MRI : Theory and Application

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MRI Theory and Application

• REFS
• Principles of MRI, D.G. Nishimura
• Elster, QA in MRI
• http//www.cis.rit.edu/htbooks/nmr and
  www.cis.rit.edu/htbooks/mri

G. R. Moran, 2003
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After the 10 cent intro

• MRI mainly focuses on water protons (spin ½) and
  measures T1 and T2 as a function of position
• Different tissues have different T1/T2
• Magnetization relaxes different amounts in
  different positions ? provides
  contrast
• We can adjust this more later

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Someone check the patient
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OK. We can look at patients too.
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And, with the advent of rapid sequences
Normal
Infarct
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But. As nice as these images are, they raise some
questions - hopefully

• What exactly are T1 and T2?
• What is resonance?
• How do you measure T1 and T2 as a function of
  position and convert this to an image?
• What kind of hardware is required?
• etc

These are the questions we will answer here.
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Basic NMR

• We are mainly imaging water protons in the body,
  and protons have nuclear spin, I1/2
• Jtotal angular momentum
• J?I (more on this later)
• µ is called the total magnetic dipole moment
• µ?J??I ?(protons) 42.58MHz/T
• Think of the protons as small magnets having a
  magnetic moment, µ

OR E -µB
If BB0z E -??B0Iz
Spin up (1/2)
Spin down (-1/2)
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What is Resonance?

• In Quantum mechanics, Iz just returns the value
  of the nuclear spin (-1/2)

E- ½??B0
E -½??B0
?E E- - E ??B0 ??0
Where ?0 ?B0 is the Larmor frequency
or resonant frequency
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OK. Hold that thought.

• How many things have I said at this point that
  are not quite correct?
• -- Skip to overheads for a moment

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Relaxation
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T1, the Spin-Lattice Relaxation Time

• Occurs when a proton encounters another magnetic
  field fluctuating near ?0
• Typically another proton, or electron
• To produce a field fluctuating near ?0, molecules
  must be moving or tumbling near ?0
• Dipole-dipole interaction
• Resonance is like a swing!

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T2, the spin-spin relaxation time

• Does not require a change in energy wrt B0
• An intrinsic process that causes the spins to
  lose their phase coherence in the transverse
  plane
• Slowly fluctuating fields in tissues cause spins
  to experience slightly different fields
• Magnetic susceptibility differences
• Dipole-dipole interaction

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Molecular Motion?

• Slow molecular motion produces slowly fluctuating
  fields
• These motions are more effective in T2 relaxation
• Result in short T2
• In solids, T2 can be so short that signal is lost
• If molecular motion is rapid, protons sample many
  environments and local variations average out
• T2 less effective
• T2 T1

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For Example
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The Obvious Question?
The obvious question now is, how do we measure T1
and T2? Well, from our solution to the Bloch
Equation following a 90 degree pulse
Mz(0)0 Thus Mz(t) M0 (Mz(0) M0)e-t/T1 Or
Mz(t) M0 (1-e-t/T1)
The magnetization in the x-y plane decays away,
then the z-Magnetization Begins to recover with
T1.
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Aside
Of course we could have applied a 180 degree
pulse, completely inverting M0. Then Mz(0) -
M0 , and Mz(t) M0 (1-2e-t/T1) Back
to how we measure T1. I said that we only detect
a signal if we have magnetization in the x-y
plane. Thus the recovering magnetization would
induce no signal. We cant see it!
We have to get the recovering magnetization into
the x-y plane at various times in its recovery to
see it!
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What about T2?
Consider what happens immediately following the
90 degree pulse
What if we hit the Spins with a 180 Degree
pulse Instead?
We would get an echo!! The 90-180 sequence is
thus called the spin echo.
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OK. Why is this relevant?
A CPMG sequence is a 90-180-180-180-etc
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Chemical Shift

• I introduced the concept of ?o for a few reasons.
• One is chemical shielding/shift
• If all spins feel the same Bo, then they resonate
  at the same ?o
• Thus an RF pulse at ?o will tilt ALL the spins in
  the sample.
• However electrons on molecules can become
  polarized and shield the nucleus.

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Shielding
-
-

• Polarized electrons shield nucleus
• Actual field at nucleus may appear less

-
-
Bo
-
µ
-
-
-
-
Beff Bo (1-s) ?eff ?o (1-s)
s is the chemical shielding - depends on molecule
s is very small (ppm), otherwise these changes
would destroy our ability to do MRI (?o not the
same everywhere)
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Chemical Shift
? 2pf ? Bo (1-s)

• To measure s absolutely, we would need an
  unshielded, or bare nucleus.
• This doesnt exist in nature, right?
• Thus we measure wrt a standard.

d s(standard) s(sample) in ppm Or d
?(sample) ?(reference) / ?(reference) x
106 For example.
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Can we do some imaging now?

