Biophysical Journal Volume 106 April 2014 1555–1556
1555
New and Notable Drifting Through the Beehive Bradley J. Roth* Department of Physics, Oakland University, Rochester, Michigan
Spiral waves are thought to underlie many heart arrhythmias, including fibrillation (1,2). Some of the earliest experimental recordings of spiral waves indicated that sometimes they drift (3), meaning that the core of the spiral wave not only meanders in a spirographlike pattern but also ambles along, on average, in one direction. This is not unlike the motion of an electron in a copper wire, with a random thermal motion—akin to the meandering of a spiral wave, but less organized—and a slower drift speed in the direction of an applied electric field. What causes the drift of a spiral wave? One important factor is heterogeneity of tissue properties. The resulting drift has two components: one along the direction of the heterogeneity, and another perpendicular to it. Consider a spiral wave rotating in the x-y plane. If the tissue properties vary with x, then the core of the spiral wave can drift parallel to the y axis. Whether it is in the positive or negative direction along this axis depends on whether the spiral wave rotates clockwise or counterclockwise (4). The core can also drift parallel to the x axis, usually toward the region of longest action potential duration (5). In this issue of the Biophysical Journal, Calvo et al. (6) use computer simulations to analyze the drift of a spiral wave in the atrium, where there exists a marked gradient of tissue properties. In their title, Calvo et al. (6) label their model as representing atrial fibrillation, although perhaps ‘‘atrial flutter’’
Submitted February 27, 2014, and accepted for publication March 6, 2014. *Correspondence: [email protected] Editor: Andrew McCulloch. Ó 2014 by the Biophysical Society 0006-3495/14/04/1555/2 $2.00
is the more appropriate term. Your opinion about the importance of this simulation for atrial fibrillation may depend on your point of view about how fibrillation is sustained. Rogers and Ideker (7) compare the competing hypotheses by invoking two metaphors: a rabbit warren and a beehive. In the rabbit warren analogy, parent wavefronts break up into daughter wavefronts, which break up again and again, like ‘‘rabbits breeding in a warren’’ (7). Fenton et al. (8) have preformed elegant simulations illustrating this type of behavior. The alternative view is that there exists a mother rotor, the ‘‘queen bee’’ governing the beehive, acting as the source of wave fronts that sometimes fail or break up as they propagate outward (8). This academic debate over the mechanism that sustains atrial fibrillation has a translational counterpart: investigators have obtained clinical data that support both the rabbit warren (9) and the beehive (10) hypotheses. If you favor the second metaphor, then for you, the study of Calvo et al. (6) examines how the mother rotor drifts through the beehive. The most important membrane current distributed heterogeneously in the study of Calvo et al. is the time-independent inward rectifier, IK1 (11). This potassium current plays a crucial role both for determining the resting potential and for speeding the phase-three repolarization of the action potential. A larger IK1 corresponds to a shorter action potential duration. The current is inwardly rectifying, meaning that for hyperpolarization, the current is outward and large, but for depolarization, the current is inward and small; it contributes little or nothing during the action potential plateau. An earlier study showed that a heterogeneous distribution of IK1 might be critical during ventricular fibrillation (12). The article of Calvo et al. (6) can be considered as an analogous investigation for the atrium. Another important precursor to this study was that performed by Ten Tusscher and Panfilov (5),
