A medical monitoring apparatus and a method for surveillance of patients submitted to a plurality of extracorporeal treatment sessions executed by at least one extracorporeal blood treatment machine is disclosed. An infrastructure including a plurality of blood treatment machines and the monitoring apparatus is also disclosed. The monitoring apparatus and the method are configured for determining presence of peaks in the values taken over time by a characteristic (Cd(t)) of the dialysis liquid during a same treatment session and for determining presence of peaks in the values taken over time by the parameter (BV%(t)) related to blood volume change during the same treatment session. Based on the detection of the above peaks the apparatus and method verify presence and cause of a condition of recirculation.
