A method of detecting an indication of a potential intradialytic morbid event (IME) by monitoring a patients condition during excess fluid removalby ultrafiltration during a hemodialysis treatment includes determining the patients relative blood volume (RBV), and removing a portion of the volume of excess fluid from blood of the patient at an initial ultrafiltration rate while periodically monitoring a second derivative over time of the relative blood volume (SDRBV). The method then includes continuing to remove excess fluid from blood of the patient at the same ultrafilration rate, or, optionally, incrementally increasing the ultrafiltration rate. The method further includes triggering an alarm for an IME for the patient if the SDRBV is in a range of between a low SDRBV alarm level and a high SDRBV alarm level, and, alternatively or additionally monitoring the patients normalized blood pressure ratio, and taking a remedial action if the alarm is triggered.