Optimizing Defibrillation Therapy
Several multicenter clinical trials have provided consistent evidence that implantable defibrillation therapy prolongs patient life. This convincing demonstration of efficacy has led to a nearly exponential growth, over the last decade, in the number of patients receiving implantable devices. Currently, approximately 0.2 million implantable cardioverter-defibrillators (ICDs) are implanted every year throughout the world. Although ICD therapy has proven to be efficient and reliable in preventing sudden cardiac death,138 with success rates clearly superior to other therapeutic options such as pharmacological antiarrhythmia therapy,139 it is far from ideal. There are several known adverse effects secondary to the administration of electrical shocks; the most prominent are linked to electroporation140 (ie, the formation of pores in the cellular membrane that allow the free and indiscriminate redistribution of ions, enzymes, and large molecules between intracellular and interstitial space) and its aftereffects, which are indirectly caused by the high field strengths required to terminate arrhythmias such as ventricular fibrillation (VF) with sufficiently high probability. More importantly, psychological effects on patients play a nonnegligible role. Conscious patients may perceive shock delivery as extremely painful, which leads to traumatization and reduction in quality of life. Although pain may be tolerable in those cases where shock delivery terminates an otherwise lethal arrhythmia, this is less likely in those cases where inadequate shocks were delivered due to high-voltage component malfunctions of the device. A recent meta-analysis of industrial reports3 concluded that such malfunctions are much more frequent than expected, with thousands of patients being affected. Further, clinical data from ICD trials suggested that six of seven shocks delivered can be classified as inadequate, indicating that the amount of overtreatment in the ICD population is significant.139
A substantial reduction in shock energy can only be achieved by full appreciation of the mechanisms by which a shock interacts with the heart and by devising novel therapeutic approaches on their basis. However, despite major advances in both experimental technology and computational modeling, our understanding of the biophysical basis of defibrillation remains incomplete. Further progress has been hampered by the inability of current experimental techniques to resolve electrical events in 3D during and after shock delivery with sufficiently high spatiotemporal resolution. Current mapping techniques are limited to record electrical activity from cardiac surfaces only and thus are incapable of detecting electrical events in the depth of the myocardium, which may exist there without any signature at the surfaces.26 Computer models were introduced as a means to overcome experimental limitations, allowing the observation of electrical events within the depth of the myocardium. Initially, monodomain models were used, but theory and simulations predicted shock-induced changes in transmembrane voltage, ΔVm, only along tissue boundaries and conductive discontinuities in the heart. These predictions contradicted experimental studies that had established that a critical mass of the tissue of approximately 95%141,142 has to be affected by a sufficiently strong gradient of >5 V/cm143,144 to be effective. Later, the "missing link"145 that could explain shock-induced polarizations in the far field was discovered with the advent of the bidomain model, which predicted the existence of "virtual electrodes" (ie, polarizations that occur far from any physical electrode).85
Conceptually, defibrillation can be considered to be a two-step process. First, the applied shock drives currents that traverse the myocardium and cause complex polarization changes in transmembrane potential distribution.81 Second, postshock active membrane reactions are invoked that eventually result either in termination of fibrillation in the case of shock success or in reinitiation of fibrillatory activity in the case of shock failure. Using computer models to analyze the etiology of "virtual electrode polarization" (VEP) patterns during the shock application phase revealed that shape, location, polarity, and intensity of shock-induced VEP are determined by both the cardiac tissue structure and the configuration of the applied field.81,146,147 Based on theoretical considerations, VEPs can be classified either as "surface VEP," which penetrates the ventricular wall over a few cell layers, or as "bulk VEP," where polarizations arise throughout the ventricular wall.148,149 Analysis of the bidomain equations revealed that a necessary condition for the existence of the bulk VEP is the presence of unequal anisotropies in the myocardium. Sufficient conditions include either spatial nonuniformity in applied electric field or nonuniformity in tissue architecture, such as fiber curvature, fiber rotation, fiber branching and anastomosis, and local changes in tissue conductivity due to resistive heterogeneities. A mathematical rationale supporting these notions is given in the "Theoretical Considerations for Low-Voltage Defibrillation" section.
