Quantification of repolarization reserve to understand interpatient variability in the response to proarrhythmic drugs: a computational analysis

Abstract

Background: "Repolarization reserve" is frequently invoked to explain why potentially proarrhythmic drugs cause, across a population, a range of changes to cardiac action potentials (APs). However, the mechanisms underlying this interindividual variability are not understood quantitatively.

Objective: The purpose of this study was to perform a novel analysis of mathematical models of ventricular myocytes to quantify repolarization reserve and gain insight into the factors responsible for variability in the response to proarrhythmic drugs.

Methods/results: In several models of human or canine ventricular myocytes, variability was simulated by randomizing model parameters and running repeated simulations. With each randomly generated set of parameters, APs before and after simulated 75% block of the rapid delayed rectifier current (I(Kr)) were calculated. Multivariable regression was performed to determine how much each model parameter attenuated or exacerbated the AP prolongation caused by the I(Kr)-blocking drug. Simulations with a human ventricular myocyte model suggest that drug response is influenced most strongly by (1) the density of I(Kr), (2) the density of slow delayed rectifier current I(Ks), (3) the voltage dependence of I(Kr) inactivation, (4) the density of L-type Ca2+ current, and (5) the kinetics of I(Ks) activation. The analysis also identified mechanisms underlying nonintuitive behavior, such as ionic currents that prolong baseline APs but decrease drug-induced AP prolongation. Finally, the simulations provided quantitative insight into conditions that aggravate the drug response, such as silent ion channel mutations and heart failure.

Conclusion: These modeling results provide the first thorough quantification of repolarization reserve and improve our understanding of interindividual variability in adverse drug reactions.

Figure 1. Multivariable regression to quantify repolarization reserve

(A) Model parameters (X), simulation results (Y) and parameter sensitivities (B) are collected in matrices with the indicated structures and relationships. Values in matrices are represented using the indicated color table. (B) Three trials with similar baseline APDs and responses to HERG block (75% reduction in G_Kr) that are either typical (ΔAPD=23.7 ms, top), smaller than normal (ΔAPD=15.9 ms, middle), or larger than normal (ΔAPD=45.3 ms, bottom).

Figure 2. Cell-to-cell variation in the response to HERG block

(A) Distribution of ΔAPD from a set of 300 trials performed with the TNNP model, illustrating sample-to-sample variability in the drug response. (B) Baseline APD versus ΔAPD in simulations with the TNNP model shows a lack of correlation in this model.

Figure 3. Results of multivariable regression

(A) Elements of the matrix B, indicating how each model parameter influences ΔAPD, are plotted in descending order of importance. Green bars indicate parameters for which an increase leads to greater ΔAPD whereas red bars indicate parameters for which an increase leads to smaller ΔAPD. (B) Model validation of interesting regression analysis predictions. Voltage dependence of I_Kr activation (V_xr1) is the least important parameter whereas voltage dependence of I_Kr inactivation (V_xr2) is the third most important contributor. Simulations show APs before and after HERG block, shifting either V_xr1 or V_xr2 by +20 mV.

Figure 4. Counterintuitive contributors to HERG block

(A) Regression coefficients for APD (abscissa) plotted versus regression coefficients for ΔAPD (ordinate). (B) Increasing L-type Ca²⁺ current (G_Ca) by 3 times increases baseline APD but decreases ΔAPD (top). This occurs because increased G_Ca leads to an elevated plateau potential (middle) and increased activation of I_Ks (bottom).

Figure 5. Matrix multiplication to understand complex phenotypes

When multiple parameters change in a particular condition, the net effect on ΔAPD can be calculated as the matrix product of the change in parameters and the relevant parameter sensitivities. In all panels, values in matrices are represented using the red blue color table shown at the top left. Images are scaled from −0.6 to +0.6. (A) Parallel changes in G_Ca and G_Ks lead to no net change in APD but additive changes in ΔAPD. ΔAPD= 55 ms when G_Ca and G_Ks are decreased by 40% and 60% respectively. (B) Changes in I_Ks associated with a silent mutation in KCNQ1 that leads to both decreased conductance and activation at more positive potentials. The changes in G_Ks and V_xs contribute roughly equally to the increase in ΔAPD. (C) Simulation of decreased repolarization reserve in heart failure. Changes in four model parameters were simulated (as per Winslow et al). Each change is multiplied by its corresponding parameter sensitivity, and the overall change in ΔAPD can be calculated as the sum of these products.