Multiple Coherence Pathways
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Transcript of Multiple Coherence Pathways
Multiple Coherence Pathways
Simple spin echo
TE TE
a b c d
spinecho90y 180x
TE TE
a b c d
Hahnecho90y 90x
TM TE
90x
e f
stimulatedecho
Hahn (90-90) and stimulated (90-90-90)echoes
Hennig Fig. 2
QuickTime™ and a decompressor
are needed to see this picture.
Repeated flip =90o
QuickTime™ and a decompressor
are needed to see this picture.
Repeated flip =40o
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?
Shortcomings of vector representation
Vector representation (e.g., Bloch): [Mx My Mz]
Problems:
1. Evolution of magnetization (in absence of RF) has 2 independent components (transverse & longitudinal), but vectors have 3
2. 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
Alternate representation of magnetization
Problem 1: Evolution of magnetization has 2 independent components (transverse & longitudinal), but vectors have 3
Replace: [Mx My Mz]
With: [F=Mx+iMy 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
Alternate representation of magnetization
Problem 1: Evolution of magnetization has 2 independent components (transverse & longitudinal), but vectors have 3
Replace: [Mx My Mz]
With: [F=Mx+iMy Mz]
Effect of RF pulse:
F+ = F cos2(/2) + F* sin2(/2) - i Mz sin()
Mz+ = Mzcos2(/2) - Mzsin2(/2) - i (F-F*) sin()
0o 180o 90o
Single RF pulse acts like 3 separate pulses
flip angle (degrees)
fract
ion
Fractional components in arbitrary RF pulse
Configuration theory (coherence pathways)
Problem 2: Vectors fundamentally represent single isochromats, where MRI essentially always encounter distributions
Mz
Mz
Mx
Mx
* typos in Hennig?
Hennig,Fig 4
Hennig, Eqs 8-11
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
RF pulses
Echoformation
time
phase evolution
exchange betweenconfigurations
Track flow of magnetization between configurations
Fn+ = Fn-1 cos2(/2) + Fn* sin2(/2) + Zn sin()
(Fn*) + = Fn+1* cos2(/2) + Fn-1* sin2(/2) + Zn* sin()
Zn+ = Zn cos() + (Fn* - Fn) sin() (see Eq 13-15)
Track flow of magnetization between configurations
Time evolution of signal dynamics
Time evolution of signal dynamics
Differs from previous via starting conditions (i.e., preparatory pulses)
Time evolution of signal dynamics
Differs from first via flip angle