The cellular response depends on VEP magnitude and polarity as well as on preshock state of the tissue. APD can be either extended (by positive VEP) or shortened (by negative VEP) to a degree that depends on VEP magnitude and shock timing, with strong negative VEP completely abolishing (de-exciting) the action potential, thus creating postshock excitable gaps. As demonstrated in bidomain modeling studies,26,150 the postshock VEP pattern is also the major determinant of the origin of postshock activations. In those regions where shock-induced virtual anodes and virtual cathodes are in close proximity, a "break" excitation at shock-end (ie, the "break" of the shock) can be elicited. The virtual cathode serves as an electrical stimulus eliciting a regenerative depolarization and a propagating wave in the newly created excitable area. Whether or not break excitations arise depends on whether the transmembrane potential gradient across the border spans the threshold for regenerative depolarization.151 The finding of break excitations, combined with the fact that positive VEP can result in "make" excitations (where "make" refers to the onset of a shock) in regions where tissue is at or near diastole, resulted in a novel understanding of how a strong stimulus can trigger the development of new activations.
According to VEP theory, mechanisms for shock success or failure are multifactorial depending mainly on postshock distribution of Vm as well as timing and speed of propagation of shock-induced wave fronts. Whether the depolarization of the postshock excitable gap is achieved in time critically depends on number and conduction velocity of postshock activations, as well as the available time window that is bounded by the instant at which refractory boundaries enclosing the excitable regions recover excitability. All factors ultimately depend on shock strength. Increasing shock strength results in higher voltage gradients across borders between regions of opposite polarity, leading to more break excitations,151 which then start to traverse the postshock excitable gap earlier116 and at a faster velocity,151 as well as extending refractoriness to a larger degree.152
Optimization Strategies for Lowering Defibrillation Threshold
Although ICD therapy has improved over the years, no major breakthrough was achieved that would allow the lowering of defibrillation threshold (DFT) substantially. Incremental technical refinements were implemented that led to smaller, longer lasting devices and less invasive implantation procedures. Many parameters such as size, geometry, and location of coils and can relative to the heart, as well as the waveform of the delivered pulse and the timing of the shock, play an important role in determining DFT. The large number of parameters and their nontrivial relationship renders optimizing an ICD configuration a challenging task. A large body of research exists that deals with optimization of shock waveforms. It has been demonstrated that biphasic153-155 or multiphasic156-158 waveforms defibrillate at a lower threshold than monophasic waveforms and that truncated exponential pulses further increase the efficiency.159 In addition to shock waveforms, optimization of lead placement has also seen increases in defibrillation efficacy. However, despite the many optimizations, shock energies delivered by current ICDs remain more than one order of magnitude too high to render defibrillation painless.
Although VEP theory provides a sound framework to describe mechanisms underlying success and failure of defibrillation shock in a high-voltage regimen, the theory does not lend itself easily to derive strategies that would facilitate defibrillation in a low-voltage regimen. Approaches to lower DFT by using more creative protocols are under examination; however, so far, only antitachycardia pacing (ATP) has gained clinical relevance. ATP is clinically applied with high success rates of 78% to 91% with VTs in the range of 188 to 200 beats/min and with similar success rates with faster VTs (200-250 beats/min).2 Although the underlying mechanisms are not fully understood, the therapy aims at eliciting new wave fronts by pacing the excitable gap instead of trying to reset the tissue via a strong shock. For ATP to work, it is assumed that the organizing center of a reentry is accessible from a chosen pacing site. With reentries characterized by a fairly stable cycle length, a proper timing for a pacing pulse can be chosen by delivering a series of pulses at a pacing frequency that is higher than the intrinsic frequency of the circuit such that each pacing pulse is delivered progressively closer to the wave back of the reentry. Once a stimulus falls sufficiently close to the wave back, a unidirectional block occurs, and extinction of the arrhythmia is accomplished by collision with the approaching wave front. Empirically, it has been shown that success rates are highest at approximately 88% of the cycle length with ventricular rates <250 beats/min.2 For faster activation rates or for more complex arrhythmias, ATP is more likely to fail, and a high-energy defibrillation shock has to be delivered, even if the arrhythmia has not degenerated into VF.
