principles of magnetic resonance imaging · principles of magnetic resonance imaging klaus...

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Radiologische Physik

Biomedical Magnetic Resonance: 1 Introduction

Principles of Magnetic Resonance Imaging

Klaus Scheffler, PhDRadiological PhysicsUniversity of Basel

University HospitalBasel

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Magnetic Resonance Imaging

Contents:

1 Introduction

2 Nuclear Magnetic Moments

3 Motion of Magnetization

4 Excitation and reception

5 Magnetic Resonance Imaging

6 Contrast


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Biomedical Magnetic ResonanceHistory:


198119791974

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Biomedical Magnetic ResonanceToday:


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Biomedical Magnetic Resonance: 2 Nuclear Magnetic Moments

Nuclear Magnetic Moments

Properties of a nucleus:


Nuclues is charged (multiples of e+)

Some nuclei have a spin angular momentum J:J = ħI (I multiples of ½)

Then, they have a dipolar magnetic moment : = J = ħIFor example: 1H, 13C, 19F, 31P

ħ = Planck‘s quantum constant = gyromagnetic ration

+

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Nucleus in a magnetic field:


We assume I=½ (1H, 13C, 19F, 31P)

Then, the magnetic moment along the field is:

z = ħm = ±½ħ

The magnetic moment z is parallel orantiparallel to the field B0

B0 B0

z = ½ħ z = -½ħ



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Nucleus in a magnetic field:


In an external magnetic field,spin up or spin down are associated todifferent energy levels:

Em = -zB0 = -ħB0m, m = ±½.

E = +½ħB0 , E = -½ħB0

E = ħB0



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01/2 1/2 2 B S

n Bn n nk T

01/2 1/2 2 B S

n Bn n nk T

In thermal equilibrium, there are different probabilitiesfor spin up and down occupation (Boltzmann statistics).The difference in occupation n is given by:

kB : Boltzmann constantTS: Temperature


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Macroscopic magnetization:

Visible magnetization:

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0 0 0 0( )2 4z z S

B S B S

n B nM n B T Bk T k T

0 izi

M

Sum (macroscopic Magnetization along B0):

0(TS): magnetic susceptibilitykB : Boltzmann constant


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Biomedical Magnetic Resonance: 3 Motion of Magnetization

Motion of Magnetization


Magnetization and magnetic field:

S

N

= =

M0

N

S

=

N

S

EW=

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Radiologische PhysikUniversity Hospital

Basel


N

S

B0

N

S

B0

N

S

B0



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Basel


B0

M0

B0

M0

B0

M0

?



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Basel

Nuclues is charged (multiples of e+)

Some nuclei have a spin angular momentum J:J = ħI (I multiples of ½)

Then, they have a dipolar magnetic moment : = J = ħI


+


ΣM0

=



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M0

=


N

S

B0

M0



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Magnetization and magnetic field:gravity

N

S

B0

N

S

B0

gravity

B0

M0



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Motion of magnetization: precession

( )d Bdt



B

d

d Bdt

d

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Motion of magnetization: precession



( )d Bdt

d Bdt

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Motion of magnetization: precession ( )d Bdt



d Bdt

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B0 B0

Bx(t) = 2B1cos(t)

B0

Excitation and Reception

Biomedical Magnetic Resonance: 4 Excitation and Reception

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FID: free induction decay

B0

precession of magnetization

a) on-resonance, b) off-resonance, c) spectrum

Excitation and Reception

Biomedical Magnetic Resonance: 4 Excitation and Reception

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Biomedical Magnetic Resonance: 5 Magnetic Resonance Imaging


Imaging = spatial discrimination


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Bloch equation

= B

dMdt

M B ( )

Larmor equation

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Magnetic Field Gradients

x

B 0 = B0

B0

Sample in a homogenous magnetic field B0

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x

B(x) = B0 + xGx

B0

Sample in a magnetic gradient field B0 + B

am

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BB

xx

yyMagneticMagnetic fieldfield IsoIso--FluxFlux GraphGraph

Problem: 2D Problem: 2D oror higherhigher -- FrequenciesFrequencies ambiguousambiguous

xx

yy

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Swichable, linear magnetic field gradientsindependently in x, y and z direction

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BaselMagnetic Resonance Imaging


Spatially resolved reception

GradientGradient

x2x2

x1x1

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Spatial encoding: the Fourier Transform

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RF excitation

z gradient

x gradient

GradientGradient

x2x2

x1x1

MR signal

FT

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Back projection: imaging sequence

RF excitation

z gradient

x gradient

y gradient

Signal acquisition sinogram

FT

recon

k

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Imaging in k-space

2DFT2DFT

k-space image

i2 kxS(k) (x) e dx -i 2(x) S(k) e dkkx

S(k) = S(k(t)) = S(t)

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Properties of k-space

kx

ky

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Properties of k-space

8 x 8512 x 512

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Imaging in k-space

k-space

i2 kxS(k) (x) e dx

S(k) = S(k(t)) = S(t)

RF excitation

z gradient

x gradient

y gradient

Signal acquisition

t

0

1( ) (t) dt2

k t G

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Imaging in k-space: gradient echo (GE) sequence

k-space

i2 kxS(k) (x) e dx

S(k) = S(k(t)) = S(t)

RF excitation

z gradient

x gradient

y gradient

Signal acquisition

t

0

1( ) (t) dt2

k t G

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Imaging in k-space: gradient echo (GE) sequence (EPI)

k-space

i2 kxS(k) (x) e dx

S(k) = S(k(t)) = S(t)

RF excitation

z gradient

x gradient

y gradient

Signal acquisition

t

0

1( ) (t) dt2

k t G

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Imaging in k-space: gradient echo (GE) sequence (spiral EPI)

k-space

i2 kxS(k) (x) e dx

S(k) = S(k(t)) = S(t)

RF excitation

z gradient

x gradient

y gradient

Signal acquisition

t

0

1( ) (t) dt2

k t G

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Imaging in k-space: spin echo (SE) sequence

k-space

i2 kxS(k) (x) e dx

S(k) = S(k(t)) = S(t)

RF excitation

z gradient

x gradient

y gradient

Signal acquisition

t

0

1( ) (t) dt2

k t G

90°

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k-space

i2 kxS(k) (x) e dx

S(k) = S(k(t)) = S(t)

RF excitation

z gradient

x gradient

y gradient

Signal acquisition

t

0

1( ) (t) dt2

k t G

90°

180°

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k-space

i2 kxS(k) (x) e dx

S(k) = S(k(t)) = S(t)

RF excitation

z gradient

x gradient

y gradient

Signal acquisition

t

0

1( ) (t) dt2

k t G

90°

180°

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Contrast

Biomedical Magnetic Resonance: 6 Contrast

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BaselContrast

Relaxation in living tissue

T1: recovery of longitudinal magnetization

T2* : loss of phase coherence of transverse magnetization

T2`

staticdephasing

randomdephasing

T2

T2*

x

z

T1 T2*

M

2

2

1

/

/

/0 0( )

t Tx xi

t Ty yi

t Tz zi

M M e

M M e

M M M e M


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Spin Echoes


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Relaxation in living tissue

Contrast


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Contrast of imaging sequences

k-space RF excitation

z gradient

x gradient

y gradient

Signal acquisition

Repeat hundreds of times

Contrast


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Contrast of imaging sequences:TR~T1>T2

t

MzM0

0 1 2 3 4 5 6 7 8

M0cos

Mt

M0sin

RF (flip angle )

Contrast


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200 500 1000 3000 6000

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70

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TRTE

Contrast


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