FEM Based Design and Simulation Tool for MRI Birdcage ... · FEM Based Design and Simulation Tool...

IntroductionMotivation

MethodsExperimental Results

Conclusion

FEM Based Design and Simulation Tool forMRI Birdcage Coils Including Eigenfrequency

Analysis

Necip Gurler and Yusuf Ziya Ider

Electrical and Electronics Engineering DepartmentBilkent University, Ankara, TURKEY

11.10.2012Milan, Italy

Necip Gurler COMSOL CONFERENCE EUROPE 2012

Excerpt from the Proceedings of the 2012 COMSOL Conference in Milan

Conclusion

Outline1 Introduction

RF coils in MRIRF birdcage coilsDesign and simulation of RF birdcage coils

2 MotivationReview of previous studiesProblem definitionOur work

3 MethodsFEM Models of Birdcage CoilsFrequency Domain AnalysisEigenfrequency AnalysisSoftware Tool

4 Experimental Results5 Conclusion

Conclusion

What Do the RF Coils Serve in MRI?

generate RF magnetic field (B1 field) at the Larmorfrequencyreceive RF signals at the same frequency

Source of figures: http://www.cis.rit.edu/htbooks/mri/chap-9/chap-9.htm

Conclusion

RF Birdcage Head Coil Example

Source of figure: http://www.healthcare.philips.com

Conclusion

RF Birdcage Coils

Conclusion

RF Birdcage Coils

based on the lumped element delay line (Hayes et al., 1985)

Conclusion

RF Birdcage Coils

widely used in MRI

Conclusion

RF Birdcage Coils

widely used in MRI

Advantages

Conclusion

RF Birdcage Coils

widely used in MRI

Advantages

very homogeneous RF magnetic field

Conclusion

RF Birdcage Coils

widely used in MRI

Advantages

high signal-to-noise ratio (SNR)

Conclusion

RF Birdcage Coils

widely used in MRI

Advantages

high signal-to-noise ratio (SNR)

quadrature excitation and reception capability

Conclusion

Birdcage Coils Consist of...

Conclusion

two circular end rings connected by N equally spacedrungs (or legs)

Conclusion

two circular end rings connected by N equally spacedrungs (or legs)

capacitors on the rungs or end rings or both

Conclusion

Resonance Behavior of Birdcage Coils

A birdcage coil with N number of rungs andequal valued capacitors has

Conclusion

N/2 resonant modes (m=1,2... N/2)

Conclusion

degenerate mode pairs - two modes with the samefrequency

Conclusion

end ring resonant mode (m=0)

Conclusion

end ring resonant mode (m=0)currents only flow in the end rings - Helmholtz pair

Conclusion

Which Resonant Mode is used in MRI?

most homogeneous B1 field

sinusoidal current distribution in the rungs for m = 1 mode

Source of figure: M. Lupu, MAGMA, 2004, 17, 363-371

Conclusion

Designing a RF Birdcage Coil

In order to generate a homogeneous B1 field at the desiredfrequency;

use the correct capacitance valuecalculate an initial capacitance valuetuning and matching procedures

knowing resonant modes of the birdcage coiltuning and matching procedures can be done withoutinterfering with the other modesm=0 mode is used in open MRI systems

Conclusion

Simulating a RF Birdcage Coil

Solving for the electromagnetic fields of a birdcage coil at thespecified frequency.

B1 field distribution inside the coil

specific absorption rate (SAR) at any object

variation of any electromagnetic field variables with respectto frequency

Conclusion

Review of previous studiesProblem definitionOur work

Conclusion

Studies on Designing a Birdcage CoilTropp, 1989analyzing low-pass birdcage resonator - using lumped circuitelement model and perturbation theory

Jin, 1989resonant modes calculation - lumped circuit element model

Pascone et al., 1991analyzing both low-pass and high-pass birdcage coil - usingtransmission line theory

Leifer, 1997resonant modes calculation - using discrete Fourier transform

Chin et al., 2002capacitance calculation - lumped circuit element model

Conclusion

Jin, 1989resonant modes calculation - lumped circuit element model

Conclusion

Jin, 1989 - MRIEM Software Toolresonant modes calculation - lumped circuit element model

