Machine learning in drug development: Characterizing the effect of 30 drugs on the QT interval using Gaussian process regression, sensitivity analysis, and uncertainty quantification

Abstract

Prolonged QT intervals are a major risk factor for ventricular arrhythmias and a leading cause of sudden cardiac death. Various drugs are known to trigger QT interval prolongation and increase the proarrhythmic potential. Yet, how precisely the action of drugs on the cellular level translates into QT interval prolongation on the whole organ level remains insufficiently understood. Here we use machine learning techniques to systematically characterize the effect of 30 common drugs on the QT interval. We combine information from high fidelity three-dimensional human heart simulations with low fidelity one-dimensional cable simulations to build a surrogate model for the QT interval using multi-fidelity Gaussian process regression. Once trained and cross-validated, we apply our surrogate model to perform sensitivity analysis and uncertainty quantification. Our sensitivity analysis suggests that compounds that block the rapid delayed rectifier potassium current I _Kr have the greatest prolonging effect of the QT interval, and that blocking the L-type calcium current I _CaL and late sodium current I _NaL shortens the QT interval. Our uncertainty quantification allows us to propagate the experimental variability from individual block-concentration measurements into the QT interval and reveals that QT interval uncertainty is mainly driven by the variability in I _Kr block. In a final validation study, we demonstrate an excellent agreement between our predicted QT interval changes and the changes observed in a randomized clinical trial for the drugs dofetilide, quinidine, ranolazine, and verapamil. We anticipate that both the machine learning methods and the results of this study will have great potential in the efficient development of safer drugs.

Keywords: Cardiac electrophysiology; Drug development; Finite element analysis; Gaussian process regression; Machine learning; Sensitivity analysis; Torsades de pointes; Uncertainty quantification.

Figure 1:. Methods overview.

Using machine learning techniques, we combine data from different levels of fidelity and characterize the effect of drugs on the QT interval. The input to our model are drug-induced channel block recordings from single cell patch clamp electrophysioloy [10]. From this input, we simulate the effect of drugs using a high fidelity three-dimensional heart model [65] and a low fidelity one-dimensional cable model [66]. From N_H = 45 high and N_L = 400 low fidelity simulations, we calculate high and low fidelity electrocardiograms from which we extract the drug-modulated QT interval lengths. From these results, we build a surrogate model using multi-fidelity Gaussian process regression [50]. Once we have trained our regression, we perform a sensitivity analysis and propagate the uncertainty from the drug-induced channel block recordings into the QT interval.

Figure 2:. Drug-induced ion channel block.

Human ventricular cardiomyocytes model, left, and Purkinje fiber model, right. The ventricular cell model distinguishes between endocardial, midwall, and epicardial cells and has 15 ionic currents and 39 state variables [45]; the Purkinje cell model has 14 ionic currents and 20 state variables [71]. We selectively block ionic currents and determine the fractional block from single cell experiments [10] using a Hill model.

Figure 3:. High fidelity three-dimensional heart model.

Our high fidelity model is a fully three-dimensional representation of the human ventricles discretized with 6,878,459 regular linear hexagonal finite elements, 7,519,918 nodes, and 268,259,901 internal variables [65]. For each high fidelity simulation, we simulate five heart beats, calculate the electrocardiogram, and extract the QT interval as the time difference between the onset of the QRS complex and the peak of the T wave [64].

Figure 4:. Multi-fidelity Gaussian process regression.

We combine the electrocardiograms of N_H = 45 high fidelity three-dimensional heart simulations, top, with N_L = 400 low fidelity one-dimensional cable simulations, bottom, to extract QT intervals for our multi-fidelity Gaussian process regression.

Figure 5:. Sensitivity of QT interval with respect to individual current blocks.

Blocking the I_Kr, I_Nap, I_K1and I_Ks currents prolongs the QT interval; blocking the I_to, I_NaL and I_CaL currents shortens the QT interval. Blocking the rapid delayed rectifier potassium current I_Kr has the largest effect on the QT interval. Bars represent the modified mean of the elementary effect index μ*, signs are assigned from μ, error bars represent the standard deviation σ.

Figure 6:. Main effects analysis of QT interval for individual current blocks.

Blocking the rapid delayed rectifier potassium current I_Kr prolongs the QT interval the most; blocking the L-type fast calcium current I_CaL decreases the QT interval the most. Gray lines represent the 200 trajectories used for the simulation, colored lines represent the average main effect.

Figure 7:. Uncertainty quantification in block-concentration characteristics of the drug ranolazine.

For three different experiments of ranolazine-induced blockage of the rapid delayed rectifier potassium current I_Kr [10], we calibrate three sets of Hill parameters (brown, red, and orange curves) and perform a best fit for all three experiments (black curve). To account for the uncertainty in the data, we use a hierarchical Bayesian model and infer a posterior distribution of the Hill model parameters to generate 500 Hill curves (gray curves).

Figure 8:. Uncertainty propagation of block-concentration characteristics for ranolazine at its free plasma concentration into the QT interval.

We apply the posterior distribution of current block from the hierarchical Bayesian model, left, to our surrogate model and propagate the uncertainty into the QT interval. From this QT interval distribution, we compute a probability density function, right, using a Gaussian kernel density estimation. For clear visualization, we only plot the channels with significant blockage, the rapid delayed rectifier potassium current I_Kr and the late sodium current I_NaL.

Figure 9:. Uncertainty propagation of block-concentration characteristics for 30 compounds at their free plasma concentration into the QT interval.

Color bars indicate the 95% confidence intervals and gray lines indicate the mean. All drugs are displayed at their free plasma concentration C_max, except dofetilide* and quinidine*, which are displayed at 0.9 C_max and 0.4 C_max to avoid extrapolation.

Figure 10:. Probability of QT interval change for 30 compounds across a range of compound concentrations.

Mean QT interval changes are shown as solid black lines and 95% confidence intervals are shown as dotted lines; gray regions are used when the blocks exceeded the range used to build the surrogate model.

Figure 11:. Validation of QT interval change predictions for the compounds dofetilide, quinidine, ranolazine, and verapamil.

These compounds block channels with opposing effects on the QT interval. Dofetilide is a selective I_Kr blocker, quinidine primarily blocks I_Kr, I_to and I_Ks, ranolazine blocks I_NaL and I_Kr, and verapamil blocks I_CaL and I_Kr. Mean QT interval changes are shown as solid black lines and 95% confidence intervals are shown as dotted lines; gray dots are data points from a randomized clinical trial and error bars are their 95% confidence intervals [28].