Bart van de Bank B.vandeBank@rad.umcn.nl

Ingmar Voogt I.J.Voogt@umcutrecht.nl

Michel ItaliaanderM.Italiaander@umcutrecht.nl

MR Hardware

RF Coils

Program:2

13:30 – 14:15

MR Hardware

14:15 – 15:00

RF Coils

15:00 – 17:00

RF Practice

Learning objectives3

After this lecture you should know:

The properties of a RF coil

The different coil types that are being used in MRI

Be able to define the coil setup suitable for your own experiments

and be able to develop a (simple) coil

RF Coils

4

Physics (only a few)

Coil types

How to build one?

Resonance

Larmor

Principles

B1 field

Limitations

Resonance (phenomenon)5

The ability of a system to store energy

Kinetic, electric, etc.

“Galoping Gertie”

Opened July 1940

Suspension bridge 1.6km length (3rd longest in the world)

The bridge to MR7

0B

Larmor equation8

0B

9

B0Mz Z’

Y’

10

MXY

RF Coil

Mz

ΔθZ’

Y’

11

RF Coil

Mz

MXY

Z’

Y’

B1 field12

Determine the strength of the B1 field.

Example:

We want to have a 90° flip for 1H MRI at 3T and the pulse will take 100 μs. What amplitude should the pulse have?

What flip angle we have if we lengthen the pulse to 400 μs?

B1 field13

Determine the strength of the B1 field.

Example:

We want to have a 90° flip for 1H MRI at 3T and the pulse will take 100 μs. What amplitude should the pulse have?

What flip angle we have if we lengthen the pulse to 400 μs?

Some equations14

Maxwell’s equations

Gauss’s law

Gaus’s law for magnetism

Faraday’s law

Ampere’s law (corrected)

Biot-Savart’s law*

Relation between currents and their magnetic fields.

Righthand rule

Determination of B1 Direction

* NB. approximation only at low field

RF Coils

15

Some physics

Coil types

How to build one?

Solenoid

Surface

Helmholtz

Alderman-Grant

Bollinger

Birdcage

Arrays

Antenna’s

Microstrips

Soleniod coil16

Benefits

Homogeneous B1-field

High B1-field strength

Drawbacks

Axial access only

B1 always perpendicular to B0

High inductance L (LF)

Source: www.hyperphysics.phy-astr.gsu.edu

Surface (flat) coil17

Benefits

Superb SNR

Inherent localization

Drawbacks

Inhomogeneous B1-field

Limited penetration depth

Source: AJR june 2007 vol 188 no 6 1568-1572

Helmholtz coil18

Benefits

Open access

Fairly homogeneous B1-field

Reasonable SNR

Drawbacks

Long lead conductors

Alderman-Grant (saddle) coil19

Benefits

Volume setup

Open design

Easy to construct

Drawbacks

Inhomogeneous B1-field

Only applicable for small objects

Source: www.cis.rit.edu

Bollinger (cosine) coil20

Benefits

Volume setup

Fairly Homogenous B1 field

Open design

Drawbacks

Complexer design

Birdcage coil21

Benefits

Volume setup

Superb homogeneity

Applicable at high-field

Drawbacks

Very complex design

Double resonant tough

Array coils22

Benefits

Superb SNR

Large FOV

Applicable at high-field

Applicable for parallel imaging

Drawbacks

Complex design

RF-coupling

Antenna’s23

Benefits

(relative) Simple design

Propagating EM Wave

(poynting vector)

Combined with surface coils

Drawbacks

Only applicable at high field

Microstrips (radiative antenna)24

Benefits

B1 directed into tissue

E-field in substrate

Very high Q

Drawbacks

Coupling in arrays

RF Coils

25

Some physics

Coil types

How to build one?

Components

Resonance circuitry

Quality

Build your own loop coil

Geometry

Loopsize

Quality factor

Tuning

Loading

Matching

Balancing

Trapping

Quadrature

Multi nuclei

Detune

Components & Impedance26

Inductor [H]

Impedance:

Rule of thumb: 1 nH/mm

Capacitor [F]

Impedance:

Resistor [Ω]

Impedance:

Total Impedance (=frequency profile)

circuit-dependent!

C

pF

L_coi l

nH1 2

R

ohm

Resonance circuit27

Resonance condition:

CL1 2

C

L1 2

Serial resonance Parallel resonance

Quality factor28

Q-factor reveals the quality of the resonant circuit

High Q Low loss or small bandwidth

Low Q High loss or high bandwidth

Frequency

30MHz 50MHz 70MHz 90MHz 100MHz

VDB(L1:2)

-10

0

10

20

30

40

50

Frequency

30MHz 50MHz 70MHz 90MHz 100MHz

VDB(L1:2)

-10

0

10

20

30

40

50

Build your own coil I29

1. Determine loopsize

Region of interest

Target depth

2. Create loop

Determine inductance

Estimation: Rule of thumb

Determination: Use capacitor

Determine Q

Connect to system?

