Transcript Electrical eddy currents in the human body: MRI scans and

Electrical eddy currents in
the human body: MRI
scans and medical implants
Brent Hoffmeister
Rhodes College
Department of Physics
Research interests and
collaborators

Ultrasonic bone assessment



Ultrasound therapy for osteoarthritis

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Dr. Karen Hasty (U. Tennessee)
Ultrasonic imaging of cardiac electrical stimulation

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Dr. Sue Kaste (St. Jude), Dr. Kendall Waters (NIST)
Students: Andy Whitten, Julie Javarone, Chad Jones, Garney
Caldwell, Jeff France, John Janeski, David Johnson
Dr. Bob Malkin (Duke), Amy Curry (U. Memphis)
Students: Steve Smith, Will McKinney, Stu Johnston, Erin
Sylvester, John Sexton, Chip Hartigan, Taylor Whaley
Magnetic Stimulation


Dr. Bob Malkin (Duke)
Student: Drew Shores
Magnetic stimulation

Problem

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
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
MRI scans expose patients to time varying magnetic
fields
Faraday’s Law - time varying magnetic fields induce
electrical “eddy” currents
Induced currents can cause muscle contraction,
nerve stimulation, magnetophosphenes, cardiac
arrhythmias
Effect of medical implants unknown
Goal

Model how implants affect magnetically induced
currents in the body
MRI
Y gradient
coil
Z gradient
coil
Transceiver
X gradient
coil
Main
coil
Patient
MRI Magnetic Fields
Coil
f (Hz)
Function
Bioeffect
Main
0
Align proton
spins
?
Transceiver
~10 MHz
“Pluck” proton
spins
xyz gradient
~ 1 kHz
Localize
proton signal
RF heating
Nerve, muscle
and cardiac
stimulation
Particularly interesting implant
Pacemakers and MRI
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Concerns about sources of electromagnetic interference in
patients with pacemakers.
Safe performance of magnetic resonance imaging on five
patients with permanent cardiac pacemakers.
Loss prevention case of the month: not my responsibility!
Interference with cardiac pacemakers by magnetic resonance
imaging: are there irreversible changes at 0.5 tesla?
MR imaging and cardiac pacemakers: in vitro evaluation and in
vivo studies in 51 patients at 0.5 T.
Magnetic resonance imaging of the brain at 1.5 tesla in patients
with cardiac pacemakers: can it be done?
MRI in patients with cardiac pacemakers: in vitro and in vivo
evaluation at 0.5 tesla.
Magnetic resonance imaging and cardiac pacemaker safety at
1.5-Tesla
In vivo heating of pacemaker leads during magnetic resonance
imaging.
Research question

Most of the research has focused on problems
associated with RF fields.

Less research on switched gradient fields, and
even less on interaction with implants.

Will metal and plastic objects in the chest
increase the danger of switched gradient field
stimulation?

The physics…
Faraday’s Law
 
d  
 E  dl   dt  B  da

 
B
 E  
t
Induced electric field
Increasing
uniform B
Conducting
cylinder
(patient’s body)
 
d  
 E  dl   dt  B  da
dB 2
E 2r 
r
dt
r dB
E
2 dt
Eddy currents
Electric field
r dB
J  E  
2 dt
Conductivity
Current density
What’s going to happen?
Metal/plastic
object
Metal or plastic?
 Both
interesting
 Plastics not studied
 (plastics easier too)
Approach
 Develop
an analytical model based on
Faraday’s law to predict current densities
in the vicinity of a plastic implant.
 Compare
model to experiment and finite
element analysis.
Experimental model
Helmholtz coils
(MRI Z-coils)
60 Hz AC
Dish of physiologic saline
(patient)
Apparatus
Measurement system
Helmholtz
coils
Field probe
Saline
dish
Voltmeter
High impedance
amplifier
Shielded cable
to amplifier
Probe tips
Twisted
insulated wires
1.00 cm
“Implant” geometry?
 Pick
something easy to start with.
 Ideas?
Saline dish
?
Effect of plastic “implant”
+
+
+
Emag
Echg
Analytic model - approach
y
+
+
+

