2. 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.
3. Software Used
COMSOL Multiphysics 5.1
AC/DC Module
Magnetic Fields, No Currents package (mfnc)
Magnetic Fields package (mf)
Licensed from MIT
4. 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*
5. 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
6. 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
7. List of all Simulations
(some with descriptive
names)
8. First approach– 2 opposing sets of 2
4x1x1” N52 magnets
Relatively short magnets
North Poles faced inward
(towards other set of magnets)
Not successful – magnets
were not tall enough
Not thick enough
Takeaways – try taller
and thicker magnets
9. 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
10. 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)
11. 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)
12. 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
13. 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
14. 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
15. 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
16. 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 triangle
Cut Line 3:
Cut Line 4:
17. 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
18. 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
21. 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
22. 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
23. 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?
24. 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?
25. 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
26. 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
27. 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
28. 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
29. 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
30. Golay Coil Results
All simulations can be found in the mpi_sims folder
Some results:
31. 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
