## 4 Discussion
### Effect of Extracellular Potassium Concentration on Arrhythmia Vulnerability  
The simulation results suggested that the relationship between the vulnerability of ventricular arrhythmias and extracellular potassium concentration was bell shaped with a peak in susceptibility at 12 mM. When the extracellular potassium concentration increased from 9 mM to 12 mM, the vulnerability window increased significantly and the duration of reentrant activation also increased. This phenomenon was due to the increase of repolarization dispersion caused by the increase of extracellular potassium concentration, which was beneficial to the formation and maintenance of reentry. The dispersion of repolarization could be measured by the APD distribution [29]. Figure 7 shows the APD distribution at different extracellular potassium concentrations after the S1 stimulation. When the extracellular potassium concentration was increased to 12 mM, the isochron density of APD increased, that is, the dispersion of repolarization increased, resulting in an increase in the vulnerability of ventricular arrhythmias. When the extracellular potassium concentration increased from 12 mM to 15 mM, both of the vulnerability window and the duration of reentrant activation decreased. The main reason was that with the further increase of extracellular potassium concentration, the effective refractory period of cardiomyocytes increased significantly, which hindered the propagation of reentrant wavefront. Extracellular potassium concentration is the  
Figure 7: The APD distribution at different extracellular potassium concentrations after S1 stimulation. The extracellular potassium concentrations of were (**a**) 9 mM and (**b**) 12 mM, respectively. most important influencing factor of the effective refractive period (ERP) in single cell kinetics [30]. As shown in Figure 8a, four points of ABCD were selected in different locations of the ICZ and BZ. This manuscript compared the action potential duration and the effective refractory period of the four points and further explored the mechanism of the change of the effective refractory period. Figure 8b illustrated the steady state values of action potential period and effective refractory period of ABCD at different extracellular potassium concentrations when the length of S1 stimulation cycle was 600 ms. With the increase of extracellular potassium concentration, the action potential duration of each point was shortened, while the effective refractory period was prolonged. For the case of [K\({}^{+}\)]\({}_{\text{o}}\) = 9 mM, the effective refractory period of point D was 149 ms. However, when [K\({}^{+}\)]\({}_{\text{o}}\) =15 mM, the effective refractory period of point D increased significantly, reaching 375 ms. The extension of the effective refractory period was due to the electrical remodeling of the ventricle, that is, abnormal activity of ion channels in cardiomyocytes led to electrical abnormalities. This manuscript studied the change of gated channels of INa which mainly affected the Phase 0 depolarization. The activation gates and the fast inactivation gates of INa under different extracellular potassium concentration were showed in Figure 8c,d, respectively. When the extracellular potassium concentration increases from 12 mM to 15 mM, the activation gate recovered earlier, while the inactivation gate recovered later and reached a lower steady state. The delayed recovery of the INa current led to prolonged refractory period. Prevention and elimination of abnormal activities of ion channels could be the target of clinical treatment.