BE 581

Intro to MRI

What is MRI?

• Magnetic Resonance Imaging

• Based on NMR: Nuclear Magnetic Resonance

• Chapters 14 (NMR) and 15 (MRI)

What is MRI?

• An imaging modality that uses a magnetic field and radio frequency to image soft tissue

• Non ionizing radiation - not enough energy to remove electrons from atoms

• Non ionizing radiation - may have enough energy for excitation to a higher energy state

What can we see with MRI?

• In general soft tissue– Internal Organs– Muscles– Brain – Tumors– Inflammation

What can we see with MRI?

• With a contrast agent (MRAngiography)– Gadolinium + cherate– Blood vessels– Aneurisms– Blockage

What can we see with MRI?

• FunctionalMRI (FMRI)– Hemodynamic response of brain/spinal cord– Uses oxygenated hemoglobin as a marker– Response to a stimulus

MRI video

• http://www.imrser.org/PatientVideo.html

• Lucas Parra lecture at City College NY

• http://www.youtube.com/watch?v=4uzJPpC4Wuk&feature=related

MRI process

• Patient in magnetic field– Precession of protons

• Send radio frequency– Precession is in phase (synchronization)

• Turn off radio signal– Decay of synchronization

• Collection of resonance signal– Coherent precession induces current in

detection coil

NMR

NMR

Nuclear Magnetic Resonance

Hydrogen NucleiHydrogen NucleiHydrogen Nuclei (Protons)

Axis of Angular Momentum (Spin), Magnetic Moment

External Magnetic Field

Spins PRECESS at a single frequency (f0), but incoherently − they are not in phase

Hydrogen NucleiHydrogen Nuclei

Irradiating with a (radio frequency) field of frequency f0, causes spins to precess coherently, or in phase

Hydrogen NucleiHydrogen Nuclei

Magnetic Field IMagnetic Field I

N

Smagnetic field lines

By staying in the interior region of the field, we can ignore edge effects.

But how do we describe magnetic fields and field strengths quantitatively?

Magnetic Field IIMagnetic Field II

N

S

q

v

An electric charge q moves between the N and S poles with velocity v.

If the charge is crossing magnetic field lines, it experiences a force F.F

B

F = qv x B

Thus F is perp both v and B.

• F[N] = q[A.s]v[m.s-1]B• For consistency, units of B must be N.(A . m)-1

• 1 N.(A.m)-1 1 T (tesla) Kg (A s2)-1

• If a current of 1 A flows in a direction perpendicular to the field lines of a 1 T magnetic field, each one-meter length of moving charges will experience a magnetic force of 1 N

Magnetic Field IIIMagnetic Field III

Magnetic Field B

• B goes by several different names in physics literature:– Magnetic field– Magnetic induction– Magnetic induction vector– Magnetic flux density

Nuclear Spin

• Spin: subatomic property of the nucleus– Quantized (Hydrogen proton I=1/2)

• Angular momentum J of spinning mass

I spin energy levelmI magnetic quantum number

can be +1/2 or -1/2

Magnetic moment

• The spinning of the charge generates magnetic moment µ

is the gyromagnetic ratio and it’s an intrinsic property of each nucleus

µ = J

Material NMR properties

• Only non zero spin atoms generate an MRI signal

• 1H, 13C, 31P etc.

spin

1H (proton)

• MRI is based on the abundance of this proton in the human body

Precession

• A second order motion- the rotation of a rotating object (~ wobble)

Precession

• A spin in a uniform magnetic field Bo precesses at a frequency o (Larmor frequency)

o= Bo

• Quantum mechanics dictates that µz and Jz

can only be

µz= Jz= hmI / 2

mI= +/- 1/2 (for I=1/2)

Spin Energy states

• Due to the quantization of the spin there are only 2 possible energy states for the proton - parallel and antiparallel

Zeeman effect -loss of a degenerate state

E= µzBo= +/- hBo / 4

B=0

B>0

Degenerate state

B

parallel

antiparallel

Boltzman distribution

• It’s the relative population difference between two energy states

• nupper/nlower = exp(-E/KbT)

• Kb Boltzman constant =1.38 1023 J/K

• T temperature -> this is the reason why it’s hard to to MRI, you need a lot of ENERGY and low temp -> freeze patients?

