The Basics of Magnetic Resonance Imaging

Transcription

1 The Basics of Magnetic Resonance Imaging Nathalie JUST, PhD CIBM-AIT, EPFL Course Chemistry 1

2 Course Chemistry 2

3 MRI: Many different contrasts Proton density T1 weighted T2 weighted Angiography Diffusion FLAIR weighted weighted Course Chemistry 3

4 Magnetic field strength, magnetic dipole? Earth s magnetic field : 25mT (Equator) to 70mT (Surface) [0.25 to 0.70G] Household refrigerator magnet: 10mT Clinical magnet: 1.5-3T Animal magnets: up to 17T Others: >30T Course Chemistry 4

5 The MRI scanner and its essential components It s a complex machine Major elements of MRI : Nucleus Magnet RF coil Gradient coil Cut-open in real life Course Chemistry Schematic depiction of all MRI components 5

6 1-1. Nuclear Magnetism Classical and quantum-mechanical view Nucleus angular momentum L (here called P) Rotation of electrical charge (nucleus) Rotating current Dipole moment P nucleus P m = NMR-active isotopes and their gyromagnetic ratio g Magnetic moment m of individual spin in induction field B o m gp g: gyromagnetic ratio (empirical constant) The angular momentum P of a nucleus is quantized: P z has 2I + 1 values (m): h P 2p Isotope I I 1 Spin ½: P=h3/4p Net Spin (I) P h 2p z m I gyromagnetic ratio g/2p [MHz T -1 ] 1 H 1/ Abundance / % 2 H P 1/ Na 3/ N 1/ C 1/ Course Chemistry 19 F 1/

7 Energy of nuclear spins in magnetic field Unequal population of Energy levels Energy of a magnetic dipole in magnetic field B 0 (classical) E m B 0 m cos B0 mz B0 Quantum mechanical description: E I h g m 2p I B Boltzmann statistics/distribution: Unequal population of energy levels N N e E Energy is minimal, when µ B 0 (Where is that used?) m B 0 1 h g B 4p h 4p m I =-I,,I E2 g B0 E kt 0 m=-1/2 (N 1 spins) Eg m=1/2 (N 2 spins) Transitions between E 1 and E 2 induced by photons hn = E h 2p B0 k : Boltzmann's constant (1.4x10-23 J/Kelvin) NB. At 310K : ~1 in 10 6 excess protons in low energy state (1Tesla) N 1 ~N 2 ~N/2 (N = no of spins) Non-ionizing radiation NMR Course Chemistry 7 7

8 Precession and Larmor frequency If the net magnetization is placed in the XY plane it will rotate about the Z axis at a frequency equal to the frequency of the photon which would cause a transition between the two energy levels of the spin. This frequency is called the Larmor frequency. w gb 0 f g 2 B 0 p Course Chemistry 8

9 Rotating Frame of Reference It is convenient to define a rotating frame of reference which rotates about the Z axis at the Larmor frequency. We distinguish this rotating coordinate system from the laboratory system by primes on the X and Y axes, X'Y'. A magnetization vector rotating at the Larmor frequency in the laboratory frame appears stationary in a frame of reference rotating about the Z axis. In the rotating frame, relaxation of M Z magnetization to its equilibrium value looks the same as it did in the laboratory frame. A transverse magnetization vector rotating about the Z axis at the same velocity as the rotating frame will appear stationary in the rotating frame. Course Chemistry 9

10 Start with thermodynamic equilibrium magnetization M 0 Reference frame rotating with w L (onresonance) Apply additional, constant magnetic field with magnitude B 1 (in xy plane) for time Flipping magnetization over in the rotating reference frame x M 0 z B 1 a Rotating reference frame y What motion can be observed for M? dm dt γb1 M M 0 precesses about B 1 Magnetization rotates about B 1 with angular velocity gb 1 Frequency gb 1 /2p period T = 2p/gB 1 Course Chemistry Definition Flip angle = angle of rotation a induced by B 1 applied for seconds Special cases of a: 90 0 : Full excitation (all M 0 is rotated into transverse plane, xy, i.e. M 0 M xy ) : Inversion (M z -M z ) B 1 = radiofrequency (RF) field (why?) Lab frame: B 1 (t)=b 1 (cosw L t,sinw L t) g ~ 42MHz/Tesla w L /2p ~ 100MHz 10

11 1-5. Relaxation governs the return to equilibrium M 0 Thermodynamic equilibrium z M 0 RF pulse(s) B 1 After excitation z x Relaxation T 1, T 2 M xy y B 1 x y B Transverse magnetization: (along x and y-axis, on resonance) Exponential decay of M xy dm x( t) M x( t) dt T 2 dm y ( t) M y ( t) dt T 2 M xy ( t) M xy (0) e t T 2 Course Chemistry Equations formally equivalent to linear attenuation coefficient (x-ray) (same solution) 11

