**3. Rotors and heart geometry**

Rotors are common to many biological, chemical and physical excitable media and their dynamics have been researched intensively. The specific anatomical structure of the cardiac chambers is likely to be a crucial factor in determining the fibrillatory behavior. The hetero‐ geneity of the ventricular anatomy is likely to play an important role in rotor dynamics. For example, the thicker left ventricular wall may manifest the complex dynamics of 3-dimensional scroll waves much more readily than the thinner right ventricle and the atrial walls. There is a left-to-right gradient of dominant frequencies, suggesting that the left heart may be playing the leading role in maintaining fibrillation. [11] Kim et al. suggested that sink-to-source mismatch between areas with different thickness in the ventricle may serve to anchor rotors [13] and these rotors may span the thickness of the ventricular wall. For instance, the papillary muscles in the LV may help to stabilize rotors.[11,14]

A thickness threshold is sought at which complex and changing short-period wave behavior abruptly becomes more organized into simple drifting spiral waves of slightly longer period. [15 16] Such a threshold was indeed found in canine ventricles and bears the same relation to rotor period and representing about 1/π times the distance a spiral wave propagates during one rotation period.[16] This distance is the nominal diameter of the rotor, the source of the reentrant activation front. In three dimensions, this source is not, as in two dimensions, a small 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 ventricular wall more often degenerates to fibrillation. [16,19]

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 decreases VF rate and increases VF organization.[11]

## **4. Geometry and defibrillation**

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]

Rotors are common to many biological, chemical and physical excitable media and their dynamics have been researched intensively. The specific anatomical structure of the cardiac chambers is likely to be a crucial factor in determining the fibrillatory behavior. The hetero‐ geneity of the ventricular anatomy is likely to play an important role in rotor dynamics. For example, the thicker left ventricular wall may manifest the complex dynamics of 3-dimensional scroll waves much more readily than the thinner right ventricle and the atrial walls. There is a left-to-right gradient of dominant frequencies, suggesting that the left heart may be playing the leading role in maintaining fibrillation. [11] Kim et al. suggested that sink-to-source mismatch between areas with different thickness in the ventricle may serve to anchor rotors [13] and these rotors may span the thickness of the ventricular wall. For instance, the papillary

A thickness threshold is sought at which complex and changing short-period wave behavior abruptly becomes more organized into simple drifting spiral waves of slightly longer period. [15 16] Such a threshold was indeed found in canine ventricles and bears the same relation to rotor period and representing about 1/π times the distance a spiral wave propagates during one rotation period.[16] This distance is the nominal diameter of the rotor, the source of the reentrant activation front. In three dimensions, this source is not, as in two dimensions, a small

**3. Rotors and heart geometry**

30 Cardiac Defibrillation

muscles in the LV may help to stabilize rotors.[11,14]

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, in the presence of an electric field, discontinuities in tissue conductivity, such as blood vessels, changes in fiber direction, fatty tissue and intercellular clefts, induce a redistribution of intracellular and extracellular currents that can locally hyperpolarize or depolarize the cells. At the depolarization threshold, an excitation wave is emitted.[6,20,21] Conceptually, defib‐ rillation can be considered to be a two-step process. Firstly, the applied shock drives currents that traverse the myocardium and cause complex polarization changes in transmembrane potential distribution. Secondly, post-shock active membrane reactions are invoked that eventually result either in termination of ventricular fibrillation in the case of shock success, or in reinitiation of fibrillatory activity in the case of shock failure.[22]

Detailed analysis of VEP etiology demonstrated that both applied field [24] and tissue structure are major determinants of the shape, location, polarity and intensity of the shock-induced polarization.[24,27] The cellular response to shock-induced VEP depends on the strength and polarity of the shock, as well as on the electrophysiological state of the cell at the time of shock delivery.[27] There is a relationship between the response of the tissue to an electric field and the spatial distribution of heterogeneities in the scale-free coronary vascular structure. In response to a pulsed electric field, these heterogeneities serve as nucleation sites for the generation of intramural electrical waves that can generate tissue depolarization. These intramural wave sources permit targeting of electrical turbulence near the cores of the vortices of electrical activity that drive complex fibrillatory dynamics. Simultaneous and direct access to multiple vortex cores results in rapid synchronization of cardiac tissue and therefore, efficient termination of fibrillation. Using this control strategy, Luther et al. demonstrated lowenergy termination of fibrillation in vivo. Their results give new insights into the mechanisms and dynamics underlying the control of spatio-temporal chaos in heterogeneous excitable media and provide new research perspectives towards alternative, life-saving low-energy

Defibrillation and Cardiac Geometry http://dx.doi.org/10.5772/55120 33

**5. Geometry and lead positioning for cardiac defibrillation**

Most models used to describe defibrillation view the myocardial mass as an isotropic conduc‐ tive domain and use the critical mass hypothesis to define successful defibrillation. According to this hypothesis the success of a defibrillation shock depends on rendering a critical mass of the myocardium inexcitable, such that fibrillation wavefronts have no myocardium to depolarize and propagate through.[19] It has been found that raising the extracellular potential gradient above a critical level renders myocardium refractory.[31] Frazier et al.[32] have found the critical level of potential gradient to be close to 5 V/cm, and a commonly accepted value

