Humberto Arce

Alternans and higher-order rhythms in an ionic model of a sheet of ischemic ventricular muscle

Life-threatening arrhythmias such as ventricular tachycardia and fibrillation often occur during acute myocardial ischemia. During the first few minutes following coronary occlusion, there is a gradual rise in the extracellular concentration of potassium ions ([K(+)](0)) within ischemic tissue. This elevation of [K(+)](0) is one of the main causes of the electrophysiological changes produced by ischemia, and has been implicated in inducing arrhythmias. We investigate an ionic model of a 3 cmx3 cm sheet of normal ventricular myocardium containing an ischemic zone, simulated by elevating [K(+)](0) within a centrally-placed 1 cmx1 cm area of the sheet. As [K(+)](0) is gradually raised within the ischemic zone from the normal value of 5.4 mM, conduction first slows within the ischemic zone and then, at higher [K(+)](0), an arc of block develops within that area. The area distal to the arc of block is activated in a delayed fashion by a retrogradely moving wavefront originating from the distal edge of the ischemic zone. With a further increase in [K(+)](0), the point eventually comes where a very small increase in [K(+)](0) (0.01 mM) results in the abrupt transition from a global period-1 rhythm to a global period-2 rhythm in the sheet. In the peripheral part of the ischemic zone and in the normal area surrounding it, there is an alternation of action potential duration, producing a 2:2 response. Within the core of the ischemic zone, there is an alternation between an action potential and a maintained small-amplitude response ( approximately 30 mV in height). With a further increase of [K(+)](0), the maintained small-amplitude response turns into a decrementing subthreshold response, so that there is 2:1 block in the central part of the ischemic zone. A still further increase of [K(+)](0) leads to a transition in the sheet from a global period-2 to a period-4 rhythm, and then to period-6 and period-8 rhythms, and finally to a complete block of propagation within the ischemic core. When the size of the sheet is increased to 4 cmx4 cm (with a 2 cmx2 cm ischemic area), one observes essentially the same sequence of rhythms, except that the period-6 rhythm is not seen. Very similar sequences of rhythms are seen as [K(+)](0) is increased in the central region (1 or 2 cm long) of a thin strand of tissue (3 or 4 cm long) in which propagation is essentially one-dimensional and in which retrograde propagation does not occur. While reentrant rhythms resembling tachycardia and fibrillation were not encountered in the above simulations, well-known precursors to such rhythms (e.g., delayed activation, arcs of block, two-component upstrokes, retrograde activation, nascent spiral tips, alternans) were seen. We outline how additional modifications to the ischemic model might result in the emergence of reentrant rhythms following alternans. (c) 2000 American Institute of Physics.

Triggered alternans in an ionic model of ischemic cardiac ventricular muscle

It has been known for several decades that electrical alternans occurs during myocardial ischemia in both clinical and experimental work. There are a few reports showing that this alternans can be triggered into existence by a premature ventricular contraction. Detriggering of alternans by a premature ventricular contraction, as well as pause-induced triggering and detriggering, have also been reported. We conduct a search for triggered alternans in an ionic model of ischemic ventricular muscle in which alternans has been described recently: a one-dimensional cable of length 3 cm, containing a central ischemic zone 1 cm long, with 1 cm segments of normal (i.e., nonischemic) tissue at each end. We use a modified form of the Luo-Rudy [Circ. Res. 68, 1501-1526 (1991)] ionic model to represent the ventricular tissue, modeling the effect of ischemia by raising the external potassium ion concentration ([K(+)](o)) in the central ischemic zone. As [K(+)](o) is increased at a fixed pacing cycle length of 400 ms, there is first a transition from 1:1 rhythm to alternans or 2:2 rhythm, and then a transition from 2:2 rhythm to 2:1 block. There is a range of [K(+)](o) over which there is coexistence of 1:1 and 2:2 rhythms, so that dropping a stimulus from the periodic drive train during 1:1 rhythm can result in the conversion of 1:1 to 2:2 rhythm. Within the bistable range, the reverse transition from 2:2 to 1:1 rhythm can be produced by injection of a well-timed extrastimulus. Using a stimulation protocol involving delivery of pre- and post-mature stimuli, we derive a one-dimensional map that captures the salient features of the results of the cable simulations, i.e., the {1:1-->2:2-->2:1} transitions with {1:1<-->2:2} bistability. This map uses a new index of the global activity in the cable, the normalized voltage integral. Finally, we put forth a simple piecewise linear map that replicates the {1:1<-->2:2} bistability observed in the cable simulations and in the normalized voltage integral map. (c) 2002 American Institute of Physics.

MINIMUM ENERGY CONFIGURATIONS OF ATOMS ADSORBED ON A LATTICE

Abstract The minimum energy arrangements of atoms adsorbed on a crystalline surface display a very rich set of geometries originated from the competition between the adsorbate-adsorbate interaction, and the tendency to occupy the most favorable adsorption sites over the substrate. We develop a method to obtain these geometries for rational coverages assuming the adsorbates occupy symmetric sites and that they form a lattice commensurate with the substrate, allowing for multi-atomic primitive cells. We obtain results for adsorption on a square lattice with truncated-dipolar interactions. We propose a new truncation scheme which we compare with previous ones, and we explore the effects of changing the range of the potential. The ordered phases we obtain agree with experiments performed for K over Ir(001) and Cs over Rh(001). Furthermore, our results supply some insight on the absence of observed ordered phases for some rational coverages.

Minimum energy 2D patterns of atoms adsorbed on a hexagonal lattice

Abstract We obtain the lowest energy 2D arrangements of atoms adsorbed on a hexagonal lattice, assuming rational coverage and a repulsive dipolar adsorbate-adsorbate interaction. To this end we exhaustively explore the ordered arrangements compatible with the coverage, including those that have multiatomic unit cells. For some coverages (θ = 1/3, 1/4 and 1/7) we find a well defined ground state, and for others a nearly infinite degeneracy related to the possibility of creating dense arrays of linear defects with a negligible energy cost. We compare our results with some experimental determinations of surface structures in alkali overlayers on fcc (111) and hcp (0001) metal faces. Except for those systems that form islands, we have found agreement between our predicted ground states and experiment. Furthermore, no ordered structures with the coverages of our near degenerate states have been observed.

Recurrence Analysis of Cardiac Restitution in Human Ventricle

The cardiac restitution curve describes functional relationships between diastolic intervals and their corresponding action potential durations. Although the simplest relationship is that restitution curves are monotonic, empirical studies have suggested that cardiac patients present a more complex dynamical process characterized, for instance, by a non-monotonic restitution curve. The purpose of this chapter is to analyze the dynamical properties of a non-monotonic cardiac restitution curve model derived from previously published clinical data. To achieve this goal, we use Recurrence Quantitative Analysis combined with Lyapunov exponents and Supertrack Functions in order to describe the complex dynamics underlying non-monotonic restitution curves. We conclude by highlighting that a consequence of the advanced complex dynamics that emerges from the aforementioned non-monotonicity, is the increasing risk of alternant rhythms.