A tale of two fibrillations.
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Action Potentials↗
Biomedical subjects
Alan Garfinkel
Publications and source records attributed to Alan Garfinkel.
Mechanism for spiral wave breakup in excitable and oscillatory media.
We study spiral wave breakup using a Fitzhugh-Nagumo-type system. We find that spiral wave breakup can occur near the core or far from it in both excitable and oscillatory regimes. There is a faraway breakup scenario in both excitable and oscillatory media that depends on long wavelength modulation modes. We observed three distinct scenarios, including one that involves breakup that does not develop into turbulence. However, we find that the mechanisms behind these three scenarios are the same: they are caused by the interaction between the dispersion relation and the asymptotic behavior of the modulation mode. The difference in phenomenology is due to the asymptotic behavior of the modulation mode.
Biophysics↗
Novel approaches to identifying antiarrhythmic drugs.
Currently, device therapy with implantable cardioverter-defibrillators is the only proven effective therapy for sudden cardiac death. However, new insights into the mechanisms of ventricular fibrillation, particularly the role of dynamic factors that cause wave instability, are providing conceptual advances toward developing effective new pharmacotherapy.
Action Potentials↗
Emergent oscillations in a mathematical model of the human menstrual cycle.
BACKGROUND: The aim of this study was to develop a mathematical model of the hypothalamo-pituitary-gonadal axis that would reflect available data in humans. METHODS: A model of hormonal relationships at the early follicular and midluteal phases of the human menstrual cycle is proposed. FINDINGS: Two distinct temporal patterns of oscillatory behavior have been demonstrated for both pituitary and gonadal steroids in the early follicular phase: first, rapid oscillations in gonadotropin releasing hormone, follicle stimulating hormone and luteinizing hormone (Q approximate to 1 hour) that were an immediate consequence of the programmed equations. Second, there were slower, undulating, emergent rhythms in luteinizing hormone and follicle stimulating hormone, and also in estrogen, having oscillatory periods of 2-12 hours. There was also a longer-period (Q2-3 days) emergent rhythm in progesterone. In the mid-luteal phase, estrogen and progesterone rhythms were correlated, and all hormones showed an approximately 6-hour periodicity. CONCLUSIONS: To our knowledge, the oscillatory behavior of peripheral sex steroids in the follicular phase has not been previously noted.
Bipolar Disorder↗
Understanding biological complexity: lessons from the past.
Advances in molecular biology now permit complex biological systems to be tracked at an exquisite level of detail. The information flow is so great, however, that using intuition alone to draw connections is unrealistic. Thus, the need to integrate mathematical biology with experimental biology is greater than ever. To achieve this integration, obstacles that have traditionally prevented effective communication between theoreticians and experimentalists must be overcome, so that experimentalists learn the language of mathematics and dynamical modeling and theorists learn the language of biology. Fifty years ago Alan Hodgkin and Andrew Huxley published their quantitative model of the nerve action potential; in the same year, Alan Turing published his work on pattern formation in activator-inhibitor systems. These classic studies illustrate two ends of the spectrum in mathematical biology: the detailed model approach and the minimal model approach. When combined, they are highly synergistic in analyzing the mechanisms underlying the behavior of complex biological systems. Their effective integration will be essential for unraveling the physical basis of the mysteries of life.
Animals↗
Effects of the excitation-contraction uncouplers diamine monoxime (DAM) and cytochalasin D (CytoD) on induced arrhythmias in the rabbit ventricle.
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Action Potentials↗
Frequency analysis of ventricular fibrillation in Swine ventricles.
It has been suggested from frequency analysis that cardiac fibrillation is driven by stable intramural reentry, with wavebreak occurring due to failure of 1:1 propagation. We tested this hypothesis with a combined experimental and theoretical approach. Optical mapping was performed on epicardial, endocardial, and transmural cut surfaces of fibrillating swine ventricles. Wavelets were characterized, the frequency content of optical signals analyzed, and space-time plots (STPs) constructed to detect Wenckebach-like conduction. The findings were compared with simulations in 2D and 3D cardiac tissue using the Luo-Rudy action potential model. The incidence of reentry in the cut transmural surface (11.8% in right ventricle, 14.3% in left ventricle) was similar to that on the endocardial surface (13.1%, P=NS) but greater than on the epicardial surface (7.7%, P<0.01). Frequency spectra of optically recorded membrane voltage were organized into spatial domains with the same dominant frequency, but these domains were nonstationary. In STPs, pseudo-2:1 conduction block was caused by double potentials arising when reentry occurred on the recording site rather than true Wenckebach conduction. The latter was observed in 11 of 166 STPs but did not occur at borders of high-to-low frequency domains. In simulations, similar findings were obtained when action potential duration (APD) restitution slope was steep. Stationary dominant frequency domains with Wenckebach conduction patterns were observed only in the presence of shallow APD restitution slope and marked nonuniform tissue heterogeneity. In conclusion, stable intramural reentry as the engine of fibrillation was not observed. Our findings support the idea that dynamic wavebreak plays a fundamental role in the generation and maintenance of ventricular fibrillation.
Action Potentials↗
Electrical restitution and cardiac fibrillation.
Combined experimental and theoretical work has shown that restitution properties of the cardiac action potential duration and conduction velocity contribute to breakup of reentrant wavefronts during cardiac fibrillation independent of preexisting electrophysiologic heterogeneities in the tissue. Developing therapies that favorably alter these cardiac electrical restitution properties are a promising new approach to preventing fibrillation.
Electrophysiology↗
Effects of amiodarone on wave front dynamics during ventricular fibrillation in isolated swine right ventricle.
