# Review of MRI Physics - Working.ppt

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```					Introduction to MRI Physics
Ian Miller

July 11, 2007
Goal of Today’s Lecture
• Relate the concepts of MRI physics to things that engineers
• Lay the groundwork for more detailed understanding of
more complicated imaging techniques
•   Fast spin echo
•   Echo planar imaging
•   Volume imaging
•   3D time of flight
•   Diffusion
•   …
Why this is an Intimidating Topic
• There are a myriad of basic physics principles involved,
each of which is individually important and hard to skip over
• Need to simultaneously consider two scales
• single particles
• aggregates of billions of particles
• There are multiple dimensions involved to keep straight
• The math is complicated for non-engineers, and most of it is
vector-based
• It’s easy to convince yourself you “get it”
Organization of Discussion
•   Review of Relevant Basic Physical Principles
•   Magnetism
•   Resonance
•   Image Creation
•   T1 and T2
•   Anatomy of an MR Scanner
•   Future Topics
Current is the Flow of Charged Particles
• Abbreviated “I”
Where
• Q is charge
• t is time

sodium
atom

sodium
ions
4
3
2
1
6
5

6 atoms
3 seconds
Every Current Creates a Magnetic Field
B
I

• The current and the magnetic field have to be
perpendicular at all points. Therefore
• Straight currents magnetic field loops surrounding them
• Current loops have straight magnetic fields going through them

I
B
Thermal Energy is Stored as Molecular Motion
• At 0 K, all molecular motion ceases.
• As heat is added, the molecules move around, absorbing
the heat in various ways:

• The second law of thermodynamics requires that all
available mechanisms of thermal energy storage be used
• For simpler molecules, the available options are fewer
Protons are Spinning Charges
• Protons have charge and are constantly spinning

• The charge can be thought of as distributed

This is a magnetic moment
Precession
• Precession refers to a change in the direction of the axis of
a rotating object.
• torque-free
• torque-induced

• It occurs when spinning objects experience a moment
outside the plane of rotation
• It’s all made up of photons
• It all moves at the same speed
• The difference between light we see (visible electromagnetic
radiation) and any other type is the frequency at which the
photon oscillates

x-rays

visible
light

Light Absorption by e- is Quantized
• Recall valence shell electron theory from high school
chemistry

• You can get an electron to “jump up” to the next level by
supplying energy at the exact wavelength required
Absorption Spectra Show Quantization

visible
light

The parts that are missing
were absorbed by the
electrons
Emission Spectra Show Quantization

Emission
Experiment

Absorption Experiment
The requirement for the
precise amount of energy
needed is quantization
Exponential Change is Convenient to Study
• Exponential change occurs when the rate of change of a
quantity is proportional to the quantity itself

• k can be
• Positive (exponential growth)
• Negative (exponential decay)
• We should love exponential change because it is relatively
easy to study
• If you plot the quantity against time, k can be readily
calculated with a few data points, and there is only one
degree of freedom
• You often already know two boundary conditions
• q at time zero
• q at time infinity
• You only need one more!
Recap of Review Material
• Current is the Flow of Charged Particles
• Every Current Creates a Magnetic Field
• Perpendicular at all points to the current
• Thermal Energy is Stored as Molecular Motion
• Protons are Spinning Charges
• Protons have a current loop
• Protons have a magnetic moment along the axis of rotation
• Precession
• Occurs when a spinning object experiences a moment out of the
plane of rotation
•   Electromagnetic Radiation is Just Light
•   Light Absorption by particles is Quantized
•   Absorption Spectra Show Quantization
•   Emission Spectra Show Quantization
•   Exponential Change is Convenient to Study
Now we need to scale up to the bulk / macroscopic scale
Magnetic Resonance Imaging
• At rest, all protons spin (and translate) because of the
presence of thermal energy. The proton of a single
hydrogen atom in the vacuum of space will spin for this
reason.

