The Lorentz force (the force acting on currents in a magnetic field) plays an increasingly larger role in techniques to image current and conductivity. This review will summarize several applications involving the Lorentz force, including (1) magneto-acoustic imaging of current; (2) “Hall effect” imaging; (3) ultrasonically-induced Lorentz force imaging of conductivity; (4) magneto-acoustic tomography with magnetic induction; and (5) Lorentz force imaging of action currents using magnetic resonance imaging.The review was easy to write, because it consisted primarily of the background and significance section of a National Institutes of Health grant proposal I wrote several years ago (and which is now funded). The review describes ground-breaking work by many authors, but here I want to highlight studies by three talented undergraduate students who worked with me at Oakland University during several summers.
Kaytlin Brinker
Kayt studied a method to measure conductivity called Magneto-Acoustic Tomography with Magnetic Induction, or MAT-MI (Brinker and Roth, “The Effect of Electrical Anisotropy During Magnetoacoustic Tomography with Magnetic Induction,” IEEE Transactions on Biomedical Engineering, Volume 55, Pages1637–1639, 2008). This technique was developed by Bin He and his group at the University of Minnesota. You apply two magnetic fields, one static and one changing with time. The rapidly changing magnetic field induces eddy currents in the tissue, which then experience a Lorentz force from the static field, causing the material to move and initiating a sound wave. Measurement of the acoustic signal allows you to gain information about the conductivity distribution. Kayt’s task was to determine how anisotropy (the conductivity depends on direction) would influence MAT-MI. She “found that when imaging nerve or muscle, electrical anisotropy can have a significant effect on the acoustic signal and must be accounted for in order to obtain accurate images.”Nancy Tseng
Nancy, who had just graduated from high school when she worked with me, analyzed a technique originally pioneered by Han Wen and then developed further by Amalric Montalibet. A sound wave is propagated through the tissue in the presence of a magnetic field. The Lorentz force causes charge separation, inducing an electrical potential and current. Measurement of the electrical signal provides information about the conductivity. Tseng looked at this effect in anisotropic tissue (Tseng and Roth, “The Potential Induced in Anisotropic Tissue by the Ultrasonically-Induced Lorentz Force,” Medical and Biological Engineering and Computing, Volume 46, Pages 195–197, 2008). She found “a novel feature of the ultrasonically-induced Lorentz force in anisotropic tissue: an oscillating electrical potential propagates along with the ultrasonic wave.” The effect has not yet been measured experimentally, but represents a fundamentally new mechanism for the induction of bioelectric signals.Kevin Schalte
Kevin derived a tomographic method to determine tissue conductivity using the ultrasonically-induced Lorentz force (Roth and Schalte, “ Ultrasonically-Induced Lorentz Force Tomography,” Medical and Biological Engineering and Computing, Volume 47, Pages 573-577, 2009). “The strength and timing of the electric dipole caused by the ultrasonically-induced Lorentz force determines the amplitude and phase of the Fourier transform of the conductivity image. Electrical measurements at a variety of [ultrasonic] wavelengths and directions are therefore equivalent to mapping the Fourier transform of the conductivity distribution in spatial frequency space. An image of the conductivity itself is then found by taking the inverse Fourier transform.” I would never have undertaken this project had I not been a coauthor on the 4th edition of Intermediate Physics for Medicine and Biology. Only by working on the textbook did I come to fully understand and appreciate the power of tomography (see Chapter 12 on Images and Section 16.9 about Computed Tomography).I often read about how the United States is falling behind other nations in math and science, but working with outstanding undergraduates such as these three gives me confidence that we remain competitive.
Finally, let me reproduce the all-important acknowledgments section of the minireview:
I thank Steffan Puwal and Katherine Roth [my daughter] for their comments on this manuscript. I also thank Bruce Towe, Han Wen, Amalric Montalibet and Xu Li for permission to reproduce their figures in this review. This work was supported by the National Institutes of Health grant R01EB008421.
Oakland University, because of the Professors there, has such a unique blend of so many different pieces or building blocks to expand upon. I have new problems today, and out of the blue you remind me - sending me back to the fundamental basics. I really miss all of the great conversations that took place every single day at OU. I can never leave my physics books. There is just so much work to do.
ReplyDelete