Conclusion

Lumped Circuit Element Model

end rings and rungs are modeled as inductors

self and mutual inductances are calculated usinghandbook formulas

equivalent circuit model (LC network) is solved usingKirchoff’s voltage and current laws

Conclusion

Figure: Equivalent lumped circuit element models for low-passand high-pass birdcage coils

Conclusion

Limitation of Lumped Circuit Element Model

There are some limitations of using lumped circuit elementmodel

heavily depends on the inductance calculations

Conclusion

There are some limitations of using lumped circuit elementmodel in the capacitance and resonant modes calculations:

Conclusion

heavily depends on the inductance calculations which aremade under the quasi-static assumption

Conclusion

Example: L = 0.002l[

+ 0.5]

Conclusion

+ 0.5]

frequency ↑

Conclusion

+ 0.5]

frequency ↑ error ↑

Conclusion

Modelling a Transmission Line as a Lumped CircuitElement

Deutsch et al., 1997There is an important criterion

Conclusion

Deutsch et al., 1997There is an important criterion - used for determining whether awire can be modeled as lumped circuit element or not -

Conclusion

Deutsch et al., 1997There is an important criterion - used for determining whether awire can be modeled as lumped circuit element or not - which isgiven as

Conclusion

Deutsch et al., 1997There is an important criterion - used for determining whether awire can be modeled as lumped circuit element or not - which isgiven as

length of wire ≤λ

20where λ is the wavelength.

Conclusion

What Have We Done in this Study?

Conclusion

We have first developed FEM models of low-pass andhigh-pass birdcage coils in COMSOL Multiphysics.

Conclusion

Using these models;

Conclusion

Using these models;

Two FEM based simulation methods

Conclusion

Using these models;

Frequency Domain Analysis

Conclusion

Using these models;

Frequency Domain AnalysisEigenfrequency Analysis

Conclusion

Using these models;

Software Tool

Conclusion

Using these models;

Software Tool

FEM-FDA-EFAT

Conclusion

Using these models;

Software Tool

FEM-FDA-EFAT

A handmade low-pass birdcage coil is constructed.

Conclusion

FEM Models of Birdcage CoilsFrequency Domain AnalysisEigenfrequency AnalysisSoftware Tool

Conclusion

Geometry

Conclusion

Geometry

low-pass and high-pass birdcage coils are geometricallymodeled in the simulation environment

Conclusion

Geometry

low-pass and high-pass birdcage coils are geometricallymodeled in the simulation environment

Conclusion

Adding Physics

Conclusion

Adding Physics

Radio Frequency Branch → Electromagnetic WavesInterface

Conclusion

Adding Physics

solves the electromagnetic wave equation for the timeharmonic and eigenfrequency problem

Conclusion

Adding Physics

solves the electromagnetic wave equation for the timeharmonic and eigenfrequency problem

∇× µ−1r (∇× E)− k2

ǫr −jσωǫ0

Conclusion

Boundary Conditions

Conclusion

Boundary Conditions

boundaries of rungs, end rings, capacitor plates and RFshield are assigned to Perfect Electric Conductor (PEC)

Conclusion

Boundary Conditions

n × E = 0

Conclusion

Boundary Conditions

n × E = 0

Conclusion

Boundary Conditions

Conclusion

Boundary Conditions

we need to prevent reflections from the outer boundary ofthe solution domain

Conclusion

Boundary Conditions

we need to prevent reflections from the outer boundary ofthe solution domainscattering boundary condition → for boundaries

Conclusion

Boundary Conditions

we need to prevent reflections from the outer boundary ofthe solution domainscattering boundary condition → for boundariesperfectly matched layer → for domain

Conclusion

Boundary Conditions

we need to prevent reflections from the outer boundary ofthe solution domainscattering boundary condition → for boundariesperfectly matched layer → for domain

Conclusion

Boundary Conditions

Conclusion

Boundary Conditions

In frequency domain analysis, lumped port boundarycondition is used for voltage excitation (Zport =

VportIport

Conclusion

Boundary Conditions

VportIport

Conclusion

Boundary Conditions

VportIport

In eigenfrequency analysis, no source is appliedNecip Gurler COMSOL CONFERENCE EUROPE 2012