12 Relaxation Mechanisms: T1 and T2 processes Relaxation: Absorption of energy is spontaneous not relaxation Relaxation occurs after a sample has been stimulated by local magnetic fields at the Larmor frequency These fields are produced by the molecules themselves which are modulated by molecular motion and structure Spin-Lattice Relaxation (T1): Loss of energy resulting from the pulse to the surroundings as thermal Energy Rate of return of the Mz magnetization to its equilibrium value (M0) Spin-spin Relaxation (T2): Loss of phase coherence between the spins after the 90º pulse T1=T2 in pure liquids T2<T1 in biological samples M exp( t / TC) T2 is very short in solid states (less than 1ms) T1 can be very long in slolid states (>1min) Course Chemistry 12

13 Bloch Equations add relaxation terms (T 1, T 2 ) to the fundamental Eq of motion of magnetization: dm z ( t) dt dm x ( t) dt dm y ( t) dt g[ M ( t) B ( t) M ( t) B ( t)] x y g[ M ( t) B ( t) M ( t) B ( t)] y z g[ M ( t) B ( t) M ( t) B ( t)] z x y z x - γb M Substituting =-gb 0 +w RF (B 0 =B z is not time-dependent) yields: g x y z M z ( t) M T 1 M x (t) T 2 M y T 2 (t) Rotating reference frame [ M x 1 M y x ( t) B1 ( t) M yb ( t)] y y ( t) gm B1 ( t) z 0 along z along x along y B 1 : RF field in rotating frame x gm z ( t) B1 ( t) M x Course Chemistry γb 1 Felix Bloch Physics 1952 M

14 Free Induction Decay (FID) The NMR signal detected following a pulse is a function of time. If 1 type of nucleus in a uniform field, it is a single exponentially decaying signal, whose frequency depends on its resonance frequency: FID M ( t) M (0) e iwt t / T Transverse xy magnetization xy M xy ( t) M xy (0) e iwt e e t / T M x t M y T 2 T t Longitudinal magnetization (after 90 0 RF excitation) 0.6 M z 0.4 T M z t / T1 ( t) M (1 e ) 0 M xy Course Chemistry 14

15 Fourier Transform Course Chemistry 15

16 Increasing the magnetic field strength B 0 increases sensitivity MRI of the lower abdomen MRI of the breast (1.5 vs 3 Tesla) MRI of the spine fmri of the brain (1.5 vs 4 Tesla) cle/research/38414 maximum possible MR signal: determined by equilibrium nuclear magnetization M 0 Course Chemistry 16 16

17 MRI contrast depends on experimental parameters I. Time after excitation TE TE=25 ms 50 ms 75 ms 100 ms Course Chemistry 17 17

18 II. Flip angle a and time between excitations TR ms a a a deg pulse Course Chemistry 18 18

19 Magnetic susceptibility (χ) Extent to which a substance becomes magnetized when placed in an external field Electromagnetic interactions take place between the matter and the field These interactions concentrate or disperse the lines of the magnetic field Due to action of orbital or delocalized eletrons within the matter They induce an internal magnetization Mi that either augments or opposes the magnetic field Magnetic field Mi Mi Diamagnetic χ < 0 Paramagnetic χ>0 Course Chemistry 19

20 Magnetic properties of Matter Magnetic property Direction of Magnetic field /B0 Relative Magnetic Susceptibility Materials Diamagnetic Opposiste -1 Water, Most organic molecules, inert gases Paramagnetism Same 10 Ions, salts and chelates of metals (Cr, Fe Cu, Gd, Dy) Superparamagnet ism Same 5000 Small Fe3SO4 particles Ferromagnetism Same Larger Fe3SO4 particles Course Chemistry 20

21 Example of paramagnetic contrast agent: Gadolinium Most widely used as MR contrast agent Facilitates the relaxation of tissue hydrogen protons: Enhancement of T1 relaxation The electrons of Gd interact with the resonating protons allowing a more rapid relaxation Gd is part of the lanthanides Gd has 7 unpaired electrons in its 4f orbitals Electrons possess a magnetic moment that is larger than that of the protons DTPA ( diethylenetriamine penta acetic acid) is a ligand serves as a chelator Course Chemistry 21

22 The relaxivity of MRI contrast agents depends on the molecular structure and kinetic of the complex. To increase the number of water molecules that are in the inner sphere of the complex, or to slow down the molecular rotational correlation time, are possibilities to improve the water relaxivity. Relaxivity units ( r1, r2 ) are mm -1 * sec -1 (at varying temperatures). Course Chemistry 22

23 Course Chemistry 23

24 Course Chemistry 24

25 Negative Contrast agent: Superparamagnetic iron oxide particles Gradient echo R2* Spin echo R2 Before Injection After Course Chemistry 25

26 References (the basics of MRI) Course Chemistry 26