An apparatus and methods for performing ablation of myocardial tissues are disclosed. The apparatus includes a plurality of ablation electrode configurations to which nanosecond pulsed electric fields are applied. The methods relate to therapies to treat cardiac arrhythmias, such as, atrial fibrillation and scar-related ventricular tachycardia, amongst others. The affected myocardial tissues are ablated creating a plurality of lesions enabled by the nanosecond pulsed electric fields applied to either penetrating electrodes, endo-endo electrodes, or endo-epi electrodes. Different electrophysiological tests are performed to assess the application of nanosecond pulsed electric field ablation to specific desired tissue location within the heart. Test results show the potential to overcome limitations of current ablation therapies, thereby providing patients and doctors a superior treatment for cardiac arrhythmias.