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Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation. (English) Zbl 1069.92503

Summary: Wave propagation in ventricular muscle is rendered highly anisotropic by the intramural rotation of the fiber. This rotational anisotropy is especially important because it can produce a twist of electrical vortices, which measures the rate of rotation (in degree/mm) of activation wavefronts in successive planes perpendicular to a line of phase singularity, or filament. This twist can then significantly alter the dynamics of the filament. This paper explores this dynamics via numerical simulations. After a review of the literature, we present modeling tools that include: (i) a simplified ionic model with three membrane currents that approximates well the restitution properties and spiral wave behavior of more complex ionic models of cardiac action potential (Beeler-Reuter and others), and (ii) a semi-implicit algorithm for the fast solution of monodomain cable equations with rotational anisotropy. We then discuss selected results of a simulation study of vortex dynamics in a parallelepipedal slab of ventricular muscle of varying wall thickness (S) and fiber rotation rate \((\theta_z)\).
The main finding is that rotational anisotropy generates a sufficiently large twist to destabilize a single transmural filament and causes a transition to a wave turbulent state characterized by a high density of chaotically moving filaments. This instability is manifested by the propagation of localized disturbances along the filament and has no previously known analog in isotropic excitable media. These disturbances correspond to highly twisted and distorted regions of filament, or “twistons,” that create vortex rings when colliding with the natural boundaries of the ventricle. Moreover, when sufficiently twisted, these rings expand and create additional filaments by further colliding with boundaries. This instability mechanism is distinct from the commonly invoked patchy failure or wave breakup that is not observed here during the initial instability. For modified Beeler-Reuter-like kinetics with stable reentry in two dimensions, decay into turbulence occurs in the left ventricle in about one second above a critical wall thickness in the range of 4-6 mm that matches the experiment. However this decay is suppressed by uniformly decreasing excitability. Specific experiments to test these results, and a method to characterize the filament density during fibrillation are discussed. Results are contrasted with other mechanisms of fibrillation and future prospects are summarized.

MSC:

92C30 Physiology (general)
92C05 Biophysics
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References:

