Electroporation and Shock-Induced Transmembrane Potential in a Cardiac Fiber During Defibrillation Strength Shocks

Abstract

Experimental studies have shown that the magnitude of the shock-induced transmembrane potential (Vm) saturates with increasing electric field strength. This study uses a mathematical model to investigate the effects of electroporation and membrane kinetics on Vm in a cardiac fiber. The model consists of the core conductor equation for a one-dimensional fiber, where excitability is represented by the Luo-Rudy dynamic model (1994-1995) and electroporation is described by a membrane conductance that increases exponentially with Vm squared. For shocks delivered during the plateau of an action potential, the model reproduces the experimentally observed saturation of Vm with a root mean square error of 4.27% and a correlation coefficient of 0.9992. For shocks delivered during diastole, the saturation of Vm is qualitatively reproduced even when the sodium and calcium channels are inactivated. Quantitative replication of the response to diastolic shocks is hindered by the choice of electroporation parameters (optimized for shocks delivered during the plateau) and differences in the membrane kinetics between model and experiment. The complex behavior of Vm during large shocks is due to a combination of electroporation, electrotonus, propagation, and active membrane kinetics. The modeling results imply that the experimentally observed saturation of Vm is due to electroporation of the lipid bilayer.

Advantage of four-electrode over two-electrode defibrillators

“…(5) describes the first-order kinetics of the pore density. The parameter values α = 200 cm −2 ms −1 ; β = 6.25 10 −5 mV −2 and N 0 = 1.5 10 5 cm −2 used here are the same as in the original paper by De Bruin and Krassowska [30]. The strength of this electroporation current depends on the opening and resealing of pores and has a nonlinear dependence on V m as shown in Eq.(5).…”

“…This behavior was not captured with the first available mathematical physiological models of the membrane kinetics. De Bruin and Krassowska [30] suggested that this behavior can be attributed to the electroporation phenomenon and they developed a mathematical model in which electroporation current (i ep ) is taken into account [30]:…”

“…where the conductance g p (V m ) is modeled as an instantaneous function of the transmembrane potential [30] and N is the membrane pore density. Eq.…”

Modeling Defibrillation

“…Another serious difficulty is the use of state-of-the-art ionic models which incorporate now up to several tens of state variables of ever increasing stiffness. These models are developed and tested within the normal physiological range of action potentials, however, during the shock administration transmembrane voltages may rise significantly beyond this range, even when ionic models are augmented with additional currents such as electroporation currents (DeBruin & Krassowska, 1998) or hypothetical potassium currents (Cheng, Tung & Sobie, 1999). Although these currents kick in at elevated transmembrane voltages to cap the rise of V m at a few hundreds of mV, transmembrane voltages still rises well beyond the physiological range which could potentially entail undesirable behavior of the model equations.…”

“…Although ICD therapy has proved to be efficient and reliable in preventing sudden cardiac death (Bardy et al, 1993), with success rates clearly superior to other therapeutic options such as pharmacological anti-arrhythmia therapy (Zipes et al, 1997), it is far from ideal. There are several known adverse effects secondary to the administration of electrical shocks, the most prominent are linked to electroporation (DeBruin & Krassowska, 1998), (i.e. 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 after-effects which are indirectly caused by the high field strengths required to terminate arrhythmias such as ventricular fibrillation (VF) with sufficiently high probability.…”