A proposed blood treatment apparatus includes a blood treatment unit, at least one fluid pump and at least one blood pump. The fluid pumps are configured to pass blood treatment fluid through the blood treatment unit, while the blood pumps are configured to extract untreated blood from a blood source, e.g. a patient, pass the extracted blood through the blood treatment unit and deliver treated blood to a target vessel, e.g. likewise represented by a patient. Each blood pump includes a pumping chamber, which is separated into a first accumulation container and a second accumulation container by a flexible member. The flexible member is further movable within the pumping chamber so as to vary a volume relationship between the first and second accumulation containers. The second accumulation container is configured to receive an amount of blood treatment fluid to act on the flexible member and thus pump blood from the first accumulation container.