Global Optimization of Ventricular Myocyte Model to Multi-Variable Objective Improves Predictions of Drug-Induced Torsades de Pointes

Abstract

In silico cardiac myocyte models present powerful tools for drug safety testing and for predicting phenotypical consequences of ion channel mutations, but their accuracy is sometimes limited. For example, several models describing human ventricular electrophysiology perform poorly when simulating effects of long QT mutations. Model optimization represents one way of obtaining models with stronger predictive power. Using a recent human ventricular myocyte model, we demonstrate that model optimization to clinical long QT data, in conjunction with physiologically-based bounds on intracellular calcium and sodium concentrations, better constrains model parameters. To determine if the model optimized to congenital long QT data better predicts risk of drug-induced long QT arrhythmogenesis, in particular Torsades de Pointes risk, we tested the optimized model against a database of known arrhythmogenic and non-arrhythmogenic ion channel blockers. When doing so, the optimized model provided an improved risk assessment. In particular, we demonstrate an elimination of false-positive outcomes generated by the baseline model, in which simulations of non-torsadogenic drugs, in particular verapamil, predict action potential prolongation. Our results underscore the importance of currents beyond those directly impacted by a drug block in determining torsadogenic risk. Our study also highlights the need for rich data in cardiac myocyte model optimization and substantiates such optimization as a method to generate models with higher accuracy of predictions of drug-induced cardiotoxicity.

Keywords: cardiac modeling; cardiotoxicity; in silico drug trial; long QT; model optimization; safety pharmacology.

Figure 1

Sensitivity of baseline ORd model to select conductances. (A) The APD of the baseline model has a strong sensitivity to the conductance of I_Kr. (B) The calcium transient (quantified here as systolic [Ca²⁺]_i) depends sensitively on G_CaL, G_NCX, and G_NaK. (C) The level of [Na⁺]_i depends mainly on G_NaK. Conductances were varied by ±20% (light blue/red) and ±50% (dark blue/red) of baseline values.

Figure 2

APD values of optimized models. Horizontal lines give control APD₉₀ (black) as well as APD₉₀ surrogates for QT interval prolongation in LQT patients (colored). These APD values form the optimization objective in the simplest case (“APD_LQT”). For the multi-variable optimization (“multi-var”), the objective also include constraints on [Ca²⁺]_i and [Na⁺]_i. Dots give APD₉₀ values under control simulations (black) and during LQT simulations (LQT1, red; LQT2, blue; LQT3, green). The overestimation of the LQT2 response and the underestimation of the LQT1 response in the baseline ORd model are eliminated in the optimized models. Relative APD₉₀ prolongation in the baseline model is 3.0, 43.8, and 15.8%, for LQT1, LQT2, and LQT3, respectively. For the multi-variable optimized model, relative APD₉₀ prolongation is 14.9, 22.9, and 18.6% for LQT1-3, while for the APD_LQT-optimized model the corresponding values are 14.5, 19.4, and 17.0%. The target QT interval values are 12.2, 16.6, and 16.2%.

Figure 3

Action potentials, calcium transients, and [Na⁺]_i in optimized models. (A) Optimized models have similar action potentials under control conditions, but the different parameter sets underlying the different solutions give rise to some waveform variation. (B) Despite having comparable action potentials, models optimized without constraints on [Ca²⁺]_i and [Na⁺]_i can have widely different calcium transients. Shaded areas give constraints on minimum and maximum [Ca²⁺]_i (0.05–0.15 and 0.3–0.7μM, respectively). (C) Without constraints on [Ca²⁺]_i and [Na⁺]_i, optimization can result in models with very low [Na⁺]_i levels. Shaded area indicate constraint on [Na⁺]_i (7–10mM). “APD_LQT±βAdr” designates the original optimization to clinical LQT data under normal and β-adrenergic stimulation conditions by Mann et al. (2016).

Figure 4

Prediction of TdP risk from model simulations. (A) Baseline ORd model with epicardial myocyte parameter settings (the epicardial configuration is shown here as it was determined to give the best classification in Lancaster and Sobie, . Using the endocardial baseline model yields very similar results). (B) APD_LQT±βAdr optimized model. (C) Multi-variable optimized model. (D) APD_LQT optimized model. Dotted lines indicate no-drug control values of APD₅₀ and diastolic [Ca²⁺]_i. Colors for the different models correspond to the color scheme in Figure 3. Solid lines give decision boundaries between torsadogenic (open circles) and non-torsadogenic drugs (filled circles). Dashed lines demarcate regions within which the categorization error remains below a threshold value (E^*). Using the multi-variable optimized model, all drugs that prolong APD₅₀ by more than 5 ms are known TdP risk drugs. Verapamil (marked by black dot) is an example of a TdP negative drug that significantly prolongs the AP in the baseline and APD-optimized models but not in the multi-variable optimized model.

Figure 5

Ionic mechanisms of repolarization dynamics during verapamil application. (A) Baseline model. (B) Multi-variable optimized model. Verapamil (simulated as a scaling of G_CaL by 0.64, a scaling of G_Kr by 0.55, and a scaling of G_Na by 0.998) decrease I_Kr by similar amounts in the baseline and in the multi-variable optimized models. However, due to the up-regulated I_CaL and I_NCX in the optimized model, it sustains a larger loss of inward current than the baseline model. Further, the increased I_Ks in this model provides a repolarization reserve. Together, these effects lead to a maintained APD₅₀ value and an only slightly increased value of APD₉₀.