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Wireless communications technologies can support efficient healthcare services in medical and patient-care environments. However, using wireless communications in a healthcare environment raises two crucial issues. First, the RF transmission can cause electromagnetic interference (EMI) to biomedical devices, which could critically malfunction. Second, the different types of electronic health (e-Health) applications require different quality of service (QoS). In this paper, we introduce an innovative wireless access scheme, called EMI-aware prioritized wireless access, to address these issues. First, the system architecture for the proposed scheme is introduced. Then, an EMI-aware handshaking protocol is proposed for e-Health applications in a hospital environment. This protocol provides safety to the biomedical devices from harmful interference by adapting transmit power of wireless devices based on the EMI constraints. A prioritized wireless access scheme is proposed for channel access by two different types of applications with different priorities. A Markov chain model is presented to study the queuing behavior of the proposed system. Then, this queuing model is used to optimize the performance of the system given the QoS requirements. Finally, the performance of the proposed wireless access scheme is evaluated through extensive simulations.