A mechanism for the upper limit of vulnerability

Bidomain modeling of electrical and mechanical properties of cardiac tissue

Throughout the history of cardiac research, there has been a clear need to establish mathematical models to complement experimental studies. In an effort to create a more complete picture of cardiac phenomena, the bidomain model was established in the late 1970s to better understand pacing and defibrillation in the heart. This mathematical model has seen ongoing use in cardiac research, offering mechanistic insight that could not be obtained from experimental pursuits. Introduced from a historical perspective, the origins of the bidomain model are reviewed to provide a foundation for researchers new to the field and those conducting interdisciplinary research. The interplay of theory and experiment with the bidomain model is explored, and the contributions of this model to cardiac biophysics are critically evaluated. Also discussed is the mechanical bidomain model, which is employed to describe mechanotransduction. Current challenges and outstanding questions in the use of the bidomain model are addressed to give a forward-facing perspective of the model in future studies.

The Relationship Between Cardiac Vulnerability and Restitution Properties of the Ventricular Activation Recovery Interval

INTRODUCTION

The restitution of the action potential duration (APD) is an important contributor to ventricular fibrillation (VF) initiation by a single critically timed ectopic beat. We hypothesized that a steep slope of the activation recovery interval restitution curve was related to the upper limit of vulnerability (ULV).

METHODS AND RESULTS

Fifty-four consecutive patients with implantable cardioverter defibrillators (ICDs) implanted between April 2012 and July 2013 were included. At the implantation, pacing from the right ventricular (RV) coil to an indifferent electrode inserted in the ICD pocket was performed, and the unipolar electrograms from the RV coil were simultaneously recorded. We assessed the standard restitution by introducing extra-stimuli, while measuring the activation recovery interval (ARI). Our protocol for the vulnerability test consisted of delivering three 15 J shocks on the T-peak and within ±20 milliseconds of it. If VF was not induced by that procedure, a ULV of ≤15 J was defined. The relationship between the ULV and maximum slope of the restitution curve was analyzed. A restitution curve could finally be obtained in a total of 40 patients. The background characteristics were similar between the two groups. The maximum slope of the restitution curve was steeper in the ULV > 15 J group than ULV ≤ 15 J group (1.55 ± 0.45 vs. 0.91 ± 0.64, P < 0.05). A maximum slope exceeding 1.0 was the optimal point for discriminating patients with a ULV > 15 J from a ULV ≤ 15 J (sensitivity 61.5% and specificity 96.3%).

CONCLUSION

The maximum slope of the restitution curve was significantly related to the ULV. High defibrillation threshold patients could be detected by the ARI dynamics.

Diastolic field stimulation: the role of shock duration in epicardial activation and propagation

Detailed knowledge of tissue response to both systolic and diastolic shock is critical for understanding defibrillation. Diastolic field stimulation has been much less studied than systolic stimulation, particularly regarding transient virtual anodes. Here we investigated high-voltage-induced polarization and activation patterns in response to strong diastolic shocks of various durations and of both polarities, and tested the hypothesis that the activation versus shock duration curve contains a local minimum for moderate shock durations, and it grows for short and long durations. We found that 0.1-0.2-ms shocks produced slow and heterogeneous activation. During 0.8-1 ms shocks, the activation was very fast and homogeneous. Further shock extension to 8 ms delayed activation from 1.55 ± 0.27 ms and 1.63 ± 0.21 ms at 0.8 ms shock to 2.32 ± 0.41 ms and 2.37 ± 0.3 ms (N = 7) for normal and opposite polarities, respectively. The traces from hyperpolarized regions during 3-8 ms shocks exhibited four different phases: beginning negative polarization, fast depolarization, slow depolarization, and after-shock increase in upstroke velocity. Thus, the shocks of >3 ms in duration created strong hyperpolarization associated with significant delay (P < 0.05) in activation compared with moderate shocks of 0.8 and 1 ms. This effect appears as a dip in the activation-versus-shock-duration curve.

A Simplified Approach for Simultaneous Measurements of Wavefront Velocity and Curvature in the Heart Using Activation Times

The velocity and curvature of a wave front are important factors governing the propagation of electrical activity through cardiac tissue, particularly during heart arrhythmias of clinical importance such as fibrillation. Presently, no simple computational model exists to determine these values simultaneously. The proposed model uses the arrival times at four or five sites to determine the wave front speed (v), direction (θ), and radius of curvature (ROC) (r₀). If the arrival times are measured, then v, θ, and r₀ can be found from differences in arrival times and the distance between these sites. During isotropic conduction, we found good correlation between measured values of the ROC r₀ and the distance from the unipolar stimulus (r = 0.9043 and p < 0.0001). The conduction velocity (m/s) was correlated (r = 0.998, p < 0.0001) using our method (mean = 0.2403, SD = 0.0533) and an empirical method (mean = 0.2352, SD = 0.0560). The model was applied to a condition of anisotropy and a complex case of reentry with a high voltage extra stimulus. Again, results show good correlation between our simplified approach and established methods for multiple wavefront morphologies. In conclusion, insignificant measurement errors were observed between this simplified approach and an approach that was more computationally demanding. Accuracy was maintained when the requirement that ε (ε = b/r₀, ratio of recording site spacing over wave fronts ROC) was between 0.001 and 0.5. The present simplified model can be applied to a variety of clinical conditions to predict behavior of planar, elliptical, and reentrant wave fronts. It may be used to study the genesis and propagation of rotors in human arrhythmias and could lead to rotor mapping using low density endocardial recording electrodes.

