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Vulnerability to re-entry in simulated two-dimensional cardiac tissue: Effects of electrical restitution and stimulation sequence
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10.1063/1.2784387
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    Affiliations:
    1 Cardiovascular Research Laboratories, Department of Physiological Science, and Department of Molecular, Cellular, and Integrative Physiology, David Geffen School of Medicine at UCLA, University of California, Los Angeles, California 90095, USA
    2 Cardiovascular Research Laboratories and Department of Physiological Science, David Geffen School of Medicine at UCLA, University of California, Los Angeles, California 90095, USA
    3 Cardiovascular Research Laboratories, Department of Medicine (Cardiology), and Department of Physiology, David Geffen School of Medicine at UCLA, University of California, Los Angeles, California 90095, USA
    4 Cardiovascular Research Laboratories, Department of Medicine (Cardiology), and Department of Physiological Science, David Geffen School of Medicine at UCLA, University of California, Los Angeles, California 90095, USA
    5 Cardiovascular Research Laboratories and Department of Medicine (Cardiology), David Geffen School of Medicine at UCLA, University of California, Los Angeles, California 90095, USA
    a) Author to whom correspondence should be addressed. Telephone: 310-794-6050. FAX: 310-206-9133. Electronic mail: zqu@mednet.ucla.edu
    Chaos 17, 043115 (2007); http://dx.doi.org/10.1063/1.2784387
/content/aip/journal/chaos/17/4/10.1063/1.2784387
http://aip.metastore.ingenta.com/content/aip/journal/chaos/17/4/10.1063/1.2784387
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

APD and CV restitution curves. (a) The APD restitution curves for control (square), shallow slope (circles), and steep slope (triangle). Control parameters were stated in Methods with . For shallower, , , the time constants of the and gates are sped up 2.8 times, i.e., , and . For steeper, , , and , where and are gating variables of the slow inward current, . (b) Control (square) and broadened (circle) CV restitution curves. Broadening of CV restitution is achieved by slowing the gate of the channel fivefold, i.e., . Slowing of the recovery of the channel was observed in cells from ischemic tissue (Refs. 75 and 76 ).

Image of FIG. 2.
FIG. 2.

Vulnerability to re-entry in heterogeneous tissue. (a) The vulnerable period of S1S2 intervals for different radius of the heterogeneous region with . Region 1: S2 propagates successfully throughout the tissue without block. Region 2: localized block occurs to S2 but no re-entry is formed. Region 3: localized block of S2 resulting in figure-of-eight re-entry. Region 4: S2 fails to elicit a propagating wave. (b) The vulnerable period of the S1S2 intervals for different . To modify , in the heterogeneous area is varied from to . Regions 1–4 have the same behaviors as in the corresponding regions in A. Regions 5 and 6: localized conduction block occurs to S2 but no re-entry forms. (c) Voltage snapshots showing initiation of re-entry by the S2 extrasystole, for , , and . (d) Voltage snapshots showing tip collision due to tip-tip interaction when the circular heterogeneous area is too small or is too large, , , and . (e) Voltage snapshots showing tip collision due to tip-tip interaction when is too long. , , and . (f) Voltage snapshots showing wave front-wave back interaction. , , and . is the time interval between S1 and S2. Both S1 and S2 were applied at the lower-left corner of the tissue. The gray scale for the voltage snapshots is from as shown on the right, and was used for other figures in this paper. The time above each panel is the time after the beginning of the last S1 stimulation, and the same for other figures.

Image of FIG. 3.
FIG. 3.

Role of symmetry. (a) Asymmetric heterogeneity with its boundary generated by an absolute sinusoidal function on top of a semicircle with a radius of . Shown are voltage snapshots for (re-entry), (tip-tip), and (front-back). (b) Asymmetric stimulation protocol by making S1 a planar wave from the left edge of the tissue with S2 from the lower-left corner. Shown are voltage snapshots for (re-entry), (tip-tip), and (front-back). For both a and b, the bottom panel is a snapshot of an S1 beat and was used for the heterogeneous region.

Image of FIG. 4.
FIG. 4.

Role APD restitution in wave front-wave back interactions. (a) APD from the center (open square) and outside (filled square) of the circular heterogeneous area with as was changed. (b) The maximum slope of the APD restitution curves from inside and outside of the heterogeneity. (c) Bar graph shows the S1S2 intervals at which re-entry (black) occurs or does not occur due to tip fusion (gray) or wave front-wave back interactions (striped). Failure of S2 to propagate is in white. Target wave propagation (without re-entry) occurs above the wave front-wave back interaction area. (d) APD distributions for the S1 beat for (solid line) and (dashed line) along the diagonal of the tissue [dotted line in Fig. 3(f) ]. and . (e) Same as D but for the S2 beat. S2 is blocked at the heterogeneity (arrow), so that APD is zero from that point onwards. (f) A snapshot illustrating S2 wave block and re-entry. In the case of steep APD restitution slope, the APD gradient from the S1 beat was too steep, causing wave front-wave back interactions (double lines). For shallow APD restitution, however, the APD gradient was smaller, and allowed the S2 to propagate through the central common pathway and initiate re-entry (not shown).

Image of FIG. 5.
FIG. 5.

Vulnerable window vs location of the S2 extrastimulus in heterogeneous tissue. S1 was given at the lower left corner of the tissue, while the pacing location of S2 was moved along the diagonal of the tissue. (a) . (b) . Region 1: S2 propagates successfully throughout the tissue without block. Region 2: localized block occurs to S2 but no re-entry is formed. Region 3: localized block of S2 resulting in figure-of-eight re-entry. Region 4: S2 fails to elicit a propagating wave. The gray bars indicate the heterogeneous regions along the diagonal line.

Image of FIG. 6.
FIG. 6.

Induction of re-entry by the S1S2S3 protocol in homogenous tissue. (a) Voltage snapshots showing unidirectional conduction block induced by the S1S2S3 protocol in which S1 is applied at the lower-left corner and S2 and S3 are applied at the center of the tissue. (b) Voltage snapshots showing initiation of re-entry. (c) Voltage snapshots showing tip fusion. (d) and (e) The vulnerable window in the S1S2 interval ( -axis) and S2S3 interval ( -axis) parameter space with control CV restitution (d) and broad CV restitution (e). For a and c, and , and for B, and . Region 1: S3 propagates successfully throughout the tissue without block. Region 2: localized block occurs to S3 but no re-entry is formed. Region 3: localized block of S3 resulting in figure-of-eight re-entry. Region 4: S3 fails to elicit a propagating wave. Region 5: S2 fails to elicit a propagating wave.

Image of FIG. 7.
FIG. 7.

Voltage snapshots for the S1S2S3 protocol in homogenous tissue with flat APD restitution slope. and .

Image of FIG. 8.
FIG. 8.

Induction of re-entry by the S1S2S3 protocol in homogenous tissue with steep APD restitution slope. (a) The vulnerability window of re-entry (black). Labels are the same as in Figs. 6(d) and 6(e) . (b) Voltage snapshots showing re-entry. and . (c) Voltage snapshots showing tip fusion. and .

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/content/aip/journal/chaos/17/4/10.1063/1.2784387
2007-11-15
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Vulnerability to re-entry in simulated two-dimensional cardiac tissue: Effects of electrical restitution and stimulation sequence
http://aip.metastore.ingenta.com/content/aip/journal/chaos/17/4/10.1063/1.2784387
10.1063/1.2784387
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