High-Gradient FFL Simulations for Human-Sized MPILucas Jenkins, MGH Wald Lab

Background and Goals

For Magnetic Particle Imaging, an integral part of the hardware setup is the main magnetic gradient

The strength of the magnetic field gradient is directly correlated to the possible resolution of the Magnetic Particle Image

Previous MPI scanners have all had bores that would fit rats The goal of these simulations was to create a high gradient in a human-

sized bore.

Software Used

COMSOL Multiphysics 5.1 AC/DC Module

Magnetic Fields, No Currents package (mfnc) Magnetic Fields package (mf)

Licensed from MIT

Location of .mph Files From Simulations Stored on MIT Linux box jotunn.mit.edu:2 /

home clzimmer

mpi_sims Anything with prefix “Lucas”

To see all: $ls /home/clzimmer/mpi_sims/Lucas*

Materials Simulated: Permanent Magnets

Used in mfnc module Magnet specs from http://www.magnet4less.com/index.php?cPath=1_122 N52 Grade Neodymium Magnets used – remnant flux density BrMax =

14,800 gauss = 1.48 T Some arc magnets used – but for the most part, combinations of 4cm x

1cm x 1/2cm N52 magnets used to create different geometries Other important property for permanent magnets: μrelative

Neodymium μrelative = 1.05 Air μrelative = 1 For simulations with iron yolks - μrelative of iron can vary with field strength – I

chose an intermediate value from what I had seen for Low Carbon Cold Rolled (aka laminated) Annealed Steel of μrelative = 1200

Approaches for Permanent Magnets

Many different geometries of permanent magnets were simulated 1.) Arc Magnets 2.) 2 opposite sets of Magnets *** 3.) Magnets set up at Vertices of Equilateral Triangle 4.) Quadrupole Magnet Some geometries were also simulated with an iron yolk around the

magnets to concentrate the flux lines

***Most successful method for FFL

List of all Simulations (some with descriptive names)

First approach– 2 opposing sets of 2 4x1x1” N52 magnets Relatively short magnets North Poles faced inward(towards other set of magnets) Not successful – magnetswere not tall enough Not thick enough Takeaways – try tallerand thicker magnets

Results from first attempt – more of a field free point than FFL

Red arrows are flux density norms (small fields)

Y-Z Plane View X-Z Plane View X-Y Plane View

First Results (continued)Cut lines endpoints (cm): Y Field and Gradient (0, -15, 5.08) (0, 15, 5.08) **z=5.08cm is centered in z dir

Z Field and Gradient (0, 0, -10) (0, 0, 20) X Field and Gradient (-10, 0, 5.08) (10, 0, 5.08)

Second approach – 2 Opposing Tall Arc-Shaped Magnets

Again, North poles faced inwards Geometric Properties (arcs are identical but opposite): ID of arc: 10.16cm OD of arc: 17.78cm y coordinate of the center of each arc: ±9cm (x=0) Inner arc angle = 180° Extrusion Height: 60cm

Intermediate Geometric Step (distances in cm)

Arc Magnet Results Better than small magnets Arc shape did not seem to help Height and thickness made main difference Gradient strengths still too weak

Again, red arrows are flux density norms

Y-Z Plane ViewX-Z Plane ViewX-Y Plane View

Arc Magnet Results (continued)Cut lines endpoints (cm): Y Field and Gradient (0, -30, 30) (0, 30, 30) **z=30cm is centered in z dir

Z Field and Gradient (0, 0, 10) (0, 0, 50) X Field and Gradient (-10, 0, 5.08) (10, 0, 5.08)

Low x and y gradients at center = unfit for MPI

Third Approach: Triangular Setup Place groups of magnets at vertices of

equilateral triangle with side length=36cm. Groups of:

single 1x1” N52 magnets 2 side by side 1x1” N52 magnets And a 2x2 square of 1x1” N52 magnets

Were used in these simulations Results from 2x2 square (best results)

are shown Extrusion Height (z-dir) = 60mm

Triangular Approach Results Magnetic fields from each group of magnets were directed at center of

triangle – however, this meant that the fields were not evenly opposed As can be seen in the Y-Z plane view, flux distributions were uneven

Y-Z Plane ViewX-Z Plane ViewX-Y Plane View

Triangular Flux Density Plots

We struggled to plot the gradients along non-axial lines in COMSOL, but given the similar flux density curves for the y-axis field and the field along Cut Lines 3 and 4, we assume that the gradient curves along Cut Lines 3 and 4 were similar to the Y Gradient, as the geometric and magnetic properties of the magnets at each vertex of the triangle were identical.