An alternative approach to avoid high-energy shocks has been suggested by Ripplinger et al,160 which targets arrhythmias driven by reentrant cores attached to anatomic obstacles. The proposed therapy is based on destabilizing such a reentry by unpinning the reentrant core from the anatomic obstacle. The unpinned reentry either self-terminates when encountering a tissue boundary or repins and anchors to another heterogeneity. The unpinning mechanism relies on the formation of VEPs of opposite polarity in the far field in response to an applied electric field. As predicted by VEP theory, areas of depolarization and hyperpolarization form around tissue heterogeneities including those that anchor the core of a reentry. Depending on the timing of the pulse, the reentrant core either shifts its phase or detaches from the obstacle. Because unpinning relies on the VEP mechanism of excitation, simultaneous excitation of all reentrant cores can be achieved, independently of a chosen electrode location. In vitro studies in rabbits demonstrated that unpinning could be achieved with shock strengths ≤2.4 V/cm.160 Success rates in terminating reentry depend critically on the timing of the unpinning pulse relative to the phase of the reentry. When unpinning shocks were applied uniformly throughout all phases of reentry, the success rate was only 13.1%. Hence, choosing the optimal phase for shock delivery is important. However, the phase of reentry is difficult to establish in vivo, and in the presence of multiple reentries, the timing of the unpinning pulse cannot be optimal for all reentrant circuits. Besides, in a whole heart model where heterogeneity is omnipresent, immediate repinning after detachment is not unlikely, which requires the repeated application of the therapy.
An alternative approach to terminate arrhythmias sustained by reentrant mechanism is to use a feedback-driven pacing protocol to control and eliminate reentry cores, by moving them until they hit inexcitable obstacles or each other, and annihilate. The mechanism used for influencing the direction of drift of the reentrant core relies on a phenomenon of resonant drift161,162 (ie, the drift of reentrant waves when periodic, low-energy shocks are applied in resonance with the period of the reentry). A feedback algorithm163 is required to maintain the resonance, which is implemented as a sensing electrode that serves to derive trigger signals for the pacing electrodes. A recent theoretical study that used a realistic anisotropic bidomain model of cardiac tissue with microscopic heterogeneities and realistic cellular kinetics confirmed earlier experimental and theoretical reports that were based on overly simplified models of cardiac tissue (such as the Belousov-Zhabotinsky reaction or monodomain models using a FitzHugh-Nagumo kinetics) that resonance drift pacing can be indeed used to move organizing centers of arrhythmias.133 Simulations showed that termination can be achieved with high probability and within a sufficiently short time frame at a fraction of the conventional single-shock defibrillation strength. The direction of drift can be controlled by choosing a delay between detection of the trigger signal at the sensing electrode and delivery of a pacing pulse. For arrhythmias where the organizing center is anatomically anchored, unpinning is required first to induce drift via resonance drift pacing.
Neither ATP nor unpinning or resonance drift is likely to be efficient with more complex activation patterns (ie, in the presence of multiple anatomical or functional reentrant circuits or during fibrillatory activity). Recently, Fenton et al132 proposed a strategy for such a scenario. A train of low-voltage field stimuli is applied at a fast rate to cause changes in polarizations, ΔVm, in the far field along conductive discontinuities of the myocardium. Discontinuities within excitable regions at which ΔVm is sufficiently large to be suprathreshold act as virtual electrodes, which become sites of wave-front emission. With sufficiently high field strengths, many virtual electrodes are formed, which progressively entrain the tissue until synchrony is achieved everywhere. The efficiency of the method has been demonstrated experimentally in vitro for thin-walled atrial preparations at very low field strengths of ≤1.6 V/cm. Whether the method can be applied with similarly low field strengths to ventricular arrhythmias where reentrant activity may occur within the thick ventricular walls has not yet been established.
Theoretical Considerations for Low-Voltage Defibrillation
At the very core of any attempt to understand the mechanisms underlying defibrillation shock and failure is the mechanistic link by which externally applied electric fields, E = −∇Φe, transduce into changes in membrane polarization. Surface VEPs arise due to current redistribution near boundaries separating myocardium from blood in cavities or vessels or from a surrounding bath. Due to the arrangements of myocytes that tend to be aligned parallel to the organ surfaces, the attenuation of surface VEPs with distance to a boundary is governed by the transverse space constants λt and λn. That is, within a few space constants, typically <1 mm, surface VEP drops off to zero, leaving tissue unaffected by the shock, despite the presence of an extracellular potential gradient ∇Φe. Hence, surface VEPs alone are insufficient to affect a critical mass of the tissue, and defibrillation success depends critically on the formation of bulk VEPs. According to bidomain theory, bulk VEPs exist only in the presence of unequal anisotropy ratios. Sufficient conditions for the existence of bulk VEPs are most easily understood by rewriting Equation 14–6:
which reveals that the term S, referred to as activating function,81,164 acts to induce changes in Vm. As shown by Sobie et al,81 S can be decomposed into:
That is, field-induced changes in Vm are driven either by the component S1, the spatial variation in the intracellular conductivities (∇·σi) weighted by the applied electric field ∇Φe, or by the component S2, the spatial variation in the applied electric field ∇(∇Φe) weighted by the intracellular conductivity tensor σi. By inspecting Equations 14–15 and 14–16, it becomes immediately evident that unequal anisotropy ratios are a necessary condition for bulk VEP because S disappears from the parabolic part of the bidomain equations.
