Topological Constraint on Scroll Wave Pinning

Pertsov, Arkady M.; Wellner, Marcel; Vinson, Michael; Jalife, José

doi:10.1103/physrevlett.84.2738

Cited by 52 publications

(43 citation statements)

References 10 publications

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“…The different experimental preparations may contribute to this difference. Modeling studies 40 have shown that the filament of the 3D scroll wave tends to attach to an external boundary, such as the cut edge of a ventricle wedge, which may increase the incidence of reentry observed on the boundary.…”

Section: Discussionmentioning

confidence: 99%

Intramural Foci During Long Duration Fibrillation in the Pig Ventricle

Huang

et al. 2008

Circulation Research

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Abstract-For more than 50 years, it has been assumed that ventricular fibrillation (VF) is maintained solely by reentry in the working myocardium. This hypothesis has never been tested by recording VF with electrodes spaced sufficiently close to map activation sequences in 3D. We recorded the first 10 minutes of electrically induced VF from the anterior left ventricular (LV) free wall near the insertion of the anterior papillary muscle in 6 pigs. A 3D transmural unipolar electrode array consisting of a 9ϫ9 array of needles with 2-mm spacing and 6 electrodes 2 mm apart on each needle was used for recordings. Automatic analyses were performed to recognize 3D reentry and foci. Our results showed that intramural reentry is present early but not late during VF in the mapped region. The incidence of reentry in working myocardium decreases almost to 0 after 3 minutes of VF. In contrast, intramural foci are present during early VF and, as VF continues, increase in incidence, so that by 10 minutes of VF, 27% of wavefronts arise from intramural foci. These results suggest that, particularly after the first 3 minutes of VF, mechanisms other than local reentry in the working myocardium maintain VF in the anterior LV free wall near the root of the anterior papillary muscle.

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Section: Discussionmentioning

confidence: 99%

Intramural Foci During Long Duration Fibrillation in the Pig Ventricle

Huang

et al. 2008

Circulation Research

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“…Today's developing technique of cardiac tissue transillumination (25,26) allows some visualization of the filament; its data should become more accurately interpretable with the help of the method described here, possibly combined with known topological constraints (27). In actual heart tissue, the fiber architecture can often be considered given (28).…”

Section: Discussionmentioning

confidence: 99%

Minimal principle for rotor filaments

Wellner

Berenfeld

Jalife

et al. 2002

Proc. Natl. Acad. Sci. U.S.A.

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Three-dimensional rotors, or scroll waves, provide essential insight into the activity of excitable media. They also are a suspected cause in the formation and maintenance of ventricular fibrillation, whose lethality is well known. It is therefore of considerable interest to find out what configurations can be adopted by such pathologies. A scroll's behavior is embodied in its organizing center or filament, a largely quiescent tube about which the scroll rotates. Predicting filament shape has normally required computer-intensive simulations of the whole scroll in time. We have found a fast and robust principle that yields the prediction for stationary filaments on a purely geometrical basis, blind to the reaction parameters of the medium. The procedure is to calculate the filament shape as a minimal path. We work in singly diffusive media whose diffusivity tensor-and no other feature-varies spatially. Mathematical and numerical evidence is presented for the proposition that a stable filament is a geodesic in a three-dimensional space whose metric is given by the inverse diffusivity tensor of the medium. Away from the boundaries, a stable filament is unaffected by the reaction parameters. The algorithmic aspects of this work are subsidiary to our main purpose of drawing attention to the universal and unexpectedly exact fit of an elementary geodesic principle within reaction-diffusion theories.

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“…The scroll wave rotate about a linelike filaments called vortex filament, and usually can be defined in terms of a phase singularity. In three-dimensional excitable media, the vortex filament is commonly a closed ring, and these vortex filaments can form linked and knotted rings which contract to compact, particle-like bundles [10,11,12,13,14,15,16,17,18,19,20,21].…”

Section: Introductionmentioning

confidence: 99%

Branch Processes of Vortex Filaments and Hopf Invariant Constraint on Scroll Wave

Zhu¹,

Ren²,

Mo³

2009

Commun. Theor. Phys.

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In this paper, by making use of Duan's topological current theory, the evolution of the vortex filaments in excitable media is discussed in detail. The vortex filaments are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation points of a complex function Z( x, t). It is also shown that the Hopf invariant of knotted scroll wave filaments is preserved in the branch processes (splitting, merging, or encountering) during the evolution of these knotted scroll wave filaments. Furthermore, it also revealed that the "exclusion principle" in some chemical media is just the special case of the Hopf invariant constraint, and during the branch processes the "exclusion principle" is also protected by topology.

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Topological Constraint on Scroll Wave Pinning

Cited by 52 publications

References 10 publications

Intramural Foci During Long Duration Fibrillation in the Pig Ventricle

Intramural Foci During Long Duration Fibrillation in the Pig Ventricle

Minimal principle for rotor filaments

Branch Processes of Vortex Filaments and Hopf Invariant Constraint on Scroll Wave

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