Find charge density of
accumulated charge

Use Coulomb’s law to
find Echg

Enet = Emag - Echg
P
x
Conservation of charge
Surface charge
density
d f
dt
Saline
conductivity

n
 J saline   Emag  Echg
Normal
component
At interface

i
yB0




( f   b ) 
cost 
( f   b )
2 dt 2 0
2
2 0
y dB
Free and bound
charge
Bound charge
Electric susceptibility
of water

b   0 Emag  E

n
chg i
 yB0


  0 
cost 
( f  b ) 
2 0
 2

Differential equation…
d f
2  yB0



cost 
f
dt
2   2
2 0



…and steady state solution
 f t   y 0B0 cost
Simplifying assumption
80
 (2   ) 0  
1.2 S/m
2 60 Hz
Coulomb’s Law
Echg 
1
4 0
L

L
W
W
f
y
 2
dydz
2
2
2
2
2 1/ 2
x  y  z (x  y  z )
L
B0 cost W
y2

dydz
3
2


2
2
2
W
4


x

y

z
L
y
z
P
x
Plastic
y
x
2L
2W
Echg
Echg

 L  L2  x 2  W 2  
W log


2
2
2

  L  L  x  W  
B0 cost



2



LW

 2 x arctan
2
2
2 
 x L  x  W 

Done!
Enet  Emag  Echg
x dB

 Echg
2 dt
x
 B0 cost  Echg
2
Compare to experiment…
Experiment
Electric Field (V/m)
0.025
0.02
0.015
0.01
0.005
0
0
0.01
0.02
0.03
Position (m)
Not done…
0.04
0.05
What’s wrong?
 Math
OK
 Approximations OK
 Input parameters OK
Saline-air interface
++ + +
+
plastic
+ ++ + +
Side view
+
+
+
+
+
+
Saline-dish bottom interface
A fix
 Use
a deep beaker instead of a dish.
Suspended from fishing line
plastic
These interfaces far away
from measurement region
Theory and experiment
Electric Field (V/m)
0.025
Beaker of Saline
0.02
0.015
0.01
0.005
Experimental
Analytical
0
0
0.01
0.02
0.03
Position (m)
0.04
0.05
Another fix
 Let
W go to infinity in the model
L
Echg
B0 cos t
y

dydz
3
2


2
2
2
W
4


x

y

z
L
W
Plastic
2L
2
2W
Theory and experiment
0.025
Electric Field (V/m)
Dish of Saline
0.02
0.015
0.01
Experimental
0.005
Analytic Model
0
0
0.01
0.02
0.03
Position (m)
0.04
0.05
Generalizing the geometry
Enet  Emag  Echg 
y
x
 B0 cost  Echg
2
L2

L1
x dB
 Echg
2 dt
P
where
x
Echg
B0 cost


2





L2  L1 x sin  2
 cos 
2 x arctan
2
 L1 L2  x  L2  L1 x cos 2 


 2L  L sin  2

2
1


2
2


 L2  x  2 L2 x cos 2 
 sin 
 x log 2

2


L

x

2
L
x
cos

2
1
 1



Theory and experiment
0.025
 = 90 deg
 = 45 deg
0.02
Electric Field (V/m)
0.02
0.015
0.01
0.005
0.015
0.01
0.005
Experimental
Experimental
Analytical
Analytical
0
0
0
0.01
0.02
0.03
0.04
0
0.05
0.01
0.02
0.03
Position (m)
Position (m)
0.025
 = 15 deg
0.02
Electric Field (V/m)
Electric Field (V/m)
0.025
0.015
0.01
0.005
Experimental
Analytical
0
0
0.01
0.02
0.03
Position (m)
0.04
0.05
0.04
0.05
What we know so far

Plastics can significantly
alter eddy current patterns

Basic effect: eddy currents
are forced to flow around
the plastic

Effect can be understood as
result of charge
accumulation at interfaces
Clinical significance
 Plastics
might redirect eddy currents
toward sensitive tissues
Heart
Torso
Future work
 Metal
implants
 More realistic geometries
 More realistic B(t)