Magnetic Resonance Imaging

Time Domain NMR Signal

Rotating transverse magnetization will induce current in coil of wire.

The plot of current as a function of time will be M_y(t) or a sine wave.

This wave will decay exponentially with time constant T₂*.
This wave is called a free induction decay (FID).

The FID is converted into a frequency domain spectrum.

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+/- Frequency Convention

Positive n

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Negative n

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Pulse Sequence

A set of RF pulses applied to a sample to produce a specific form of NMR signal

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TimingDiagram

A multiple axis plot of various aspects of a pulse sequence versus time

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90-FID Sequence (one-pulse sequence)

x'y'z Picture

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90^o pulse

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Precession

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Decay of magnetization

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Timing Diagram

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Signal (S)

S(TR) = k r ( 1 - e^TR/T1 )

where:

TR = repetition time
k = proportionality constant
r = spin density

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The Spin-Echo Sequence

x'y'z Picture

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90^o pulse

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magnetization begins to dephase

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180^o pulse

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echo

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Timing Diagram

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Signal (S)

S(TR,TE) = k r ( 1 - e^-TR/T1 ) e^-TE/T2

TE = echo time

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The Inversion Recovery Sequence

x'y'z Picture

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180^o pulse

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spin-lattice relaxation

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90^o pulse & dephase...

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Timing Diagram

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Signal (S) when the sequence is not repeated.

S(TI) = k r ( 1 - 2e^TI/T1 )

where: TI = inversion time

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Signal when the sequence is repeated.

S(TI,TR) = k r ( 1 - 2e^TI/T1 + e^-TR/T1)

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Note:

TI_(S=0) = T₁ ln2

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Copyright © 2000 J.P. Hornak.
All Rights Reserved.