Research Interests

My research focuses on bioelectric phenomena, such as the electrical activity of nerve and muscle. A particular interest of mine is electrical stimulation of the heart. Electric fields can cause the heart to contract, and can even induce abnormal behavior such as cardiac arrhythmias and fibrillation. Moreover, strong electrical shocks can stop abnormal and potentially fatal electrical behavior (a process called "defibrillation"). My goal is to understand the fundamental physics that underlies electrical stimulation and defibrillation of the heart. For a non technical description of my research, see the article "Shocking Rhythms" in the January 27, 1996 issue of Science News.

I use the "bidomain model" to study cardiac tissue. The bidomain model is a mathematical model that determines the electrical potential inside and outside heart cells. One important feature of cardiac tissue is that it is anisotropic: the electrical conductivity depends on direction. What makes cardiac tissue different than other anisotropic materials is that it has two conductivities: one for the space inside of the cells, and one for the space outside. Both spaces are anisotropic, but not to the same degree: the space inside cells is strongly anisotropic, while the space outside cells is weakly anisotropic. This difference in anisotropy results in a wide variety of interesting behavior. For instance, when electrical current is injected into the heart through a small electrode, the change in transmembrane potential (the difference in potential between the inside and outside of the cells) does not fall off smoothly with distance from the electrode, but instead has a complex distribution with regions of both depolarization (positive transmembrane potential) and hyperpolarization (negative transmembrane potential). These regions of depolarization and hyperpolarization result in four different mechanisms for electrical excitation. Which mechanism excites the heart depends on the polarity of the current, the duration of the current pulse, and the timing of the pulse. The strength-interval curve for cardiac tissue (the minimum current that can excite the heart as a function of the time between the current pulse and the previous heartbeat) has a complex shape which has been measured for decades but was never understood. I have predicted the shape of the strength-interval curve using the bidomain model, and found good agreement between my predictions and experimental observations. I have also predicted that if cardiac tissue is stimulated twice through a single electrode, the heart may beat many times because an arrhythmia is induced. Drs. John Wikswo and Marc Lin of Vanderbilt University recently verified this prediction experimentally. I have only described a few of the interesting predictions of the bidomain model. For a more detailed review, see the paper I published with John Wikswo in the Proceedings of the IEEE (vol. 84, pp. 379-391, 1996).

The bidomain model consists of two coupled, nonlinear partial differential equations. Although a few analytical solutions to these equations have been found, in general the equations must be solved numerically. In my research, I simulate what happens in cardiac tissue using numerical calculations. Many of these simulations require high-power computers and new algorithms. Therefore, the tools I use in my research are those of "Computational Physics".

Recent Publications

Hildebrandt, M. C. and B. J. Roth, 2001, A simulation of protective zones during quatrefoil reentry in cardiac tissue. J. Cardiovasc. Electrophysiol., 12:1062-1067.

Patel, S. G. and B. J. Roth, 2001, How epicardial electrodes influence the transmembrane potential during a strong shock. Annals Biomed. Eng., 29:1028-1031.

Janks, D. and B. J. Roth, 2002, Averaging over depth during optical mapping of unipolar stimulation. IEEE Trans. Biomed. Eng., 49:1051-1054.

Roth, B. J., 2002, Artifacts, assumptions, and ambiguity: Pitfalls in comparing experimental results to numerical simulations when studying electrical stimulation of the heart. Chaos, 12:973-981.

Murdick, R. and B. J. Roth, 2003, Magneto-encephalogram artifacts caused by electro-encephalogram electrodes. Med. & Biol. Eng. & Comput.,41:203-205.

Roth, B. J. and D. Langrill Beaudoin, 2003, Approximate analytical solutions of the bidomain equations for electrical stimulation of cardiac tissue with curving fibers. Phys. Rev. E, 67:051925.

Roth, B. J. and S. G. Patel, 2003, Effects of elevated extracelllar potassium ion concentration on anodal excitation of cardiac tissue. J. Cardiovasc. Electrophysiol., 14:1351-1355.

Roth, B. J.,  2004,  Art Winfree and the bidomain model of cardiac tissue. J. Theor. Biol., 230:445-449.

Murdick, R. A. and B. J. Roth,  2004,  A comparative model of two mechanisms from which a magnetic field arises in the heart. J. Appl. Phys., 95:5116-5122.

Liau. J., J. Dumas, D. Janks, B. J. Roth, and S. B. Knisley, 2004,  Cardiac optical mapping under a translucent stimulation electrode.  Ann. Biomed. Eng., 32:1202-1210.

Langrill Beaudoin, D. and B. J. Roth,  2004,  Effect of plunge electrodes in active cardiac tissue with curving fibers.  Heart Rhythm, 1:476-481.

Patel, S. G. and B. J. Roth,  2005,  Approximate solution to the bidomain equations for defibrillation problems.  Phys. Rev. E,  71: 021908.

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