The invention relates to a medical aspiration system having a catheter with at least two lumens, wherein a first lumen forms an aspiration lumen which is connected to an aspiration unit for suction removal of substances from a blood vessel through an inlet opening in the aspiration lumen, and a second lumen forms an infusion lumen through which a substance can be supplied to the blood vessel through an outlet opening in the infusion lumen, wherein the outlet opening in the infusion lumen is arranged in a region between the inlet opening of the aspiration lumen and a position proximal to the inlet opening in the aspiration lumen. The invention is characterized in that the infusion lumen is connected to a cooling unit, which supplies a cooled liquid for administration through the infusion lumen.