In Silico Modeling and Validation of the Effect of Calcium-Activated Potassium Current on Ventricular Repolarization in Failing Myocytes

The Effect of Calcium-Activated Potassium Channels (SK Channels) on Repolarization in Failing Ventricular Myocytes—A Computational Modeling Study

Research Background and Academic Significance

Heart failure (HF) is a severe and prevalent cardiac disease, characterized by a comprehensive deterioration of the heart’s electrophysiological and contractile functions. This pathological state not only leads to diminished cardiac pumping, failing to meet physiological and metabolic demands, but also often co-occurs with other metabolic or cardiac diseases, of which atrial fibrillation (AF) is the most common. Notably, the coexistence of AF in patients with reduced ejection fraction heart failure further increases the risk of mortality. Therefore, in-depth understanding of the electrophysiological features and regulatory mechanisms of the heart under heart failure conditions is of great significance for reducing the risk of fatal arrhythmias in patients and for improving therapeutic strategies.

In cardiac electrophysiology research, small conductance calcium-activated potassium channels (SK channels) have recently received increasing attention. SK channels are a subgroup of potassium-selective ion channels, and mechanistically, they lack voltage sensors and are solely regulated by intracellular calcium concentration. SK channels are widely expressed in both human atrium and ventricle, though their physiological and pathological roles have yet to be fully elucidated. Research has confirmed that SK channels are “dormant” in healthy cardiac tissue but are upregulated (increased expression and calcium sensitivity) under various cardiac disease states such as heart failure and atrial fibrillation, indicating a special role in disease. For example, literature reports show that SK channel blockade in heart failure conditions can prolong ventricular action potential duration (APD), while having no significant effect under healthy conditions. These findings suggest that SK channel upregulation under pathological conditions might be an adaptive response to impaired repolarization reserve, aiming to shorten APD and restore cardiac electrical stability. However, the pro- or anti-arrhythmic roles of SK channels in heart failure-related arrhythmias remain unclear, constituting a key challenge in both basic and clinical electrophysiology.

Traditional experimental methods (such as patch-clamp technique) have revealed portions of the mechanisms; however, due to limited sample sizes and the difficulty in establishing disease models, they cannot comprehensively clarify the role of SK channels in heart failure. Thus, in silico models based on computational simulation have become a hot topic, enabling dynamic simulation of cardiac action potential kinetics from cellular to tissue level, revealing how changes in various ionic currents lead to arrhythmogenesis. Especially for human heart failure ventricular cell electrophysiological models, although many disease-specific models exist, most do not explicitly include the SK current mechanism. Therefore, quantitative description and validation of SK channels mark a significant breakthrough for advancing research on heart failure-induced electrical remodeling.

Source, Authors, and Publication Information

This study is entitled “In silico modeling and validation of the effect of calcium-activated potassium current on ventricular repolarization in failing myocytes,” authored by Marta Gómez, Jesús Carro, Esther Pueyo, Alba Pérez, Aída Oliván, and Violeta Monasterio. The primary research teams are from the Computing for Medical and Biological Applications Group at Universidad San Jorge, Spain, the Aragón Institute of Engineering Research (I3A) at Universidad de Zaragoza, IIS Aragón, and CIBER de Bioingeniería, Biomateriales y Nanomedicina. The paper is published in the IEEE Journal of Biomedical and Health Informatics (Vol. 29, No. 9, September 2025), and is backed by extensive experimental and computational expertise as well as multiple research grants from Spain (MICIU/AEI, ERDF/EU, Gobierno de Aragón, etc.).

Detailed Research Process and Methods

1. Collection and Organization of Experimental Data

The paper first collects and organizes the only two available experimental data sets on SK channel regulation in human heart failure ventricular myocytes, used for model construction and parameter calibration:

a) Blockade Dataset (BD)

This data originates from a study by Bonilla et al. published in 2014. The experimental subjects were left ventricular mid-myocardial cells (n=7) from late-stage heart failure patients. Using patch-clamp techniques, changes in action potential duration (APD50 and APD90) were recorded at different heart rates (0.5, 1, and 2 Hz) after application of the SK channel-specific blocker apamin. Three cells were excluded from analysis due to occurrence of late phase-3 early afterdepolarizations (EADs) after drug treatment. The data demonstrated that SK channel blockade significantly prolongs APD.

b) Activation Dataset (AD)

The second set includes samples from left ventricular papillary muscle and endocardial tissue from heart failure patients. Tissue sampling was performed by experienced cardiothoracic surgeons, involving 3 mid-myocardial and 23 endocardial specimens. Tissue slices (350 μm thick) were treated with the SK channel activator ska-31, and APD80 changes at different heart rates were measured using optical voltage mapping. Details of solution composition and staining methods highlight the rigor of the experimental design.

