A computationally efficient electrophysiological model of human ventricular cells

Abstract

-Recent experimental and theoretical results have stressed the importance of modeling studies of reentrant arrhythmias in cardiac tissue and at the whole heart level. We introduce a sixvariable model obtained by a reformulation of the PriebeBeuckelmann model of a single human ventricular cell. The reformulated model is 4.9 times faster for numerical computations and it is more stable than the original model. It retains the action potential shape at various frequencies, restitution of action potential duration, and restitution of conduction velocity. We were able to reproduce the main properties of epicardial, endocardial, and M cells by modifying selected ionic currents. We performed a simulation study of spiral wave behavior in a two-dimensional sheet of human ventricular tissue and showed that spiral waves have a frequency of 3.3 Hz and a linear core of ϳ50-mm diameter that rotates with an average frequency of 0.62 rad/s. Simulation results agreed with experimental data. In conclusion, the proposed model is suitable for efficient and accurate studies of reentrant phenomena in human ventricular tissue. action potential; computer simulation; mathematical model; reentrant arrhythmia; spiral wave THE HISTORY of modeling biological excitable media such as nerve and heart tissue started 50 years ago with the Hodgkin-Huxley model of the giant squid axon (19). The first model of cardiac tissue (Purkinje fibers) was proposed by Noble in 1962 (30) and consisted of four variables. During the following decades, the experimental techniques for studying the properties of the cell membrane were improved continuously, leading to new cardiac tissue models of increasing accuracy, e.g., the phase- The Priebe-Beuckelmann (PB) model is based on the phase-2 LR model. However, five major ionic currents, including the fast (I Kr ) and slow (I Ks ) components of the delayed rectifier K ϩ current, the L-type Ca 2ϩ current (I Ca ), the transient outward K ϩ current (I to ), and the inward rectifier K ϩ current (I K1 ), are based on experimental data obtained on human myocytes. In addition, parameters of the intracellular Ca 2ϩ concentration ([Ca 2ϩ ] i ) handling were changed in such a way that simulated transients are comparable to observed experimental data on human myocytes (4). The remaining currents have been adjusted from the LR model, with their amplitude scaled to fit human cell data.Priebe and Beuckelmann developed their model to compare the electrophysiological properties of failing and nonfailing ventricular myocytes. It can be used for accurate simulations of the ionic currents and concentrations in a single cell during electrical activity. Our objective, however, is to simulate reentrant sources of arrhythmias in two (2-D) and three dimensions (3-D), which are believed to underlie most ventricular tachycardias and ventricular fibrillation (18,21,43). Although the PB model is based on experimental measurements in human heart tissue, we refrained from using it for the study of reentrant arrhythmias for several reasons. F...

Turbulent electrical activity at sharp-edged inexcitable obstacles in a model for human cardiac tissue

“…Time t is measured in milliseconds, voltage V in millivolts, conductances (GX) in nanosiemens per picofarad, the intracellular and extracellular ionic concentrations (Xi, Xo) in millimoles per liter, and current densities (IX) in microamperes per unit area in square centimeters, as used in second-generation models (see, e.g., Refs. 7,35,36,67). For a detailed list of the parameters of this model and the equations that govern the spatiotemporal behaviors of the transmembrane potential and currents see, e.g., References 61 and 67.…”

Cardiac cell modelling: Observations from the heart of the cardiac physiome project

“…In addition, some gating variables with slow time constants may not vary enough to affect the model behaviour significantly and can be eliminated; similarly, currents with very small amplitudes in some cases also can be eliminated without significantly affecting most cellular properties. The Bernus et al (2002) reduction of the Priebe-Beuckelmann human ventricular model is an example of a reduced model that obtains good agreement with the original model, as shown in Figure 3. In this case, the number of variables was reduced from 17 to six by eliminating four of the original nine gating variables and by treating all ionic concentrations as constants.…”

“…These models are intended primarily for use in tissue simulations where multicellular effects are being investigated and computational efficiency becomes important. In some cases, simplified or minimal models can be used to represent the overall membrane dynamics under various conditions, including pharmaceutical agents or mutations, by fitting model parameters directly from experimental data, a process that becomes faster and more straightforward when the number of parameters is reduced significantly (often by an order of magnitude) (Bueno-Orovio et al 2008, Bernus et al 2002. These model variations then can be simulated in tissue to study tissue-level phenomena, including wave stability and dynamical bifurcations (see, for example, the paper in this issue).…”

“…Principal component analysis or sensitivity analysis can be used for removal of parameters or model parts to which the output is insensitive (e.g. Fink and Noble 2009, Bernus et al 2002, Schmidt et al 2008. Lately, a similar approach of invariant manifold reductions for Markov models has been used (Keener 2009).…”

ECG simulations with realistic human membrane, heart, and torso models

“…Each cell was represented by a model of the human ventricular cell membrane described recently by Bernus et al [1]. This membrane model is a compromise between the accuracy obtained by its ancestor, the Priebe-Beuckelmann model [2], and the efficiency required by a large-scale heart model.…”