Relevance to Low-Voltage Defibrillation
Recently proposed low-voltage defibrillation strategies such as unpinning160 or antifibrillatory pacing132 rely on the presence of minimum field strengths either to unpin an anatomically anchored core or to elicit a sufficiently large number of activations via VEP mechanisms that act to entrain and synchronize the tissue. With traditional single-shock defibrillation strategies, it is assumed that a minimum gradient of 5 V/cm is required to facilitate successful defibrillation.165 With low-voltage strategies, the required minimum gradient seems to be lower, in the range between 1.6 and 2.4 V/cm. Designing an electrode configuration that ensures the required minimum gradients in an in vitro setup is easily achieved with large plate electrodes, where the field strength is constant throughout the tissue. This is clearly not the case when ICD configurations for in vivo use are under consideration. For technical reasons, size, shape, and location of the electrodes are subjected to limitations. Standard ICD configurations use fairly small coils, which lead to highly heterogeneous fields in their immediate vicinity. Further, due to the small size, field strength drops off rapidly with distance, leading to very high gradients in the near field, but the bulk of the tissue experiences much weaker field strengths below 10 V/cm,166,167 which is also below the electroporation threshold.168
Quantitative investigation of shock-tissue interaction within the heart and how this depends on specific electrode configurations could lead to important advances in ICD technologies and protocols with direct clinical relevance.169 However, predicting the exact electrical potential gradient distribution or activating function for determining changes in polarization in the presence of applied extracellular fields in vitro or in vivo in 3D at a sufficiently high spatiotemporal resolution is currently beyond the capabilities of any available clinical or experimental modality. In this scenario, computer modeling is the only choice for acquiring such information.
Indeed, the importance of predicting such factors has been recognized in earlier combined experimental and theoretical studies.146 However, the applied experimental technique provided only a fairly small epicardial field of view, and consistent with this experimental setup, the computational model represented the cardiac structure as a 2D patch that matched the experimental field of view. More recent computational studies to quantify DFT within 3D models have been highly simplified,169 fully relying on the critical mass hypothesis and ignoring the current view based on VEP theory. Further, these models are monodomain and disregard most structural and functional details that are known to be key determinants of shock outcome. Nonetheless, such models have been applied in a clinical study to provide metrics for relative comparison of electrode performance.169
Recent developments in computational cardiac modeling, as described earlier in this chapter, have significantly advanced our ability to simulate the electrical behavior of myocardial tissue within anatomically detailed whole ventricular models. Not only do such models provide us with knowledge of the response of both the extracellular and transmembrane potentials to an electrical stimulus throughout the fully 3D volume of the ventricles, but, due to the inherent detail and complexity of the models, they also allow us to assess the mechanisms by which fine-scale anatomical structures within the heart interact with strong electrical fields. Such micro-anatomically realistic models are currently being used by our groups to quantitatively predict DFT and tissue damage for clinically relevant electrode configurations and shock waveforms to rationalize placement and geometry of ICD cans and coils. Preliminary results from these investigations are presented in the following section.
The anatomically highly detailed MR-based computational model of the rabbit ventricles, described previously in the "Construction of Models of the Cardiac Anatomy" section, was used to simulate a typical ICD setup, as shown in Fig. 14–8A. The stimulus catheter is inserted into the RV, applying a stimulus to the endocardial surface of the RV close to the apex. A grounding electrode is placed close to the base of the LV, in line with typical clinical configurations. A strong electrical stimulus of variable strength, in the form of a current injection, is applied to the tissue via the catheter.
A. Shown is the electrode configuration corresponding to an implantable cardioverter-defibrillator (ICD) set up, with a grounding (GND) electrode at the base of the left ventricle and a catheter inserted into the right ventricular (RV) cavity, applying a stimulus directly to endocardial surface at the apex of the RV. B. Shown is the effect of applying a current injection stimulus of 50 × 108 A/μm3 via the electrode configuration shown in A, with the left image showing the gradient of the extracellular potential (∇Φe) within the ventricular cavities, where the color scale has been chosen to saturate at 4 V/cm; the center image showing the extracellular potential (Φe); and the right image showing the transmembrane potential (Vm).
