Spatiotemporal Dynamics of Damped Propagation in Excitable Cardiac Tissue Veniamin Y. Sidorov, 1 Rubin R. Aliev, 1 Marcella C. Woods, 2 Franz Baudenbacher, 1 Petra Baudenbacher, 1 and John P. Wikswo 1,2,3 1 Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA 2 Department of Biomedical Engineering, Vanderbilt University, Nashville, Tennessee 37235, USA 3 Department of Molecular Physiology and Biophysics, Vanderbilt University, Nashville, Tennessee 37235, USA (Received 10 June 2002; revised manuscript received 29 August 2003; published 13 November 2003) Compared to steadily propagating waves (SPW), damped waves (DW), another solution to the nonlinear wave equation, are seldom studied. In cardiac tissue after electrical stimulation in an SPW wake, we observe DW with diminished amplitude and velocity that either gradually decrease as the DW dies, or exhibit a sharp amplitude increase after a delay to become an SPW. The cardiac DW-SPW transition is a key link in understanding defibrillation and stimulation close to the refractory period, and is ideal for a general study of DW dynamics. DOI: 10.1103/PhysRevLett.91.208104 PACS numbers: 87.19.Hh, 47.54.+r, 82.40.Ck, 89.75.Kd Introduction.— The physics of the propagation of con- tinuous waves in passive (linear) media has been studied exhaustively and exhibit reflection, refraction, and inter- ference. In the classic example of electromagnetic (EM) waves in vacuum, waves of all frequencies propagate with the same phase velocity, so that a solitary EM pulse can propagate without distortion and can pass through another pulse unchanged. In lossy media, where energy is dissipated, wave amplitude decays as it propagates. In dispersive media, where wavelength depends upon propa- gation velocity, the wave shape can change with time and anomalous dispersion can occur. In active (nonlinear) media, for which losses in the media are accompanied by the release of stored energy, solitary waves of a particular shape can propagate with- out distortion. The wave shape is determined by the governing nonlinear differential equations. Propagating nerve and cardiac action potentials (APs) are examples of solitary waves for which nonlinearities determine bio- logically important phenomena [1]: AP initiation re- quires a suprathreshold electrical stimulus, which in turn depends upon both the stimulus duration and the elapsed time since the previous AP. A minimum time interval, termed the absolute refractory period (ARP), must separate the leading edges of sequential APs, re- gardless of stimulus strength. Because of the ARP, upon collision APs will annihilate each other. Despite the common assumption that the AP has a constant shape and a uniform conduction velocity, experiments reveal that an AP following immediately after another AP will have a deformed shape (termed restitution) and reduced propagation velocity (termed dispersion) as com- pared to one after a longer separation in time [2]. Most of these phenomena are evident, for example, in reentrant cardiac arrhythmias [3]. Reduction of the threshold can increase the sensitivity to extraneous electrical activity and can lead to the spontaneous generation of waves that form expanding target patterns. AP annihilation upon collision results in a volume of tissue being refractory, so that any conduction through that region is blocked for a time longer than the ARP. Conduction block can lead to an AP that propagates over a closed path to form a vortex or more complex reentrant patterns [4]. A reduction in the ARP can lead to higher reentry frequencies, as seen in fibrillation, the most dangerous pattern of all cardiac reentries. Finally, there is an ongoing controversy as to whether reexcitation following an unsuccessful defibril- lation shock arises from an unstable point focus (trig- gered activity), an intramural reentry not visible from the epicardium, or slow propagation in the electrically al- tered postshock tissue [5,6]. In this Letter, we demonstrate experimentally that nonuniform propagation and AP amplitude decay can play an important role in both conduction block and delayed activation. We used isolated rabbit hearts and applied a conditioning electrical stimulus (S 1 ), which produced a solitary AP propagating with constant shape and amplitude. Following a specified interval, we applied a second stimulus (S 2 ), which launches another wave into the wake of the initial one. This protocol is of special interest to the study of the vulnerability of the heart to the initiation of self-maintained, high frequency wave sources that have long been regarded as a precursor to dangerous cardiac arrhythmias [7–9]. A widely accepted mathematical description of vulnerability assumes that the effect of stimulation depends on the S 2 timing: an S 2 soon after S 1 dies out, because it is applied to abso- lutely refractory tissue; an S 2 long after S 1 freely propa- gates, because it is applied to resting tissue; an S 2 applied close to the boundary of absolute refractoriness may result in a discontinuous front that evolves into reentry (see Ref. [8] for details). This description bears its roots in the simple cellular automata model by Wiener and Rosenblueth [9], which assumes only discrete states of the medium occur; i.e., a wave either has a constant shape and propagates steadily, or it disappears. However, as mentioned above, theoretical and experimental observa- tions indicate that the shape, amplitude, and velocity of a PHYSICAL REVIEW LETTERS week ending 14 NOVEMBER 2003 VOLUME 91, NUMBER 20 208104-1 0031-9007= 03=91(20)=208104(4)$20.00  2003 The American Physical Society 208104-1 Sidorov,VY, Aliev,RR, Woods,MC, Baudenbacher,F, Baudenbacher,P, Wikswo,JP. Spatiotemporal Dynamics of Damped Propagation in Excitable Cardiac Tissue. Phys.Rev.Lett., 91, 208104-1-208104, 2003 (Posted with Permission) Posted with permission