A Theoretical Model of Magneto-Acoustic Imaging of Bioelectric Currents

Twenty years ago, I became interested in magneto-acoustic imaging, primarily influenced by the work of Bruce Towe that was called to my attention by my dissertation advisor and collaborator John Wikswo. (See, for example, Towe and Islam, “A Magneto-Acoustic Method for the Noninvasive Measurement of Bioelectric Currents,” IEEE Trans. Biomed. Eng., Volume 35, Pages 892–894, 1988). The result was a paper by Wikswo, Peter Basser, and myself (“A Theoretical Model of Magneto-Acoustic Imaging of Bioelectric Currents,” IEEE Trans. Biomed. Eng., Volume 41, Pages 723–728, 1994). This was my first foray into biomechanics, a subject that has become increasingly interesting to me, to the point where now it is the primary focus of my research (but that’s another story; for a preview look here).

A Treatise on the Mathematical
Theory of Elasticity,
by A. E. H. Love.

I started learning about biomechanics mainly through my friend Peter Basser. We both worked at the National Institutes of Health in the early 1990s. Peter used continuum models in his research a lot, and owned a number of books on the subject. He also loved to travel, and would often use his leftover use-or-lose vacation days at the end of the year to take trips to exotic places like Kathmandu. When he was out of town on these adventures, he left me access to his personal library, and I spent many hours in his office reading classic references like Schlichting’s Boundary Layer Theory and Love’s A Treatise on the Mathematical Theory of Elasticity. Peter and I also would read each other’s papers, and I learned much continuum mechanics from his work. (NIH had a rule that someone had to sign a form saying they read and approved a paper before it could be submitted for publication, so I would give my papers to Peter to read and he would give his to me.) In this way, I became familiar enough with biomechanics to analyze magneto-acoustic imaging. Interestingly, we published our paper in the same year Basser began publishing his research on MRI diffusion tensor imaging, for which he is now famous (see here).

As with much of my research, our paper on magneto-acoustic imaging addressed a simple “toy model”: an electric dipole in the center of an elastic, conducting sphere exposed to a uniform magnetic field. We were able to calculate the tissue displacement and pressure analytically for the cases of a magnetic field parallel and perpendicular to the dipole. One of my favorite results in the paper was that we found a close relationship between magneto-acoustic imaging and biomagnetism.

“Magneto-acoustic pressure recordings and biomagnetic measurements image action currents in an equivalent way: they both have curl J [the curl of the current density] as their source.”

For about ten years, our paper had little impact. A few people cited it, including Amalric Montalibet and later Han Wen, who each developed a method to use ultrasound and the Lorentz force to generate electrical current in tissue. I’ve described this work before in a review article about the role of magnetic forces in medicine and biology, which I have mentioned before in this blog. Then, in 2005 Bin He began citing our work in a long list of papers about magnetoacoustic tomography with magnetic induction, which again I've written about previously. His work generated so much interest in our paper that in 2010 alone it was cited 19 times according to Google Scholar. Of course, it is gratifying to see your work have an impact.

But the story continues with a more recent study by Pol Grasland-Mongrain of INSERM in France. Building on Montalibet’s work, Grasland-Mongrain uses an ultrasonic pulse and the Lorentz force to induce a voltage that he can detect with electrodes. The resulting electrical data can then be analyzed to determine the distribution of electrical conductivity (see Ammari, Grasland-Mongrain, et al. for one way to do this mathematically). In many ways, their technique is in competition with Bin He’s MAT-MI as a method to image conductivity.

Grasland-Mongrain also publishes his own blog about medical imaging. (Warning: The website is in French, and I have to rely on Google Translate to read it. It is my experience that Google has a hard time translating technical writing). There he discusses his most recent paper about imaging shear waves using the Lorentz force. Interestingly, shear waves in tissue is one of the topics Russ Hobbie and I added to the 5th edition of Intermediate Physics for Medicine and Biology, due out next year. Grasland-Mongrain’s work has been highlighted in Physics World and Focus Physics, and a paper about it appeared this year in Physical Review Letters, the most prestigious of all physics journals (and one I’ve never published in, to my chagrin).

I am amazed by what can happen in twenty years.


As a postscript, let me add a plug for toy models. Russ and I use a lot of toy models in IPMB. Even though such simple models have their limitations, I believe they provide tremendous insight into physical phenomena. I recently reviewed a paper in which the authors had developed a very sophisticated and complex model of a phenomena, but examination of a toy model would have told them that the signal they calculated was far, far to small to be observable. Do the toy model first. Then, once you have the insight, make your model more complex.