• Everything thus far applies equally as well to
  NMR as to MRI
• The key difference lies in the answer to, How do
  we encode positional information?
• We have seen what T1 and T2 are, and hopefully
  can see some of their value
• BUT. How do we measure them at many locations
  over a given volume at the same time?

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Topics Remaining

• MRI Basics
• Pulse Sequences
• T1/T2 weighting
• Hardware
• Applications
• Safety
• Artifacts

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MRI Basics
OR How do we encode positional information?

• Consider a cubic volume that has 1mm3 voxels.
• Each voxel has its own magnetization vector
• These vectors are initially aligned with the
  field, B0.

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What happens if we 1) Apply a 90 degree pulse?
All of the magnetization vectors are oscillating
at ?0, so all of the vectors are tilted into the
x-y plane (very nearly)
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2) We want to image a single slice through the
object. What if we were to add a small amount to
the field so that it varied with z position?
B(z) B0 Gz z ?(z) ?0 ?Gz z
Typically, gradient strengths are 10mT/m
1G/cm whereas B0 1-3T
So, d?/dz ? Gz 4.258 kHz/cm That means that a
physical width of 1cm corresponds to a
frequency width of 4.3kHz.
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2 Comments

• We can select which physical slice we want by
  choosing the appropriate frequency with our 90
  degree pulse.
• The physical width of the slice, ?z, will be
  determined by the bandwidth of the RF pulse.
• Why a sinc?

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Slice Selection
So, lets turn on this Gz, and apply a sinc shaped
pulse at ?0, with some bandwidth corresponding to
?z. What happens?
Will all of the spins be tilted thru 90 degrees?
Note that we will only see signal from the
affected spins (only ones in x-y plane) We have
tilted spins in, or excited a single slice.
Now the problem is a 2 dimensional one.
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Pulse Sequence So Far
Now what? We have excited a single slice, now we
need to resolve x and y.
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What if we do nothing?
If we just sit back and wait, we will simply just
detect a FID from all of the spins we have
excited in the slice, as they decay back to
equilibrium.
FID All of the spins in the slice have the same
resonant frequency so all contribute similarly to
the FID. What if we turned on an x gradient, Gx,
while this was happening instead? Well. The
nuclear spins would have a different resonant
frequency depending upon their x position. So
what?
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Turn on a Gx
B(x) B0 Gx x ?(x) ?0 ?Gx x
Think about the received signal from a single
oscillator at x,y Signal
m(x,y) e-i?t The total received signal will be a
sum of all of these in the slice
S ?x?y m(x,y) e-i?t dx dy
?x?y m(x,y) e-i?ot e-i?Gx xt dx dy
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Fourier Transforms
The resulting signal S ?x?y m(x,y) e-i?Gx xt
dx dy (2-D) looks very much like the Fourier
Transform of m(x,y) F(kx) ? f(x) e-i2pkx x dx
(1-D) Because the signals exponential factor
only depends upon x (not y), the signal is really
just a 1-D FT of m(x,y). If we receive the
signal, then do an inverse FT, we dont get
m(x,y), but a sum of m(x,y) over y.
This makes sense right? The gradient only makes
the resonant frequency a function of x. So when
we look at a single frequency, we see the signal
from one x-position, but all y positions in the
volume.
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Readout Gradient

• The x gradient is called the readout gradient,
  because we apply it while reading the signal
• Only during this time does the resonant frequency
  change with x position
• Pulse sequence so far

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The last piece

• Well, what about y?
• Can we apply a Gy during readout too?
• No.
• The resonant frequency may not be unique across
  the sample

• We do apply a Gy,
• but in a different way.

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Apply a Gy

• We apply a Gy as soon as the slice is selected
• We only apply it for a time, ty.