[1] DOI: 10.1142/S0218127496000163 · doi:10.1142/S0218127496000163
[2] DOI: 10.1063/1.166297 · doi:10.1063/1.166297
[3] DOI: 10.1063/1.166307 · Zbl 1069.92501 · doi:10.1063/1.166307
[4] DOI: 10.1063/1.166290 · doi:10.1063/1.166290
[5] DOI: 10.1038/355349a0 · doi:10.1038/355349a0
[6] DOI: 10.1161/01.CIR.91.9.2454 · doi:10.1161/01.CIR.91.9.2454
[7] DOI: 10.1172/JCI119159 · doi:10.1172/JCI119159
[8] DOI: 10.1113/jphysiol.1962.sp006849 · doi:10.1113/jphysiol.1962.sp006849
[9] DOI: 10.1113/jphysiol.1977.sp011853 · doi:10.1113/jphysiol.1977.sp011853
[10] DOI: 10.1098/rstb.1985.0001 · doi:10.1098/rstb.1985.0001
[11] DOI: 10.1161/01.RES.68.6.1501 · doi:10.1161/01.RES.68.6.1501
[12] DOI: 10.1161/01.RES.74.6.1071 · doi:10.1161/01.RES.74.6.1071
[13] DOI: 10.1109/5.486738 · doi:10.1109/5.486738
[14] DOI: 10.1113/jphysiol.1978.sp012576 · doi:10.1113/jphysiol.1978.sp012576
[15] Elharrar V., Am. J. Physiol. 244 pp H782– (1983)
[16] DOI: 10.1161/01.CIR.93.3.603 · doi:10.1161/01.CIR.93.3.603
[17] DOI: 10.1002/aja.1001010103 · doi:10.1002/aja.1001010103
[18] Nielsen P., Am. J. Physiol. 260 pp H1365– (1991)
[19] DOI: 10.1002/cpa.3160420106 · Zbl 0664.92005 · doi:10.1002/cpa.3160420106
[20] DOI: 10.1007/BF00163916 · Zbl 0744.92015 · doi:10.1007/BF00163916
[21] DOI: 10.1161/01.CIR.90.6.3076 · doi:10.1161/01.CIR.90.6.3076
[22] DOI: 10.1161/01.RES.72.4.744 · doi:10.1161/01.RES.72.4.744
[23] DOI: 10.1016/0167-2789(95)00059-D · doi:10.1016/0167-2789(95)00059-D
[24] DOI: 10.1016/0002-9149(75)90865-6 · doi:10.1016/0002-9149(75)90865-6
[25] DOI: 10.1161/01.CIR.85.2.680 · doi:10.1161/01.CIR.85.2.680
[26] DOI: 10.1126/science.7973648 · doi:10.1126/science.7973648
[27] DOI: 10.1137/1032001 · Zbl 0711.35067 · doi:10.1137/1032001
[28] DOI: 10.1016/0375-9601(85)90315-9 · doi:10.1016/0375-9601(85)90315-9
[29] DOI: 10.1016/0167-2789(88)90080-2 · Zbl 0645.76052 · doi:10.1016/0167-2789(88)90080-2
[30] DOI: 10.1016/0167-2789(89)90255-8 · Zbl 0666.76117 · doi:10.1016/0167-2789(89)90255-8
[31] DOI: 10.1137/1034001 · Zbl 0773.35030 · doi:10.1137/1034001
[32] DOI: 10.1098/rsta.1994.0070 · Zbl 0862.92002 · doi:10.1098/rsta.1994.0070
[33] DOI: 10.1139/p90-100 · Zbl 0991.92501 · doi:10.1139/p90-100
[34] DOI: 10.1038/345419a0 · doi:10.1038/345419a0
[35] Mironov S., J. Physiol. (London) 100 pp 1975– (1996)
[36] DOI: 10.1063/1.166306 · doi:10.1063/1.166306
[37] DOI: 10.1126/science.270.5239.1222 · doi:10.1126/science.270.5239.1222
[38] DOI: 10.1063/1.166289 · Zbl 1069.92506 · doi:10.1063/1.166289
[39] DOI: 10.1063/1.166291 · Zbl 1069.92510 · doi:10.1063/1.166291
[40] DOI: 10.1142/S0218127491000142 · Zbl 0749.92009 · doi:10.1142/S0218127491000142
[41] DOI: 10.1142/S0218127491000336 · Zbl 0875.92027 · doi:10.1142/S0218127491000336
[42] DOI: 10.1063/1.166206 · doi:10.1063/1.166206
[43] DOI: 10.1007/BF02368286 · doi:10.1007/BF02368286
[44] DOI: 10.1016/0375-9601(93)90921-L · doi:10.1016/0375-9601(93)90921-L
[45] DOI: 10.1103/PhysRevLett.71.1103 · Zbl 0972.92502 · doi:10.1103/PhysRevLett.71.1103
[46] DOI: 10.1063/1.166024 · doi:10.1063/1.166024
[47] DOI: 10.1063/1.166295 · doi:10.1063/1.166295
[48] DOI: 10.1016/S0006-3495(61)86902-6 · doi:10.1016/S0006-3495(61)86902-6
[49] DOI: 10.1063/1.165844 · Zbl 1031.76502 · doi:10.1063/1.165844
[50] Panfilov A., Dokl. Akad. Nauk SSSR 274 pp 1500– (1984)
[51] DOI: 10.1016/0167-2789(91)90003-R · Zbl 0733.92007 · doi:10.1016/0167-2789(91)90003-R
[52] DOI: 10.1007/BF00697663 · doi:10.1007/BF00697663
[53] DOI: 10.1016/0167-2789(92)90052-O · Zbl 0780.92014 · doi:10.1016/0167-2789(92)90052-O
[54] DOI: 10.1161/01.CIR.78.5.1277 · doi:10.1161/01.CIR.78.5.1277
[55] DOI: 10.1016/S0022-5193(05)80750-7 · doi:10.1016/S0022-5193(05)80750-7
[56] DOI: 10.1161/01.RES.66.2.367 · doi:10.1161/01.RES.66.2.367
[57] DOI: 10.1103/PhysRevLett.70.2182 · doi:10.1103/PhysRevLett.70.2182
[58] DOI: 10.1016/0167-2789(94)90228-3 · Zbl 0824.35129 · doi:10.1016/0167-2789(94)90228-3
[59] DOI: 10.1016/0167-2789(88)90062-0 · Zbl 0656.76018 · doi:10.1016/0167-2789(88)90062-0
[60] Jr R. G., Am. J. Physiol. 272 pp H1826– (1997)
[61] DOI: 10.1098/rspa.1992.0084 · doi:10.1098/rspa.1992.0084
[62] DOI: 10.1016/0378-4371(92)90252-L · doi:10.1016/0378-4371(92)90252-L
[63] DOI: 10.1016/0960-0779(95)95761-F · Zbl 0925.92056 · doi:10.1016/0960-0779(95)95761-F
[64] DOI: 10.1103/PhysRevLett.79.665 · doi:10.1103/PhysRevLett.79.665
[65] DOI: 10.1103/PhysRevLett.72.164 · doi:10.1103/PhysRevLett.72.164
[66] DOI: 10.1142/S0218127496001582 · Zbl 1298.35008 · doi:10.1142/S0218127496001582
[67] DOI: 10.1021/j100339a047 · doi:10.1021/j100339a047
[68] DOI: 10.1103/PhysRevLett.77.2105 · doi:10.1103/PhysRevLett.77.2105
[69] DOI: 10.1063/1.166294 · doi:10.1063/1.166294
[70] Dillon S., Circulation 72 pp 1116– (1985)
[71] DOI: 10.1017/S0022112072002307 · Zbl 0237.76010 · doi:10.1017/S0022112072002307
[72] DOI: 10.1017/S0022112082003462 · doi:10.1017/S0022112082003462
[73] DOI: 10.1063/1.166292 · Zbl 1069.92500 · doi:10.1063/1.166292
[74] DOI: 10.1137/0147038 · Zbl 0649.34019 · doi:10.1137/0147038
[75] DOI: 10.1016/S0022-5193(05)80465-5 · doi:10.1016/S0022-5193(05)80465-5
[76] DOI: 10.1103/PhysRevE.53.1740 · doi:10.1103/PhysRevE.53.1740
[77] DOI: 10.1172/JCI113945 · doi:10.1172/JCI113945
[78] DOI: 10.1016/0002-8703(64)90371-0 · doi:10.1016/0002-8703(64)90371-0
[79] DOI: 10.1161/01.RES.79.3.493 · doi:10.1161/01.RES.79.3.493
[80] DOI: 10.1016/0167-2789(94)90171-6 · Zbl 0826.35128 · doi:10.1016/0167-2789(94)90171-6
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.