The Y Axis Field and Cut Lines 3 and 4 emanated from magnet groups at the vertices of the triangleCut Line 3:

Cut Line 4:

Triangular Magnets Takeaways

Gradients too small Fields do not cancel effectively at center R^2 decreasing field effects seem to dominate flux decrease as opposed

to true cancellations – theme of all simulations so far = low slope magnetic fields

Unfit for human MPI

Two Sets of Opposing Magnets pt. II Two sets of opposing magnets – taller with different geometric layout 3 magnets in the back and 4 in the front (1”x1” N52) 70cm extrusion

Optimized Opposing Magnets Results

Y-Z Plane ViewX-Z Plane ViewX-Y Plane View

Optimized Opposing Magnets Results (cont.)

Optimized Opposing Magnets Results First Example of actual Free Field “Line” in Spectrum/Arrow plots Gradient Strength of 0.5 T/m still relatively low – thicker magnets may

help? Gradients of at least 1-2 T/m desired Optimized opposite magnets do not quite reach desired gradients -

quadrupole magnets were attempted next

Quadrupole Magnetic Setup Quadrupole Magnets are a rough

approximation to a k=3 Halbach cylinder, leaving no field in the center of the bore

Our quadrupole setup used the same 4+3 1x1” groups of magnets placed on the vertices of an imaginary square of diagonal 36 cm

This setup left ~18.5 cm between each corner magnet – enough room for an average human head to slide in sideways while leaving the FFL approximately at the center of the head

Extrusion height of 70 cm

Quadrupole Magnets Results

Y-Z Plane ViewX-Z Plane ViewX-Y Plane View

Most clear free field line for permanent magnets Promising Results – line is very uniform for whole length of magnet – can

shorten magnet?

Quadrupole Magnets Results Magnetic Flux density curve look uniform for 30 cm around center of

magnet in z direction – x and y flux density curves are nearly identical Gradient strengths approaching desired levels – could possibly be

increased with Iron Yolk?

Yolked Quadrupole Setup Quadrupole magnets are in same arrangement as previous simulation Iron Yolk placed around Magnets with hole through direction which

allows head entrance Cold Rolled (laminated) annealed steel used in

simulation with μrelative = 1200 Goal with yolk is to concentrate flux lines within

the yolk, ideally increasing gradient Note – yolked simulations for dual opposite

magnets in same folder, not as successful

Yolked Quadrupole results

Y-Z Plane ViewX-Z Plane ViewX-Y Plane View

Slightly more uniform gradients – gradient falls off more slowly in z-dir compared to no yolk

Yolked Quadrupole results Gradients are >1 T/m – possibly high enough for

human sized MPI (althought maybe claustrophobic). Yolk seems to add ~0.3 T/m to gradient at center

Electromagnetic Simulations

Not as many simulations done as for static magnetic fields Copper coils with cross section of 1.25mm were used as inductors Golay gradient coils were simulated – inverse Helmholtz coils remain a

future simulation Due to COMSOL’s use of Magnetic Potential to calculate Magnetic Flux,

the magnetic flux elements calculated in the AC/DC mf module needed to be mapped to a coefficient PDE so that Lagrangian elements could be used to calculate the gradient of the magnetic flux density

Golay Coil Setup

8 sets of 17.5cm radius arcs – connected by straight lines as shown. Arc angle is 120 degrees

Current flows in the same direction on the 2 upper inner arcs, and in the opposite direction on the 2 lower inner arcs

Coils excited with 100V at the center of the outside arc

Golay Coil Results

All simulations can be found in the mpi_sims folder Some results:

Golay Coil Results

Higher gradients can be created with electromagnets than permanent magnets

Electromagnets are more complex to simulate in COMSOL Future efforts would go towards mastering the Magnetic Fields interface

in COMSOL, and simulating inverted Helmholtz coils