The wider adoption of mobile Health video communication systems in standard clinical practice requires real-time control to provide for adequate levels of clinical video quality to support reliable diagnosis. The latter can only be achieved with real-time adaptation to time-varying wireless networks' state to guarantee clinically acceptable performance throughout the streaming session, while conforming to device capabilities for supporting real-time encoding. We propose an adaptive video encoding framework based on multi-objective optimization that jointly maximizes the encoded video's quality and encoding rate (in frames per second) while minimizing bitrate demands. For this purpose, we construct a dense encoding space and use linear regression to estimate forward prediction models for quality, bitrate, and computational complexity. The prediction models are then used in an adaptive control framework that can fine-tune video encoding based on real-time constraints. We validate the system using a leave-one-out algorithm applied to ten ultrasound videos of the common carotid artery. The prediction models can estimate structural similarity quality with a median accuracy error of less than 1%, bitrate demands with deviation error of 10% or less, and encoding frame rate within a 6% margin. Real-time adaptation at a group of pictures level is demonstrated using the high efficiency video coding standard. The effectiveness of the proposed framework compared to static, nonadaptive approaches is demonstrated for different modes of operation, achieving significant quality gains, bitrate demands reductions, and performance improvements, in real-life scenarios imposing time-varying constraints. Our approach is generic and should be applicable to other medical video modalities with different applications.