Wireless Body Area Networks are composed of sensor nodes that may be implanted in the body or worn on it. A node is composed of a sensing unit, a processor and a radio unit. One of the nodes, the sink, acts as a gateway between the body area network and other networks such as the Internet. We propose a routing protocol that constructs paths between nodes such that the final network topology is a tree rooted at the sink. The protocol's aim is to increase network lifetime and reliability, and to adapt to network conditions dynamically. Moreover, the protocol enables communications between nodes and sink both in the upstream direction, from nodes to sink, and in the downstream direction from sink to nodes. When the network tree is constructed, a node chooses its parent, i.e., next hop to sink, by using one of various criteria. Namely, these are the number of hops between parent and sink, energy level of parent, received signal strength from parent, number of current parent's children, and a fuzzy logic function that combines multiple criteria. Moreover, as time progresses the tree structure may dynamically change to adapt to conditions such as the near-depletion of a routing node's energy. Simulation results show improvements in network lifetime and energy consumption over the older version of the protocol.