ACTION POTENTIAL DURATION HETEROGENEITY IN A COMPUTER MODEL OF THE ATRIA

Edward J. Vigmond¹, Samuel Kuo² and Natalia A. Trayanova^2
1Department of Electrical and Computer Engineering, University of Calgary,
2500 University Dr. NW,Calgary, CANADA, T2N 1N4
²Department of Biomedical Engineering, Tulane University,
New Orleans, USA, 70118

Abstract: Atrial fibrillation is the most common form of cardiac arrhythmia yet it remains poorly understood. Two differing views exist as to the nature of the underlying activity sustaining the fibrillation: (1) Moe’s multiple wavelet hypothesis suggests that multiple meandering wavefronts exist which continuously fractionate and collide, while (2) Lewis’s mother wavelet hypothesis posits a stable circuit of of which break unstable daughter wavelets. Vagal stimulation converts flutter into fibrillation by reducing action potential duration (APD) but does so in a spatially nonuniform way. This study uses a morphologically realistic computer representation of the atria to examine reentrant activity resulting from vagal stimulation of a flutter circuit. Vagal stimulation was incorporated by introducing islands of reduced APD which were varied in number, size and extent of APD reduction. With uniform APD, reentry was not induced. Adding small vagal effects established a stable flutter which was anchored around the superior vena cava. Increasing vagal stimulation caused the flutter circuit to spawn small wavelets, usually two. Further APD reduction once again established a stable rotor. Results suggest fibrillation is caused by a mother wavelet since anatomical considerations restrict reentrant pathways given the wavelength of the tissue.

INTRODUCTION

Atrial fibrillation (AF) is the most common form of cardiac arrhythmia yet remains poorly understood. It impacts severely on health, increasing the incidence of stroke and reducing cardiac function. One route to fibrillation is the breakdown of a stable flutter circuit, but there are two views as to the nature of the activation pattern underlying fibrillation. The first, the multiple wavelet theory, holds that AF is the result of a critical number of selfperpetuating but highly unstable wavefronts which constantly collide and fractionate, producing an everchanging, chaotic excitation pattern[1]. The second view posits the existence of a stable mother wavelet continually spawning unstable daughter wavelets which quickly annihilate themselves by running into refractory tissue[2]. Both mechanisms produce irregular electrograms as recorded during bouts of AF.

Figure 1: Interconnectedcable model. Sample shells from the left and right atrium and the conducting sheath of the coronary sinus (CS). Openings for the pulmonary veins (PV) and the superior vena cava (SVC) are indicated.

One factor which has been implicated in the conversion of flutter into fibrillation is action potential duration (APD) heterogeneity brought about by vagal stimulation[3]. Vagal stimulation releases acetylcholine (ACh) which decreases APD in a dose dependent manner. In addition, ACh is released from discrete nerve endings which are sparsely distributed, resulting in pockets of reduced APD. Hence, APD is highly nonuniform during vagal stimulation.

The study aims to determine the effect of APD dispersion on a flutter circuit, and specifically, whether the fibrillation resulting from vagal effects is due to a set of chaotically meandering wavefronts or, is consistent with the mother wavelet hypothesis. A computationally efficient computer model which incorporates the major morphological features of the atria has been previously developed[4] and will be used here. In addition, the APD dispersion patterns needed to produce fibrillation will be determined and any resultant activation patterns examined.

METHODS

A computer model of the atria was constructed using the interconnected cable method[4], which described the atria by a set of one dimensional cables which were connected by fixed resistances representing gap junctions. The cables represented muscle fibers and followed physiological paths.

Orifices for veins and coronary sinus were introduced by distorting the cables in the region of the opening. The model comprised the right and left atria, Bachmann’s Bundle, the crista terminalis, discrete pectinate muscles, the conducting rim of the fossa ovalis (FO), and the muscular sheath of the coronary sinus (CS). Conduction from the right to left atrium was through a discrete number of regions: (1) Bachmann’s Bundle; (2) the conducting rim of the FO; and, (3) the muscular sheath of the CS. The left and right atrium were made of a number of layers. Each cable was segmented into 100 µm lengths yielding a model with 320,000 nodes. Ionic current dynamics in the model was described by the RamirezCourtemanche set of equations[5] which resulted in 27 differential equations per computational node. Model parameters were chosen so that activation times matched those measured experimentally. Simulation of 1 second required 1.5 hours of wall clock time on 8 R10000 MIPS processors.

