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










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




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RF Birdcage Head Coil Example

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




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RF Birdcage Coils




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RF Birdcage Coils

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




Conclusion


RF Birdcage Coils


widely used in MRI




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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...




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




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

capacitors on the rungs or end rings or both




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Resonance Behavior of Birdcage Coils

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




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




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degenerate mode pairs - two modes with the samefrequency




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end ring resonant mode (m=0)




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




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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




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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


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

Jin, 1989 - MRIEM Software Toolresonant 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


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


Lumped Circuit Element Model

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




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Limitation of Lumped Circuit Element Model

There are some limitations of using lumped circuit elementmodel

heavily depends on the inductance calculations




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

heavily depends on the inductance calculations




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




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Example: L = 0.002l[

ln(

2lB

)

+ 0.5]




Conclusion






ln(

2lB

)

+ 0.5]

frequency ↑




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ln(

2lB

)

+ 0.5]

frequency ↑ error ↑




Conclusion


Modelling a Transmission Line as a Lumped CircuitElement

Deutsch et al., 1997There is an important criterion




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




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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




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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.




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What Have We Done in this Study?




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




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Using these models;




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Using these models;

Two FEM based simulation methods




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Using these models;


Frequency Domain Analysis




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Using these models;


Frequency Domain AnalysisEigenfrequency Analysis




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Using these models;



Software Tool




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Using these models;



Software Tool

FEM-FDA-EFAT




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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









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Geometry




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Geometry

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




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Adding Physics




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Adding Physics

Radio Frequency Branch → Electromagnetic WavesInterface




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Adding Physics


solves the electromagnetic wave equation for the timeharmonic and eigenfrequency problem




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Adding Physics


solves the electromagnetic wave equation for the timeharmonic and eigenfrequency problem

∇× µ−1r (∇× E)− k2

0

(

ǫr −jσωǫ0

)

E = 0




Conclusion


Boundary Conditions




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Boundary Conditions

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




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Boundary Conditions

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

n × E = 0




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Boundary Conditions




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Boundary Conditions

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




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Boundary Conditions

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




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Boundary Conditions

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




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Boundary Conditions




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Boundary Conditions

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

VportIport

)




Conclusion


Boundary Conditions

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

VportIport

)

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



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Mesh




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Mesh

(Element Size) <<λ5




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Simulation of a Birdcage Coil




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solves for the electromagnetic fields in the solution domain




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at the desired frequency (or frequencies)




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for the specified capacitance value




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In Frequency Domain Analysis;




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loaded (or unloaded) birdcage coils




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shielded (or unshielded) birdcage coils




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shielded (or unshielded) birdcage coils

linear or quadrature excitation




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Simulation Results




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Simulation Results

three different scenarios;




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Simulation Results


unloaded and unshielded 8-leg low-pass birdcage coil




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Simulation Results



unloaded and shielded 8-leg low-pass birdcage coil




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Simulation Results




loaded and shielded 16-leg high-pass birdcage coil




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Simulation Results





electromagnetic field distributions




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Simulation Results






H+ and H−




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Simulation Results






H+ and H−

H+ =Hx + iHy

2H− =

(Hx − iHy )∗

2




Conclusion


Simulation Results






H+ and H−

H+ =Hx + iHy

2H− =

(Hx − iHy )∗

2

E-field




Conclusion


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




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H+ and H− → for linear excitation




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H+ and H− → for quadrature excitation




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Electric field → for linear and quadrature excitation




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H+ uniformity → for quadrature excitation




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




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

H+ uniformity → for quadrature excitation




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




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Geometric model




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




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




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SAR distribution of an object




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SAR =σ|E|2

ρ

σ: conductivity, ρ: density




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SAR =σ|E|2

ρ

σ: conductivity, ρ: density

Normalized SAR distribution → for quadrature excitation




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Normalized SAR distribution → for quadrature excitation




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Conclusion


Resonant Mode Analysis of a Birdcage Coil




Conclusion



calculates the resonant modes of the birdcage coil




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




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




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Eigenfrequency Analysis in COMSOL Multiphysics




Conclusion



use developed FEM models of birdcage coils




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add eigenfrequency study




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add eigenfrequency studyspecify number of eigenfrequencies




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add eigenfrequency studyspecify number of eigenfrequenciesspecify a frequency point

add eigenvalue solver




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add eigenfrequency studyspecify number of eigenfrequenciesspecify a frequency point

add eigenvalue solverchange the linearization point (if necessary)




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Simulation Results




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Simulation Results

two different scenarios;




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Simulation Results






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Simulation Results



unloaded and shielded 16-leg high-pass birdcage coil




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Simulation Results




observed electromagnetic variables




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Simulation Results





H+ at these resonant modes




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Simulation Results





H+ at these resonant modes

surface current density




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Conclusion



H+ → for all resonant modes




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




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

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




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Conclusion


Software Tool for Designing and Simulating a BirdcageCoil




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PURPOSE:




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PURPOSE:

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




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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




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PURPOSE:


developed software tool




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PURPOSE:


developed software tool

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




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Properties of the sofware tool




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developed in MATLAB




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developed in MATLAB

has graphical-user-interface (GUI)




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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




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developed in MATLAB


modeling the coil geometry




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developed in MATLAB


modeling the coil geometryadding physics and boundary condition




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developed in MATLAB


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




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developed in MATLAB


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




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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




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Conclusion

Handmade Low-pass Birdcage Coil




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




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Conclusion

Experimental Results and Comparison with NumericalAnalyses

for the resonant modes




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S11 of the coil for five different capacitance values




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




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Jin’s software tool, MRIEM




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




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Conclusion

Measured and Calculated Resonant ModesResults for Low-pass Birdcage Coil




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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




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Results for 10pF





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Results for 3.3pF





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Results for 1.8pF





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Results for 1pF





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Percentage error

Error rate (%) = 100 ×

∣

∣

∣

∣

fmeas − fcalc

fmeas

∣

∣

∣

∣




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Percentage error rate for FEM-EFAT and MRIEM




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Conclusion

Conclusion




Conclusion

Conclusion

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




Conclusion

Conclusion


Frequency Domain Analysis




Conclusion

Conclusion


Frequency Domain Analysiselectromagnetic fields solutions of a birdcage coil for anyscenario




Conclusion

Conclusion



Eigenfrequency Analysis




Conclusion

Conclusion



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




Conclusion

Conclusion




Conclusion

Conclusion

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




Conclusion

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

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...


fem based design and simulation tool for mri birdcage ... · fem based design and simulation tool...

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