Multiple Coherence Pathways

Simple spin echo

TE TE

a b c d

spinecho

90y 180x

TE TE

a b c d

Hahnecho

90y 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)

frac

tion

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