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Magnetic Resonance Tomography (MRT) Overview
Patients undergoing an MRTlie flat on a scanning table and are placed in a magneticfield created by a HUGE magnet
Picker Eclipse 1.5T
Whole-body MRT drawbacks
• They can cost up to several million dollars
• Because of the small bore of the magnet some patientsexperience claustrophobia during the exam
Medical journals report a 35% patients experiencing severeanxiety
• Recently has been discovered a side effect of MR known as “Tissue heating”Some patient undergoes an augment in the temperature ofsome body parts
A New MR device
• Permits the diagnosis of single body parts (foot, forearm,hand, …) without requiring the patient to be inserted into it
• Features a large magnetic field uniformity region
• Has an affordable price even for small clinical houses
• Improved precision of the MR devise
Optimal Design Problem
- Low cost- Low weight- High field uniformity- Big uniformity region
Multipolar magnet design
one half of the multipolar magnet
z
y x
~460mm
max 300mm~360mm
Magnetic Resonance apparatus featuring
n. m
agne
ts=3
n. rings=6
n.mag
nets=
4
half magnet
Design Variables
Positions of the ringsalong the X-axis
X
x1 x2 x3 x4 x5 x6
Angular positions of each row of small magnets 1ϕ 2ϕ
3ϕ
4ϕ
Design Variables
Offsets of the 4 outermost rings w.r.t. the 2 innermost ones
Xb1 b2 b3 b4
r
Radius of magnets
Design Variables
0
100
200
300
-200
0
200
-200
-100
0
100
200
0
100
200
300
-200
0
200
3D model
Objective Function
The objective function measures the non-uniformity of themagnetic field within a specified target region which is
cylinder with elliptical base of dimensionsheigth: 120mmsemi-axes: 60mm x 50mm
directed along the X-axis
( )( ) ( )( ) ( )( ) ( )( )( )
( )21
2)(2)(2)(
xB
xBxBxBxBxU
Z
N
i
iY
iXZ
iZ
p
∑=
++−=
( )( )
p
N
i
iZ
Z N
xBxB
p
∑== 1
)(
Magnetic field as uniform as possible and directed along the Z axis
Comercial Devices
Have a field non-uniformity of ~51ppm
Ideal value is U(x)=0 (global minimum)
The Optimization Algorithm should havethe ability to locate a global minimum with
high precision
Magnetic Resonance Results
We tried to solve it using alg. DDFSA and got
18ppm non-uniformity in 19408 function evals
nr=5nm=3r=22
f=51 ppm
Starting point
nr=7nm=3r=27
f=18 ppm
Final point
Magnetic Resonance Results
( ) ( )( )*
**
xBxBxB
Z
ZZ −Behavior of on the ZY plane
51ppm configuration 18ppm configuration
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