M. Lustig, EECS UC Berkeley Principles of MRI EE225E / BIO265 Lecture 16 Instructor: Miki Lustig UC Berkeley, EECS 1 M. Lustig, EECS UC Berkeley Projct • Work as a team of two – Oral presentation (20min) – Or, Report as a wikepedia entry • Work shared equally, presentation time as well • Level of presentation -- assume textbook level of knowledge • Grading based on accuracy, clarity and normalized by scope • Work: –Implementation –Review of advanced topics/papers - could be from your own research 2 M. Lustig, EECS UC Berkeley Things to do: • Pick a partner (use Piazza) • Pick a topic (list on website) • Write a short proposal - – 1-2 paragraphs – References • Send me the proposal by Fri 29th. 3 M. Lustig, EECS UC Berkeley Echoes • Early in NMR people noticed the following odd behavior (Hann, 1950) Two 90° excitations, separated by T cause large signal to form at 2T, Why? 4
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M. Lustig, EECS UC Berkeley
Principles of MRIEE225E / BIO265
Lecture 16
Instructor: Miki LustigUC Berkeley, EECS
1
M. Lustig, EECS UC Berkeley
Projct
• Work as a team of two– Oral presentation (20min) – Or, Report as a wikepedia entry
• Work shared equally, presentation time as well• Level of presentation -- assume textbook level of
knowledge• Grading based on accuracy, clarity and normalized by
scope• Work:
–Implementation–Review of advanced topics/papers - could be from your
own research
2
M. Lustig, EECS UC Berkeley
Things to do:
• Pick a partner (use Piazza)• Pick a topic (list on website)• Write a short proposal -
– 1-2 paragraphs– References
• Send me the proposal by Fri 29th.
3
M. Lustig, EECS UC Berkeley
Echoes
• Early in NMR people noticed the following odd behavior (Hann, 1950)
Two 90° excitations, separated by T cause large signal to form at 2T, Why?
4
�(~r, t) =
Z t
0!(~r, ⌧)d⌧
�(~r, t) = !E(~r)t| {z } + !cst|{z} + �
Z t
0
~G(⌧)~rd⌧
| {z }
M. Lustig, EECS UC Berkeley
Phase Evolution of Spins
off-res chem-shiftencoding gradients
Each of these make s(t) dephase
5
�(~r, t) = �
Z t
0
~G(⌧)~rd⌧
~G(t)
M. Lustig, EECS UC Berkeley
Gradient Echoes
Consider a special case where: !E(~r) = 0, !cs = 0
is an inhomogeneity we can control!
6
M. Lustig, EECS UC Berkeley
Gradient Echoes
Large signal
Low signal
7
M. Lustig, EECS UC Berkeley
Spin Bench Simulation
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�(t)�G
x
x1
�G
x
x2
M. Lustig, EECS UC Berkeley
Gradient Echo
k-space
kx
(t)t
t=TE
We get a large signal when we cross k-space origin
Phase diagram: x1>0, x2<0, phase evolution at each position:
9
!E(~r) !cs(~r)
M. Lustig, EECS UC Berkeley
Gradient Echo
• All Spins have zero-phase at t=TE• The signal adds coherently, producing a