Nonlinear Dynamics and Chaos in Cardiac Arrhythmias Violet Redensek

Basic Electrical Processes of the Heart and Cardiac Arrhythmias

1.The SA (sinoatrial) node -The natural pacemaker of the heart, the SA node generates electrical impulses and initiates the heartbeat 2. The AV (atrioventricular) node -The AV node is activated by the electrical signals of the SA node. It delays the electrical impulse to ensure that the atria have ejected the blood into the ventricles before the ventricles contract

In electrically excitable muscles cells, such as those of the heart, there is a period of time, known as the refractory period, where the cell is incapable of repeating a specific action Essentially a recovery period In cardiac cells, the refractory period is related to the ion currents that flow into and out of the cell The action potential of the cell cannot be initiated again until the cell returns to its resting potential

Cardiac Alternans A cardiac alternan is an abnormality where one or more properties of the heartbeat alternate from beat to beat, creating a period-doubling oscillation (remember period-doubling is a hallmark of the onset of chaos) In a electrocardiogram (ECG), the T wave represents the electrical repolarization of the ventricles after each contraction Clinical trials have showed a clear correlation of T-wave alternans and arrhythmias, and an increased risk for sudden death

Concordant and Disconcordant Alternans Concordant alternans occur when the alternans are in phase throughout the whole cardiac tissue Disconcordant alternans occur when the alternans are out of phase, so the timing is not homogeneous throughout the cardiac tissue This can happen when the time interval for electrical stimulation is shorter than the refractory period- the propagation of cardiac excitation fails if the wavefront encounters a region that is still in refractory

Disconcordant Alternans and Lethal Arrhythmias An experiment was done to test the link between T-wave alternans and heterogeneity in cardiac cells The (guinea pig) heart was regulated by a pacemaker – When the heart rate was fast enough, concordant alernans appeared – Raising the heart rate further produced discondordant alternans – Raising the heart rate still further produced fibrillations

Symmetry Breaking Cardiac tissue is normally in a translationally invariant homogeneous cardiac state, where refractoriness is spatially uniform Spontaneous symmetry breaking produces arrhythmogenic dispersion of refractoriness, where the refractoriness is not longer spatially uniform Disconcordant alternans create or accentuate the dispersion of refractoriness

Simulation of the sudden onset of disconcordant alternans. Red line separates the two disconcordant regions.

Cable Equation 1-Dimensional cardiac electrical activity can be described by the cable equation C (dV m /dt)=α (d 2 V m /dt 2 ) - I(V m, y 1, y 2,…) – V m is membrance voltange, C is capacitance, I is the ion current in a cell, and y i describes how the ion flow rate through the membrane depends in a time-dependent and nonlinear way on V m

Application Analyzing the nonlinearity in cardiac electrical processes will allow for a better understanding of how cardiac arrhythmias arise, a better understanding of the differences between benign and fatal arrhythmias, and developing more effective therapies for treating and preventing life-threatening arrhythmias

Simulation of regular period pacing with and without feedback control

Proposal Look at alternans in other wave patterns besides the T-wave Look at Poincare Plot of Heart Rate Variability (HRV), and other variables What dynamical physiological features must be taken into account to simulate and better understand the nonlinear functions leading to alternans and arrhythmias? – Electrical signals from the brain, etc

Questions?

References Karma, Alain, and Robert F. Gilmour. "Nonlinear Dynamics of Heart Rhythm Disorders." Phys. Today Physics Today 60.3 (2007): Web. 12 Feb Goldberger AL, Amaral LAN, Glass L, Hausdorff JM, Ivanov PCh, Mark RG, Mietus JE, Moody GB, Peng C-K, Stanley HE. PhysioBank, PhysioToolkit, and PhysioNet: Components of a New Research Resource for Complex Physiologic Signals. Circulation 101(23):e215-e220 [Circulation Electronic Pages; (June 13) (June 13) Homoud, M.d. Munther K. "Introduction to Electrocardiography." (2008): n. pag. Tufts-New England Medical Center, Spring Web. 14 Feb