Figure 14–8B shows the resulting distribution of extracellular potential gradient ∇Φe (left), extracellular potential Φe (center), and transmembrane potential Vm (right) throughout the volume of the ventricular model following the application of a 50 × 108 A/μm3 stimulus.
As can be seen from Fig. 14–8B, detailed information can be obtained regarding the prediction of voltage gradients for suprathreshold activations. These preliminary simulation results demonstrate, perhaps unsurprisingly, that the critical field strength isosurface (shown as 4 V/cm in Fig. 14–8B, left) is very close to the site of shock delivery, even though gradients in the immediate vicinity of the electrode are fairly high. The Vm panel also demonstrates how the model can be used to predict anatomical locations at which VEP-triggered activations arise.
Although preliminary, these initial simulations demonstrate the utility of such a modeling approach to provide a detailed analysis of electric potential distributions within the ventricular tissue during ICD protocols and to assess their dependency on specific lead placements. The flexibility of the model used here will also facilitate future investigations of novel ICD configurations to be tested in silico, providing the potential to optimize ICD configurations and protocols to improve success while reducing shock energy and tissue damage. Our initial results suggest how alterations in electrode placement may result in significant changes in distribution and heterogeneity of electric fields and activating function within the myocardial mass, which can thus be a major determinant of the DFT as well as spatial distribution and severity of tissue damage secondary to adverse shock effects. The bidomain nature of our model also allows for the computation of vulnerability grids for arrhythmia induction following shock application in order to accurately determine DFT, as well as allowing computation of the activating function to quantify shock-tissue interaction as a function of electrode configuration. Finally, the high level of anatomical detail contained within the model will provide knowledge of how anatomical heterogeneity within the ventricles influences the shock response, which is of great importance in the development of patient-specific therapies.
Elucidating the Role of the Purkinje Network
Electrophysiological properties of PS cells are distinct from those of ventricular myocytes, with prominent variations in numerous ionic currents.170-172 PS fibers respond to electrical fields differently from the endocardium upon which they run because of cellular differences173 and because they are oriented in different directions than the myocardial fibers. Because the PS is a network of 1D cables, they should also be more prone to field excitation than 3D tissue.32 Moreover, the myocardial response resulting from a particular shock depends on the orientation of the stimulating field; thus, different shocks may elicit distinct contributions from the PS, which could have implications for clinical techniques, where field direction is constrained by physical limitations.
Despite ever-accumulating evidence that the PS promotes and sustains arrhythmias174 and is the source of postshock activations that may contribute to the failure of defibrillation,175 no studies have directly observed the PS response to normal-strength stimuli at the organ level and the associated impact on shock outcome. Studies of field effects on papillary-Purkinje preparations173 have used strong shocks to study electroporation but have disregarded the effects of weaker shocks on the PS-ventricular system as a whole, which are certainly clinically relevant. Measurements of PS electrical activity are difficult to obtain experimentally because fibers are fine and penetrate into the myocardium where the PMJs are situated. Optical mapping is problematic because the PS signal is overwhelmed by the myocardial signal at the organ scale. Computer modeling offers a noninvasive alternative to experimentation for ascertaining contributions of the PS to the whole heart response to defibrillation-strength shocks.
In this section, we demonstrate how the computer model developed as described in the preceding sections can be used to assess the role of the PS during defibrillation. Using our model, we will investigate the various issues raised. By applying large electric fields to the ventricles and observing behavior of the system with and without the PS, we will clearly identify its role.
We hypothesize that the PS is easily activated by electrical fields, which leads to far-field myocardial depolarizations emanating from PMJs during defibrillation. This is a distinct phenomenon from VEP effects but would produce complementary results. The strength and orientation of the applied field are expected to determine the postshock excitable gap and affect transmission characteristics; thus, shock features will mediate PS contributions. A computer model of 3D rabbit ventricles was used to study the response of quiescent tissue to various defibrillation shocks, with and without a detailed representation of the PS.
