Transcript BE 581

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=4uzJ
PpC4Wuk&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 Nuclei
Hydrogen Nuclei (Protons)
Axis of Angular Momentum
(Spin), Magnetic Moment
Hydrogen Nuclei
Spins PRECESS at
a single frequency
(f0), but incoherently
− they are not in
phase
External Magnetic Field
Hydrogen Nuclei
Irradiating with a
(radio frequency)
field of frequency f0,
causes spins to
precess coherently,
or in phase
Magnetic Field I
magnetic field lines
S
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?
N
Magnetic Field II
S
B
If the charge is crossing
magnetic field lines, it
experiences a force F.
v
F
An electric charge q
moves between the N
and S poles with velocity
v.
q
F = qv x B
N
Thus F is perp both
v and B.
Magnetic Field III
•
•
•
•
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 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 level
mI 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
spin
• Only non zero spin atoms generate an
MRI signal
• 1H, 13C, 31P etc.
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
Degenerate state
anti
parallel
parallel
B=0
B
B>0
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
B
Nuclear magnetic
moment is a bar
magnet
• When placed in a magnetic field it is forced to
align
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
f o=
Bo/2 linear
• 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 degrees
Flip Mz = My
180 degrees
flip 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]
Exponential decay
with T2 time constant
• Magnetization over time
Exponential decay
with 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 oscillation
Induced 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
  t 
M z t   M o 1 e T1 


t

 
M z t   M o 1 2e 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)
s(t)=
• Mxy(0) is magnitude of Mx, My at t=0
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