MOM 2006 journal for pdf.pmd - University of Michigan-Flint

Results
Figure 2 shows phase plane plots (Φ m
versus ∂Φ m
/∂t) of the action potential at the locations
marked “a”, “b”, and “c” in Fig. 1. The maximum rate of change is different between the upper
(“c”, 287 V/s) and lower (“a”, 267 V/s) edges. The time constant of the foot of the action
potential, τ foot
, can be found by fitting the initial rise (from -79 to -69 mV) of the action potential
to an exponential. In a phase plane plot, an exponential increase appears as a straight line. The
foot of the action potential along the upper edge (“c”, 0.22 ms) is smaller than the time constant
along the lower edge (“a”, 0.29 ms).
The results depend on the conductivities of the cardiac tissue. When the conductivities were
adjusted so the tissue had equal anisotropy ratios (σ iL
=0.2, σ eL
=0.2, σ iT
=0.032, and σ eT
=0.032
S/m), the differences between the two edges disappeared. The results also depend on the angle
that the fibers make with the boundary. Angles from 0 to 90° were simulated, with 75° showing
the most significant effect. Finally, the behavior is different between the upper and lower edges.
When a vector pointing from the sealed boundary into the tissue along the fibers makes an obtuse
angle with the direction of propagation (like on the top edge), the rate of rise of the action
potential is faster, and the time constant of the action potential foot is smaller, than when such a
vector makes an acute angle with the direction of propagation (like on the bottom edge).
Discussion
The rate of rise of the action potential, and the time constant of the action potential foot, are
sensitive to boundary effects. Previous studies (Roth, 1991; Roth, 2000) have shown that a
conducting bath perfusing the tissue surface can affect the action potential upstroke. This study
finds similar results for a sealed boundary with fibers approaching the surface at an angle. The
effect disappears when equal anisotropy ratios are present or when the fibers are parallel or
perpendicular to the surface. The changes in the action potential are not large, but may be
detectable in experiments using a “wedge preparation”, in which the heart wall has been cut and
the transmembrane potential is recorded on the cut surface (Akar and Rosenbaum, 2003; Fast et
al., 2002).
Acknowledgements
This research was supported by the National Institutes of Health (R01 HL57207) and the
SMaRT program an RED site at Oakland University funded by the National Science Foundation
under Grant No. DMR-0552779. We thank Andrew King for his comments and suggestions.
Meeting of Minds 2006 66