Net Magnetic   Net Magnetic
Field (M)      Field (M)

• Entropy dictates that the spins within a group of protons are
not organized
• Going from a single proton to a group of protons will yield all
possible orientations (which sum to zero)
MRI: Application of a Magnetic Field
• Now let’s return to what happens with a proton when you
apply an external magnetic field

• There are two
effects here
• Alignment of spins
with the external
magnetic field
• Precession,
because the
moment
experienced by the
proton is out of the
B0                  plane of rotation
They are related,
but different
MRI: Determinants of Spin Rate
• The speed of precession of a spinning body in a field is
called the Larmor frequency, and we know a few things
• Zero when B0 = 0
• Increases as magnetic field increases
• We could do an experiment and plot the relationship
between B0 and precessional frequency

wL       Slope = gyromagnetic ratio

B0
•   Larmor freqency, and is dictated by

• For protons wL is approximately 42 MHz/Tesla
B0
MRI: Scaling up to Populations
Single Proton   Population of Protons
No External Field

M
M
External Field = B0

M                                                                 M
Simplification
• We can’t stop a proton from spinning, so let’s simplify our
diagram

will now be

will now be
MRI: Scaling up to Populations
• In a big population of protons, more line up with the field
than against, but there is a distribution of both
• Thermodynamics will tell us what the ratio is
External Field = B0

B0                              M
Difference in Energy Levels
This is 500 ppm (small!)
k = Boltzmann
Constant

100,000

100,000                   100,000
100,000
Net = 0        100,006
MRI works because we have

100,000               100,0020

100,050

B0
1 T, 37C
We’ve Seen This Before

• The excitation of proton spins is a quantized system
• So what is the frequency (v) needed to cause this excitation?
MRI: Combining Precession and Quanta

wL
Slope = gyromagnetic ratio

B0

• Gyromagnetic ratio = gamma = 42.58 MHz/T
• The excitation frequency (for an individual proton) is going to
depend on the magnetic field (the individual proton)
experiences
• This is the Resonance frequency
• MRI
Understanding Resonance by Analogy

• The proton is like a tetherball
• If you hit the tetherball at random intervals, it’s net vector is
random
• If you hit the tetherball at exactly the right interval (equal to
it’s period of rotation around the pole), each hit is additive
and makes the ball go higher and higher
• Think about the different scales: single tetherball vs. billions
of tetherballs
MRI: Identifying the EMF of Interest
Simplification
• We’ve used B0 enough that we know what it is: a
homogeneous external magnetic field
External Field = B0

will now be
B0
Recipe for an NMR Experiment
1)   Put sample in big magnetic field
2)   Transmit radio waves into sample (saturate the protons)
3)   Turn off radio wave transmitter
•    Emission experiment
•    Who cares? (what are the applications of spectra?)
•    Immediately recognized that it could tell us about the local
magnetic environment of hydrogen protons

You get a spectrum
because each hydrogen
atom has a different local
B0                           environment
Optimizing the NMR Experiment
• Parallelizing the process: shooting the whole spectrum at
once
• We would like to
•   Take a complex EMF wave
•   (Group of photons with different Frequencies)
•   Break it up into component frequencies
•   Use components to predict identity
• We don’t have a prism for radio waves
• Enter… the Fourier Transform
• Put in amplitude-time data
• Get out amplitude-frequency data

the-art computer
processors
Optimizing the NMR Experiment

B0

A prism is an example of a fourier transform
So is the cochlea
Lauterbur’s Insight
• Conventional NMR used spectra to make
in a uniform magnetic field
with position, then the resonant frequency
in a uniform population of protons
• Great idea…
MRI: Slice Selection
• The Larmor frequency is dependent on B0, the external
magnetic field

• By varying B0 over the subject, we can choose a frequency
that will only excite a particular part of the subject

• Different values of B0
will tune the photons
to require different
energies (w)
• If we only give one
frequency of EMF,
only one slice will be
Z       excited”
MRI: Slice Selection
• Now we have an excited plane of protons
• We reset B0 so that the field is uniform
• We wait for the energy to be re-transmitted as a radio signal

