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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
  and neurophysiologists already understand
• 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
Electromagnetic Radiation is Just Light
• 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




                         radio waves
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
  about it
   • 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
                                      Avagadro’s numbers of protons

      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
4)   Receive radio waves re-transmitted by subject (“relaxation”)
•    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




                                              Made possible by state-of-
                                                 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
  inferences about local magnetic perturbations
  in a uniform magnetic field
• If the magnetic field was instead made to vary
  with position, then the resonant frequency
  spectrum would instead tell you about location
  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
  radiofrequency EMF
• 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
                        midstream: the protons are already
                        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)
• Instead, we will introduce a gradient in the y direction
  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
  when the protons relax (…the readout gradient)
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
  using orthogonal radio antennas.
                             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
               Radiofrequency in



                                       Spin alignment (work)
                                      Sp
                                        in
                                           -S
                                             pi
                                                n
                                                    re
                                                      la        Spin alignment (work)
                                                         xa
          Radiofrequency out                             tio
                                                            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
              Radiofrequency in



                                  Spin alignment (work)




                                                           T2*
        Radiofrequency      random                static
              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
                       • Magnetic field gradient system
                       • Computer system.
What We’ve Covered
• Reviewed the most fundamental rules that govern MR
  phenomena
• Identified how to excite selected photons using
  supermagnets and radio waves
• 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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