For wireless medical video communications, the emerging high-efficiency video coding (HEVC) standard and network standards support low-delay and high-resolution video transmission, at the clinically acquired resolution and frame rates. Ultimately, the goal is to support remote diagnosis for emergency incidents in standard clinical practice. Clinical video quality assessment needs to be clearly defined in terms of clinical criteria. This paper investigates the advantages of the HEVC standard over the H.264/AVC standard and the wireless transmission of high-resolution stroke ultrasound videos over mobile WiMAX networks. We test different HEVC modes that include high-efficiency and low-complexity configurations combined with low-delay and random access. The results are compared against similar H.264/AVC configurations. The experimental evaluation demonstrates significant reductions in bitrate requirements for equivalent clinical quality of approximately 37%. Moreover, careful selection of network parameters based on objective and subjective clinical criteria demonstrates that mobile WiMAX can be used to communicate low-delay H.264/AVC ultrasound video at the clinically acquired resolution.