Abstract Addressing the study of antiarrhythmic drug is today more complex than ever, due to the changes drastically experienced by the appearance of different studies where the proarrhythmic action of these types of drugs has been verified. These results force to redefine the antiarrhythmic therapy. For this reason, the aim of this PhD thesis is to develop a mathematical model of the sodium channel blockade by lidocaine and to determine the proarrhythmic effect of this drug under pathological conditions as ischemia. In this work, we have developed a model of the effect of lidocaine. We model the use and pH dependent through the use of the genetic algorithms to adjust the association and dissociation rate constants of the differential equations. Thus, this model provides a useful tool to study the effect of the drug in different pathologies. We observed that lidocaine reduced the fast sodium current, the maximum upstroke velocity and the conduction velocity. These effects were increased when the frequency of stimulation and the pH diminished. We have shown that the refractory period increased raised only at high frequencies and high concentration of drug. Additionally, we found that under ischemic conditions and in the presence of lidocaine, the vulnerability to re-entry increased, tending to widen the vulnerable window as the drug concentration increased. Thus, this drug presents a proarrhythmic effect under these conditions. This effect is produced by the reduction on conduction velocity in the different zones of ischemic tissue. Also, we studied the action of lidocaine when it was combined with class III antiarrhythmic drugs. Our results suggest that under acute ischemic conditions, the combined action of the blockade of the rapid delayed rectifier potassium current and lidocaine diminishes the vulnerability to re-entry, ratifying in this way the proarrhythmic effect produced by lidocaine. In conclusion, the lidocaine under simulated acute ischemic conditions shows a proarrhythmic effect, due to its reduction on the conduction velotity, which is much higher than the effect on the effective refractory period. In conclusion, lidocaine under conditions of acute ischemia has a pro-arrhythmic effect due to enhance the start of re-entries. Although, lidocaine tends to turn situations from unidirectional blockage to bidirectional blockage, making difficult to break the reentry. This behaviour confers an antiarrhythmic effect.