Conclusion

(Element Size) <<λ5

Conclusion

(Element Size) <<λ5

Conclusion

Simulation of a Birdcage Coil

Conclusion

solves for the electromagnetic fields in the solution domain

Conclusion

at the desired frequency (or frequencies)

Conclusion

for the specified capacitance value

Conclusion

In Frequency Domain Analysis;

Conclusion

loaded (or unloaded) birdcage coils

Conclusion

shielded (or unshielded) birdcage coils

Conclusion

shielded (or unshielded) birdcage coils

linear or quadrature excitation

Conclusion

Simulation Results

Conclusion

Simulation Results

three different scenarios;

Conclusion

Simulation Results

unloaded and unshielded 8-leg low-pass birdcage coil

Conclusion

Simulation Results

unloaded and shielded 8-leg low-pass birdcage coil

Conclusion

Simulation Results

loaded and shielded 16-leg high-pass birdcage coil

Conclusion

Simulation Results

electromagnetic field distributions

Conclusion

Simulation Results

H+ and H−

Conclusion

Simulation Results

H+ and H−

H+ =Hx + iHy

2H− =

(Hx − iHy )∗

Conclusion

Simulation Results

H+ and H−

H+ =Hx + iHy

2H− =

(Hx − iHy )∗

E-field

Conclusion

Simulation Results - 1st ScenarioUnloaded and Unshielded 8-leg Low-pass BC

Conclusion

H+ and H− → for linear excitation

Conclusion

H+ and H− → for linear excitation

Conclusion

H+ and H− → for quadrature excitation

Conclusion

H+ and H− → for quadrature excitation

Conclusion

Electric field → for linear and quadrature excitation

Conclusion

Electric field → for linear and quadrature excitation

Conclusion

H+ uniformity → for quadrature excitation

Conclusion

Simulation Results - 2nd ScenarioUnloaded and Shielded 8-leg Low-pass BC

Conclusion

Simulation Results - 3rd ScenarioLoaded and Shielded 16-leg High-pass BC

Conclusion

Geometric model

Conclusion

H+ → for unloaded and loaded case (quadrature excitation)

Conclusion

H+ → for unloaded and loaded case (quadrature excitation)

Conclusion

H− → for unloaded and loaded case (quadrature excitation)

Conclusion

H− → for unloaded and loaded case (quadrature excitation)

Conclusion

SAR distribution of an object

Conclusion

SAR =σ|E|2

σ: conductivity, ρ: density

Conclusion

SAR =σ|E|2

σ: conductivity, ρ: density

Normalized SAR distribution → for quadrature excitation

Conclusion

Normalized SAR distribution → for quadrature excitation

Conclusion

Resonant Mode Analysis of a Birdcage Coil

Conclusion

calculates the resonant modes of the birdcage coil

Conclusion

calculates the resonant modes of the birdcage coil and theelectromagnetic field distributions at these resonantmodes

Conclusion

calculates the resonant modes of the birdcage coil and theelectromagnetic field distributions at these resonantmodes for the given capacitance value

Conclusion

Eigenfrequency Analysis in COMSOL Multiphysics

Conclusion

use developed FEM models of birdcage coils

Conclusion

add eigenfrequency study

Conclusion

add eigenfrequency studyspecify number of eigenfrequencies

Conclusion

add eigenfrequency studyspecify number of eigenfrequenciesspecify a frequency point

add eigenvalue solver

Conclusion

add eigenfrequency studyspecify number of eigenfrequenciesspecify a frequency point

add eigenvalue solverchange the linearization point (if necessary)

Conclusion

Simulation Results

Conclusion

Simulation Results

two different scenarios;

Conclusion

Simulation Results

Conclusion

Simulation Results

unloaded and shielded 16-leg high-pass birdcage coil

Conclusion

Simulation Results

observed electromagnetic variables

Conclusion

Simulation Results

H+ at these resonant modes

Conclusion

Simulation Results

H+ at these resonant modes

surface current density

Conclusion

H+ → for all resonant modes

Conclusion

Simulation Results - 2nd ScenarioUnloaded and shielded 16-leg High-pass BC

Conclusion

H+ and surface current densities → for m=0 mode

Conclusion

H+ and surface current densities → for m=0 mode

Conclusion

Software Tool for Designing and Simulating a BirdcageCoil

Conclusion

PURPOSE:

