Approximately 20% of intensive care patients in Germany require mechanical ventilation due to illness or post-operative conditions, which impairs their ability to communicate effectively. This poses significant challenges for patients and their caregivers. Augmentative and alternative communication concepts from other fields can be adapted to the context of intensive care to support ventilated patients. We developed an assistive system designed for the needs of the user group that is controlled by a ball-shaped interaction device. In this paper we introduce the central element of the assistive system, a radial menu technique called Compass Menu. It is systematically described using a taxonomy of menu properties. Our prototype was evaluated by six HCI experts in a pilot study. They evaluated how well design decisions made in development met previously identified menu design objectives as well as usability, applicability, user experience, and aesthetics. For the evaluation, we developed a comprehensive questionnaire tailored to menu design. The results indicate that the menu design could be suitable for implementation in interactive systems that support mechanically ventilated intensive care patients.