Investigating the role of the coronary vasculature in the mechanisms of defibrillation

BACKGROUND

The direct role of coronary vessels in defibrillation, although hypothesized to be important, remains to be elucidated. We investigated how vessel-induced virtual electrode polarizations assist reentry termination.

METHODS AND RESULTS

A highly anatomically detailed rabbit ventricular slice bidomain computer model was constructed from 25-μm magnetic resonance data, faithfully representing both structural and electric properties of blood vessels. For comparison, an equivalent simplified model with intramural cavities filled in was also built. Following fibrillation induction, 6 initial states were selected, and biphasic shocks (5-70 V) were applied using a realistic implanted cardioverter-defibrillator electrode configuration. A fundamental mechanism of biphasic defibrillation was uncovered in both models, involving successive break excitations (after each shock phase) emanating from opposing myocardial surfaces (in septum and left ventricle), which rapidly closed down excitable gaps. The presence of vessels accelerated this process, achieving more-rapid and successful defibrillation. Defibrillation failed in 5 cases (all because of initiation of new activity) compared with 8 with the simplified model (5/8 failures because of surviving activity). At stronger shocks, virtual electrodes formed around vessels, rapidly activating intramural tissue because of break excitations, assisting the main defibrillation mechanism, and eliminating all activity <15 ms of shock end in 60% of successful shocks (36% in simplified model). Subsequent analysis identified that only vessels >200 μm in diameter participated through this mechanism. Consequently, wavefronts could survive intramurally in the simplified model, leading to reentry and shock failure.

CONCLUSIONS

We provide new insight into defibrillation mechanisms by showing how intramural blood vessels facilitate more-effective elimination of existing wavefronts, rapid closing down of excitable gaps, and successful defibrillation and give guidance toward the required resolution of cardiac imaging and model generation endeavors for mechanistic defibrillation analysis.

How hyperpolarization and the recovery of excitability affect propagation through a virtual anode in the heart

Researchers have suggested that the fate of a shock-induced wave front at the edge of a "virtual anode" (a region hyperpolarized by the shock) is a key factor determining success or failure during defibrillation of the heart. In this paper, we use a simple one-dimensional computer model to examine propagation speed through a hyperpolarized region. Our goal is to test the hypothesis that rapid propagation through a virtual anode can cause failure of propagation at the edge of the virtual anode. The calculations support this hypothesis and suggest that the time constant of the sodium inactivation gate is an important parameter. These results may be significant in understanding the mechanism of the upper limit of vulnerability.

High defibrillation threshold: the science, signs and solutions

Defibrillation threshold (DFT) testing has traditionally been an integral part of implantable cardioverter defibrillator (ICD) implantation. With the increasing number of patients receiving ICDs, physicians are encountering high DFT more often than before. Tackling the problem of high DFT, warrants an in-depth understanding of the science of defibrillation including the key electrophysiological concepts and the underlying molecular mechanisms. Numerous factors have been implicated in the causation of high DFT. Due consideration to the past medical history, pharmacotherapy, laboratory data and cardiac imaging, help in assessing the pre-procedural risk for occurrence of high DFT. Drugs, procedural changes, type and location of ICD lead system are some of the key players in predicting DFT during implantation. In the event of encountering an unacceptably high DFT, we recommend to follow a step-wise algorithm. Ruling out procedural complications like pneumothorax and tamponade is imperative before embarking on a search for potentially reversible clinical or metabolic derangements. Finally, if these attempts fail, the electrophysiologist must choose from a wide range of options for device adjustment and system modification. Although this review article is meant to be a treatise on the science, signs and solutions for high DFT, it is bound by limitations of space and scope of the article.

Shock induced electrical activation in structurally detailed models of pig left-ventricular tissue

Detailed models of sample specific structures in pig left-ventricular tissue have been constructed. These models include epicardial and endocardial surfaces, fiber and sheet orientations, vessels and cleavage planes with significant dimensions. This work shows that it is possible to extract from 3D tissue images reduced dimension descriptions of cleavage planes in the heart wall. These descriptions are used to analyze the response of tissue to electrical shocks of varying strengths. The presence of explicit discontinuities in the heart significantly reduces the time required for transmural activation and provides a basis for understanding successful defibrillation.