Not ready, yet!

Electrical Model

V_RF

R_Sy stem

50

L_Coil

nH

1

2

R_Coil

OhmT1

L_Coil

nH

1

2

R_Coil

OhmL_Coil

nH

1

2

50 R

Target (visual) depth

Optimal coil radius

2R0

Rcoil

(<<1Ω)

Inductance (L)ZL=jωL (L~1nH/mm)

(Z~300Ω @5cm, 300MHz)

Current I

High Q Low R

Q = ωL/Rcoil

P = U * I ?

[kW]

50Ω

U

Build your own coil II30

3. Tune the loop

Larmor frequency of interest

4. Determine Q

Differentiate between

Unloaded

Loaded

5. Connect to system?

Yes

Rcoil

Current I

ZL=jωL

Electrical ModelR_Coil

OhmC_Tune

pF

L_Coil

nH

1

2

R_Coil

OhmL_Coil

nH

1

2

TUNE

ZCt=-j/ωCt

C

ω0 ω

Qunloaded = ωL/Rcoil

Tissue

(conductivity

permeability)

Rtissue

Qloaded = ω L/(Rcoil+Rtissue)

C_Tune

pF

R_Tissue

Ohm

R_Coil

OhmL_Coil

nH

1

2

Zt=?

R_Tissue

OhmC_Tune

pF

L_Coil

nH

1

2

R_Coil

Ohm

Build your own coil III

The magic 50 ohms31

R_s ystem

50

0

R_loadn

0

V_RF

0

1

2

3

4

5

6

0 20 40 60 80 100

R [Ohm]P

[m

W]

Pow

er

R [Ω]50 Ω

RLoad < RSystem

RLoad = RSystem

RLoad > RSystem

Build your own coil IV32

6. Match the coil

Determine total impedance)//( tissuecoilLCt RRZZZ

Electrical Model

Rcoil

Current I

ZL=jωL

TUNE

ZCt=-j/ωCt

Tissue

(conductivity

permeability)

Rtissue

Zt=?

R_Tissue

OhmC_Tune

pF

L_Coil

nH

1

2

R_Coil

Ohm

Zt=1/(1/(jωL+R)+jωC)

= a + jB

Re(Zt)=50 = a

Im(Zt)=0 ≠ B

Zt=50+jX

jB

-jB

Z_Replace

50 + jB

ω

no match

matched

50 + jB

C_Match

-jBZ_Replace

tissuecoilLC

tRRZZ

Z

11

tissuecoilLC

tissuecoilLCt

RRZZ

RRZZZ

jbaZ t

Build your own coil V33

Tissue

(conductivity

permeability)

2Ct

2Ct Cm

2Cm

2Cm

Ct

50

Build your own coil - summary34

Matching

C

Tuning

C

Loop

L+R

GND

Matching

Tuning

Build your own coil

Quadrature35

I

I

-1

0

1

0

-1

0

1

0

90o

delay

+

Transmit ?

Hybride

box

Receive

Build your own coil

Multi nuclei36

Measure different nuclei with MR

31P, 23Na, 19F, 13C etc.

Design decisions

single / multi coil arrangement

single / multi probe input

relative coil efficiency

Always need 1H coil

shimming, decoupling, localization, magnetization

transfer, multi-nuclei (time interleaved),

quantification, ...

Build your own coil

Multi nuclei37

=

C

orL

1 2

C_HFC_LF

L_coil1 2

L_coil1 2

L_parallel1 2

L_coil1 2

C_LF

C_HF

+

@ High

Frequency

@ Low

Frequency

Build your own coil

Detuning38

Homogeneous excitation & localized

acquisition (high SNR):

Separate Tx and Rx coil

But make sure that:

During Tx: no B1 field coupling

During Rx: no noise coupling

2C

4C

4C

L/2

L/2

Ldec

PINmatch

tune

Forward Bias

Reversed Bias

Literature39

Haase, A., F. Odoj, et al. (2000). "NMR probeheads for in vivo

applications." Concepts in Magnetic Resonance 12(6): 361-388.

Mispelter, J., Lupu, M. & Briguet, A. NMR Probeheads for biophysical

and biomedical experiments; Imperial College Press (2006)

Build your own coil

Workshop40

Split in 6 groups

Every group builds a coil

Practice will be in room: P59, Gebouw de Valk

(Building 304), 1st floor

Please,be very careful with the equipment

41