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In this work, we focus on Body Area Networks (BANs) for real-time data streaming applications, where the realtime nature of data streams is of critical importance for providing a useful and efficient sensorial feedback for the user while system lifetime should be maximized. Thus, bandwidth, throughput and energy efficiency of the communication protocol must be carefully optimized. In this paper, we present an Energy-Balanced Rate Allocation and Routing Protocol (EBRAR). EBRAR selects routes based on the residual energy, thus, instead of continuously routing data through an optimized (energy efficient) fixed path, the data is transported more intelligently and the burden of forwarding the data is more equally spread among the nodes. Another unique property of EBRAR is its ability to provide adaptive resource allocation. Our experimental results show that the proposed protocol performs well in terms of energy balance, network lifetime and utility.