A blood treatment apparatus (1) comprising: - a blood circuit that includes an arterial line (7) intended to draw blood from a patient and a venous line (6) intended to return blood to the patient； - a filter (2) having a main chamber (3) and a secondary chamber (4) separated by a semipermeable membrane (5), and - a treatment solution supply system configured to supply treatment solution within the apparatus ( 1) of blood treatment through an access (10) of treatment solution to the secondary chamber (4) of the filter (2), in which the treatment solution supply system comprises: a first intermediate container (11 ) and a second intermediate container (12)； - a source (60) of treatment solution； - a first gravimetric scale (21) configured to weigh the first intermediate vessel (11)； - a second gravimetric scale (22) configured to weigh the second intermediate vessel (12)； - a source flow controller (33) configured to supply treatment solution from the source (60) of treatment solution to the first intermediate vessel (11) weighed by the first gravimetric scale (21) and to the second intermediate vessel (12) weighed by the second gravimetric scale (22)； - a sterilization filter (80) located between the source (60) of the treatment solution and the access (10) of the treatment solution so that the treatment solution supplied to the access (10) of the treatment solution from the source ( 60) of treatment solution pass through the sterilization filter (80)； - an output controller (31) configured to control the flow of treatment solution from the first intermediate container (11) and the second intermediate container (12) to the access (10) of the treatment solution； - a container selection controller (32) located in a treatment solution path between the source flow controller (33) and the output controller (31)； - a control unit (41) operatively linked to the first gravimetric scale (21), the second gravimetric scale (22), the source flow controller (33), the container s
