Abstract: A method for operating a portable dialysis device, comprising the following steps: continuously and alternately filling and emptying a hydraulic chamber with hydraulic fluid by a pump, wherein upon filling the hydraulic chamber, an at least partially flexible delivery membrane is moved towards a blood chamber adjoining the hydraulic chamber, in which blood is received, and wherein the blood flows tangentially along an inner wall of the blood chamber through an inlet side, whereby the blood chamber is compressed to eject the blood, and enhancing a return flow of the blood from the blood chamber while avoiding dead points in the flow in the blood chamber, and wherein upon emptying the hydraulic chamber, the delivery membrane is moved away from the blood chamber so that the blood chamber expands to receive the blood, so that a continuous, alternate compression and expansion of the blood chamber by the delivery membrane occurs, such that a continuous uninterrupted exchange of the blood in the blood chamber is per

Abstract: A portable dialysis device that can be continuously worn in and/or on the body of a patient, with a blood chamber in which the patient's blood can be received, a hydraulic chamber which can be filled with a hydraulic fluid and which adjoins the blood chamber, an at least partially flexible delivery membrane which is arranged between the hydraulic chamber and the blood chamber and which, when the hydraulic chamber is filled with hydraulic fluid, is movable in the direction of the blood chamber in such a way as to cause a compression of the blood chamber and therefore an ejection of the blood located therein, a pump for controllable filling and/or emptying of the hydraulic fluid in the hydraulic chamber, such that blood can in this way be conveyed into the blood chamber and/or out of the latter, a filter membrane which is arranged between the blood chamber and the hydraulic chamber and through which waste substances in the blood can be removed to the hydraulic fluid located in the hydraulic chamber, such that t