Embodiments of the invention relate to an extracorporeal perfusion apparatus comprising an extracorporeal blood circuit for conveying blood, a filtrate circuit for conveying blood plasma, and a controller, wherein the filtrate circuit is connected to the extracorporeal blood circuit by means of a filter, wherein the filter has a sieving coefficient of 5% for substances having a molar mass of 340,000 g/mol (relative molecular mass of 340 kDa), and wherein a depletion agent comprising a first carrier having a neutral, hydrophobic surface is arranged in the filtrate circuit, wherein the perfusion apparatus comprises a dispensing means for feeding an endotoxin-binding lipopeptide into the extracorporeal blood circuit, wherein the endotoxin-binding lipopeptide is selected from the group consisting of polymyxins, polymyxin derivatives, prodrugs thereof, and a combination thereof.
