RAPID COMMUNICATIONS PHYSICAL REVIEW E 91, 030901(R) (2015) Interaction of scroll waves in an excitable medium: Reconnection and repulsion Nirmali Prabha Das and Sumana Dutta * Department of Chemistry, Indian Institute of Technology Guwahati, Guwahati 781039, India (Received 3 August 2014; published 18 March 2015) Scroll waves of reentrant activity and their interactions pose a serious threat to cardiac health. In experiments with the Belousov-Zhabotinsky reaction we demonstrate the interaction of scroll waves. We show that depending on their mutual orientation, two scroll rings can push each other away and rupture on touching the system boundary, or they can reconnect to form a single, large ring. Reconnection only occurs when the filaments lie within one core length of each other. The reconnected filament has extended lifetimes, which could have serious implications in systems where they occur. The experimental results are explained on the basis of a simple numerical model. DOI: 10.1103/PhysRevE.91.030901 PACS number(s): 05.45.−a, 87.19.Hh, 82.40.Ck, 82.40.Qt Spiral waves occur in systems ranging from biology [1] to astrophysics [2], and fluids [3] to superconductors [4]. Scroll waves are the three-dimensional (3D) counterparts of spiral waves, which rotate around a one-dimensional singularity, known as its filament [5]. Their presence in the cardiac tissues is many times the cause of arrhythmias and tachycardias, which finally lead to heart failure [6,7]. So the interaction of scroll waves may have far-reaching consequences on cardiac activity. In fluids and liquid crystals, there is evidence of vortex interaction leading to interesting phenomena like filament reconnection [8–10]. If likewise, scroll rings interact and reconnect, then small rings may merge and form large ones that will have enhanced lifetimes. If this happens in heart tissues, it will ensure a long life of the filaments which in turn will have a detrimental effect on cardiac health. The work reported here is motivated by these concerns. Though the study of scroll waves has been ongoing for quite a few decades [11], only a few computational studies of their interactions have been made [12–14]. Some experiments on the interaction of two-dimensional (2D) spiral cores [15,16] and 3D filaments have been carried out more recently [17], but no instances of scroll-wave reconnection have yet been demonstrated. In this Rapid Communication, we report the experimental evidence of scroll-wave reconnection. Our results demonstrate that when two scroll rings are brought close enough, they can either attract each other, and reconnect to form a large scroll ring, or they can repel so that they rupture on touching the boundaries. We also carry out simple numerical simulations that help explain the filament behavior in our experiments. Both the phenomena will have important consequences on the nature and lifetime of the scroll waves. For our studies in scroll-wave interaction, we use the three-dimensional Belousov-Zhabotinsky reaction, which is a simple laboratory model where scroll waves can be directly observed [18–23]. Our experimental system was embedded in a 0.8% w/v agar gel matrix. The mixture contained 0.04 M sodium bromate, 0.04 M malonic acid, 0.16 M sulphuric acid, 0.5 mM ferroin, and 0.1 mM SDS (sodium dodecyl sulfate). SDS was added to prevent the formation of CO 2 bubbles during the later stages of the experiment. For the first set of experiments, we initiated two nonrotating semispherical waves * sumana@iitg.ernet.in some distance apart, touching the tip of a silver wire into a 5-mm-thick Belousov-Zhabotinsky (BZ) gel layer. When the two waves expanded to their required size, and were approximately 1–2 mm apart, another layer of BZ gel was poured over this layer. The semispherical waves curled into the top layer and formed a pair of scroll waves with circular filaments. Both the filaments were coplanar and had a similar sense of rotation. In order to study scroll-wave interactions between filaments having an opposite sense of rotation, we prepared two gel layers, each with a thickness of about 5 mm, in two separate Petri dishes. Two nonrotating half spheres were generated in each one by initiation with a silver wire. When the waves reached desirable dimensions, we placed one Petri dish over the other. The waves curled into the facing gel layer and formed two scroll rings, whose filaments are placed one over the other. We illuminated our experimental system from below, using diffused white light and monitored it from above with a charge coupled device camera (mvBlueFOX 220a) through a blue filter. The images were recorded onto a computer at an interval of 2 s and the data analyzed using MATLAB codes. In our analysis of the filament interactions, we have assigned a direction along the tangent to the filament at a particular point, via the right-hand rule [14]. This utilizes the curl of the motion of the constituent spirals around the said point on the filament. Thus a unique direction of travel along the ring is defined. The two scroll rings that are formed side by side on the gel, have a clockwise sense of rotation when viewed from the top, while the scroll rings that are formed with their kernels facing each other, have an opposite sense of rotation. Figure 1 summarizes the results of experiments involving interacting scroll rings with the same sense of rotation. During the scroll initiation process, if the half-spherical waves are too close, on pouring the second gel layer over them the wave fronts merge, and a single scroll wave is formed. When we increase the distance between the wave fronts, two independent scroll rings are generated. However in most cases, the distance between them keeps on increasing, as they shrink under their positive filament tension, known to exist for the filaments in the BZ system. Only within a very specific range of interfilament distance, do the two filaments undergo reconnection. Figure 1 is such an example where scroll-wave reconnection has been observed. Figure 1(a) shows the initiation of two scroll waves formed at a close proximity. The dark region in Fig. 1(e) marks 1539-3755/2015/91(3)/030901(4) 030901-1 ©2015 American Physical Society