• The results are not
SX                          very exciting
• The whole signal is at
the frequency we put
in
• It starts loud, and
exponentially decays

SY

X
Z       Y
Questions?
MRI: What We Have So Far
• We have selectively charged a slab of brain with
• We turned off the magnet, and got signals back from all over
the slab
• What we need is to know where each signal came from

Z

• Right now, all we can “see” is the net magnetization vector,
but we can see it in several directions: x, y, z
• Therefore we can measure signal averaged over the whole
slice
• That’s not a very interesting picture
A Trick Necessary to Continue

• The energy absorbed by an excited particle is determined by
the field it is acting against in order to become excited
• Electrons: attraction with nucleus
• Spinning top: gravity
• Protons in NMR: magnetic field
• Note that the last one is very easily manipulated
Changing the Rules in Midstream

• By changing the strength of the magnetic field (re-writing the
rules of attraction in mid-stream), the protons can be
manipulated “on the fly”
• Increase the field to increase precession speed
• Increase the field to increase their resonance frequency
• Consider increasing gravity on a spinning top
MRI: Getting Coordinates in Plane (X)
• We need to revisit Lauterbur’s idea with the trick we just
learned in order to use frequency to map location
• Once we get the spins saturated, we can vary B0 over x
• B0 still points in the same direction,
but make it stronger on one side of
the patient than the other
• This is changing the rules in
saturated / excited, and now we’re
altering the field on them
• We know from our simple experiments
that the protons exposed to the
weaker field will precess less quickly

Z
X
MRI: Getting Coordinates in Plane (X)

• Protons will spontaneously
revert to the lower energy
state
• Protons at x=0 will be relaxing
Z                          in a strong field, and give off
high-frequency EMF
• Protons at x=1 will be relaxing
in a weak field, and give off
Z
low-frequency EMF
net
magnetization•   Then we can use the FT to
vector, M       separate the frequencies and
identify the signal strength at
each x-coordinate
X
MRI: Getting Coordinates in Plane (X)
• All frequencies in the output signal come at once, and is a
plot of signal strength per unit time

Z
net
magnetization
vector, M

X

• Now, the frequency of
the emission tells us the
aggregate signal for
each x-column
MRI: Getting Coordinates in Plane (Y)
• Tying the x coordinate to the frequency is called frequency
encoding
• It would be nice if we could just do the same thing with the Y
direction, but we can’t
• Since magnetic field vectors add,
putting a second gradient in the y
direction is indistinguishable from
doing a single gradient at an
angle
• No new information is captured,
and the Fourier Transform can’t
Y

distinguish them unless the
frequencies are unique
X
A Transient Gradient Changes the Phase
• If we change the field strength on a magnet that is already
precessing, we can make its precession change speed
• If we increase it again, it speeds back up

B0                               B0

• This is what we mean when we say that two
protons are out of phase
MRI: Getting Coordinates in Plane (Y)
temporarily
• This slows changes the speed for a moment, but then the
frequency returns to what it had been
• Holding back some spins in this way creates a phase shift in
the spins, which we can exploit later

Y                                    Y

X                                     X
MRI: Getting Coordinates in Plane (Y)
• This technique gives us an extra degree of freedom
• The Fourier transform does not know how to process phase
information, but it does preserve it
• We then do a second Fourier transform in order to obtain
the information we want
• Let’s use an example to understand the 2D Fourier
Transform
The 2-D Fourier Transform

1D FT
by row

Plot A-t
FT
by column
The 2-D Fourier Transform

1D FT
by row

Plot A-t
FT
by column
MRI: What we End Up With
• We now have a plot of signal as a function of time at each
individual voxel
• We know that the signal will decay unequally in different
tissues, so we get signal-vs-position plots at multiple time
points, calculate the rate of decay, and give that pixel a
shade near white if the decay constant is large, and a shade
near black if the decay constant is short
• In actuality, the phase-encoding step is done first, because
the magnetic gradient it requires is transient. The frequency-
encoding step is done last, because it needs to be active
Energy Accounting 101
• It is possible to exhaustively inventory where all of the
energy of the RF pulse goes (1st law of thermodynamics)

