Niels Otani: Cardiac research

I am currently following several lines of research in the cardiac area, all oriented towards understanding, visualizing and controlling abnormal, rapid, and often life-threatening cardiac rhythms, including ventricular tachycardia, and atrial and ventricular fibrillation. Below, I list and briefly describe each of these lines of research, and provide lists of the papers we have published on each topic.

New defibrillation methods

The current method of choice for terminating ventricular fibrillation is cardioversion. (This is the method you see on TV: the paddles are applied to the chest, a big electrical shock is delivered, etc.) Unfortunately, this method is damaging to the heart and traumatic for the patient (if conscious). Additionally, patients that are carrying around implantable defibrillators (ICDs) that deliver these shocks automatically often live in fear of their devices. We have been trying to develop methods that employ lower energy shocks that have the potential for being much kinder to the patient in all these categories.

Depolarization pattern induced by a weak shock in the presence of spiral wave reentry. From Otani, IEEE Trans. Biomed. Eng. (2011); see Fenton et al., Circulation (2009).

Control of cardiac rhythm

We are using mathematical methods to develop new ways to control some of the fundamental patterns of action potential formation and propagation. An example of one such pattern, spiral wave reentry, is shown in the figure below. We hope that these methods will, in turn, lead to new therapies to control abnormal rapid cardiac rhythms. I have been primarily been using linear eigenmode theory in these studies. Additionally, I have been working with Laura Munoz, a mechanical engineer in our group, to develop methods based on tools borrowed from the field of control theory.

Top row: Uncontrolled spiral wave breaks up. Bottom row: Spiral wave controlled by an electrical stimulus maintains its shape. From Allexandre and Otani, Phys. Rev. E (2004).

A novel imaging method for visualizing action potentials using ultrasound

It is widely believed that spiral wave reentry (as described above) is responsible for tachycardia and fibrillation in the various myocardial tissues of the heart. Yet, these waves have never been seen in three dimensions, inside the heart walls. The leading method for visualization of these action potential waves, optical mapping, can only see wave activity on the surfaces of the heart. Thus, we can only suspect, but do not know for sure, that spiral waves are even present during these life-threatening arrhythmias.

We have been investigating a new imaging modality for seeing these waves at depth. We propose to calculate the patterns of action potential propagation from the mechanical contractions they produce, as visualized through the use of ultrasound. Ultrasound has no problem seeing deep into the walls of the heart. So far, we have demonstrated that it is possible to calculate the active stress inherent in action potentials from the mechanical strains the induce. This sort of calculation cannot, in general, be done. However, for the case of the heart, we show that such a calculation is possible, due to the fact that, in the heart, stress must be oriented parallel to the length of muscle fibers.

(a) Input data: A plane wave of constant active stress propagates through a cube of myocardial tissue (a single cross section of the cubic system shown). (b) Input data shown in panel (a) is used to calculate the deformation it produces in the tissue (the "forward" problem). (c) 15% noise is added to the myocardial fiber direction angles to represent uncertainty in their measurement. The deformations in panel (b) are then used to back-calculate where the active stresses, and by implication, where the action potentials, must have been (the "inverse" problem). From Otani et al., Ann. Biomed. Eng. (2010).

How ventricular fibrillation might be initiated

We have discovered that certain patterns of electrical stimuli can reliably throw the heart into ventricular fibrillation (VF). We call the time intervals with which these stimuli are delivered the "magic numbers," because the intervals are remarkably predicted by a comparatively simple theory that ignores the complexities of the actual situation. Our research in this area has consisted of the development of the theory itself, its predictions as calculated with computer models, and experiments demonstrating the validity of the theory.

Top row: A series of rapid stimuli in a short-long-short-intermediate pattern in the right ventricle (RV) results in VF. Bottom row: By the time rapid stimuli have propagated to the left ventricle (LV) the pattern of intervals has changed to long-short-long-short, demonstrating that non-trivial dynamics is present. From Gelzer et al., Circulation (2008).

I have also used the same "magic numbers" dynamics to develop a method that may be useful in terminating fibrillation, as described in this paper:

The dynamics of action potentials

It is widely believed that an alternation in the duration of successive action potentials is a precursor to the initiation of dangerous rhythms, including ventricular fibrillation. This alternation, called alternans, is predicted by nonlinear dynamical theory to be dependent on a key property of the cardiac cells called action potential duration (APD) restitution. I have studied many aspects of this effect, including how it generalizes to propagating action potential waves, how it interacts with other dynamical properties of cells including, specifically, one called "memory," how it might be produced by the functional properties of the ion channels, and more.

Generalized restitution function in 3 dynamical dimensions, as traced out by experimental data. From Otani and Gilmour, J. Thoret. Biol. (1997).
Mechanism by which alternans is produced in the Fox-McHarg-Gilmour ion channel model. From Otani et al., Heart Rhythm (2005).

Properties of rotating waves in the heart

Self-sustaining rotating action potential waves called spiral waves are thought to underlie many abnormal rapid cardiac rhythms, including ventricular tachycardia, and atrial and ventricular fibrillation. We have studied a number of the key properties of these waves including their statistical properties, their tendency to wobble (called "meandering") and the dynamics of what is happening at the center of rotation.

Behavior of two aggregate quantities we call "predator" and "prey," used to characterize the statistical properties of spiral wave turbulence in the heart. Top panel: Both quantities alternate between two types of behavior: Type(i): low-amplitude, nearly periodic oscillation, and Type(ii): large-amplitude, aperiodic oscillation. Bottom panel: Frequency power spectrum is quite different for the two types of behavior: Harmonic bands (horizontal lines) for Type(i) behavior; Low-frequency bursts (red spots) and loss of band structure for Type(ii) behavior. From Otani et al., Phys. Rev. E (2008).

Properties of action potential propagation in the heart

The behavior of propagating action potentials near walls and non-conducting boundaries causes major departures from the behavior predicted by theories based on single cell and spatially uniform models. I have done some exploration into these effects.

An action potential propagating from the lower-left corner is able to "tunnel" into a circular region across a boundary that contains no gap junctions. From Otani, Comput. in Cardiol. (2011).

Properties of the SA node, AV conduction, and atrial fibrillation

With Dr. Syndey Moise, we are looking at patterns of arrhythmia produced by the SA node and AV nodal block. We have also examined variations in spectral entropy that occur during atrial fibrillation in both the presence and absence of certain drugs.

MAP recordings from the left and right atrium of a German Shepherd dog during atrial fribrillation. Note that the recording from the right atrium seems to display more disorganization. Spectral entropy from the left (blue) and right (red) atrium. The higher spectral entropy in the right atrium captures in a rigorous, quantitative way the feature we see informally as higher disorganization in right atrium MAP recording. From Pariaut et al., Am. J. Vet. Res. (2008).

Computer modeling of problems in cardiac electrophysiology

We have looked into certain computational aspects of action potential propagation modeling. We have found that it is important to respect charge conservation in computer models of finite spatial extent. We have also found that superimposing a secondary, binary tree structure on the cells that make up a conventional, computational grid structure in space is useful in implementing a variable timestep algorithm. (Timesteps that can change dynamically can save considerable computational time, since the timescales in action potential propagation vary tremendously from one part of the action potential to another.)

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