While body sensor networks (BSNs) have proven to be a feasible solution for long-term vigilant health monitoring, limited battery life remains one of the main factors that has impeded their widespread adoption. Energy harvesting technologies bring an opportunity to address this issue by enabling the development of self-powered BSNs. However, the dynamic nature of energy harvesting sources poses a challenge to self-powered vigilance. In this paper, an application-driven dynamic power management (DPM) method for self-powered BSNs is presented that optimally adapts system operation to energy availability while meeting application requirements for vigilant monitoring. Vigilant Atrial Fibrillation (AF) monitoring is investigated as an example case study, and a simulation using real-world energy harvesting profiles is executed to validate the model and the optimal solution.