Artificial intelligence (AI), distributed computing, and the Internet of Medical Things are joining forces to advance medical imaging. Investigating how distributed AI processes spanning edge, fog, and cloud infrastructures can benefit from aggregate programming approaches is central to identifying new research options. Such an investigation, based on existing bibliographic data, revealed four primary research areas: (i) IoT-based distributed intelligence, (ii) self-organizing systems, (iii) programming and computational field models, and (iv) cloud, fog and systems integration. Several common issues that can be set in relation with the four directions include interoperability, explainability, real-time edge intelligence, and clinical validation. Common issues that can be identified across these clusters include interoperability, explainability, real-time edge intelligence, and clinical validation. Our investigation also highlights how scalable, privacy-preserving, and interpretable medical imaging systems may benefit from the aggregate paradigms by mapping conceptual foundations and research trends.