who varied the magnitude of IK1 throughout a sheet of cardiac tissue and thereby induced spiral wave drift. They concluded that IK1 heterogeneities ‘‘lead to drift of spiral waves toward regions of longer period’’ (5). Calvo et al. represent the atrium as a two-dimensional sheet of cardiac tissue, with the left atrium (large IK1) on the left side and the tissue surrounding the pulmonary veins (small IK1) on the right side. As you might expect, they observe a shorter action potential duration on the left than on the right, and the spiral-wave core drifts rightward. When ferreting out the mechanism of this drift, they do not focus on the action potential duration as much as the minimum diastolic transmembrane potential, or, in other words, how close the action potential returns to rest between excitations. A lower diastolic potential results in a more fully recovered sodium channel, making the tissue more excitable. Calvo et al. claim that excitability is the key factor that best predicts the drift direction. While the report of Calvo et al. answers some questions, it leaves other issues unresolved. For instance, they do not emphasize the component of drift perpendicular to the IK1 gradient, even though it is present in their simulations. Indeed, their Fig. 7 B suggests that in some cases this component may be more pronounced than the drift toward the pulmonary veins. Moreover, other factors besides IK1 can affect the movement of the spiral-wave core. Rogers and McCulloch (13) showed that heterogeneities in fiber orientation can induce drift, and my own work with Victor LeBlanc suggests that drift can arise from the different degrees of anisotropy in the intracellular and extracellular spaces (14). Indeed, the drift of spiral waves is a complex subject, with many underlying mechanisms (15). Calvo et al. have provided valuable insight into one aspect of
http://dx.doi.org/10.1016/j.bpj.2014.03.006
1556
spiral wave drift that may be important during atrial fibrillation. REFERENCES 1. Panfilov, A. V. 2009. Theory of reentry. In Cardiac Electrophysiology: From Cell to Bedside, 5th Ed. D. P. Zipes and J. Jalife, editors. Saunders, Philadelphia, PA, pp. 329–337. 2. Fenton, F. H., E. M. Cherry, and L. Glass. 2008. Cardiac arrhythmia. Scholarpedia. 3:1665. 3. Davidenko, J. M., A. V. Pertsov, ., J. Jalife. 1992. Stationary and drifting spiral waves of excitation in isolated cardiac muscle. Nature. 355:349–351. 4. Fast, V. G., and A. M. Pertsov. 1990. Drift of vortex in the myocardium [Dreĭf vikhria v miokarde]. Biofizika. 35:478–482. 5. Ten Tusscher, K. H. W. J., and A. V. Panfilov. 2003. Reentry in heterogeneous cardiac tissue described by the Luo-Rudy ventricular
Biophysical Journal 106(8) 1555–1556
Roth action potential model. Am. J. Physiol. Heart Circ. Physiol. 284:H542–H548.
without focal impulse and rotor modulation). J. Am. Coll. Cardiol. 62:138–147.
6. Calvo, C. J., M. Deo, ., O. Berenfeld. 2014. Attraction of rotors to the pulmonary veins in paroxysmal atrial fibrillation: a modeling study. Biophys. J. 106:1811–1821.
11. Anumonwo, J. M. B. 2009. Biophysical properties of inwardly rectifying potassium channels. In Cardiac Electrophysiology: From Cell to Bedside, 5th Ed. D. P. Zipes and J. Jalife, editors. Saunders, Philadelphia, PA, pp. 139–147.
7. Rogers, J. M., and R. E. Ideker. 2000. Fibrillating myocardium: rabbit warren or beehive? Circ. Res. 86:369–370. 8. Fenton, F. H., E. M. Cherry, ., S. J. Evans. 2002. Multiple mechanisms of spiral wave breakup in a model of cardiac electrical activity. Chaos. 12:852–892.
12. Samie, F. H., O. Berenfeld, ., J. Jalife. 2001. Rectification of the background potassium current: a determinant of rotor dynamics in ventricular fibrillation. Circ. Res. 89:1216–1223.
9. Cuculich, P. S., Y. Wang, ., Y. Rudy. 2010. Noninvasive characterization of epicardial activation in humans with diverse atrial fibrillation patterns. Circulation. 122:1364– 1372.
13. Rogers, J. M., and A. D. McCulloch. 1994. Nonuniform muscle fiber orientation causes spiral wave drift in a finite element model of cardiac action potential propagation. J. Cardiovasc. Electrophysiol. 5:496–509.
10. Narayan, S. M., D. E. Krummen, ., J. M. Miller. 2013. Direct or coincidental elimination of stable rotors or focal sources may explain successful atrial fibrillation ablation: on-treatment analysis of the CONFIRM trial (Conventional ablation for AF with or
14. LeBlanc, V. G., and B. J. Roth. 2003. Meandering of spiral waves in anisotropic tissue. Dyn. Cont. Discr. Impuls. Systems B Appl. Algor. 10:29–42. 15. Biktashev, V. N. 2007. Drift of spiral waves. Scholarpedia. 2:1836.
