There is disclosed herein a blood circuit assembly (17) for a dialysis unit, comprising: an organizing tray (171) including circuit tube engagement members (174) each_having a hole through which a respective circuit tube passes, the engagement members engaging with the respective circuit tubes to allow the circuit tubes to be pulled and stretched for engagement with an occluder (513) of the dialysis unit; a pair of pneumatic pumps (23) mounted to the organizing tray for circulating blood received from a patient through a circuit including a dialyzer (14) and back to the patient; an air trap (19) mounted to the organizing tray arranged to remove air from blood circulating in the circuit; a pair of dialyzer connections arranged to connect to the inlet and outlet of the dialyzer (14); and a pair of blood line connectors (203, 204), one inlet blood line connector for receiving blood from the patient and providing blood to the pneumatic pumps and the other outlet blood line connector for returning blood to the patient. A related method of mounting a blood circuit assembly onto a dialysis unit is also disclosed.