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!