1555
New and Notable Drifting Through the Beehive Bradley J. Roth* Department of Physics, Oakland University, Rochester, Michigan
Spiral waves are thought to underlie many heart arrhythmias, including fibrillation (1,2). Some of the earliest experimental recordings of spiral waves indicated that sometimes they drift (3), meaning that the core of the spiral wave not only meanders in a spirographlike pattern but also ambles along, on average, in one direction. This is not unlike the motion of an electron in a copper wire, with a random thermal motion—akin to the meandering of a spiral wave, but less organized—and a slower drift speed in the direction of an applied electric field. What causes the drift of a spiral wave? One important factor is heterogeneity of tissue properties. The resulting drift has two components: one along the direction of the heterogeneity, and another perpendicular to it. Consider a spiral wave rotating in the x-y plane. If the tissue properties vary with x, then the core of the spiral wave can drift parallel to the y axis. Whether it is in the positive or negative direction along this axis depends on whether the spiral wave rotates clockwise or counterclockwise (4). The core can also drift parallel to the x axis, usually toward the region of longest action potential duration (5). In this issue of the Biophysical Journal, Calvo et al. (6) use computer simulations to analyze the drift of a spiral wave in the atrium, where there exists a marked gradient of tissue properties. In their title, Calvo et al. (6) label their model as representing atrial fibrillation, although perhaps ‘‘atrial flutter’’
Submitted February 27, 2014, and accepted for publication March 6, 2014. *Correspondence: [email protected] Editor: Andrew McCulloch. Ó 2014 by the Biophysical Society 0006-3495/14/04/1555/2 $2.00
is the more appropriate term. Your opinion about the importance of this simulation for atrial fibrillation may depend on your point of view about how fibrillation is sustained. Rogers and Ideker (7) compare the competing hypotheses by invoking two metaphors: a rabbit warren and a beehive. In the rabbit warren analogy, parent wavefronts break up into daughter wavefronts, which break up again and again, like ‘‘rabbits breeding in a warren’’ (7). Fenton et al. (8) have preformed elegant simulations illustrating this type of behavior. The alternative view is that there exists a mother rotor, the ‘‘queen bee’’ governing the beehive, acting as the source of wave fronts that sometimes fail or break up as they propagate outward (8). This academic debate over the mechanism that sustains atrial fibrillation has a translational counterpart: investigators have obtained clinical data that support both the rabbit warren (9) and the beehive (10) hypotheses. If you favor the second metaphor, then for you, the study of Calvo et al. (6) examines how the mother rotor drifts through the beehive. The most important membrane current distributed heterogeneously in the study of Calvo et al. is the time-independent inward rectifier, IK1 (11). This potassium current plays a crucial role both for determining the resting potential and for speeding the phase-three repolarization of the action potential. A larger IK1 corresponds to a shorter action potential duration. The current is inwardly rectifying, meaning that for hyperpolarization, the current is outward and large, but for depolarization, the current is inward and small; it contributes little or nothing during the action potential plateau. An earlier study showed that a heterogeneous distribution of IK1 might be critical during ventricular fibrillation (12). The article of Calvo et al. (6) can be considered as an analogous investigation for the atrium. Another important precursor to this study was that performed by Ten Tusscher and Panfilov (5),