Magnetization

• The Boltzman distribution characterizes the number of parallel and antiparallel spin

• When B=1.5T applied to 1 million protons there are only 5 more parallel than antiparallel

• Typical volume for MRI is 1021 protons

Magnetization

• This difference generates bulk magnetization Mo in z direction (N nuclei)

Classical physics interpretation

• valid when E << KbT

• When placed in a magnetic field it is forced to align

N

S

Nuclear magneticmoment is a bar magnet

B

Classical physics interpretation

• Spin provides angular momentum, interaction with Bo -> Torque -> precession

• The small difference in population of energy levels produces a small net magnetization Mz

Larmor frequency

• When proton are irradiated with EM radiation at a frequency fo we have resonance

E = hfo= (h/2)Bo

The Larmor frequency is

o= Bo angular

fo= Bo/2linear

• Larmor frequency ->wobbling frequency

Use of RF pulse

• Bulk magnetization Mz

• A pulse of frequency o is able to flip M

Use of RF pulse

• A pulse of frequency o is able to flip M

• The flip angle depends on amplitude and length of the pulse

90 degreesFlip Mz = My

180 degreesflip Mz = -Mz

Use of RF pulse

• It is fundamental that the RF pulse is applied at the resonant frequency o

• Nothing would happen otherwise RESONANT FREQUENCY

• Quantum mechanics: A photon with energy equal to E can promote lower energy protons to higher energy

Block Equation

• Bulk magnetization M=[Mx,My,Mz]

• Magnetization over time

Exponential decaywith T2 time constant

Exponential decaywith T1 time constant

Block Equation - T2 decay

• A RF pulse generate the transverse Mx My component

• When RF is off Mx and My will decay exponentially (tc=T2) back to Mz

Block Equation - T2 decay

Damped oscillationInduced on a receiver coil

Free precession -T2 decay

• Why does this happen?1 Spin - Spin relaxation– Each spin sees other magnetic field

generated by other spins (decay T2)

2 Bo is not perfectly homogeneus (T+2)

shorter than T2 (100 times)

TOTAL EFFECT

Block Equation - T1 decay

90 pulse

180 pulse

€

Mz t( ) = Mo 1− e−t

T1 ⎛

⎝ ⎜

⎞

⎠ ⎟

Mz t( ) = Mo 1− 2e−t

T1 ⎛

⎝ ⎜

⎞

⎠ ⎟

Free precession - T1 decay

• The spin give/loose energy to the environment (lattice)

• Spin-lattice relaxation

• The system return to equilibrium state after a pulse

• Time necessary to recover 63% of longitudinal magnetization Mz

Free precession - T1 decay

• Water has long T1

• Adding protein reduces T1 length

• Contrast agents are sometime used to decrease T1

Free Induction Decay (FID)

• We can measure these relaxation state with a R coil tuned at the resonant frequency (o = 3.87 MHz for 1H)

• Mxy(0) is magnitude of Mx, My at t=0

s(t)=

Homework 1 (due 10/6)

• Research values of Mo, T2 and o and trace the T2 relaxation in Matlab

Homework 2 (due 10/6)

• Do the same for T1 relaxation

Homework 3

• Find the energy difference between low and high energy state of a proton in a 5 Tesla magnetic field

Homework 4

• What kind of magnets (How many Tesla?) are the basis of commercially available MRI?

• Consider clinical MRI, small (arm/leg MRI) and animal MRI

Images References

• Wikipedia.org

• http://www.radiologyinfo.org/en/info.cfm?pg=angiomr&bhcp=1

• MRI physics class by Lucas Parra CCNY