In a recent study Yang et al. examined the effect of coil position on active-can single-coil ICD defibrillation efficacy by using a finite difference thoracic model which incorporated realistic geometries and conductive inhomogeneities of human thoracic tissues. [34] Four electrode configurations with the coil placed, respectively, in the right ventricular (RV) apex, in the middle of RV cavity, along the free wall in RV, or along the septal wall in RV, were simulated and their defibrillation efficacies were evaluated based on a set of metrics including voltage defibrillation threshold (VDFT) and current defibrillation threshold. It was found that the

optimal electrode configuration is to position the coil in the middle of the RV cavity.

in myocardial tissue as its resistivity value is one-third larger than blood's.

The RV cavity-to-can configuration had more endocardium exposed to the more uniform and relatively high voltage gradient fields. Other configurations exposed only endocardic surfaces near the electrodes to high voltage gradient fields and the voltage gradient drops more quickly

Aguel et al[35] used a high-resolution finite element model of a human torso that includes the fiber architecture of the ventricular myocardium to find the role of lead positioning in a

defibrillation techniques.[6]

for critical myocardial mass is 95%. [33]

Over a decade ago, bidomain simulations[23] followed by optical mapping studies [24,25] demonstrated that the membrane response in the vicinity of a strong unipolar stimulus involved simultaneous occurrence of positive (depolarizing) and negative (hy‐ perpolarizing) effects in close proximity. This finding of 'virtual electrodes' was in con‐ trast with the established view [26] that tissue responses should only be depolarizing (hyperpolarizing) if the stimulus was cathodal (anodal).[27] Essentially, the virtual elec‐ trode polarization (VEP) theory states that adjacent areas of opposite polarizations exist around the tip of the pacing electrode.[28] Sepulveda et al. [23] showed that the region depolarized (excited) by a strong stimulus has a dog-bone shape, with its long axis per‐ pendicular to the direction of the myocardial fibers. Regions of hyperpolarization (called virtual anodes) exist adjacent to the electrode along the fiber direction. A virtual anode is an example of a virtual electrode. Many researchers have observed these regions of de‐ polarization and hyperpolarization experimentally. [25,29] Depolarization can excite a cell and conversely, hyperpolarization can de-excite a cell. The cellular response to shock-in‐ duced VEP depends on the strength and polarity of the shock, as well as on the electro‐ physiological state of the cell at the time of shock delivery. Positive VEP can result in regenerative depolarization in regions where tissue is at or near diastole; such activation is termed 'make' because it takes place at the onset (make) of the shock. A strong nega‐ tive VEP can completely abolish the action potential (i.e. regenerative repolarization), thus creating post-shock excitable gaps in the virtual anode regions. The close proximity of a de-excited region and a virtual cathode has been shown, in both modelling studies and optical mapping experiments,[25] to result in an excitation at shock end (termed 'break' excitation, i.e. at the break of the shock). The virtual cathode serves as an electri‐ cal stimulus eliciting a regenerative depolarization and a propagating wave in the newly created excitable gap.[27] For a defibrillation shock to succeed, it must extinguish exist‐ ing VF activations throughout the myocardium (or in a critical mass of it), as well as not initiate new fibrillatory wavefronts.[27] A shock succeeds in extinguishing fibrillatory wavefronts and not initiating new re-entry if make/break excitations manage to traverse the shock-induced excitable gaps before the rest of the myocardium recovers from shockinduced depolarization.[27] Defibrillation failure has been explained by one (or both) of the following mechanisms: (I) the shock fails to extinguish all or a sufficient amount of fibrillatory electrical activity and (2) newly created shock-induced wavebreaks by nearthreshold stimulating fields occurring at existing excitable gaps.[30]

Detailed analysis of VEP etiology demonstrated that both applied field [24] and tissue structure are major determinants of the shape, location, polarity and intensity of the shock-induced polarization.[24,27] The cellular response to shock-induced VEP depends on the strength and polarity of the shock, as well as on the electrophysiological state of the cell at the time of shock delivery.[27] There is a relationship between the response of the tissue to an electric field and the spatial distribution of heterogeneities in the scale-free coronary vascular structure. In response to a pulsed electric field, these heterogeneities serve as nucleation sites for the generation of intramural electrical waves that can generate tissue depolarization. These intramural wave sources permit targeting of electrical turbulence near the cores of the vortices of electrical activity that drive complex fibrillatory dynamics. Simultaneous and direct access to multiple vortex cores results in rapid synchronization of cardiac tissue and therefore, efficient termination of fibrillation. Using this control strategy, Luther et al. demonstrated lowenergy termination of fibrillation in vivo. Their results give new insights into the mechanisms and dynamics underlying the control of spatio-temporal chaos in heterogeneous excitable media and provide new research perspectives towards alternative, life-saving low-energy defibrillation techniques.[6]