who varied the magnitude of IK1 throughout a sheet of cardiac tissue and thereby induced spiral wave drift. They concluded that IK1 heterogeneities ‘‘lead to drift of spiral waves toward regions of longer period’’ (5). Calvo et al. represent the atrium as a two-dimensional sheet of cardiac tissue, with the left atrium (large IK1) on the left side and the tissue surrounding the pulmonary veins (small IK1) on the right side. As you might expect, they observe a shorter action potential duration on the left than on the right, and the spiral-wave core drifts rightward. When ferreting out the mechanism of this drift, they do not focus on the action potential duration as much as the minimum diastolic transmembrane potential, or, in other words, how close the action potential returns to rest between excitations. A lower diastolic potential results in a more fully recovered sodium channel, making the tissue more excitable. Calvo et al. claim that excitability is the key factor that best predicts the drift direction. While the report of Calvo et al. answers some questions, it leaves other issues unresolved. For instance, they do not emphasize the component of drift perpendicular to the IK1 gradient, even though it is present in their simulations. Indeed, their Fig. 7 B suggests that in some cases this component may be more pronounced than the drift toward the pulmonary veins. Moreover, other factors besides IK1 can affect the movement of the spiral-wave core. Rogers and McCulloch (13) showed that heterogeneities in fiber orientation can induce drift, and my own work with Victor LeBlanc suggests that drift can arise from the different degrees of anisotropy in the intracellular and extracellular spaces (14). Indeed, the drift of spiral waves is a complex subject, with many underlying mechanisms (15). Calvo et al. have provided valuable insight into one aspect of
http://dx.doi.org/10.1016/j.bpj.2014.03.006
1556
spiral wave drift that may be important during atrial fibrillation. REFERENCES 1. Panfilov, A. V. 2009. Theory of reentry. In Cardiac Electrophysiology: From Cell to Bedside, 5th Ed. D. P. Zipes and J. Jalife, editors. Saunders, Philadelphia, PA, pp. 329–337. 2. Fenton, F. H., E. M. Cherry, and L. Glass. 2008. Cardiac arrhythmia. Scholarpedia. 3:1665. 3. Davidenko, J. M., A. V. Pertsov, ., J. Jalife. 1992. Stationary and drifting spiral waves of excitation in isolated cardiac muscle. Nature. 355:349–351. 4. Fast, V. G., and A. M. Pertsov. 1990. Drift of vortex in the myocardium [Dreĭf vikhria v miokarde]. Biofizika. 35:478–482. 5. Ten Tusscher, K. H. W. J., and A. V. Panfilov. 2003. Reentry in heterogeneous cardiac tissue described by the Luo-Rudy ventricular
Biophysical Journal 106(8) 1555–1556
Roth action potential model. Am. J. Physiol. Heart Circ. Physiol. 284:H542–H548.
without focal impulse and rotor modulation). J. Am. Coll. Cardiol. 62:138–147.
6. Calvo, C. J., M. Deo, ., O. Berenfeld. 2014. Attraction of rotors to the pulmonary veins in paroxysmal atrial fibrillation: a modeling study. Biophys. J. 106:1811–1821.
11. Anumonwo, J. M. B. 2009. Biophysical properties of inwardly rectifying potassium channels. In Cardiac Electrophysiology: From Cell to Bedside, 5th Ed. D. P. Zipes and J. Jalife, editors. Saunders, Philadelphia, PA, pp. 139–147.
7. Rogers, J. M., and R. E. Ideker. 2000. Fibrillating myocardium: rabbit warren or beehive? Circ. Res. 86:369–370. 8. Fenton, F. H., E. M. Cherry, ., S. J. Evans. 2002. Multiple mechanisms of spiral wave breakup in a model of cardiac electrical activity. Chaos. 12:852–892.
12. Samie, F. H., O. Berenfeld, ., J. Jalife. 2001. Rectification of the background potassium current: a determinant of rotor dynamics in ventricular fibrillation. Circ. Res. 89:1216–1223.
9. Cuculich, P. S., Y. Wang, ., Y. Rudy. 2010. Noninvasive characterization of epicardial activation in humans with diverse atrial fibrillation patterns. Circulation. 122:1364– 1372.
13. Rogers, J. M., and A. D. McCulloch. 1994. Nonuniform muscle fiber orientation causes spiral wave drift in a finite element model of cardiac action potential propagation. J. Cardiovasc. Electrophysiol. 5:496–509.
10. Narayan, S. M., D. E. Krummen, ., J. M. Miller. 2013. Direct or coincidental elimination of stable rotors or focal sources may explain successful atrial fibrillation ablation: on-treatment analysis of the CONFIRM trial (Conventional ablation for AF with or
14. LeBlanc, V. G., and B. J. Roth. 2003. Meandering of spiral waves in anisotropic tissue. Dyn. Cont. Discr. Impuls. Systems B Appl. Algor. 10:29–42. 15. Biktashev, V. N. 2007. Drift of spiral waves. Scholarpedia. 2:1836.
