In wireless body area sensor networks (WBASNs), energy efficiency is an area of extreme significance. At first, we present a mathematical model for a non-invasive inductive link which is used to recharge the battery of an implanted biomedical device (pacemaker). Afterwards, we propose a distance-aware relaying energy-efficient (DARE) and mutual information-based DARE (MI-DARE) routing protocols for multihop mobility-aware body area sensor networks (MM-BASNs). Both the routing protocols and the non-invasive inductive link model are tested with the consideration of eight patients in a hospital unit under different topologies, where the vital signs of each patient are monitored through seven on-body sensors and an implanted pacemaker. To reduce energy consumption of the network, the sensors communicate with a sink via an on-body relay which is fixed on the chest of each patient. The behavior (static/mobile) and position of the sink are changed in each topology, and the impact of mobility due to postural changes of the patient(s) arms, legs, and head is also investigated. The MI-DARE protocol further prolongs the network lifetime by minimizing the number of transmissions. Simulation results show that the proposed techniques outperform contemporary schemes in terms of the selected performance metrics.