Conclusion

PURPOSE:

To provide convenience for the coil designers and theresearchers in the field of MRI

Conclusion

PURPOSE:

To provide convenience for the coil designers and theresearchers in the field of MRI to use the proposedsimulation methods easily and according to the parametersthey specify

Conclusion

PURPOSE:

developed software tool

Conclusion

PURPOSE:

developed software tool

FEM based Frequency Domain and EigenfrequencyAnalysis Tool (FEM-FDA-EFAT)

Conclusion

Properties of the sofware tool

Conclusion

developed in MATLAB

Conclusion

developed in MATLAB

has graphical-user-interface (GUI)

Conclusion

developed in MATLAB

has graphical-user-interface (GUI)makes all design and simulation steps according to theuser-specified parameters by connecting to the COMSOLMultiphysics server

Conclusion

developed in MATLAB

modeling the coil geometry

Conclusion

developed in MATLAB

modeling the coil geometryadding physics and boundary condition

Conclusion

developed in MATLAB

modeling the coil geometryadding physics and boundary conditiongenerating mesh for the model

Conclusion

developed in MATLAB

modeling the coil geometryadding physics and boundary conditiongenerating mesh for the modeladding study and solver sequence

Conclusion

developed in MATLAB

modeling the coil geometryadding physics and boundary conditiongenerating mesh for the modeladding study and solver sequencecomputing the solutions

Conclusion

developed in MATLAB

modeling the coil geometryadding physics and boundary conditiongenerating mesh for the modeladding study and solver sequencecomputing the solutions

when the computation is finished, results can be observedin COMSOL Multiphysics

Conclusion

FEM-FDA-EFAT

Conclusion

FEM-FDA-EFAT

Conclusion

Handmade Low-pass Birdcage Coil

Conclusion

8-leg low-pass birdcage coil is constructed on plexiglasstube

Conclusion

Experimental Results and Comparison with NumericalAnalyses

for the resonant modes

Conclusion

S11 of the coil for five different capacitance values

Conclusion

S11 of the coil for five different capacitance valuescompare the measured resonant modes

Conclusion

Jin’s software tool, MRIEM

Conclusion

Jin’s software tool, MRIEMOur software tool, FEM-EFAT

Conclusion

Measured and Calculated Resonant ModesResults for Low-pass Birdcage Coil

Conclusion

used capacitance values

47 pF, 10 pF, 3.3 pF, 1.8 pF, 1 pF

Conclusion

Results for 47pF

Modes Measured (MHz) MRIEM (MHz) FEM-EFAT (MHz)m=1 60.75 67.46 59.1m=2 85.88 90.64 87.22m=3 93.38 102.2 101.1m=4 102.8 - 105.4

Conclusion

Results for 10pF

Conclusion

Results for 3.3pF

Conclusion

Results for 1.8pF

Conclusion

Results for 1pF

Conclusion

Percentage error

Error rate (%) = 100 ×

fmeas − fcalc

Conclusion

Percentage error rate for FEM-EFAT and MRIEM

Conclusion

We have proposed two FEM based simulation methods usingdeveloped FEM models of low-pass and high-passbirdcage coils in COMSOL Multiphysics:

Conclusion

Frequency Domain Analysis

Conclusion

Frequency Domain Analysiselectromagnetic fields solutions of a birdcage coil for anyscenario

Conclusion

Eigenfrequency Analysis

Conclusion

Eigenfrequency Analysisresonant modes of a birdcage coil and electromagnetic fieldsolutions at these resonant modes

Conclusion

A software tool is developed to make these two simulationmethods easily and according to the user-specifiedparameters

Conclusion

Experimental results show that results of the proposedsoftware tool is more accurate than the results of softwaretool which uses lumped circuit element model

Conclusion

Experimental results show that results of the proposedsoftware tool is more accurate than the results of softwaretool which uses lumped circuit element model

These methods can be adapted to design and simulateother MRI RF coils

Conclusion

One more thing...

Conclusion

One more thing...

FEM Based Design and Simulation Tool for MRI Birdcage ... · FEM Based Design and Simulation Tool...

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