**2. Geometry and pathogenesis of ventricular fibrillation**

The exact mechanism of ventricular fibrillation (VF) is still unknown. One of the most accepted hypotheses is that during VF, synchronous contraction of the muscle is disrupted by fast, vortex-like, rotating waves of electrical activity named rotors.[3-6]. The spiral wave rotates about an organizing center, or core, which is thought to be an unexcited but excitable medium that defines the primary dynamic characteristics of the wave. At the core of the vortex is a line of phase singularities (i.e. a region where the phase is undefined) named filament. It seems that, at least in the initial phases, a relatively stable circuit, called the mother rotor, maintains VF.[7] Zaitsev et al[7] used the term domain to define a region in which all of the tissue has the same peak frequency in the VF power spectrum.[8] Optical recordings during VF found that a single domain of highest peak frequency was present, named the dominant domain, and

© 2013 Blendea et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

was surrounded by domains of lower peak frequencies. Some wavefronts that arouse in the dominant domain propagate into domains with lower peak frequencies, and others block at the boundary between domains.[9] These findings suggest that that VF is maintained by a single, stationary, stable reentrant circuit, i.e., the mother rotor, in the dominant domain, which has the shortest refractory period from which activations propagate into the more slowly activating domains with longer refractory periods. Nanthakumar et al [10] demonstrated reentrant wavefronts in human VF, providing a direct demonstration of phase singularities, wavebreaks and rotor formation in severely diseased, explanted human hearts.[11] Impor‐ tantly, they found also wavefronts as large as the entire vertical length of the optical field, which suggested a high degree of organization.[10] Findings from simultaneous epicardial and endocardial multielectrode mapping in patients with cardiomyopathy [12] suggested that during induced VF episodes, stable reentrant wavefronts occur in the endocardium and the epicardium. The same authors demonstrated a stable source in the endocardium, with a highly organized pattern in the local electrogram and a simultaneous and disorganized pattern in the epicardium, consistent with the hypothesis of 3-dimensional scroll waves.[12] Thus, the shortlived rotors on the epicardial and/or endocardial surfaces are thought to be manifestations of a scroll wave organized along the fiber orientation within the wall. Massé et al also observed variable block patterns in wavefront transmission, resulting in disorganized activity and wavefront fragmentation.[12] Rotors may exist alone as stationary high-frequency mother rotors that generate wavefronts that fractionate and disorganize in its periphery. They may also manifest as drifting rotors or even as rotors that rapidly die off leaving multiple offspring wavelets that originate new short-lived rotors and new wavelets.[11]

elliptical disk but a filament.[16] If the myocardial tissue is thick enough to admit a vortex filament lying on its side, the rotor can move more freely, fragment, and close in rings.[16] In numerical experiments with uniformly anisotropic and perfectly continuous and homogene‐ ous three-dimensional excitable media, such vortex filaments spontaneously lash about unless confined to a layer thinner than about a rotor diameter.[16] Apart from reasonably steady rotation, their motion is apparently irregular. It seems that there is a thickness threshold of about one rotor diameter (3 to 10 mm, depending on fiber orientation) that complements the known area threshold for creating and sustaining a rotor (3 mm by 3 or 10 mm perpendicular to thickness, depending on fiber orientation). Together, they constitute a compact critical volume of 3 mm by 3 mm by 10 mm (about 0.1 g of tissue) beyond which reentrant tachycardia (monomorphic or polymorphic) can spontaneously become more complex (fibrillation).[16] Another finding suggesting role of tissue thickness for development of ventricular fibrillation is the observation that rotors in situ have a longer period in thinner (and more epicardial) layers.[17] Another possible contributor to the thickness effect arises from the conspicuous rotation of fiber orientation from epicardium to endocardium. It has been suggested that twist renders vortex filaments unstable.[18] There is a suggestion that thicker myocardium, bearing less twist per unit distance, would be less liable to such instabilities. The thinner right ven‐ tricular free wall is capable of supporting spiral waves more stably, and the thicker left

Defibrillation and Cardiac Geometry http://dx.doi.org/10.5772/55120 31

An interesting analysis that gives more insight into the pathogenesis of rotor is a correlation of body size, heart weight, ventricular surface area, and wall thickness in different mammali‐ ans against the minimum safely sustainable sinus rhythm interval over different species. This analysis assumes that the rotor dynamics is the same in the ventricular myocardium of different mammalian species.[16] Data from mammals including rats, guinea pigs, and man shows that rotors thus turn out to lie on the phylogenetic trend line near the transition from normal hearts that spontaneously defibrillate to normal hearts capable of sustained fibrillation. It seems that ventricles cannot stably beat faster than the rotor period unless they are too small to accommodate a rotor. Individuals susceptible to death by ventricular fibrillation have sufficient ventricular surface dimensions to accommodate a rotor pair (I to 2 cm in longitudinal fiber direction) and have a wall thickness sufficient to accommodate a vortex filament of one rotor diameter [transverse to fibers, with anisotropically reduced electrical scale, about (1 cm)/ 3 = 3 to 4 mm.[16] Structural remodeling has been shown to interfere with rotor behavior. With regards to the ventricles, it has been shown experimentally that the dynamics of VF in the presence of heart failure are different from those in the normal heart. Heart failure remodeling

The only clinically effective method for eliminating vortices in the heart is the delivery of a high-energy electric shock that depolarizes and also hyperpolarizes the tissue with a voltage gradient of about 5 V/cm.[6] In the bidomain representation, the voltage in cardiac tissue is the potential drop between the intracellular and extracellular medium. Theory predicts [20] that,

ventricular wall more often degenerates to fibrillation. [16,19]

decreases VF rate and increases VF organization.[11]

**4. Geometry and defibrillation**
