The paper presents a mathematical model of the ventricular cardiac action potential, focusing on the depolarization and repolarization phases and their interaction. The model incorporates recent single-cell and single-channel data, including the effect of changing extracellular potassium concentration ([K]o). Key features include: 1. **Ionic Currents**: - **Fast Sodium Current (INa)**: Characterized by a fast upstroke velocity (Vmax = 400 V/sec) and slow recovery from inactivation. - **Time-Independent Potassium Current (IK1)**: Includes a negative-slope phase and significant crossover as [K]o varies. - **Time-Dependent Potassium Current (IK2)**: Shows minimal crossover. - **Plateau Potassium Current (IKp)**: Activates at plateau potentials. - **Background Current (Ia)**: A constant background current. 2. **Model Formulation**: - The model uses a numerical reconstruction based on Hodgkin-Huxley-type formalism, with the rate of change of membrane potential (V) given by a differential equation involving ionic currents. - Ionic currents are determined by gating variables, which are solutions to a system of nonlinear ordinary differential equations. - The model incorporates realistic sodium channel kinetics, including a slow inactivation process, and accurately simulates the effects of changes in [K]o on action potential duration and rest potential. 3. **Results**: - **Action Potential Characteristics**: The model accurately simulates the action potential characteristics, including threshold potential, membrane depolarization rate, plateau potential, action potential duration, and resting potential. - **Recovery of Excitability**: The model demonstrates the importance of the fast depolarization and slow recovery of INa in determining membrane behavior, accurately simulating the latency to threshold and maximum upstroke velocity. - **Supernormal Excitability**: The model investigates supernormal excitability, a phenomenon observed at low [K]o concentrations. It shows that supernormality is due to the shape of the threshold potential curve during repolarization, which is influenced by the recovery of the sodium channel. - **Stimulus Duration Effects**: The model also explores the effects of stimulus duration on membrane excitability, showing that longer stimuli can lead to larger peak-to-peak amplitudes of the supernormal notch and different behavior during late phase 4 of the action potential. The model provides a detailed understanding of the mechanisms underlying various electrophysiological phenomena and their interaction, supporting experimental observations and advancing the field of cardiac electrophysiology.The paper presents a mathematical model of the ventricular cardiac action potential, focusing on the depolarization and repolarization phases and their interaction. The model incorporates recent single-cell and single-channel data, including the effect of changing extracellular potassium concentration ([K]o). Key features include: 1. **Ionic Currents**: - **Fast Sodium Current (INa)**: Characterized by a fast upstroke velocity (Vmax = 400 V/sec) and slow recovery from inactivation. - **Time-Independent Potassium Current (IK1)**: Includes a negative-slope phase and significant crossover as [K]o varies. - **Time-Dependent Potassium Current (IK2)**: Shows minimal crossover. - **Plateau Potassium Current (IKp)**: Activates at plateau potentials. - **Background Current (Ia)**: A constant background current. 2. **Model Formulation**: - The model uses a numerical reconstruction based on Hodgkin-Huxley-type formalism, with the rate of change of membrane potential (V) given by a differential equation involving ionic currents. - Ionic currents are determined by gating variables, which are solutions to a system of nonlinear ordinary differential equations. - The model incorporates realistic sodium channel kinetics, including a slow inactivation process, and accurately simulates the effects of changes in [K]o on action potential duration and rest potential. 3. **Results**: - **Action Potential Characteristics**: The model accurately simulates the action potential characteristics, including threshold potential, membrane depolarization rate, plateau potential, action potential duration, and resting potential. - **Recovery of Excitability**: The model demonstrates the importance of the fast depolarization and slow recovery of INa in determining membrane behavior, accurately simulating the latency to threshold and maximum upstroke velocity. - **Supernormal Excitability**: The model investigates supernormal excitability, a phenomenon observed at low [K]o concentrations. It shows that supernormality is due to the shape of the threshold potential curve during repolarization, which is influenced by the recovery of the sodium channel. - **Stimulus Duration Effects**: The model also explores the effects of stimulus duration on membrane excitability, showing that longer stimuli can lead to larger peak-to-peak amplitudes of the supernormal notch and different behavior during late phase 4 of the action potential. The model provides a detailed understanding of the mechanisms underlying various electrophysiological phenomena and their interaction, supporting experimental observations and advancing the field of cardiac electrophysiology.