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 Dr. Sue Kaste (St. Jude), Dr. Kendall Waters (NIST) Dr. Sue Kaste (St. Jude), Dr. Kendall Waters (NIST) Students: Andy Whitten, Julie Javarone, Chad Jones, Garney Caldwell, Jeff France, John Janeski, David Johnson Students: Andy Whitten, Julie Javarone, Chad Jones, Garney Caldwell, Jeff France, John Janeski, David Johnson  Ultrasound therapy for osteoarthritis Dr. Karen Hasty (U. Tennessee) Dr. Karen Hasty (U. Tennessee)  Ultrasonic imaging of cardiac electrical stimulation Dr. Bob Malkin (Duke), Amy Curry (U. Memphis) Dr. Bob Malkin (Duke), Amy Curry (U. Memphis) Students: Steve Smith, Will McKinney, Stu Johnston, Erin Sylvester, John Sexton, Chip Hartigan, Taylor Whaley Students: Steve Smith, Will McKinney, Stu Johnston, Erin Sylvester, John Sexton, Chip Hartigan, Taylor Whaley  Magnetic Stimulation Dr. Bob Malkin (Duke) Dr. Bob Malkin (Duke) Student: Drew Shores Student: Drew Shores

Magnetic stimulation  Problem MRI scans expose patients to time varying magnetic fields MRI scans expose patients to time varying magnetic fields Faraday’s Law - time varying magnetic fields induce electrical “eddy” currents Faraday’s Law - time varying magnetic fields induce electrical “eddy” currents Induced currents can cause muscle contraction, nerve stimulation, magnetophosphenes, cardiac arrhythmias Induced currents can cause muscle contraction, nerve stimulation, magnetophosphenes, cardiac arrhythmias Effect of medical implants unknown Effect of medical implants unknown  Goal Model how implants affect magnetically induced currents in the body 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) FunctionBioeffect Main0 Align proton spins ? Transceiver ~10 MHz “Pluck” proton spins RF heating xyz gradient ~ 1 kHz Localize proton signal Nerve, muscle and cardiac stimulation

Particularly interesting implant

Pacemakers and MRI  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

Induced electric field Conducting cylinder (patient’s body) Increasing uniform B

Eddy currents Current density Conductivity Electric field

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) Dish of physiologic saline (patient) 60 Hz AC

Apparatus

Measurement system Saline dish High impedance amplifier Helmholtz coils Voltmeter Field probe 1.00 cm Twisted insulated wires Probe tips Shielded cable to amplifier

“Implant” geometry?  Pick something easy to start with.  Ideas? ? Saline dish

Effect of plastic “implant” E mag E chg

Analytic model - approach  Find charge density of accumulated charge  Use Coulomb’s law to find E chg  E net = E mag - E chg x y P

Conservation of charge Surface charge density Free and bound charge Normal component At interfaceSaline conductivity

Bound charge Electric susceptibility of water

Differential equation… …and steady state solution

Simplifying assumption 1.2 S/m 80 2  60 Hz

Coulomb’s Law 2W 2L Plastic y z x x y P

E chg

Done! Compare to experiment…

Experiment Not done…

plastic ++++ Side view Saline-air interface Saline-dish bottom interface What’s wrong?  Math OK  Approximations OK  Input parameters OK

A fix  Use a deep beaker instead of a dish. plastic Suspended from fishing line These interfaces far away from measurement region

Theory and experiment Beaker of Saline

Another fix 2W 2L Plastic  Let W go to infinity in the model

Theory and experiment Dish of Saline

Generalizing the geometry x y P  L1L1 L2L2 where

Theory and experiment  = 90 deg  = 45 deg  = 15 deg

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 Torso Heart

Future work  Metal implants  More realistic geometries  More realistic B(t)