Two forms of spiral-wave reentry in an ionic model of ischemic ventricular myocardium

Abstract

It is well known that there is considerable spatial inhomogeneity in the electrical properties of heart muscle, and that the many interventions that increase this initial degree of inhomogeneity all make it easier to induce certain cardiac arrhythmias. We consider here the specific example of myocardial ischemia, which greatly increases the electrical heterogeneity of ventricular tissue, and often triggers life-threatening cardiac arrhythmias such as ventricular tachycardia and ventricular fibrillation. There is growing evidence that spiral-wave activity underlies these reentrant arrhythmias. We thus investigate whether spiral waves might be induced in a realistic model of inhomogeneous ventricular myocardium. We first modify the Luo and Rudy [Circ. Res. 68, 1501-1526 (1991)] ionic model of cardiac ventricular muscle so as to obtain maintained spiral-wave activity in a two-dimensional homogeneous sheet of ventricular muscle. Regional ischemia is simulated by raising the external potassium concentration ([K(+)](o)) from its nominal value of 5.4 mM in a subsection of the sheet, thus creating a localized inhomogeneity. Spiral-wave activity is induced using a pacing protocol in which the pacing frequency is gradually increased. When [K(+)](o) is sufficiently high in the abnormal area (e.g., 20 mM), there is complete block of propagation of the action potential into that area, resulting in a free end or wave break as the activation wave front encounters the abnormal area. As pacing continues, the free end of the activation wave front traveling in the normal area increasingly separates or detaches from the border between normal and abnormal tissue, eventually resulting in the formation of a maintained spiral wave, whose core lies entirely within an area of normal tissue lying outside of the abnormal area ("type I" spiral wave). At lower [K(+)](o) (e.g., 10.5 mM) in the abnormal area, there is no longer complete block of propagation into the abnormal area; instead, there is partial entrance block into the abnormal area, as well as exit block out of that area. In this case, a different kind of spiral wave (transient "type II" spiral wave) can be evoked, whose induction involves retrograde propagation of the action potential through the abnormal area. The number of turns made by the type II spiral wave depends on several factors, including the level of [K(+)](o) within the abnormal area and its physical size. If the pacing protocol is changed by adding two additional stimuli, a type I spiral wave is instead produced at [K(+)](o)=10.5 mM. When pacing is continued beyond this point, apparently aperiodic multiple spiral-wave activity is seen during pacing. We discuss the relevance of our results for arrythmogenesis in both the ischemic and nonischemic heart. (c) 1998 American Institute of Physics.

Geometric diagnostics of complex patterns: Spiral defect chaos

“…Our results for spiral defect chaos suggest that these measures should provide also insight into other complex states that exhibit chiral structures. Examples include meandering spirals and defect chaos in chemical systems, [1][2][3]28 spirals in the oscillation amplitude of whirling hexagons in rotating non-Boussinesq convection, 27 spirals in vertically vibrated material, 10 patterns of bacterial colonies, 6,7 calcium waves, 11,12 spiral waves in the heart, 49 and in aggregating amoebaes. 13,14 …”

Preventing ventricular fibrillation by flattening cardiac restitution

“…After baseline measurements, bretylium (1 g͞ml) or bretylium ϩ cromakalim (2.86 g͞ml) was added to the perfusate, and the measurements were repeated after 15 min. The concentration of bretylium was progressively increased (5,10,20, and 40 g͞ml) until VF terminated or converted to a periodic ventricular tachycardia (VT). Afterward, rapid pacing was used to test whether or not VF was inducible.…”

Initiation of Ventricular Fibrillation by a Single Ectopic Beat in Three Dimensional Numerical Models of Ischemic Heart Disease: Abrupt Transition to Chaos

“…Such localized disease has been rarely studied before, with two notable exceptions. Previously Xu and Guevara described a two dimensional numerical model with simulated ischemia produced by increasing extracellular [5]. The flat sheet had 1.25 cm square area.…”

“…Xu and Guevara, 1998 [5] Rapid pacing for induction of arrhythmias in a computational model of a 2D sheet with small square of regional "ischemia", mimicked as increased extra-cellular potassium ion concentration direction-dependent conduction velocity (30 cm/sec in the axial and hoop dimensions, 22 cm/sec in the radial dimension). For simplicity, axial and circumferential or hoop velocities are assumed in the net to be equal, in keeping with the generally helical wrapping of muscle fibers in a living heart, as well as the generally modest effects of fiber orientation noted in prior work [6,[16][17][18].…”

“…From the earliest days of computers this particular problem has seemed almost ideal for computational biology, and numerical models of many types abound [1][2][3]. Many are two dimensional sheets of interconnected cells in which waves of activation propagate [4][5][6][7][8]. Some are fully three dimensional and hint that ventricular instability may occur more readily in three dimensions than in two dimensions [9][10][11][12][13][14].…”