Reentry was initiated by applying a cross shock protocol. Propagation originated in a region corresponding to the SA node. Approximately 200 ms later, a premature S2 stimulus was delivered to the right atrial free wall, resulting in scroll wave formation. APD heterogeneity was introduced by creating islands of shortened APD as occurs under vagal stimulation. APD was decreased by increasing the conductances of the transient outward and potassium currents while decreasing the conductance of the calcium current[6]. Different APD distributions were examined to ascertain the effects on the scroll wave activity.

RESULTS

With uniform APD of 168 ms, the S1S2 protocol failed to produce a scroll wave. Even though a fairly large region was affected by S2, sufficient recovery had not occurred by the time the wavefront initiated by the S2 returned to the site of the S2. With 9 islands, a scroll wave was established when the APD was reduced to 119 ms. The wave rotated around the superior vena cava (SVC). The scroll wave had a period of 105 ms and was stable, still being present after 3 seconds. The left atrium was activated by waves travelling across from the right. The rim of the FO or the Bachmann’s bundle were the preferred pathways by which activity propagated although occasionally, the CS sheath proved to be the initiating pathway. No scroll wave was established in the left atrium under these conditions.

With the same number of islands, decreasing the APD further to 81 ms, caused small wavelets to spawn of of the scroll wave. The wavelets were short lived, quickly running into refractory tissue. At least two wavelets were usually present at any point in time. The scroll wave was less well anchored to the SVC. Decreasing the APD in the islands below 51 ms resulted in a scroll wave anchored around the SVC with a period of 138 ms, which did not spawn wavelets.

DISCUSSION

Fibrillation in this model corresponded to the mother wavelet hypothesis. A single stable scroll wave was anchored around the SVC in the right atrium. Daughter wavelets would emanate form this wavelet so that there were approximately 3 wavefronts present. The scroll wave seemed to be fixed due to the constraints imposed by the dimensions of the right atrium and the anatomical openings. Due to the wavelength of the tissue, there are a limited number of ways in which a stable scroll wave can establish itself on the right atrium. Furthermore, the openings for the veins further limit the pathways which may form. When vagal stimulation was applied, it was not uniform leaving regions of original APD which formed functional barriers and inhibited the formation of shorter circuits. Using this ionic model, the restitution properties of the tissue were not sufficiently altered to produce the breakup required for the multiple wandering wavelets type of fibrillation.

Figure 2: Multiple wavefronts on right atria under vagal stimulation. The transmembrane voltage is indicated by the grey scale.

ACKNOWLEDGMENT

This work was supported by the American Heart Association, Southern Affiliate Grant 0151084B and through a University of Calgary Startup Grant.

REFERENCES

[1] G. Moe, "On the multiple wavelet hypothesis of atrial fibrillation," Arch Int Pharmacodyn Ther., vol. 140, pp. 183–188, 1962.

[2] T. Lewis, The Mechanism and Graphic Registration of the Heart Beat. London, UK: Shaw & Sons, 3 ed., 1925.

[3] W. Smith and A. Wallace, "Management of Arrhythmias and Conduction Abnormalities," in The Heart (J. Hurst, ed.), vol. 1, ch. 27, pp. 475–485, New York: McGrawHill, Inc., 6 ed., 1986.

[4] E. Vigmond, R. Ruckdeschel, and N. Trayanova, "Reentry in a Morphologically Realistic Atria," J. Cardiovasc. Electrophys., vol. 12, no. 9, pp. 1046–54, 2001.

[5] R. Ramirez, S. Nattel, and M. Courtemanche, "Mathematical analysis of canine atrial action potentials: rate, regional factors, and electrical remodelling," Am J Physiol, vol. 279, pp. H1767–1785, 2000.

[6] J. Feng, L. Yue, Z. Wang, and S. Nattel, "Ionic mechanisms of regional action potential heterogeneity in the canine right atrium," Circ. Res., vol. 83, pp. 541–551, 1998.