Introduction to Magnetic Resonance Imaging

Bruno Quesson, CR1 CNRS

Important magnetic field (~1 Tesla)

General ElectricSiemensPhilips

MRI : Imaging of water and fat (soft tissues)

diagnostis

healthy pathological

brain

animal

breast

Fat suppression

Tunable contrasts

Multislices 2D / 3D

Any slice orientation is feasible

Functional Diagnosis

Tissue looks normal but its function is altererd– Cardiac arythmia – Perfusion : thrombosis, tissue is nomore feed with blood– Diffusion : stroke– lungs : He3 imaging– …

angiography perfusionLung, He3

Diffusion brain

Dynamic imaging (heart)

Spatial resolution can be adjusted

Embryo of mice

fMRI : functional imaging of the brain activity

signal changes with blood oxygenation– Task => use of oxygen– Indirect detection of the brain activity– Low signal variation (2%) => high filed

Dynamic imaging (kinetic) 3D imaging (cover the entire brain) Statistical analysis Associate PET (radioactivity) et EEG (electrical activity)

Interventional imaging

Definition : « guide a therapeutic procedure with the help of images»– Rapid acquisition -> real time– Real time reconstruction– Real time processing

Examples :

-to visualize catheter positioning – Substitution Xray to MRI

-to identify a lesion and to guide the puncture– Ex : breast, liver, brain tumours

Interventionnal imaging : thermometry

Pig liver

Human

temperature Thermal Dose Follow up T2 Follow up T1

HOW IS THIS POSSIBLE???

Nuclear Magnetic Resonance : NMR

Magnetic equilibrium : B0 static and intense

Perturbation of the equilibrium : Excitation B1 (energy transferred to the system)

Back to initial equilibrium state : Relaxation (energy transferred from the system)

B0 = 0

z

B0 ≠ 0

MacroscopicMagnetization M0y

x

z

y

x

zM0

zM0

zM0

B1

zM0

zM0

Emitted signal=

NMR signal

Modeling the NMR signal

Vector mathematical formalism

z

M

B0

y

x

Mz

Mx

My

Mx(t)=?

My(t)=?

Mz(t)=?

Solution of the Bloch differential equations :

Mx(t) = Mt(0).exp(-t/T2).cos(0 t)

My(t) = Mt(0).exp(-t/T2).sin(0 t)

Mz(t) = M0 – (M0 – Mz(0)).exp(-t/T1)

Transverse magnetization

Longitudinal magnetization

0 = B0

transverse magnetization : exponential decay

Helicoïdal motion

y

Mt

B0 x100

80

60

40

20

0

Mt

1.00.80.60.40.20.0

Time / s

Rotation around B0 Amplitude : exponential decay

Mt(t) = Mt(0).exp(-t/T2).exp(0 t)

Detectable signal

Longitudinal magnetization

z

B0 x

Mz

100

80

60

40

20

03.02.52.01.51.00.50.0

Mz

Time / s

Mz(t) = M0 – (M0 – Mz(0)).exp(-t/T1)

y

Typical NMR parameters at 1.5 Tesla

8550500breast

7055870cardiac muscle

951001800vitrous humor

7060775spleen

6060650kidney

6070600pancreas

7045500liver

8075934disk

951001200blood

4080830lung

10080252fat

4060400bone marrow

4060400Vertebral marrow

7045870SQuel Muscle

1001602400CSF

7090780WM

85100920GM

M0 (%)T2 / msT1 / msTissue

Longitudinal (T1) and Transverse (T2) relaxation times

M0(GM)

M0(WM)

100

80

60

40

20

0

Mz

3.02.52.01.51.00.50.0

GM WM

100

80

60

40

20

0

Mt

1.00.80.60.40.20.0

GM WM

Time / s

Difference = contrast

T1 contrast

T2 contrast

Proton Density

Acquisition sequence

Sequence = a number of events which occur at different instants

t

B1

TR

Te

S2 = M0.(1-exp(-TR/T1)).exp(-Te/T2). exp(i0t)

Te

S1 = M0.exp(-Te/T2).exp(i0t)

Which contrast ?

TR/T1

TE/T2

ContrastT1

ProtonDensity

ContrastT1 and T2

ContrastT2

0

Examples

But how a MR image is obtained???

