The Effects of Spiral Anisotropy on the Electric Potential and the Magnetic Field at the Apex of the Heart

The Effects of Spiral Anisotropy on the Electric Potential and the Magnetic Field at the Apex of the Heart.

B. J. Roth, W.-Q. Guo, and J. P. Wikswo, Jr.

Living State Physics Group, Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235

This paper describes a volume-conductor model of the apex of the heart that accounts for the spiraling tissue geometry. Analytic expressions are derived for the potential and magnetic field produced by a cardiac action potential propagating outward from the apex. The model predicts the existence of new information in the magnetic field that is not present in the electrical potential.

The apex of the heart.
From Mall, F. P. (1911) “On the Muscular Architecture of the Ventricles of the Human Heart.”
American Journal of Anatomy, Volume 11, Pages 211–266.
The geometry of a slab of cardiac tissue. The thickness of the tissue is l, the conductivity of the saline bath is σe, and the conductivity tensors of the intracellular and interstitial volumes are σ̃i and σ̃o. The variables ρ, θ, and z are the cylindrical coordinates, and the red curves represent the fiber direction. Based on Fig. 2 of Roth et al. (1988).
The current (blue) and magnetic field (green) created by an action potential propagating outward from the apex of the heart if no off-diagonal terms are present in the conductivity tensors. Based on Fig. 5a of Roth et al. (1988).
The azimuthal component of the current (blue) and the electrically silent components of the magnetic field (green) produced by off-diagonal terms in the conductivity tensor, with σe = 0. Based on Fig. 5b of Roth et al. (1988).
The total magnetic field at the apex of the heart. This figure is only qualitatively correct; the field lines may not be quantitatively accurate. Based on Fig. 5e of Roth et al. (1988).

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