Purkinje Network Activation
The angle of incidence of an electric field on a fiber determines the strength of the interaction, so it was presumed that the His/Purkinje network, with its variously oriented branches, would respond differently to various fields. The ventricles with PS were subjected to 1-ms constant electric fields of 5 V/cm in the three principal directions. As expected, the excitation patterns for each of the fields were quite distinct (Fig. 14–9). The myocardium was excited in a small number of regions. For transverse shocks, the cathodal epicardial wall, the septal wall nearest the cathode, and the endocardial wall nearest the anode were depolarized. For shocks along the major axis, the basal epicardium and apical endocardium were excited. Looking at the PS, many small regions were affected strongly. These regions corresponded to either endings or sharp curves, whereas straight regions were relatively unaffected, demonstrating once again that saw-tooth effects are not strong under constant electric fields. Excitation occurred downfield where there were abrupt changes in conductivities. Such changes encompassed bends in the branches and endings. Conversely, de-excitation occurred upfield, again at abrupt changes in geometry. Thus, looking at a field in the x-direction (see Fig. 14–9, left), the bottom ends of the network are hyperpolarized, whereas the tops are depolarized. For the other directions, similar patterns hold in the appropriate directions. A field along the x-direction appeared to activate more of the network than fields oriented along the other directions. There were more excitation regions in the PS than in the myocardium.
Electric field stimulation of the ventricles with Purkinje system. Constant electric fields were applied in the x-, y-, and z-directions. Induced transmembrane voltages are shown 1.25 ms after application of the field for the myocardium (above) and the Purkinje system (below).
The time for the entire network to activate is given in Fig. 14–10. This time varied with the direction of the field and decreased with increasing gap junction resistance. Decreasing rgj below 0.5 M Ω had essentially no effect. The total activation time was determined by the lengths of the branches, which were unaffected by the stimuli. The vast majority of the network was excited within 6 ms, with a particular branch being responsible for the remaining time. Such branches relied on activity to propagate into them and took considerably longer to activate than branches that were field stimulated at both ends. The activation time was reduced drastically for small increases in coupling resistance if that change in resistance resulted in field activation of a new branch; otherwise, the decrease in activation time was small with an increase in rgj. Fields along the y-direction took the longest time to activate the network, whereas fields in the x-direction excited the entire network faster. For the most part, increasing the gap junction resistance had a gradual effect, reducing the activation time by slightly increasing the regions depolarized by the field. The saw-tooth potential was enough to bring a near-threshold excitation portion of the membrane above threshold. With an x-directed field, there was a drastic decrease in excitation time as the resistance was increased from 1 to 2 MΩ. This corresponded to a case where the saw-tooth effect became large enough to trigger a branch that was raised to near threshold by the field. If the field failed to trigger the branch, the branch would be activated by activity propagating through the Purkinje network.
Time for the Purkinje tree to completely depolarize as a function of field direction and Purkinje system gap junction resistance.
Figure 14–11 compares the effect of shocks oriented along the long axis with and without a PS. Without a PS, initial depolarization of tissue at the ventricular base was a result of proximity to the anodal plane, which raised Vm above threshold by decreasing local Φe. The second source of activation was due to a VEP on the endocardial surface of the left ventricular apex, a consequence of hyperpolarization on the apical endocardium induced by the cathodal plane. Following the end of the shock, the pair of resultant wave fronts propagated gradually across the ventricles, completing activation in 59.5 ms.
The Purkinje system (PS) alters shock-induced ventricular activation. A 5-V/cm shock was applied to quiescent ventricles without (top) and with (bottom) PS. With a PS, far-field excitations on the endocardial surface due to activations from the PS abbreviated total activation time by 30% compared with no PS.
Although ventricular activation immediately following the shock (0 ms) was independent of the PS, strong gradients were induced within segments of the PS. Ensuing activations emanating from these excited segments markedly affected the shock response. Initial effects of the PS on myocardial activation sequence were visible shortly after the end of the shock (5 ms); numerous ventricular locations were indirectly activated by the far field as a result of propagation from excited PMJs in PS sections excited by the shock. The resultant wave fronts propagated through the myocardial wall, giving rise to epicardial breakthroughs (right ventricular free wall, 17 ms) that did not occur in the absence of a PS, because the only sources of depolarization were wave fronts propagating from the apex and base. Later still (25 ms), several regions that remained inactive in the no PS case were completely activated in the presence of a PS. Complete activation of the ventricles with PS occurred in 39.0 ms, whereas a thick band of unexcited tissue between wave fronts remained when no PS was present (40 ms).
Full details of this study are provided in the article by Boyle et al.176
Contribution to Shock Induced Reentry Initiation
We examined how the PS contributed to postshock arrhythmogenesis. A transmembrane pacing pulse was applied to the apex of the ventricles. At varying coupling intervals, cross-shocks were applied in the Y direction to induce reentry. When a PS was present compared with no PS, the window of vulnerability was narrower (10 vs 15 ms) because the ventricles depolarized and, hence, repolarized more quickly. The minimum shock strength to induce reentry was lower with a PS (3.3 V/cm vs 4 V/cm).
