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The recently released IEEE 802.15.6 standard specifies several physical (PHY) layers and medium access control (MAC) layer protocols for variety of medical and non-medical applications of Wireless Body Area Networks (WBAN). The medical applications of WBAN has several obligatory requirements and constrains viz. high reliability, strict delay deadlines and low power consumption. The standard IEEE 802.15.6 MAC scheme is not able to fulfil the all requirements of medical applications of WBAN. To address this issue we propose an IEEE 802.15.6-based MAC scheme that is the modification of superframe structure, user priorities and access mechanism of standard IEEE 802.15.6 MAC scheme. The proposed superframe has three access phases: random access phases (RAP), manage access phases (MAP) and contention access phase (CAP). The proposed four user priorities nodes access the channel during RAP using CAMA/CA mechanism with a large value of contention window. The proposed MAC scheme uses RTS/CTS access mechanism instead of basic access mechanism to mitigate the effect of hidden and expose terminal problem. Moreover, we develop an analytical model to evaluate the performance of proposed MAC scheme and solve the analytical model using Maple. The results show that the modified IEEE 802.15.6 MAC scheme achieve the better performance in terms of reliability, throughput, average access delay, energy consumption, channel utilization and fairness compared to standard IEEE 802.15.6 MAC scheme in E-health applications.