Personal health monitoring systems can offer a cost-effective solution for human healthcare. To extend the lifetime of health monitoring systems, we propose a near-threshold ultra-low- power multi-core architecture featuring low-power cores, yet capable of executing biomedical applications, with multiple instruction and data memories, tightly coupled through flexible crossbar interconnects. This architecture also includes broadcasting mechanisms for the data and instruction memories to optimize system energy consumption by tailoring memory sharing to the target application. Moreover, the architecture enables power gating of the unused memory banks to lower leakage power. Our experimental results show that compared to the state-of-the-art, the proposed architecture achieves 39.5% power savings at high workload requirements (637 MOps/s), and 38.8% savings at low workload requirements (5 kOps/s), whereby leakage power consumption dominates.