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 – … angiographyperfusionLung, He 3 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 temperatureThermal DoseFollow up T2Follow 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) B 0 = 0 z B 0 ≠ 0 Macroscopic Magnetization M0 y x z y x z M0M0 z M0M0 z M0M0 B1B1 z M0M0 z M0M0 Emitted signal = NMR signal 

Modeling the NMR signal Vector mathematical formalism z M B0B0 y x Mz Mx My Mx(t)=? My(t)=? Mz(t)=? Solution of the Bloch differential equations : Mx(t) = M t (0).exp(-t/T 2 ).cos(  0 t) My(t) = M t (0).exp(-t/T2).sin(  0 t) Mz(t) = M0 – (M0 – Mz(0)).exp(-t/T 1 ) Transverse magnetization Longitudinal magnetization  0 =  B 0

transverse magnetization : exponential decay Helicoïdal motion y MtMt B0B0 x Mt Time / s Rotation around B0Amplitude : exponential decay Mt(t) = M t (0).exp(-t/T2).exp(  0 t) Detectable signal

Longitudinal magnetization z B0B0 x Mz Mz Time / s Mz(t) = M0 – (M0 – Mz(0)).exp(-t/T 1 ) y

Typical NMR parameters at 1.5 Tesla breast cardiac muscle vitrous humor spleen kidney pancreas liver disk blood lung fat bone marrow Vertebral marrow SQuel Muscle CSF WM GM M0 (%)T2 / msT1 / msTissue

Longitudinal (T1) and Transverse (T2) relaxation times Difference = contrast T1 contrast T2 contrast Proton Density

Acquisition sequence Sequence = a number of events which occur at different instants t B1 TRTR TeTe S2 = M0.(1-exp(-TR/T1)).exp(-Te/T2). exp(i  0 t) TeTe S1 = M0.exp(-Te/T2).exp(i  0 t)

Which contrast ? TR/T1 TE/T2 Contrast T1 Proton Density Contrast T1 and T2 Contrast T2 0

Examples

But how a MR image is obtained??? MR image = map of magnetization How can we separate signal coming from different locations???? B0B0 y x z y z S1 = M0.exp(-Te/T2).exp(i  0 t) S2 = M0.exp(-Te/T2).exp(i  0 t) S3 = M0.exp(-Te/T2).exp(i  0 t) S4 = M0.exp(-Te/T2).exp(i  0 t) 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 B0B0 y x z y z S1 = M0.exp(-Te/T2).exp(i  1 t) S2 = M0.exp(-Te/T2).exp(i  2 t) S3 = M0.exp(-Te/T2).exp(i  3 t) S4 = M0.exp(-Te/T2).exp(i  4 t) 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(i  0.t) MT(z). exp(i. .Gz.z..t) dz S(kz) = exp(-t/T2).exp(i  0.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 z       

Graphical representation z kz 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 Image Fourier space “k-space”

MRI acquisition sequence t t t t B1 Gs Gp Gr TRTR TeTe Gradient echo Trajectory in the Fourier space Contrast

Contrast manipulation Preparation Acquisition (of Fourier space) t t t t B1 Gs Gp Gr TeTe Ti 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 Mz Time / s fat liver Mt fat liver Mt fat liver Mt Time / s fat liver

Selective perturbation Ex : « black blood » (BB) for cardiac imaging t t t t B1 Gs Gp Gr Ti (blood) Acquisition 180° BB prepulse Acquisition preparation t

Resulting images Without BB With BB pulse

Double inversion-recovery t t t t B1 Gs Gp Gr Acquisition 180° Motif DI Ti(1)Ti(2)

Gradient Echo sequence t t t t B1 Gs Gp Gr TRTR TeTe Gradient echo Trajectory in the Fourier space Contrast

Spin echo sequence Refocuses all magnetizations t t t t B1 Gs Gp Gr TRTR TeTe T e /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