Wireless Body Area Networks (WBANs) are introduced as an enabling technology in tele-health for patient monitoring. Designing an efficient Medium Access Control (MAC) protocol is the main challenge in WBANs because of their various applications and strict requirements such as low level of energy consumption, low transmission delay, the wide range of data rates and prioritizing emergency data. In this paper, we propose a new MAC protocol to provide different requirements of WBANs targeted for medical applications. The proposed MAC provides an efficient emergency response mechanism by considering the correlation between medical signals. It also reduces the power consumption of nodes by minimizing contention access, reducing the probability of the collision and using an efficient synchronization algorithm. In addition, the proposed MAC protocol increases the data rate of the nodes by allocating the resources according to the condition of the network. Analytical and simulation results show that the proposed MAC protocol outperforms IEEE 802.15.4 MAC protocol in terms of power consumption level as well as the average response delay. Also, the comparison results of the proposed MAC with IEEE 802.15.6 MAC protocol show a tradeoff between average response delay and medical data rate.