Introduction to Magnetic Resonance Imaging Bruno Quesson, CR1 CNRS.
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Transcript of Introduction to Magnetic Resonance Imaging Bruno Quesson, CR1 CNRS.
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
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
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)
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
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
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
Gradient Echo sequence
t
t
t
t
B1
Gs
Gp
Gr
TR
Te
Gradient echo
Trajectory in the Fourier space
Contrast