A blood treatment apparatus, including a blood treatment unit configured to receive untreated blood and fresh blood treatment fluid, and emit treated blood and used blood treatment fluid, a pair of fluid pumps configured to pass blood treatment fluid through the blood treatment unit, a pair of blood pumps configured to extract untreated blood from a blood source, pass extracted blood through the blood treatment unit and deliver treated blood to a target vessel, each blood pump including a pump chamber and a flexible member separating the pumping chamber into a first blood accumulating container and a second working fluid accumulating container where the flexible member is configured to vary a volume relationship between the first and the second accumulation containers. A control unit and a measuring device are configured to emit a feedback signal indicative of the amount of working fluid received into, or discharged from at least one of the second accumulation containers whereby the pumped mass or volume of working fluid is determined by the control unit at an arbitrary position of the flexible member.