The PS was active throughout reentry and exhibited both anterograde and retrograde conduction at PMJs. PS activity contributed to reentry dynamics in three ways (Fig. 14–12). First, PS end points conducted intramural activity retrogradely, exciting distant endocardium ahead of the wave front and effectively accelerating propagation when the original wave front merged with the new wave front. Second, retrograde activity provided an escape route for wave fronts terminating due to refractory tissue, thereby prolonging activity. Third, refractory regions surrounding PS entry points caused fractionation in wave fronts. Because PS cells have a longer intrinsic APD, this sort of wave front splitting occurred frequently.
Purkinje system (PS) contributions during reentry. A. Wave fronts can be accelerated as activity is rapidly shunted ahead because of retrograde propagation through the PS, which causes breakthroughs (black arrow tips) that eventually merge with the primary front. B. Activity from wave fronts about to be extinguished due to refractoriness (white arrows) can "escape" annihilation by entering the PS retrogradely. C. Large areas of refractoriness surrounding PS end points create functional obstacles, which can cause wave fronts to fractionate (black arrows) and provide anchoring points for reentry.
To assess how the PS contributed to the maintenance and stabilization of reentry as time progressed, the PS was disconnected at various postshock instants. Isolating the PS immediately after the shock extinguished activity. PS disconnection at 200 ms led to reentry termination at 555 ms. In contrast, PS disconnection at later stages (≥1000 ms) did not terminate reentry. Thus, once meandering wave fronts on the epicardium and the endocardium converged into stable rotors, the PS did not appear to play a direct role.
Full details of this study are provided in the article by Deo et al.177
These simulations demonstrate that the PS is a very important component in determining the response of the ventricles to defibrillation shocks and in the propagation of electrical activity in the ventricles. Thus, it is vital that the PS is included in organ-level models if fibrillation and defibrillation are to be studied.
First, the PS runs in all directions, so it will be activated in several places by electric fields regardless of the orientation of the field. The PS can be considered 1D, so it is easier to directly excite than the myocardium. Activity in the PS is widespread following shocks and spreads quickly into the myocardium to accelerate the activation of the ventricles. Compared with the myocardium, more regions were excited in the PS. In many regions where the PS was depolarized, the ventricles were not affected. The gap junction resistance played a role in determining how long it took for the entire PS to activate. Higher gap junction resistances in the PS lead to a small saw-tooth effect, which effectively increases the spatial extent of cathode make excitation.
The PS contributed to the establishment of postshock reentry. We identified several mechanisms by which this occurred. PMJs conduct both anterogradely and retrogradely, offering entry and exit points for propagating wave fronts. They effectively increase the dimensionality of the organ, leading to longer reentry times. Activity arriving through the PS was manifest on the surface as breakthroughs, which often reestablished activity after it had died out in a region. Conversely, wave fronts that appeared to be heading toward collision with refractory tissue survived by retrograde propagation. A more subtle effect led to wave-front speed up as PS wave fronts raced ahead of a myocardial wave front and emerged slightly ahead of the myocardial wave front. The longer action potential of the PS led to increased refractoriness at the PMJs, which could cause wave-front fractionation as wide wave fronts split when passing through a PMJ.
Propagation through the ventricles is complicated by the presence of the PS. Furthermore, the effects of the PS may not always be obvious or directly observable. Modeling provides a way to gauge the importance of the PS in light of experimental difficulties in measuring both global ventricular and PS behavior.
Simulations of Postinfarction Ventricular Tachycardias
Complex myocardial remodeling that occurs in postinfarcted hearts has been shown to give rise to substrates that could initiate/anchor ventricular tachycardia (VT) reentrant activity. The degree of myocardial injury in the infarcted region is dependent on tissue proximity from the site of occlusion. Tissue that experiences zero perfusion undergoes cellular necrosis and formation of scar tissue. Infarct shape analysis has demonstrated that strands of viable tissue within electrically passive scar tissue could provide alternate pathways for propagation. In addition, partial perfusion in the adjacent PZ tissue results in ion channel and gap junction remodeling that has been shown to result in slowed conduction and altered action potential morphology. The complexity of tissue remodeling within the infarct has made it difficult to elucidate the specific mechanisms that give rise to postinfarction VT and its morphology. This section will outline the application in simulation studies of an image-based 3D model of an infarcted canine heart that incorporates accurate infarct geometry and composition.
