Supporting Information

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Movie 1. Raw fluorescence from the surface of a pig heart during sustained VF. The duration of this movie is 2.5 s, and the acquisition rate was 250 frames per s; thus the movie is considerably slower than real time. The signals have been normalized such that the minimum value of each pixel over this interval corresponds to black and the maximum values for each pixel corresponds to white.

Movie 2. The same movie as in Movie 1 after a five-point median temporal filter followed by a 3 ´ 3 ´ 3 spatiotemporal boxcar filter. The data have also been masked by hand (a mask was created for each animal) to indicate the sites that were used in the analysis, e.g., the pixels recording from the atria and the pixels not focused on the heart were excluded.

Movie 3. The same data as in Movie 1 after the conversion to phase, i.e., this is a phase movie computed from the raw data.

Movie 4. The same data as in Movie 2 after the conversion to phase, i.e., this is a phase movie computed from the filtered data.

Fig. 7. Phase resetting from reconstructed state space. (Top) Transmembrane potential (Vm) action potentials from the Luo-Rudy dynamic (LRd) model (1-5), resulting from steady-state pacing at a cycle length of 350 ms. An action potential resulting from a premature stimulus is shown in gray. (Middle) Phase of signals in Top as computed from reconstructed state space, i.e., Eq. 1 with F₅₀ equal to the midpoint of Vm, -22.5 mV, and t = 3 ms (6). (Bottom) PRC generated from the data from Middle. Notice that the PRC for the premature beat (gray dots) falls on the same curve as the equally spaced beats. That is, while traditional PRCs (generated from time encoding of phase) describe the changes in the temporal sequence of a behavior (e.g., time of depolarizaton), PRCs generated from state-space encoding of phase indicate the changes in state space dynamics (see figure 1 in ref. 6). Thus a PRC generated from time encoding of phase is flat for no stimulus, a PRC generated from state-space encoding of phase is not (7). Therefore, stimulus induced changes in PRCs generated from state-space encoding of phase must be compared to that of no stimulus. For the experimental data in the article PRCs were qualitatively similar when D q was computed with values separated by 8-24 ms; clearly as this interval approached half a cycle (~45 ms) the range of D q was 2p (one cycle).

1. Luo, C. H. & Rudy, Y. (1994) Circ. Res. 74, 1071-1096.

2. Luo, C.-H. & Rudy, Y. (1994) Circ. Res. 74, 1097-1113.

3. Zeng, J., Laurita, K. R., Rosenbaum, D. S. & Rudy, Y. (1995) Circ. Res. 77, 140-152.

4. Viswanathan, P. C., Shaw, R. M. & Rudy, Y. (1999) Circulation 99, 2466-2474.

5. Faber, G. M. & Rudy, Y. (2000) Biophys. J. 78, 2392-2404.

6. Gray, R. A., Huelsing, D. J., Aguel, F. & Trayanova, N. A. (2001) J. Cardiovasc. Electrophysiol. 12, 1129-1137.

7. Oprisan, S. A., Thirumalai, V. & Canavier, C. C. (2003) Biophys. J. 84, 2919-2928.

Fig. 8. VF (state space dynamics of wave collison). (Upper) Isochrone map indicates the position of the wavefront every 8 ms during one beat. Arrows indicate the direction of propagation. (Lower) PRC generated from a 10 × 10 pixel region indicated by grid in the isochrone map. Fluorescence signals from this same region are plotted in reconstructed state space (numbers represent sequence and gray lines indicate the corresponding isochrone; dashed line indicates depolarization time).

Fig. 9. Effect of shock strength. (A) Amount of shock induced phase delay (D q > 0) for sites in early repolarization (+p /4 > q > -p /4) immediately preceding the shock (filled symbols). The amount of shock induced phase advance (D q < -p /2) for sites in late repolarization (-p /2 > q > -3p /4; open symbols). (B) Action potential duration (APD) changes resulting from the shocks. APD was computed as the time spent in the range +p /2 > q (t) > -p /2.(1) (C) Amount of shock induced excitation (F_end>F₅₀ and F_pre<F₅₀; filled symbols) and deexcitation (F_end<F₅₀ and F_pre>F₅₀; open symbols). All asterisks indicate statistical difference from preshock fraction (shown as datum for 0 V). Generally it has been thought that shocks act to depolarize heart tissue such that these mechanisms result from depolarization effects (e.g.,a critical mass of the heart must be depolarized for successful defibrillation). In fact, electric fields act to both depolarize and hyperpolarize heart tissue, and deexcitation (regenerative repolarizatiion) may also play a role in defibrillation.(2) These effects of defibrillation shocks are thought to increase with shock strength; therefore we relate our findings to these more traditional electrophysiological measures here. The defibrillation shocks acted to prolong recovery as quantified as an increase in action potential duration (APD) at all shock strengths compared to control (0 V) as shown in B. (C) Defibrillation shocks acted to increase the percentage of sites demonstrating excitation (F_end > F₅₀ and F_pre < F₅₀) and decrease the percentage of sites exhibiting deexcitation (F_end < F₅₀ and F_pre > F₅₀) as shock strength increased. It should be appreciated that we used a biphasic shock used clinically and monophasic shocks may result in more hyperpolarization, thus less APD prolongation and more dexcitation.

1. Chattipakorn, N., Banville, I., Gray, R. A. & Ideker, R. E. (2001) J. Am. College Cardiolog. 37, 135A.

2. Efimov, I. R., Gray, R. A. & Roth, B. J. (2000) J. Cardiovasc. Electrophysiol. 11, 339-353.

Fig. 10. PRCs during defibrillation (all sites). PRCs from every other episode (i.e., all even shock strengths). PRCs were generated as D q versus q _pre^, where D q = q _end – q _pre, where q _pre indicates the phase map immediately preceding the shock and q _end indicates the phase map at the end of the shock. Only every fourth point is plotted for clarity.