RF Pulses: Basic Principles

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RF Pulses Basic Principles

• David Rourke, Nottingham University

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Introduction

• Nuclear magnetic resonance
• NMR nuclei are little bar magnets
• NMR nuclei are little gyroscopes

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Bar magnet in a B field
Dipole moment m T m ? B
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Gyroscope under an external torque
Precession rotation axis rotates in direction
perpendicular to the applied force and the
previous axis direction.
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Precessing magnetic moment

• Precession always about B, angular speed ?B.
• EMF induced in coil placed perpendicular to
  precession axis (Faraday)

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Spin excitation
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Selective spin excitation

• Slice selection

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Selective spin excitation

• Pencil selection

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Selective spin excitation

• Volume selection

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Magnetic field B(r,t)

• Can (at least approximately) solve all these
  problems asB is quite flexible cf g(0,0,9.81)

• B0 and ? must match (?B0 ?)
• Generally, G(t) is fixed by the type of
  excitation required (slice, pencil, volume)
• B1(t) determines the precise excitation profile

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Bloch equations
dipole moment at some given point insample at
some instant in time
(Tm ? B d S/dt And m ? S)
(Relaxation)
Forward problem given B(r,t) and m(r,t0), find
m(r,T). Easy(ish) (numerically). Put Bloch
equarions into a numerical ode solver. Inverse
problem given m(r,t0) and desired m(r,T), find
B(r,t). Hard.
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Rotating frame (approximation)
?B0?

• For B10 and r0

• Reinterpret m (as observed in rotating frame)
• Bloch equations keep their original form,
  withmodified B

• B now slowly varying.
• RF Pulse BrfB1(t)i B2(t). Real or complex.

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Inverting Bloch equations

• In fact
• There is no known method of inverting the Bloch
  equations, in general.
• It is not known whether any given desired
  response m(r,t) can actually be achieved bya
  suitably chosen B(r,t).

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Approximations

• Small tip-angle. Can include relaxation. Works
  for slice, pencil, volume excitation.
• Neglect relaxation
• Slice selection
• Inverse scattering (SLR etc)
• Adiabatic approximation B1-insensitive

• Numerical searches used optimal control
  theory,simulated annealing, genetic algorithms
  .Mainly for slice selection.

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Small-tip-angle approximation

• Design RF pulse for slice selection.
• Distinguish spins according to z coord.
• Gradient
• B field

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STAA cont

• Bloch eqs

• ignore relaxation
• rotating frameassume pulse real (B20)

• STAA mzconstm0
• Define mmximy (complex) transverse
  magnetization

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STAA cont
?
?
?
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Sinc pulse

• Expect FTB1(t) (m01) top hat, height 1

• Expect p/2-?zGz T/2

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Perfect sinc
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Perfect pulses

• Linear phase

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Perfect pulses cont

• Self-refocused

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Conclusions

• Approximate methods of RF pulse design (STAA,
  adiabatic) very successful.
• Only analytic methods available for gt1D, or to
  make B1-insensitive pulses, or to include T1/T2
  relaxation.
• Extend inverse scattering techniques?