplitude (arb)

35000

kx

RF

0

-35000

0

5000

10000 Time (us) 15000

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20000

25000

Repeat with different phase-encoding
amplitudes to fill k-space
13


Spin Relaxation
 Spins do not continue to precess forever
 Longitudinal magnetization returns to equilibrium due to spin-lattice interactions – T1 decay
 Transverse magnetization is reduced due to both spin-lattice energy loss and local, random, spin
dephasing – T2 decay

 Additional dephasing is introduced by magnetic field inhomogeneities within a voxel – T2' decay.
This can be reversible, unlike T2 decay

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14


Bloch Equation
The equation of MR physics


  1
dM
1 
= γM × B + ( M 0 − M z ) zˆ + M ⊥
dt
T1
T2

Summarizes the interaction of a nuclear spin with the external
magnetic field B and its local environment (relaxation effects)

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15


Contrast - T1 Decay

 Longitudinal relaxation due to spin-lattice
interaction

1.0

 Mz grows back towards its equilibrium

o

180 Pulse

value, M0

Mz/M0

0.5

− t / T1


MForzshort
(t )TR,=equilibrium
M 0 (1moment
− e is reduced)

0.0
Inversion Recovery

-0.5

-1.0

0

1

2

3

4

5

t/T1

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16


Contrast - T2 Decay
 Transverse relaxation due to spin dephasing
 T2 irreversible dephasing
 T2/ reversible dephasing
 Combined effect

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0.8

Mx(t)/Mx(0)

1
1 1
= + /
*
T2 T2 T2
M ⊥ (t ) = M ⊥ (0)e

1.0

0.6
0.4
0.2
0.0

−t / T2*

0

1

2

*

t/T2

3

4

17

5


Free Induction Decay –
Gradient echo (GRE)
 Excite spins, then measure decay
 Problems:

MR signal

– Rapid signal decay
– Acquisition must be

e-t/T2*

disabled during RF
– Don’t get central
“echo” data

time
0

90 RF
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18


Spin echo (SE)
MR signal

e-t/T2
e-t/T2*
time

0

90 RF

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0

180 RF

19


MR Parameters: TE and TR
 Echo time, TE is the time from the RF excitation to the center of the echo being received.

Shorter

echo times allow less T2 signal decay

 Repetition time, TR is the time between one acquisition and the next.

Short TR values do not
allow the spins to recover their longitudinal magnetization, so the net magnetization available is
reduced, depending on the value of T1

 Short TE and long TR give strong signals

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Contrast, Imaging Parameters
S(TR , TE ) ∝ ρ(1 − e
or ρ(1 − e

− TR / T1

− TR / T1

)e

)e

− TE / T2

− TE / T2*

(SE )

(GRE)

TE
TR Image Weighting
Short Long
Proton
Short Short
T1
*
Long Long
T2, T2
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Properties of Body Tissues
Tissue

T1 (ms) T2 (ms)

Grey Matter (GM)

950

100

White Matter (WM)

600

80

Muscle

900

50

Cerebrospinal Fluid (CSF)

4500

2200

Fat

250

60

Blood

1200

100-200

MRI has high contrast for different tissue types!
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22


MRI of the Brain - Sagittal

T1 Contrast
TE = 14 ms
TR = 400 ms
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T2 Contrast
TE = 100 ms
TR = 1500 ms

Proton Density
TE = 14 ms
TR = 1500 ms
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MRI of the Brain - Axial

T1 Contrast
TE = 14 ms
TR = 400 ms
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T2 Contrast
TE = 100 ms

TR = 1500 ms

Proton Density
TE = 14 ms
TR = 1500 ms
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Brain - Sagittal Multislice T1

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