MRI Lectures

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MRI Lectures

• Disclaimer This material is not novel, but is
  collected from a variety of sources on the web.

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Principle of MRI (1)

• Certain atomic nuclei behave like a spinning top
• behave like small magnets
• Under normal circumstances
• the body is not magnetic
• the hydrogen nuclei within the body point into
  all directions randomly
• the net magnetic field strength (magnetization)
  0
• When we place an ensemble of nuclei with spin in
  a strong magnetic field
• the nuclei tend to align themselves with the
  magnetic field

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Fonar
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The MRI Operating RoomFonar OR 360

• Magnet Specs Field Strength 0.6 Tesla
  Operating Frequency 25.5 MHz Patient Gap 19
  inches Patient Access 360 degrees Treatment
  Room Specs Standard 8-foot ceiling Width 14
  Feet Length Unlimited

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GE
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Hitachi
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Hitachi
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Philips 3T MRI
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Principle of MRI (2)

• This alignment occurs
• the nuclei prefer to be in a state with the
  lowest energy
• 00 K ?all nuclei align themselves to the external
  magnetic field
• At room temperature
• the nuclei also possess thermal energy
• external magnetic field
• 0.1 tesla excess 1/106
• 1 ml H20 3 x 1022 molecules 1017 hydrogen
  atoms aligning parallel to the magnetic field

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Spin Alignment
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EM Radiation

• While the nuclei are under influence of the
  external magnetic field
• pulse of electromagnetic radiation are beamed
  into the tissue
• EM radiation is characterized by
• an electric and a magnetic component
• the magnetic component of the EM radiation exerts
  a force on the magnetic nuclei
• When the magnetic component of the EM radiation
  has a direction perpendicular to the external
  magnetic field
• cause the magnetization to precess around the
  direction of external field

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Larmor Frequency

• in such a way
• the angle between the direction of the
  magnetization and the external field will
  increase linearly with time
• only happen when the EM radiation has a certain
  frequency
• the frequency is proportional to the strength of
  the external magnetic field
• gyromagnetic ratio
• characteristic for the element (isotope)
• the range of radio frequencies 2 to 50 MHz

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Precession of Magnetization
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Principle of Gamma Camera
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A Scintigram of the Lungs
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Principle of ECG-gated Scintigraphy
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Rotating Gamma Camera
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• The Distribution of Energy
• The distribution functionThe density of states

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The Maxwell-Boltzmann Distribution

• The Maxwell-Boltzmann distribution is the
  classical distribution function for distribution
  of an amount of energy between identical but
  distinguishable particles.
• http//hyperphysics.phy-astr.gsu.edu/

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• Besides the presumption of distinguishability,
  classical statistical physics postulates further
  that
• There is no restriction on the number of
  particles which can occupy a given state.
• At thermal equilibrium, the distribution of
  particles among the available energy states will
  take the most probable distribution consistent
  with the total available energy and total number
  of particles.
• Every specific state of the system has equal
  probability.
• One of the general ideas contained in these
  postulates is that it is unlikely that any one
  particle will get an energy far above the average
  (i.e., far more than its share). Energies lower
  than the average are favored because there are
  more ways to get them. If one particle gets an
  energy of 10 times the average, for example, then
  it reduces the number of possibilities for the
  distribution of the remainder of the energy.
  Therefore it is unlikely because the probability
  of occupying a given state is proportional to the
  number of ways it can be obtained.

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Torque on a Current Loop

• Magnetic Dipole Moment µ i A
• External magnetic field B
• Magnetic Moment Torque

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Precession of Spinning Top

• Gyromagnetic Ratio ?
• Larmor Frequency ?
• ??B

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• h is Planck's Constant (equal to 6.626 x 10-34 J
  s
• ms gs mB ms.
• ms is called the spin magnetic moment, gs is the
  spin gyromagnetic ratio, mB is the Bohr magneton
  and ms is 1/2 or -1/2 (the spin of the electron
  divided by h). Of these numbers, only the Bohr
  magneton has physical units. Its value is mB e
  h / 4 p me 9.274 10-24 Am2

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• Nuclear Magnetic Moments
• The nuclei of atoms contain protons and neutrons.
  Since a neutron is electrically neutral, you
  might expect it to have no magnetic moment. In
  fact, it has a magnetic moment of -9.6624 10-27
  Am2. How can this be?
• Protons and neutrons are made up of smaller
  elementary particles called quarks. The force
  which binds the quarks together is called the
  strong force. It acts like a spring whose spring
  constant gets stronger as the distance between
  the quarks increases, so they are never seen
  alone. The quarks come in six flavors, which have
  been dubbed up, down, charm, strange, top and
  bottom.
• The proton is made of 2 up quarks and 1 down
  quark, and the neutron is made of 1 up quark and
  2 down quarks. The up quarks have an electrical
  charge of 2e/3, while the down quarks have an
  electrical charge of -e/3. All have spin quantum
  numbers of 1/2 or -1/2. This means that while the
  neutron is electrically neutral, it still has
  spinning charges within, and hence can have a
  nonzero magnetic moment.
• By the same token, the nucleus of all atoms have
  spin, since they are collections of spinning
  protons and neutrons. The nuclear magnetic moment
  of a particular atom is
• g mN I. Here the gyromagnetic ratio has a
  different value for each atom, which depends not
  only on the species but on its immediate
  environment as well, and the nuclear magneton mN
  e h / 4 p mp 5.0501 10-27 Am2, where mp is
  the mass of a proton. I is the nuclear spin the
  spin quantum number for a nucleus can be any
  number in the set I, I - 1, I - 2, ..., -I 2,
  -I 1, -I.

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Spin Up vs Spin Down

• ?E2µB
• Nuclei that are of interest in MRI
• 1H - 42.58 MHz/T
• 2H - 6.54 MHz/T,
• 31P 17.25 MHz/T,
• 23Na 11.27 MHz/T,
• 14N - 3.08MHz/T,
• 13C - 10.71 MHz/T,
• 19F - 40.08 MHz/T.