In this paper, we propose novel low-energy scheduling algorithms with low computational complexities for the heterogeneous Body Area Network (BAN) systems, considering task graphs with deadlines (timing constraints) and precedence relationships to satisfy. Our proposed novel scheme, referred to as "critical-path information track-andupdate", analyses the critical-paths, identifies the slack and distributes it over tasks such that the overall energy consumption is minimised. Our dynamic scheduling algorithm utilises the results from the static scheduling algorithm and attempts to aggressively reduce the energy consumption. Simulations for the task graph for a typical BAN application show that our static and dynamic scheduling algorithms deliver 25% and 15% more energy savings respectively compared to typical slack reclamation based scheduling algorithms.