Head-tail interactions in numerical simulations of reentry in a ring of cardiac tissue  Xiaozhong Chen, MS, Flavio H. Fenton, PhD, Richard A. Gray, PhD  Heart Rhythm  Volume 2, Issue 9, Pages 1038-1046 (September 2005) DOI: 10.1016/j.hrthm.2005.08.015 Copyright © 2005 Heart Rhythm Society Terms and Conditions

Figure 1 A: Temporal traces of the variables u, v, and w during an action potential. B: Standard action potential duration (APD) restitution curves of model 3 (M3), cytochalasin-D (CYTO), and diacetyl monoxime (DAM) models. C: Conduction velocity (CV) restitution curves of M3, CYTO, and DAM models. D: Wavelength curves of M3, CYTO, and DAM models. Heart Rhythm 2005 2, 1038-1046DOI: (10.1016/j.hrthm.2005.08.015) Copyright © 2005 Heart Rhythm Society Terms and Conditions

Figure 2 Diastolic interval (DI) range [amplitude of spatial DI profile of each beat] dynamics of diacetyl monoxime (DAM), cytochalasin-D (CYTO), and model 3 (M3). (DI range of the first beat of each length was relatively bigger compared with other beats because of the cut-induced disturbance. These beats were excluded from these figures to display the dynamic more clearly). Note different scales on the abscissa. Heart Rhythm 2005 2, 1038-1046DOI: (10.1016/j.hrthm.2005.08.015) Copyright © 2005 Heart Rhythm Society Terms and Conditions

Figure 3 A: Spatial profiles of diastolic interval (DI) of 10 continuous beats in 7-cm ring of all three models. B: Action potential duration (APD) restitution and the wavelength of APD restitution in two continuous beat in 7-cm ring of all three models. C: Conduction velocity (CV) restitution curves of beat 9 and 10 of 7-cm ring of all three models. CYTO = cytochalasin-D; DAM = diacetyl monoxime; M3 = model 3. Heart Rhythm 2005 2, 1038-1046DOI: (10.1016/j.hrthm.2005.08.015) Copyright © 2005 Heart Rhythm Society Terms and Conditions

Figure 4 Action potential duration (APD) vs vd and wd contour of diacetyl monoxime (DAM) (A), cytochalasin-D (CYTO) (B), and model 3 (M3) (C). Both vd and wd were systematically changed to obtain all possible combinations and corresponding APDs. See text for details. Heart Rhythm 2005 2, 1038-1046DOI: (10.1016/j.hrthm.2005.08.015) Copyright © 2005 Heart Rhythm Society Terms and Conditions

Figure 5 A: Multivalued diastolic interval (DI) vs. w relationship of beat 4 of 7-cm cytochalasin-D (CYTO). This is responsible for the multivalued action potential duration (APD) vs. DI relationship because w controls APD. B: The temporal traces of u and w of two points that have the same DI of 23 ms. At point 183, w starts from 0.53 and ends at 0.68 after 23 ms. At point 575, w value starts from 0.57 and ends at 0.71 after 23 ms. The same DI period with different initial value of w caused a different value of w at the time of next depolarization and resulted in different APD. C: Multivalued DI vs v relationship of beat 4 of 7-cm CYTO. This is responsible for the multivalued CV vs DI relationship because v controls CV. D: Temporal traces of u and v of two points that have the same DI of 23 ms. Point 575 spends less time in the slow region (Uv < u < Uc) and stays in the fast region (u < Uv) longer (8.6 ms) compared with point 183 (6 ms). This results in the bigger value of v at the time of depolarization and thus the bigger CV for the same preceding DI and explains the multivalued CV restitution. Heart Rhythm 2005 2, 1038-1046DOI: (10.1016/j.hrthm.2005.08.015) Copyright © 2005 Heart Rhythm Society Terms and Conditions

Figure 6 A: Spatial profiles of conduction velocity (CV) and v of a normal beat and the corresponding reset (without decoupling) beat. The reset beat has more oscillations with larger amplitudes. B: Action potential duration (APD) restitution curve of the reset beat (without decoupling) (beat 4 of 7-cm cytochalasin-D). Heart Rhythm 2005 2, 1038-1046DOI: (10.1016/j.hrthm.2005.08.015) Copyright © 2005 Heart Rhythm Society Terms and Conditions

Figure 7 A: Action potential duration (APD) restitution curves of a normal beat and the corresponding decoupled beat (beat 4 of 7-cm cytochalasin-D). The bigger distance between branches of the decoupled beat (no diffusion current) indicates diffusion current works against the branching effect. B: APD spatial profile of a normal beat and the corresponding decoupled beat (beat 4 of 7-cm cytochalasin-D). The profile of the normal beat is relatively smoother than the decoupled beat. This indicates diffusion current homogenizes the spatial APD distribution. Heart Rhythm 2005 2, 1038-1046DOI: (10.1016/j.hrthm.2005.08.015) Copyright © 2005 Heart Rhythm Society Terms and Conditions

Figure 8 A: Action potential duration (APD) restitution curves of 7-cm model 3 (M3), cytochalasin-D (CYTO), and diacetyl monoxime (DAM) ring. B: APD sensitivity to wd of 7-cm M3, CYTO, and DAM ring. C: wd sensitivity to diastolic interval (DI) of 7-cm M3, CYTO, and DAM ring. Heart Rhythm 2005 2, 1038-1046DOI: (10.1016/j.hrthm.2005.08.015) Copyright © 2005 Heart Rhythm Society Terms and Conditions