mr signal detectionfmri.ucsd.edu/ecwong/be278w12lec08.pdf · 1, then transverse magnetization m xy...
TRANSCRIPT
E. Wong, BE278, UCSD Winter 2012!
Bioengineering 278 "Magnetic Resonance Imaging"
"Winter 2012 "
Lecture 8!• RF Coils!• MR signal detection!• Reciprocity!• Resonance!• Coil Q and Noise!• Classes of RF coils!• Parallel Imaging!• Coil Geometry!• Coil Coupling!
E. Wong, BE278, UCSD Winter 2012!
MR Signal Detection!
Faraday�s Law of Induction:!
E. Wong, BE278, UCSD Winter 2012!
Reciprocity!The spatial distribution the sensitivity of an RF coil is proportional to the field generated by a unit current flowing in the coil!
For (a lot) more details, see: http://coecs.ou.edu/Tamer.S.Ibrahim/Reciprocity_In_MRI.htm!
I!
If unit current I produces a transverse RF field B1, then transverse magnetization Mxy induces:!!
€
Voltage∝ B1∫ (r)•Mxy (r)dV
B1!
Note: Only transverse components of B1 and M count!
E. Wong, BE278, UCSD Winter 2012!
RF Coil Basics: Resonance!
q I!
+!+!
-! -!
V =qC
V = L dIdt
qC= L dI
dt
I = −LC d2Idt2
I = I0eiωt
I = I0 sin(ωt +φ)
ω =1LC
C! L!
E. Wong, BE278, UCSD Winter 2012!
RF Coil Basics: Matching!
Z=R+jωL!~ (1+100j)Ω!
on resonance!
L!C!
L! L!C1!
C2!
L!C!
… or inductive!coupling !
€
Z =j
1ωL −ωC
≈ ∞
€
Z =A R − j(AωC1 −ωL)( )R2 + AωC1 −ωL( )2
−j
ωC2
A = R2 +ω 2L2
R! R! R! R!
Goals:!• Coil resonant at Larmor frequency!• Z = 50Ω:#
• Match cables!• Match preamp!
M!
E. Wong, BE278, UCSD Winter 2012!
RF Coil Q!
L!C!
• Definition: Q = # oscillations before amplitude -> 1/e!• or: 1/(fractional energy loss per oscillation)!• or: ratio of resonance frequency to width of resonance peak!
• Q(spins) = ωLT2 ~ 10 million!• Q(coil+sample) ~ 20-500!• Therefore: spins cannot be closely coupled to coil!• So, what limits coil Q?!
E. Wong, BE278, UCSD Winter 2012!
Coil losses and Sample losses!
• Sample losses are not from spins, but from random thermal motion of ions in sample!
• Goal: minimize noise by minimizing losses!• Not much control over Qsample!
• Try to get Qcoil >> Qsample!
• Maximize: (roughly) !
R!R!
€
1Qtotal
=1Qcoil
+1
Qsample
€
B1(ROI)B1 dV
∞
∫
E. Wong, BE278, UCSD Winter 2012!
Classes of RF coils!
• Transmit / Receive: Apply RF pulses and receive signal through same coil!
• * Transmit Only: Used only to apply RF pulses - typically large with uniform B1!
• * Receive Only: Used only to receive RF signal - optimized for high sensitivity!
• * Multicoil Arrays: Typically Receive Only, used to increase sensitivity over large ROI, or to implement parallel imaging!
* These need active and/or passive T/R switching!
E. Wong, BE278, UCSD Winter 2012!
Blaimer et al, Top Magn Reson Imaging 2004;15:223–236!
Parallel Imaging!
€
S j (t) = C j (r)Mxy (r)eiK (t )•rdr∫
E. Wong, BE278, UCSD Winter 2012! Blaimer et al, Top Magn Reson Imaging 2004;15:223–236!
g!
1!
4!R=2! 4!
6! 8!
€
ρ = ( ˆ C H ˆ C )−1 ˆ C H •
I
€
SNR∝ 1g R
Parallel Imaging - SENSE!
E. Wong, BE278, UCSD Winter 2012!
RF Coil Geometries!
• Surface Coil:!
• Quadrature Surface Coil:!
• Solenoid:!
• Birdcage Coil:!
Where is Bz?!
B1y! B1x!
E. Wong, BE278, UCSD Winter 2012!
RF Coil Coupling!
M~1!
M=0!
M<0!
Coupling:!• Correlates Signal!• Correlates Noise!• For M->1, coils are one coil!
TEM coil, Vaughan et al!