This thesis documents DEng research work at Chiba University which leads towards the formalization of biomedical algorithms for health care systems. The thesis title “formal and model driven design for biomedical engineering” reflects the structure of the research work. The research work was centered on two main areas (a) formal modeling and (b) functional modeling. The formal models describe how a particular system is build. In contrast, the functional models describe what system to build, i.e. the system functionality. For example, an Artificial Neural Network (ANN) algorithm describes the steps necessary to establish a specific decision making functionality. In contrast, formal modeling describes the processes which implement the functionality of the individual steps. Formal methods are used to explore design variations, such as combining multiple functional steps into one process. But the most important reason for introducing formal modeling to biomedical engineering comes from their ability to define system functionality in a clear unambiguous way. Based on the clear description it is possible to proof specific system properties. The remainder of the thesis explains how formal and model driven design leads to safe, reliable and functional biomedical systems. This work aims to benefit society with a design methodology for reliable biomedical systems. State of the art best practice design fails to deliver the highest possible levels of safety, reliability and functionality. One reason for the failure comes from the fact that biomedical systems are designed with the divide and conquer method. To be specific, divide and conquer can mean one of two things. (1) Creating problem solutions by assembling preexisting smaller systems. This method all too often leads to problem solutions which are looking for a problem. (2) Breaking up complex problems into smaller problems which can be solved with physical problem solutions. There is nothing wrong with dividing a big problem into smaller and manageable parts. However, biomedical systems get more complex and dividing these complex systems into smaller parts usually leads to island solutions. In other words, a lack of overview leads to the kind of incompatible interfaces or inconsistent workflows and piecemeal health information systems we see at the moment. My proposal is to look at systems as a whole and plan the realization of the complete system before the focus shifts to the individual parts. Every biomedical health care system in existence is a physical realization of an idea or a strategy on how to solve a medical problem. These physical problem solutions must be safe, reliable and functional. The big question is: How do we get safe, reliable and functional systems? The functionality is established through modeling. The reliability is tested by comparing the physical problem solution with the model. For most systems, the comparison takes the form of use and failure case testing. However, for complex physical systems, testing can only confirm the presence of a fault but never proof the absence of system faults. Therefore, it is impossible to establish safety through testing – the safety critical fault might lurk in an untested system state. Safety is a design property, hence the way we design a system is very important. In general every system design follows some sort of design methodology. In some cases the design methodology exists only in the brain of a single expert, who takes on all the necessary design steps. However, such a design methodology creates dangerous systems, because the safety depends on whether or not the human expert has understood all aspects of the system design. In general, decisions on incomplete data and gut feeling must be avoided for safety critical systems. With this thesis I propose a formal and model driven design methodology for biomedical systems. The idea is to extend the well-established systems engineering design methodology with formal models. The systems engineering design methodology structures the design efforts. Model driven design means to prove or at least estimate certain aspects of the system, such as safety, reliability and functionality. As part of my drive to improve the functionality of biomedical systems, I demonstrate the efficacy of functional models for diseases, such as diabetes, sleep apnoea, and epilepsy. To improve the safety, I put forward formal models which proof a specific system is deadlock and lifelock free. The structure of this thesis follows my progression through the research work. To get a feel for the unique challenges of biomedical systems design my work initially focused on biomedical signals and algorithms for Computer-Aided Diagnosis (CAD). Building up a track record in this area allowed me to progress by introducing formal and model driven design methodologies to the process which realizes biomedical systems.