The effects of acute amiodarone infusion on dynamics of ventricular fibrillation (VF) are unclear. Six isolated swine right ventricles (RVs) were studied in vitro. Activation patterns during VF were mapped optically, whereas action potentials were recorded with a glass microelectrode. At baseline, VF was associated with frequent spontaneous wave breaks. Amiodarone (2.5 microg/ml) reduced spontaneous wave breaks and increased the cycle length (CL) of VF from 83.3 +/- 17.8 ms at baseline to 118.4 +/- 25.8 ms during infusion (P < 0.05). Amiodarone increased the reentrant wave front CL (114.4 +/- 15.5 vs. 78.2 +/- 19.0 ms, P < 0.05) and central core area (4.1 +/- 3.8 vs. 0.9 +/- 0.3 mm2, P < 0.05). Within 30 min of infusion, VF terminated (n = 1), converted to ventricular tachycardia (VT) (n = 1) or continued at a slower rate (n = 4). Amiodarone flattened the APD restitution curves. We conclude that amiodarone reduced spontaneous wave breaks. It might terminate VF or convert VF to VT. These effects were associated with the flattening of APD restitution slope and increased core size of reentrant wave fronts.
Action Potentials↗
Action potential duration restitution and ventricular fibrillation due to rapid focal excitation.
The focal source hypothesis of ventricular fibrillation (VF) posits that rapid activation from a focal source, rather than action potential duration (APD) restitution properties, is responsible for the maintenance of VF. We injected aconitine (100 microg) into normal isolated perfused swine right ventricles (RVs) stained with 4-[beta-[2-(di-n-butylamino)-6-naphthyl]vinyl]pyridinium (di-4-ANEPPS) for optical mapping studies. Within 97 +/- 163 s, aconitine induced ventricular tachycardia (VT) with a mean cycle length 268 +/- 37 ms, which accelerated before converting to VF. Drugs that flatten the APD restitution slope, including diacetyl monoxime (10-20 mM, n = 6), bretylium (10-20 microg/ml, n = 3), and verapamil (2-4 microg/ml, n = 3), reversibly converted VF to VT in all cases. In two RVs, VF persisted despite of the excision of the aconitine site. Simulations in two-dimensional cardiac tissue showed that once VF was initiated, it remained sustained even after the "aconitine" site was eliminated. In this model of focal source VF, the VT-to-VF transition occurred due to a wave break outside the aconitine site, and drugs that flattened the APD restitution slope converted VF to VT despite continuous activation from aconitine site.
Aconitine↗
Electrical refractory period restitution and spiral wave reentry in simulated cardiac tissue.
Theoretical and experimental studies have shown that restitution of the cardiac action potential (AP) duration (APD) plays a major role in predisposing ventricular tachycardia to degenerate to ventricular fibrillation, whereas its role in atrial fibrillation is unclear. We used the Courtemanche human atrial cell model and the Luo-Rudy guinea pig ventricular model to compare the roles of electrical restitution in destabilizing spiral wave reentry in simulated two-dimensional homogeneous atrial and ventricular tissue. Because atrial AP morphology is complex, we also validated the usefulness of effective refractory period (ERP) restitution. ERP restitution correlated best with APD restitution at transmembrane potentials greater than or equal to -62 mV, and its steepness was a reliable predictor of spiral wave phenotype (stable, meandering, hypermeandering, and breakup) in both atrial and ventricular tissue. Spiral breakup or single hypermeandering spirals occurred when the slope of ERP restitution exceeded 1 at short diastolic intervals. Thus ERP restitution, which is easier to measure clinically than APD restitution, is a reliable determinant of spiral wave stability in simulated atrial and ventricular tissue.
Animals↗
Computerized mapping of fibrillation in normal ventricular myocardium.
It is well known that the ability to fibrillate is intrinsic to a normal ventricle that exceeds a critical mass. The questions we address are how is ventricular fibrillation (VF) initiated and perpetuated in normal myocardium, and why is VF not seen more often in the general population if all ventricles have the ability to fibrillate. To study the mechanisms of VF, we used computerized mapping techniques with up to 512 channels of simultaneous multisite recordings for data acquisition. The data were then processed for dynamic display of the activation patterns and for mathematical analyses of the activation intervals. The results show that in normal ventricles, VF can be initiated by a single strong premature stimulus given during the vulnerable period of the cardiac cycle. The initial activations form a figure-eight pattern. Afterward, VF will perpetuate itself without any outside help. The self-perpetuation itself is due to at least two factors. One is that single wave fronts spontaneously break up into two or more wavelets. The second is that when two wavelets intersect perpendicular to each other, the second wavelet is broken by the residual refractoriness left over from the first wavelet. Mathematical analyses of the patterns of activation during VF revealed that VF is a form of chaos, and that transition from ventricular tachycardia (VT) to VF occurs via the quasiperiodic route. In separate experiments, we found that we can convert VF to VT by tissue size reduction. The physiological mechanism associated with the latter transition appears to be the reduction of the number of reentrant wave fronts and wandering wavelets. Based on these findings, we propose that the reentrant wave fronts and the wandering wavelets serve as the physiological equivalent of coupled oscillators. A minimal number of oscillators is needed for VF to perpetuate itself, and to generate chaotic dynamics; hence a critical mass is required to perpetuate VF. We conclude that VF in normal myocardium is a form of reentrant cardiac arrhythmia. A strong electrical stimulus initiates single or dual reentrant wave fronts that break up into multiple wavelets. Sometimes short-lived reentry is also generated during the course of VF. These organized reentrant and broken wavelets serve as coupled oscillators that perpetuate VF and maintain chaos. Although the ability to support these oscillators exists in a normal ventricle, the triggers required to generate them are nonexistent in the normal heart. Therefore, VF and sudden death do not happen to most people with normal ventricular myocardium. (c) 1998 American Institute of Physics.
Journal Article↗