MR image = map of magnetization

How can we separate signal coming from different locations????

B0

y

x

z

y

z

S1 = M0.exp(-Te/T2).exp(i0t)

S2 = M0.exp(-Te/T2).exp(i0t)

S3 = M0.exp(-Te/T2).exp(i0t)

S4 = M0.exp(-Te/T2).exp(i0t)

S total = S1+S2+S3+S4

So what??

t

t

t

t

t

Fourier Transformation

It is NOT possible to distinguish individual signals

Let us make B0 vary in space

B0

y

x

z

y

z

S1 = M0.exp(-Te/T2).exp(i1t)

S2 = M0.exp(-Te/T2).exp(i2t)

S3 = M0.exp(-Te/T2).exp(i3t)

S4 = M0.exp(-Te/T2).exp(i4t)

S total = S1+S2+S3+S4

z

B(z) = B0 + Gz.z (z) = 0 + .Gz.z

+

Gz

So what??

t

t

t

t

Fourier Transformation

It is possible to distinguish individual signals from their spectrum in 1 direction

Profile

Mathematical description

S(Gz,t) = MT(z).exp(-t/T2).exp(i[0 + .Gz.z].t) dz

S(Gz,t) = exp(-t/T2).exp(i0.t) MT(z). exp(i..Gz.z..t) dz

S(kz) = exp(-t/T2).exp(i0.t) MT(z). exp(i.kz.z.) dz

We substitute kz = .Gz.t

S(kz) = A MT(z). exp(i.kz.z.) dz = A. FT[ MT(z) ]

Back to the profile

MT(z) = FT-1 [ S(kz) ] / A

MT(z) = A-1 . S(kz). exp(-i.kz.z.) dkz

1-We have to measure the signal for different kz (= g.Gz.t) conditions

2-We have to Fourier Transform these data sets to retrieve the profile of the object

Comparison of measurements under different Gz conditions

z

Gz

z

Gz

z

Gz

Graphical representation

zkz

Gz

0

In 2D : We have to repeat this 2 orthogonal directions

z

kz

Gz

y

Gy

ky

Gz

Gy

When the complete map is acquired, we get the image

kz

2D Fourier Transformation

ky

ImageFourier space“k-space”

MRI acquisition sequence

t

t

t

t

B1

Gs

Gp

Gr

TR

Te

Gradient echo

Trajectory in the Fourier space

Contrast

Contrast manipulation

PreparationAcquisition (of Fourier space)

t

t

t

t

B1

Gs

Gp

Gr

TeTi

t

Ex: inversion recovery (IR)

Examples of signal modulation with Inversion -Recovery

Ti = 0 s

Ti = 66 ms

Ti = 174 ms

MT(t) = MT(0).exp(-t/T2)

MT(0) = M0(1 – 2.exp(-Ti/T1))

Signal :

with :

Contrast modulation

-100

-50

0

50

100

Mz

1.21.00.80.60.40.20.0

Time / s

fat liver

100

80

60

40

20

0

Mt

0.40.30.20.10.0

fat liver

60

50

40

30

20

10

0

Mt

0.40.30.20.10.0

fat liver

100

80

60

40

20

0

Mt

0.40.30.20.10.0

Time / s

fat liver

Selective perturbation

Ex : « black blood » (BB) for cardiac imaging

t

t

t

t

B1Gs

Gp

Gr

Ti (blood)

Acquisition

180°180°

BB prepulse

Acquisitionpreparationt

Resulting images

Without BB

With BB pulse

Double inversion-recovery

t

t

t

t

B1Gs

Gp

Gr

Acquisition

180°180°

Motif DI

Ti(1) Ti(2)

Gradient Echo sequence

t

t

t

t

B1

Gs

Gp

Gr

TR

Te

Gradient echo

Trajectory in the Fourier space

Contrast

Spin echo sequence

Refocuses all magnetizations

t

t

t

t

B1

Gs

Gp

Gr

TR

Te

Te/2Te/2

Spin echo

Summary

RF pulses– Variable angles– Frequency selective or not– Spatially selective or not

Gradients

A lot of possible combinaisons

Strategy of the acquisition depends on the application