These two datasets provide “baseline” and “effect reference” for SK channel blockade and activation, forming the core basis for model calibration in this study.

2. Selection and Optimization of Baseline Cell Models

The research utilizes the O’Hara-Rudy human ventricular cell model (ORD) as the standard for healthy ventricular cell electrophysiology. The fast sodium current (INa) component is modified according to the Ten Tusscher et al. model to avoid propagation failure. For heart failure conditions, the ORDMM model (developed by Mora et al.) is adopted, based on the original ORD model but revised for maximal ionic conductances and time constants to express a heart failure phenotype, including calcium transient and dynamic abnormalities. Parameter adjustments realize heterogeneity in heart failure ventricular cells (covering endocardium, mid-myocardium, and epicardium), with interfaces reserved for embedding the SK channel mechanism.

3. SK Current (ISK) Modeling and Parameter Calibration

For quantitative description of SK current, the model adopts the ISK formula proposed by Landaw et al. as a starting point:

• ISK = GSK * XSK * (V - EK)
• XSK is the activation gating variable; its dynamics are determined by calcium sensitivity (KD) and cooperativity parameter (n). Based on human heart failure experimental data, the model adjusts these to KD=0.345μM, n=3.14, fully reflecting augmented calcium sensitivity of SK channels under heart failure conditions.
• The activation time constant (τSK) is also revised according to experimental data.

In modeling, SK channels are set to sense calcium signals in the submembrane space, following theoretical and experimental evidence of SK channel colocalization with L-type calcium channels (ICa,L).

a) Optimization of Mid-Myocardial Cell Conductance (GSK)

By simulating SK channel blockade experiments (i.e., GSK=0), comparison is made between model and BD experimental data on changes in APD50 and APD90 at each heart rate. Using Brent’s algorithm, parameter optimization seeks to minimize error in simulated and experimental relative changes (R values). The optimized GSK is determined to be 4.288 μS/μF.

b) Adjustment of Endocardial and Epicardial Cell Conductance

For endocardial and epicardial cell models, considering the heterogeneous distribution of SK channel expression across layers based on literature and experimental data, both layers’ conductance are adjusted to approximately 1.5 times that of the mid-myocardial cells (GSK=6.4μS/μF). For ska-31 activation, a uniform upregulation of GSK (by 165%) is implemented, and the model’s reliability is validated against AD experimental data.

4. Tissue-Level Fiber Model and Multi-Scale Simulation

Further, a one-dimensional (1D) transmural ventricular fiber model is constructed, comparing normal, heart failure, and heart failure + SK channel blockade conditions. The fiber is 1.7 cm long, composed of endocardial, mid-myocardial, and epicardial cells. The model uses a spatial step of 0.01 cm, and diffusion coefficients for healthy and diseased tissue are set as 0.06 mm²/ms and 0.03 mm²/ms, ensuring physiological signal propagation velocities (50 cm/s and 22.5 cm/s, respectively).

Key evaluation metrics include: - Transmural dispersion of repolarization (TDR) - QT interval (computed via pseudo-ECG)

5. Numerical Simulation Methods

Single-cell simulations use DENIS software (based on CellML standard), while fiber tissue simulations are implemented in FORTRAN using Elvira software, both adopting the Forward Euler method with a time step of 0.002ms. Stimulation is via biphasic/monophasic current pulses, all models are pre-paced for 600 cycles to reach steady state, with analyses conducted on subsequent 20 cycles.

