Analysis of the Fenton–Karma model through an approximation by a one-dimensional map

Tolkacheva, Elena G.; Schaeffer, David G.; Gauthier, Daniel J.; Mitchell, Colleen

doi:10.1063/1.1515170

Cited by 40 publications

(32 citation statements)

References 18 publications

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“…Both formulas (20) and (23) require that we know formulas for the dynamic velocity RC (since G * = c (20) and (23) show that c (20) and (23) reinforce our main point: APD restitution, not memory, is responsible for velocity rate-dependence. Regardless of how much memory is included in the mapping model, Eqs.…”

Section: B S1-s2 Pacing Protocolmentioning

confidence: 60%

“…Consequently, we use two different ionic models in our numerical simulations: a two-current ionic model [18] with no memory and a three-current ionic model [20] with some memory.…”

Section: Rate-dependent Velocity: Numerical Resultsmentioning

confidence: 99%

“…Combining Eqs. (20) and (A.9), we generate all S1-S2 wavefront velocity RCs. Likewise, combining Eqs.…”

Section: B S1-s2 Pacing Protocolmentioning

confidence: 99%

“…Figure 1a is generated using a two-current model [17,18] with no memory: the dynamic and S1-S2 RCs are indistinguishable. Figure 1 is generated using a three-current ionic model [19,20] with some memory. One can see from Fig.…”

Section: Introductionmentioning

confidence: 99%

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Rate-dependent propagation of cardiac action potentials in a one-dimensional fiber

et al. 2004

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Action potential duration (APD) restitution, which relates APD to the preceding diastolic interval (DI), is a useful tool for predicting the onset of abnormal cardiac rhythms. However, it is known that different pacing protocols lead to different APD restitution curves (RCs). This phenomenon, known as APD rate-dependence, is a consequence of memory in the tissue. In addition to APD restitution, conduction velocity restitution also plays an important role in the spatiotemporal dynamics of cardiac tissue. We present new results concerning rate-dependent restitution in the velocity of propagating action potentials in a one-dimensional fiber. Our numerical simulations show that, independent of the amount of memory in the tissue, waveback velocity exhibits pronounced rate-dependence and the wavefront velocity does not. Moreover, the discrepancy between waveback velocity RCs is most significant for small DI. We provide an analytical explanation of these results, using a system of coupled maps to relate the wavefront and waveback velocities. Our calculations show that waveback velocity rate-dependence is due to APD restitution, not memory.

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Section: B S1-s2 Pacing Protocolmentioning

confidence: 60%

“…Consequently, we use two different ionic models in our numerical simulations: a two-current ionic model [18] with no memory and a three-current ionic model [20] with some memory.…”

Section: Rate-dependent Velocity: Numerical Resultsmentioning

confidence: 99%

“…Combining Eqs. (20) and (A.9), we generate all S1-S2 wavefront velocity RCs. Likewise, combining Eqs.…”

Section: B S1-s2 Pacing Protocolmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Rate-dependent propagation of cardiac action potentials in a one-dimensional fiber

et al. 2004

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“…Like in the sheep experiment, eight paces were delivered at each BCL. Because FKCRN has only a limited memory, 24 this is sufficient to bring APD near steady state and determine the response type, while keeping computation time within reasonable limits. Eight paces may not be sufficient if a BCL falls very close to a bifurcation point, where transients are much longer.…”

Section: Pacing Protocolsmentioning

confidence: 99%

Bistability and Correlation with Arrhythmogenesis in a Model of the Right Atrium

2005

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Abstract-Rapid pacing is an important tool for understanding cardiac arrhythmias. A recent experiment involving rapid pacing of sheep atria indicated that the initiation of atrial arrhythmias may be related to the 1:1/2:1 bistability. To elucidate the mechanism of this relation, this study applied the pacing protocol from the sheep study to an idealized model of the right atrium. The model included all major anatomical features, the sino-atrial node, and the regional differences in the action potential duration (APD). A pacing protocol was applied, in which the basic cycle length (BCL) was decreased in steps of 10 ms until the response switched to 2:1, then BCL was increased. The 1:1-to-2:1 transitions occurred at shorter BCLs than the 2:1-to-1:1 transitions yielding a global bistability window of 60 ms. As in the sheep study, idiopathic waves were observed at BCLs within or near the bistability window. The model was used to quantify the types, prevalence, and persistence of idiopatic waves, study their initiation and termination, and relate them to the model components. The results demonstrate that idiopatic waveforms move with the shift of the bistability window and that they disappear when bistability is eliminated. Thus, this modeling study supports causal relationship between the 1:1/2:1 bistability and the initiation of arrhythmias.

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Anatomy of the Cardiovascular Apparatus

Thiriet

2013

Biomathematical and Biomechanical Modeling of the Circulatory and Ventilatory Systems

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Analysis of the Fenton–Karma model through an approximation by a one-dimensional map

Cited by 40 publications

References 18 publications

Rate-dependent propagation of cardiac action potentials in a one-dimensional fiber

Rate-dependent propagation of cardiac action potentials in a one-dimensional fiber

Bistability and Correlation with Arrhythmogenesis in a Model of the Right Atrium

Anatomy of the Cardiovascular Apparatus

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