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