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Phase Encoding?
Each spin, or magnetization vector in our voxels,
acquire a phase, ?ty, during this time, ty.
?ty ?0ty ?Gyyty
Hence Gy is called the phase encoding gradient. I
dont think this helps explain where the image
comes from though. Lets try it another way.
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What do the gradients do to the spins?
Now when we apply an x gradient, we have two
pieces of information. The spins are rotating at
different frequencies depending upon x, and They
start spinning at different phases depending upon
y.
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Thus the signal equation becomes
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Next

• Pros and Cons
• Some common pulse sequences
• T1/T2 weighting
• Fast pulse sequences
• Hardware
• Applications
• Safety
• Artifacts

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MRI PROS/CONS

• Excellent Soft tissue contrast and
  pathology/normal contrast
• No ionizing radiation
• NMR signal gives grey level representing
  biochemical state/enviornment of tissue
• Images represent true slices - no overlaying
  structures
• Any slice orientation
• True 3D (.5mm)3 resolution
• Many acquisition params means we are free to
  alter image S/N, contrast,resolution, time.
• No bone artifacts
• Image flow, and spectroscopy in combination with
  imaging

• No pacemakers, brain surgical clips
• Cant obtain good images near metal implants
• Long exams (15min-1hr)
• Expensive (3M siting)
• Difficult to site
• 10-100 tonnes
• RF shielded room
• Limited access
• Affects nearby equipment (CRTs, etc)
• Affected by moving ferromagnetic objects (cars,
  elevators, etc)
• Some bioeffects
• RF heat
• Nerve Stimulation
• More subtle effects
• Hazards
• Projectiles
• RF burns from ECG leads, probes, or internal
  conductors

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The Spin-Echo (90-180)

• Wait TR to reach eqm
• Then repeat with new phase
• encodes
• Then repeat for other slices

For a single slice, the total time is TRxNpe ?
1sx256 ? 4.3min
I Image intensity ? (1 e-TR/T1) e-TE/T2
Note that if TR is long, and TE is shorter, we
get a proton density weighted image
T1-weighting short TE, TR?T1 I ? 1
e-TR/T1
T2-weighting long TR, TE?T2 I ? e-TE/T2
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T1 and T2 Again
Edema blood
Fat muscle
tendons
See Handout!
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Inversion Recovery
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Rapid Imaging

• Many variations
• FLASH Fast Low Angle SHot
• FISP Fast Imaging with Steady state Precession
• EPI Echo Planar Imaging
• GRASS GRadient Acquisition in the Steady State
• SSFP Steady State Free Precession
• Et cetera
• Many of which are based upon small angle RF
  pulses which drive the spin system rapidly to a
  steady state

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T1-FARM
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Hardware
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Hardware

• Typical magnetic field strengths for MRI are
  0.5-3T
• There are smaller bore systems, for example to do
  microimaging that are in the 4-11T range
• Permanent magnet systems uncommon
• Resistive magnets
• Water/air cooled
• lt 0.3T
• Field drift
• Superconducting magnets
• Most common
• Higher, stable, homogeneous fields
• Fringe fields

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Closed Designs
Siemens Sonata 1.5T
GE Signa 3T
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Open Designs
GE Ovation 0.35T
GE Signa Openspeed 0.7T
Breast
wrist
shoulder
head
Body flex
Extremity
Coils improve resolution and S/N (filling factor)
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Intraoperative Unit
IMRIS www.imris.com 1.5T Foothills
Hospital Calgary
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Image Quality

• As field increases,
• S/N improves
• Spatial resolution improves
• But the RF absorption increases too
• Attenuates signal
• Chemical shift artifacts increase
• Spatial resolution worsened

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Applications

• Central Nervous System
• Neoplasia
• Degenerative disorders, congenital malformations
• Hemorrhage/vascular diseases
• Trauma
• Eye, spine, head and kneck
• Musculoskeletal
• Knee, ankle, foot, wrist, other joints
• Muscle disorders
• Bone marrow disorders
• Can look at fractures
• Pelvis
• Chest and Abdomen
• Cardiac

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Cardiac MRI
Reperfused
Occlusion
Baseline
So the question we have to answer is, will the
damaged tissue recover on its own? Has flow been
restored? Thus is revascularization required.
Or is the tissue permanently damaged or
infarcted?
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Contrast Enhanced MRI
Very rapid CINE movie using a T1-FARM
sequence measuring T1 as a function of position.
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Safety

• Shielding
• The outside world must be shielded from the
  magnet
• Reduce fields to lt0.5mT (FDA)
• Also moving ferromagnetic objects, cars,
  elevators, heavy equipment, can distort the main
  magnetic field
• Typically the MRI room is shielded by a faraday
  cage (80-120dB)

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Safety

• Ferromagnetic objects are bad
• Projectiles
• Implants
• Filings in eyes
• Non-hazardous foreign bodies may cause artifacts
• Pacemakers
• Bank/credit cards, electronic media, etc
• Pregnancy (will not be caused by MRI)