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Abstract
This thesis investigates an electrical instability occurring in cardiac cells that leads to a period-2 rhythm called alternans. The transition to alternans, mediated by a bifurcation, is thought to promote ventricular arrhythmias and sudden cardiac death. This research determined the bifurcation type and investigated the mechanisms that drive alternans in paced bullfrog ventricular myocardium, which may have clinical relevance in preventing the development of abnormal heart rhythms. Furthermore, this research has led to a discovery of a new bifurcation type, called an unfolded border-collision bifurcation, which may be useful to classify other systems found in nature.
To determine the bifurcation type, I used an alternate pacing method in which the underlying pacing rate, the key bifurcation parameter, was varied in a long-short pattern with various perturbation sizes prior to the bifurcation. For a cardiac system, the pacing period (the interval time between stimuli applied via an extracellular electrode with approximately 0.2 mV amplitude and 2 ms pulse width) is varied from 1000 ms, indicative of the normal pacing rate, to, at most, 250 ms in steps of 100–25 ms; after reaching steady state at each pacing period, four perturbations sizes (20, 15, 10 and 5 ms) are applied in a long-short repeating pattern to the underlying pacing period in a successive decreasing order. The response to these perturbations at each pacing period reveal the bifurcation type (based on theoretical predictions in generic models that exhibit unique bifurcation types) without having to induce the bifurcation itself.
Experimental implementation of the alternate pacing technique in bullfrog ventricular tissue piece (1 cm x 1 cm x 1 cm triangular top half of the heart with a 3mm thickness) in vitro paced with a bipolar extracellular electrode at room temperature reveals that the bifurcation to alternans is well described by a model that exhibits an unfolded border-collision bifurcation. The smooth features of the model are only detectable when the pacing period is within 25 ms or less prior to the pacing period for which the bifurcation is estimated to occur. The step size of 25 ms is the smallest value that I use experimentally to probe the region prior to the bifurcation point, giving an upper bound on the vicinity of the bifurcation point since the onset of alternans cannot be located exactly experimentally.
In cardiac cells, the change in dynamics near a bifurcation may be due to changes in ionic behavior. I hypothesize that calcium, the ion in the heart responsible for mechanical contraction, is more sensitive to the perturbations applied from alternate pacing, indicative of calcium instability promoting electrical instability. I developed a new experimental setup where I measured voltage at one spatial location via a microelectrode and calcium throughout the tissue via a calcium sensitive dye to study the connection between the onset of the unfolded border-collision bifurcation and changes in intracellular calcium concentration. The calcium sensitive dye is loaded during perfusion at 37°C and the dual-voltage calcium measurements were collected at 20°C. The calcium dye is continually excited via green LEDs (Light Emitting Diodes); in the presence of calcium, the dye fluoresces red light, which is collected via a CCD (Charged Coupled Device). I can measure the response of the dye to changes in intracellular calcium concentration (as low as 3%) spatially at a 10 micron resolution and with a sampling rate of 500 frames per second. My experimental dual measurements of calcium and voltage results suggest that changes in calcium may occur over an even narrower region (less than a 25 ms window) compared to voltage. Therefore, to continue to investigate the role of calcium, my original hypothesis must be modified to investigate changes in calcium less than 25 ms away prior to the bifurcation point. Furthermore, to continue this research, other ions in the cell, such as sodium and potassium, should be investigated to understand their role in driving electrical instability.
