Patient monitoring is becoming a requirement for offering a better healthcare to an increasing number of chronic patients whether they are living alone, or in nursing homes. Thus, it is necessary to constantly monitor their vital signs to effectively control their health condition and to provide urgent treatment while an emergency such as an abnormal variation of heart rate occurs. In recent years, wireless body sensor networks have emerged as a low cost solution for healthcare applications. However, processing the huge amount of raw data captured by bio medical sensors is a major challenge for this type of networks, along with energy, as in almost all the cases the only source of energy is battery with limited lifetime. In this paper we address how emergency alerts can be supported locally on each node of the network. Our approach proposes some criticality models which allow to reduce considerably the amount of sent data through the network, thus improving power efficiency by sending only critical measures when needed. Simulation results are presented to validate the performance of the proposed approach.