Multiple Coherence Pathways

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Multiple Coherence Pathways
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Simple spin echo
spin echo
90y
180x
d
a
b
c
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Hahn (90-90) and stimulated (90-90-90) echoes
Hennig Fig. 2
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Repeated flip ?90o
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Repeated flip ?40o
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What is an echo?

• Signal peak (in time) cause by net alignment of
  magnetization
• Spin echoes perfect alignment of isochromats
• Any distribution of isochromats is refocused
• More generally perfect alignment is not required
  to have a peak in signal
• Hahn, stimulated echoes to not have isochromats
  aligned
• Magnetization is bunched up on one side of xy
  plane
• Many echoes require distribution is isochromats
• Unlike NMR, heavy dephasing (distribution) is the
  norm in MRI
• MRI insufficient inhomogeneity to maintain
  long-term coherence
• Instead, use gradients to reliably dephase
  (spoil) and rely on short-term coherences
• Can we find a representation that is better than
  isochromat vectors?

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Shortcomings of vector representation

• Vector representation (e.g., Bloch) Mx My Mz
• Problems
• Evolution of magnetization (in absence of RF) has
  2 independent components (transverse
  longitudinal), but vectors have 3
• Fundamentally treats single isochromats, where
  MRI essentially always encounter distributions
• This is why echo evolution is so complicated to
  depict using vectors (both temporally and
  spatially)
• Phase graph representation addresses both of
  these issues

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Alternate representation of magnetization

• Problem 1 Evolution of magnetization has 2
  independent components (transverse
  longitudinal), but vectors have 3
• Replace Mx My Mz
• With FMxiMy Mz
• In absence of RF, F and Mz evolve independently
• relaxation, precession represented by scalar
  multiples
• no need to worry about coupling between Mx, My

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Alternate representation of magnetization

• Problem 1 Evolution of magnetization has 2
  independent components (transverse
  longitudinal), but vectors have 3
• Replace Mx My Mz
• With FMxiMy Mz
• Effect of RF pulse
• F F cos2(?/2) F sin2(?/2) - i Mz
  sin(?)
• Mz Mzcos2(?/2) - Mzsin2(?/2) - i (F-F)
  sin(?)

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Fractional components in arbitrary RF pulse
fraction
flip angle (degrees)
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Configuration theory (coherence pathways)

• Problem 2 Vectors fundamentally represent single
  isochromats, where MRI essentially always
  encounter distributions

Mz
Mx
Hennig, Fig 4
Mz
Mx
Hennig, Eqs 8-11
typos in Hennig?
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Configuration theory (coherence pathways)
What do Fn, Fn, Zn represent? This is just a
useful decomposition of the magnetization (e.g.,
like Fourier decomposition of an
image/object) Decomposition coefficient how
much magnetization expresses this
structure Hennig calls configurations (others
call coherences) Each configuration is a
potential echo (allow it to rephase, signal is
proportional to its coefficient) No mystical
properties (e.g., quantum mechanics not needed)!
Hennig, Fig 4
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Track flow of magnetization between configurations
phase evolution
exchange between configurations
Echo formation
time
RF pulses
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Track flow of magnetization between configurations
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Time evolution of signal dynamics
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Time evolution of signal dynamics
Differs from previous via starting conditions
(i.e., preparatory pulses)
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Time evolution of signal dynamics
Differs from first via flip angle