An artificial kidney comprises an exchanger (1) having two compartments (2, 3) separated by a semipermeable membrane (4), a first compartment (2) being connected to a circuit (5, 7) for extracorporeal blood circulation, the second compartment (3) having an outlet for draining waste liquid. Means (22, 25) are provided for controlling the flow rate (Q.sub.A) of a sterile solution containing a substance (A) to be perfused into the circuit (5, 7) for conveying a flow of blood outside the body, which flow rate is controlled as a function of the flow rate (Q.sub.OUT) of waste liquid. This kidney makes it possible to dose a substance such as a medicine, glucose or bicarbonate, accurately into the blood of a patient undergoing treatment by hemofiltration, hemodialysis, or hemodiafiltration.