The ionic kinetics in the normal and PZ myocardium were represented by the Luo-Rudy dynamic model.178 Membrane kinetics in the PZ were modified based on data from literature. Previous studies of PZ in infarcted canine hearts have reported a reduction in peak sodium current to 38% of the normal value179; a reduction in peak L-type calcium current to 31% of normal180; and a reduction in peak potassium currents IKr and IKs to 30% and 20% of the maximum,181 respectively. These modifications result in longer APD and decreased excitability compared with the normal myocardium. Mathematical description of current flow in cardiac tissue was based on the monodomain representation. To examine the arrhythmogenic propensity of the infarct substrate, an aggressive pacing protocol was delivered from the apex, similar to protocols used for clinical evaluation of patients with myocardial infarction. Pacing commenced at a basic cycle length of 250 ms for five beats (S1); 450 ms after the last S1, six stimuli were delivered at progressively shorter coupling intervals, starting at 190 ms and decreasing in steps of 10 ms. The induced activity was monitored for an additional 2.5 seconds.
Figure 14–13 illustrates the events that lead to VT induction. It depicts isochrones of activation times for time periods during the fourth stimulus of the aggressive pacing protocol and during the resulting VT. Images on the right present the intramural activation pattern on a slice through the heart, the location of which is indicated by the dashed white line on the epicardium. When the propagating wave front from the pacing site reaches the PZ, conduction significantly slows compared with the surrounding normal tissue. Faster wave fronts from the normal myocardium converge into the PZ laterally (white arrows) activating the entire PZ. The transmural view shows late activation of the PZ due to the wave front propagating from the normal myocardium. Because the PZ has a longer APD, it remains refractory, whereas the surrounding myocardium is fully recovered. As the pacing rate is increased, the wave front encounters refractory tissue, resulting in conduction block. This region of block later becomes the conduit for wave front propagation from the intramural PZ toward the surface. When pacing is completed, the activation from within the PZ tissue develops into an epicardial quatrefoil reentry. The reentry core remains within the PZ and is sustained throughout the simulation with a rotation frequency of 5 Hz.
A. Canine ventricular model of infarction containing scar (purple) and peri-infarct zone (PZ; red) regions. B. Isochrones of activation times during the fourth pacing stimulus between 2.24 and 2.54 seconds (left) and 2.75 and 3.05 seconds (right) shown on the epicardial surface and within an intramural slice.
Previous experimental studies of infarcted canine hearts have reported the induction of VT with epicardial reentry morphology.182,183 The simulations revealed that decreased excitability, longer APD, and reduced conduction velocity throughout the PZ promoted conduction block and wave break that develops into epicardial reentry. Furthermore, the simulation showed that wave break and reentry formation occurred in both the epicardial and intramural portions of the PZ. Thus, this study showcased the utility of image-based computational modeling in predicting sites of reentry formation and maintenance.
The use of modeling techniques to complement experimental work has proved to be fruitful and has become an almost indispensable tool in many studies. Despite the many limitations, which enforce trade-offs to keep simulation studies tractable, it has become widely accepted that cardiac modeling is a viable approach to gain mechanistic insights into the electrophysiological function of the heart in health and disease. Recent advancements in various disciplines that are key to further develop modeling technology will allow for the lifting of many of these restrictions. New image acquisition techniques, such as high-field MRI and DT-MRI, provide very detailed geometrical and structural descriptions of the heart at a paracellular resolution. Image processing techniques and fully automatic mesh generation techniques are available that are capable of generating micro-anatomically accurate models of the heart directly from image stacks. The introduction of optimal multigrid and multilevel preconditioning techniques improves the performance and parallel scalability of cardiac simulators, rendering large-scale parameter studies with anatomically realistic and biophysically detailed models feasible. Many of these very advanced solver techniques have been integrated in stable, mature, and easy to use toolkits.184 Current developments in HPC hardware, which aim at overcoming limitations of the current CPU-centric paradigm by using accelerator technologies such as general purpose graphics processing units, promise a tremendous boost in performance at a substantially lower price. Combining all these key technologies in a robust framework that supports researchers in performing in silico experiments with ease will require major research efforts, but the basic building blocks for such simulation tools are already available today. Although current whole heart simulators lag real time by a factor of 103 to 104, next-generation HPC hardware in conjunction with novel simulation technologies will enable research to perform in silico experiments with near real-time performance, lagging real time only by a factor of 101 to 102. Such high-performance simulation tools open new and exciting applications, such as the integration of in silico techniques into a clinical work flow to support clinicians in making better informed decisions that are not feasible today.