Invasive mechanical ventilation is the cornerstone of respiratory failure treatment. Setting ventilator parameters is a balancing act between providing adequate oxygenation and ventilation on the one hand, and minimizing lung damage and adverse cardiovascular effects on the other hand. This thesis aims to find the differences between two methods for the titration of positive end-expiratory pressure: electrical impedance tomography and esophageal pressure monitoring. Moreover, methods are proposed to suppress cardiac activity from electrical impedance tomography and esophageal pressure recordings.