A quantitative comparison of the behavior of human ventricular cardiac electrophysiology models in tissue

Abstract

Numerical integration of mathematical models of heart cell electrophysiology provides an important computational tool for studying cardiac arrhythmias, but the abundance of available models complicates selecting an appropriate model. We study the behavior of two recently published models of human ventricular action potentials, the Grandi-Pasqualini-Bers (GPB) and the O'Hara-Virág-Varró-Rudy (OVVR) models, and compare the results with four previously published models and with available experimental and clinical data. We find the shapes and durations of action potentials and calcium transients differ between the GPB and OVVR models, as do the magnitudes and rate-dependent properties of transmembrane currents and the calcium transient. Differences also occur in the steady-state and S1-S2 action potential duration and conduction velocity restitution curves, including a maximum conduction velocity for the OVVR model roughly half that of the GPB model and well below clinical values. Between single cells and tissue, both models exhibit differences in properties, including maximum upstroke velocity, action potential amplitude, and minimum diastolic interval. Compared to experimental data, action potential durations for the GPB and OVVR models agree fairly well (although OVVR epicardial action potentials are shorter), but maximum slopes of steady-state restitution curves are smaller. Although studies show alternans in normal hearts, it occurs only in the OVVR model, and only for a narrow range of cycle lengths. We find initiated spiral waves do not progress to sustained breakup for either model. The dominant spiral wave period of the GPB model falls within clinically relevant values for ventricular tachycardia (VT), but for the OVVR model, the dominant period is longer than periods associated with VT. Our results should facilitate choosing a model to match properties of interest in human cardiac tissue and to replicate arrhythmia behavior more closely. Furthermore, by indicating areas where existing models disagree, our findings suggest avenues for further experimental work.

Figure 1. Rate dependence of action potentials, primary transmembrane currents, and intracellular calcium concentration.

Action potentials, currents, and calcium transient in a single cell for the GPB (columns 1 and 3) and OVVR (columns 2 and 4) models for cycle lengths of 1000 ms (solid black), 750 ms (dashed green), 500 ms (dashed red), and 300 ms (dashed blue). Insets show peak current values for the same cycle lengths following the same color scheme. The GPB model generally shows more rate dependence; however, the OVVR model shows greater rate dependence for I_K1 and [Ca²⁺]_i. Both models show significant rate dependence for I_Ks, although the effect of rate is opposite for the two models, and for the I_CaL.

Figure 2. Transmural cell types.

(A) Epicardial and endocardial action potentials for the GPB model. (B) Epicardial, endocardial, and midmyocardial action potentials for the OVVR model. All measurements were obtained after pacing a single cell for 30 s with a CL of 1 s.

Figure 3. Action potentials for the epicardial formulations of six human ventricular models.

Action potentials in single cells (left column) and in 1D tissue (right column). Data are taken from the middle of the cable (cell 50) with a 100 cells cable after pacing for 30 s at a CL of 1 s. Because of electrotonic coupling effects, all of the model APs lose amplitude in tissue compared to single cells, with the PB model decreasing the most (23.7%) followed by the GPB model (17.6%), the TP model (12.9%), the OVVR model (12.4%), the IMW model (10.5%), and the BCF model (4.0%).

Figure 4. Rate dependence in a 1D cable for the GPB and OVVR models.

(A,D) Action potentials at cycle lengths of 1000, 600, 500, 400, and 300 ms. Compared to isolated cell APs, the upstroke amplitude is decreased because of electrotonic effects. (B,E) Steady-state and S1–S2 APD restitution curves. Steady-state restitution curves (solid lines) were obtained after pacing for 30 s and S1–S2 restitution curves (dashed lines) were obtained after 30 s of pacing for five different S1 cycle lengths. Both models show memory in APD. (C,F) Steady-state and S1–S2 CV restitution curves. The GPB model shows no apparent memory in CV, whereas the OVVR shows limited CV memory.

Figure 5. Steady-state APD and CV restitution curves for all six models in 1D epicardial cables.

(A) APD restitution curves. (B) CV restitution curves. Curves were obtained after pacing for 30 s and show significant differences among the models.

Figure 6. Alternans in the OVVR model.

Action potential traces (left) and bifurcation diagrams (right) for (A) epicardial single cell, (B) epicardial cable, (C) endocardial single cell, and (D) endocardial cable. Cycle lengths in the action potential traces are (A) 165, (B) 320, (C) 200, and (D) 310 ms.

Figure 7. Reentrant spiral wave dynamics in 2D for the GPB and OVVR models.

(A) The epicardial cell type of the GPB model features wave fronts that often stall and reform, and the dominant period is 308 ms. (B) The endocardial cell type of the GPB model shows similar stalling and recombining without breakup and a dominant period of 321 ms. (C–E) Spiral wave dynamics for (C) epicardial, (D) endocardial, and (E) midmyocardial cell types in the OVVR model. The epicardial model exhibits a quasi-breakup where a new spiral wave tip is created before the pervious one has dissipated. It has two dominant periods of 337 ms and 481 ms. The endocardial model shows similar dynamics to the epicardial formulation with a dominant period of 405 ms. The midmyocardial model features an unstable hypocycloidal trajectory with a dominant period of 430 ms. Frames in all cases correspond to 5.45, 5.50, 5.55, and 5.60 s, and tissue sizes are 14.4 cm×14.4 cm except for the OVVR epicardial cell type, where the size is 18.0×18.0 cm. Dominant periods were obtained using the full 10 s of simulation time.

Figure 8. Spiral waves for all six models using epicardial formulations.

Tissue sizes are 14.4×14.4 cm for the GPB model, 18.0×18.0 cm for the OVVR model, and 23.0 cm×23.0 cm for the PB, IMW TP, and BCF models. The spatial resolution is 0.015 cm in all cases and the time step is 0.02 ms except for the IMW model, where it is 0.01 ms. The IMW model used initial values corresponding to pacing a single cell at 3 Hz. Colorbar is in mV.

Figure 9. Action potentials for the OVVR model using the TP formulation of I_Na.

Traces show action potentials for (A) epicardial, (B) endocardial, and (C) midmyocardial cell types of the OVVR model using the TP model formulation of I_Na (green solid) compared to the original OVVR model (blue dashed). Insets show upstrokes, where the action potential shapes change most.

Figure 10. Rate adaptation and spiral wave properties for the OVVR model with the TP I_Na formulation.

(A–B) Steady-state APD restitution curves in isolated cells (A) and a one-dimensional cable (right) for epicardial (green), endocardial (red), and midmyocardial (blue) cells. Original model restitution curves are shown as dots (A) or dashed lines (B). The different I_Na formulation decreases the minimum DI that can be reached in tissue. (C) Steady-state CV restitution curves for the epicardial (green), midmyocardial (blue) and endocardial (black) cells in a one-dimensional cable. Original model CV restitution curves are shown as dashed lines. The modification increases the maximum CV by almost a factor of two. (D–F) Spiral wave snapshots, tip trajectories, and dominant periods for the epicardial, endocardial, and midmyocardial formulations of the modified model. Frames in all cases correspond to 1.85, 1.90, 1.95, and 2.00 s, and tissue sizes are 18.0×18.0 cm. Dominant periods were obtained using the full 2 s of simulation time.