the basics of magnetic resonance imagingthe basics of magnetic resonance imaging nathalie just, phd...

The Basics of Magnetic Resonance Imaging

Nathalie JUST, PhD

[email protected]

CIBM-AIT, EPFL

1 Course 2013-2014-Chemistry

mailto:[email protected]

Course 2013-2014-Chemistry 2


MRI: Many different contrasts

Proton density T1 weighted T2 weighted Angiography Diffusion FLAIR

weighted weighted

4 Course 2013-2014-Chemistry

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

Magnetic field strength, magnetic dipole?


The MRI scanner and its essential components

Cut-open in real life

It’s a complex machine …

Schematic depiction of all MRI

components

Major elements of MRI :

Nucleus

Magnet

RF coil

Gradient coil

Course 2013-2014-Chemistry 6 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

Magnetic moment m of individual spin in

induction field Bo

g: gyromagnetic ratio (empirical constant)

= P

m

P

gm

Isotope Net Spin

(I)

gyromagnetic

ratio g/2p

[MHz T-1]

Abundance /

%

1H 1/2 42.58 99.98

2H 1 6.54 0.015

31P 1/2 17.25 100.0

23Na 3/2 11.27 100.0

15N 1/2 4.31 0.37

13C 1/2 10.71 1.108

19F 1/2 40.08 100.0

NMR-active isotopes and their gyromagnetic ratio g

12

IIh

Pp

The angular momentum P of a nucleus is

quantized:

Pz has 2I + 1 values (m):

Spin ½: P=h3/4p

Iz mh

P p2


Energy of nuclear spins in magnetic field Unequal population of Energy levels

000 cos BBBE z mmm

014

Bh

E p

g

0

2BhE

pg

m=-1/2 (N1 spins)

m=1/2 (N2 spins)

Energy of a magnetic dipole in magnetic

field B0 (classical) Energy is minimal, when µ||B0

(Where is that used ?)

Quantum mechanical description:

02

Bmh

E II p

g

Boltzmann statistics/distribution: Unequal population of energy levels

k : Boltzmann's constant (1.4x10-23 J/Kelvin)

NB. At 310K : ~1 in 106 excess protons in

low energy state (1Tesla)

→ N1~N2~N/2 (N = no of spins)

mI=-I,…,I 02

4B

hE

pg

kT

E

eN

N

2

1

0B

m

NMR

Non-ionizing radiation

Transitions between E1 and E2 induced by photons

hn = E

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.


0Bw g

02

Bfp

g

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 MZ 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.



Flipping magnetization over in the rotating reference frame

Start with thermodynamic equilibrium

magnetization M0

Reference frame rotating with wL (on-

resonance)

Apply additional, constant magnetic field

with magnitude B1 (in xy plane) for time x

y

z

M0

B1

a

What motion can be observed for M ?

MBγdt

Md

1 M0 precesses about B1

Magnetization rotates about B1 with

angular velocity gB1

Frequency gB1/2p

→ period T = 2p/gB1

Definition Flip angle = angle of rotation a

induced by B1 applied for seconds

Special cases of a:

900: Full excitation (all M0 is rotated into

transverse plane, xy, i.e. M0 →Mxy)

1800: Inversion (Mz → -Mz)

B1 = radiofrequency (RF) field (why?)

Rotating reference frame

Lab frame: B1(t)=B1(coswLt,sinwLt)

g ~ 42MHz/Tesla → wL/2p ~ 100MHz


1-5. Relaxation governs the return to equilibrium M0

2T

)()( tM

dt

tdM xx

Transverse magnetization:

(along x and y-axis, on resonance)

2T

)()( tM

dt

tdM yy

x y

z

Mxy

B1 x y

z

B1

900

RF pulse(s)

B1

Relaxation

T1, T2

Thermodynamic equilibrium After excitation

Exponential decay of Mxy

2)0()(T

t

xyxy eMtM

Equations formally equivalent to linear

attenuation coefficient (x-ray) (same solution)

M0

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


)/exp( TCtM

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

T2 is very short in solid states (less than 1ms)

T1 can be very long in slolid states (>1min)


dt

tdM z )(along z

dt

tdM x )(along x

dt

tdM y )(along y

1

0

T

)( MtM z

2T

)(tM x

2T

)(tM y

)]()()()([ tBtMtBtM xyyx g

)]()()()([ tBtMtBtM yzzy g

)]()()()([ tBtMtBtM zxxz g

MBγ-

)]()()([ 11 tBMtBtM x

y

y

x g

)()( 1 tBMtM y

zy g

x

x

z MtBtM )()( 1gB1 : RF field in

rotating frame

Substituting =-gB0+wRF (B0=Bz

is not time-dependent) yields:

add relaxation terms (T1, T2) to the fundamental Eq of motion of magnetization:

Bloch Equations

MBγ 1

Rotating reference frame

Felix Bloch

Physics

1952

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


1 2 3 4 5

-0.5

0.5

1

1 2 3 4 5

-0.75

-0.5

-0.25

0.25

0.5

0.75

1Mx My

t t

T2 T2 2/)0()(

Tttixyxy eeMtM

wTransverse magnetization

2/)0()(

Tttixyxy eeMtM

w

0.2

0.4

0.6

0.8

Mz

T1 Longitudinal magnetization (after 900 RF excitation)

)1()( 1/

0

Tt

z eMtM

Mxy

Fourier Transform



Increasing the magnetic field strength B0 increases

sensitivity

http://medicalphysicsweb.org/cws/arti

cle/research/38414

MRI of the breast (1.5 vs 3 Tesla)

MRI of the lower abdomen

MRI of the spine fMRI of the brain (1.5 vs 4 Tesla)

maximum possible MR signal:

determined by

equilibrium nuclear magnetization M0


MRI contrast depends on experimental parameters I. Time after excitation TE

TE=25 ms 50 ms 75 ms 100 ms


a

II. Flip angle a and time between excitations TR

a

a deg pulse

ms

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


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)

Superparamagnetism Same 5000 Small Fe3SO4 particles

Ferromagnetism Same 25000 Larger Fe3SO4 particles

Magnetic properties of Matter

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

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).


http://www.mr-tip.com/serv1.php?type=db1&dbs=MRI

http://www.mr-tip.com/serv1.php?type=db1&dbs=Contrast%20Agents

http://www.mr-tip.com/serv1.php?type=db1&dbs=R1

http://www.mr-tip.com/serv1.php?type=db1&dbs=R2


Gradient echo

R2*

Spin echo

R2

Before Injection After

Negative Contrast agent: Superparamagnetic iron

oxide particles

References

• [email protected]

• http://www.cis.rit.edu/htbooks/mri/ (the basics of MRI)


mailto:[email protected]

http://www.cis.rit.edu/htbooks/mri/

the basics of magnetic resonance imagingthe basics of magnetic resonance imaging nathalie just, phd...

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