An extracorporeal blood treatment system includes means for withdrawing blood from a patient, and means for transporting the blood through a calcium trap. The calcium trap includes a substrate having an immobilized species, the species being adapted to reduce the calcium concentration in the blood to a concentration that prevents blood clotting in the extracorporeal blood treatment system, thereby producing calcium-depleted blood. The extracorporeal blood treatment system also includes means for treating the calcium-depleted blood downstream of the calcium trap by an extracorporeal blood treatment device, thereby producing treated calcium-depleted blood, means for infusing calcium into the treated calcium-depleted blood downstream of the extracorporeal blood treatment device to add calcium to the treated calcium-depleted blood, and means for returning treated blood back to the patient.