Spin alignment (work)

Spin alignment (work)

protons          universe
the everything else
the lattice”)
(spins)(as seen by(“the physicist)
heat
MRI: Details of the Excitation
• We can choose how much to excite the protons in the plane
• A big EMF pulse can knock all the
spins into the x-y plane
• An even bigger EMF pulse can knock
all the spins onto the –z axis
Z                                                     Z

90° Pulse

Z
initial net
magnetization
vector, M0
180° Pulse

Or anything in between
Measuring the Net Magnetization Vector
• The net magnetization vector can be measured directly by
SX

SY

X
Z       Y
• This will allow the vector within each voxel (which we’ve just
learned how to identify) to be measured in x and y
MRI: Details of the Decay
• If we start with a 180° pulse, the decay is exponential and
goes from -1 to 1 (two data points are known)

Mz
net
magnetization                        t
(M=Mz)

Z                           180° Pulse
Z
MRI: Details of the Decay
• If we perform any pulse except 180° pulse, then all protons
will get knocked into x-y plane, and precess there
• Initially, they will all be in-phase, because they are all
knocked away from Z-axis at the same time in the same
direction
• With time, they will de-phase due to two factors
• Interactions with neighboring protons (random effects)
• Imperfect homogeneity of B0 (nonrandom effects)
• This is spin-spin relaxation

Z

90° Pulse                       Mxy
net
magnetization
t
M=Mz
MRI: Details of the Decay
• De-phasing is when the signal is lost because it averages
itself out and becomes noise
• Here is a visual example of dephasing

out of phase              in phase               out of phase

• There are ways to reverse this process,
and any sequence which does so will
be called an “echo” sequence
• Once the signal is completely                         Z
dephased, we have randomness
• Even so, a non-zero net vector in the z-
direction may still exist
Revisiting Energy Accounting

Spin alignment (work)
Sp
in
-S
pi
n
re
la        Spin alignment (work)
xa
n
everything else                             protons
(“the lattice”)                            (spins)

Z
Z
heat

T1 relaxation
T2 relaxation
MRI: Details of the Decay
• We have seen two types of recovery toward equilibrium
• Mz recovery starts out low and recovers exponentially back toward
one (because z equilbrium is to line back up with B0)
• It happens with all pulse strengths
• It reflects energy loss to surrounding molecules
• Random interactions (changes moment to moment, “noise”)
• Nonrandom interactions (is static for a given molecule, “bias”)

the rate constant for this
Mz                               process is called T1
t
• Mxy recovery starts out maximal and exponentially decays toward
zero
• It happens with all pulse strengths except 180°
• It reflects energy loss back to “the universe”

the rate constant for this
Mxy                               process is called T2

t
Energy Accounting 501

Spin alignment (work)

T2*
out            effects             effects

T1 relaxation

heat
T2
relaxation
T2 Effects
• Because the static interactions are static, they can be
reversed by the 180 degree pulsation

Z
T2*
random                   static
effects                effects

T2 relaxation

T2
relaxation                180°
Pulse

Z

180°
Pulse
Echo
Another Analogy
Anatomy of a Scanner
Four main hardware components
• Main magnet
• RF system
• Computer system.
What We’ve Covered
• Reviewed the most fundamental rules that govern MR
phenomena
• Identified how to excite selected photons using
• Identified how to manipulate the excited photons in order to
“encode” positional information
• Frequency encoding
• Phase encoding
• Become familiar with 2D Fourier transforms
Future Topics to Explore
• Mechanisms of contrast
• Proton Density
• T1, T2, T2* in more detail
• Anisotropy
• Flow
• Diffusion
• Tensor mapping
• IV Contrast
• Pulse Sequence Diagram Interpretation
• Sequence selection, costs and benefits

```
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