Modeling Electromagnetic Fields An Application in MRI Kirsten

Modeling Electromagnetic Fields An Application in MRI Kirsten Koolstra April 22 nd, 2015 Challenge the future 1

Introduction Magnetic Resonance Imaging (MRI) Challenge the future 2

Introduction RF Interference in MRI Challenge the future 3

Challenge the future 4

Introduction The Effect of Dielectric Pads Challenge the future 5

Introduction The Effect of Dielectric Pads Without pad With pad Challenge the future 6

Introduction Design Procedure: Numerical Modeling Challenge the future 7

Challenges • Strong (localised) inhomogeneities in medium parameters • Large computational domain due to the body model • Accurate for low resolution! • Fast! • Take into account the boundary conditions Challenge the future 8

The Volume Integral Equation (VIE) Challenge the future 9

Different Formulations • Challenge the future 10

The Method of Moments • Challenge the future 11

Test Functions • Challenge the future 12

Basis Functions Rooftop Challenge the future 13

Basis Functions Challenge the future 14

A Closer Look EVIE Formulation • Challenge the future 15

A Closer Look Scattering on a Two-Layered Cylinder • Challenge the future 16

A Closer Look Scattering on a Two-Layered Cylinder Challenge the future 17

Some Observations 1. Contrast: Low contrast vs high contrast 2. Basis functions: Rooftop vs 2 x linear 3. Geometry: Cylinder vs square Challenge the future 18

Observation 1 Low Contrast vs High Contrast Challenge the future 19

Observation 1 Low Contrast vs High Contrast Challenge the future 20

Observation 2 Rooftop Expansion vs Linear Expansion Challenge the future 21

Observation 2 Rooftop Expansion vs Linear Expansion Challenge the future 22

Observation 3 Two-Layered Cylinder vs Two-Layered Square Challenge the future 23

Observation 3 Two-Layered Cylinder vs Two-Layered Square Challenge the future 24

What is the cause of these jumps? • Basis functions? • Formulation? • Geometry? Challenge the future 25

Fast Accurately Approach • Compare the EVIE formulation with the DVIE and JVIE formulations. • Analysing contrast dependency. • Find out what happens for different geometries. • Compare the performance of GMRES and IDR(s) methods. Challenge the future 26

Function Spaces • Challenge the future 27