Detailed Research Results

1. Model Optimization and Comparison with Experimental Data

a) Performance of the Mid-Myocardial Model

The newly optimized ORDMM-SK model, with rigorously calibrated GSK, accurately reproduces the experimental effect of SK channel blockade in prolonging APD50 and APD90 (23% and 21%, matching experimental results of 22% and 24%). In independent, larger-sample experiments (AD-mid), the model’s APD80 values at various frequencies fall within the experimental distribution range, demonstrating the model’s realism in simulating SK channel dynamics and drug intervention effects under heart failure conditions. Under slow pacing (0.5Hz), further ionic sensitivity analysis reveals that SK blockade combined with IKr reduction or increase in INaL and ICaL induces EADs, consistent with experimental observations.

b) Performance of the Endocardial Model

Through parameter search, the optimal endocardial model GSK is determined as 6.471 μS/μF, allowing simulation of AD-endo experimental APD80 distributions at multiple frequencies. Under ska-31 activation, a 165% upregulation of conductance yields excellent correspondence in APD shortening across frequencies with independent experimental data.

2. Tissue-Level Effects: Repolarization Heterogeneity and QT Interval

In transmural fiber simulations, heart failure status (FC) increases both TDR and QT interval, and SK channel blockade (FCB) further markedly increases these arrhythmia indicators. This indicates that, under heart failure, SK channel expression and function are crucial for preventing high repolarization heterogeneity and QT interval prolongation—both key predisposing factors for malignant arrhythmias.

Paper Conclusions, Scientific Value, and Application Significance

Through this study, the authors have, for the first time, clearly established and validated a quantitative kinetic model of SK channels in human heart failure ventricular myocytes, and systematically analyzed their pharmacological regulatory effects across cellular and tissue levels. Main conclusions include:

• SK channels are significantly upregulated in failing ventricular myocytes, exhibiting enhanced calcium sensitivity and higher expression.
• At the cellular level, SK channel blockade markedly prolongs APD, especially under low-frequency pacing, which can induce EADs (arrhythmogenic).
• At the tissue level, SK channels limit repolarization time dispersion and QT interval, exerting anti-arrhythmic effects; their blockade notably aggravates these risk factors.
• Pharmacological intervention of SK channels (e.g., SK blockers or activators) requires caution: SK channel activation may moderately shorten APD and improve repolarization reserve; blockade may induce malignant arrhythmias in heart failure patients. Thus, SK channels are not purely “atria-selective” targets for AF treatment—their effects in ventricles necessitate rigorous safety evaluation.
• The authors have, for the first time, proposed how SK mechanisms in such models can be precisely calibrated by experimental data, utilizing diverse simulation tools (DENIS, Elvira) and algorithms (Brent’s method) for multi-scale quantitative reproduction of cardiac electrophysiology.

Research Highlights and Innovative Features

• Rigorous Data Integration: First systematic collection and organization of human heart failure ventricular SK channel experimental data, enabling model calibration driven by real-world data.
• Multi-Level Modeling: Multi-scale simulation of SK channel dynamics from single-cell to tissue and fiber, revealing how ionic mechanisms and tissue structure jointly determine arrhythmia susceptibility.
• Fine Parameter Regulation: Targeted adjustment of SK channel abnormal expression heterogeneity in different cell layers, demonstrating the model’s broad applicability and explanatory power.
• Pharmacological Intervention Simulation: Direct simulation of the electrophysiological effects of SK channel blockade/activation, providing an efficient approach for clinical drug screening and safety assessment.

Value and Future Prospects

This study advances the development of electrophysiological models for heart failure and provides a solid theoretical foundation and simulation tools for clinical drug development and arrhythmia mechanism research. Going forward, the research team (e.g., introducing new models like tor_ord, or adopting population-based model approaches to enhance data generalizability) can further expand model applicability, improve predictive capabilities, and integrate more human experimental data to refine mechanisms of SK channels in various ventricular cell subtypes.

Moreover, the study underscores the complexity of SK channels’ global impact on ventricular and atrial electrical activity as a drug target, theoretically supporting risk assessment for atria-selective drug development strategies. With accelerated advances in computational biology and accumulation of cardiac electrophysiology data, studies like this will continue to deepen our understanding from micro-ionic mechanisms to macro-rate stability, driving precision intervention and prevention of malignant arrhythmias associated with heart failure.