A formal analysis approach for verifying the design of respiratory pacing devices

Several conditions such as central sleep apnoea and chronic hypoventilation syndrome detrimentally affect respiratory drive. A decreased or absent respiratory drive results in inadequate ventilation and undesirable changes to blood gas levels that are detrimental to health. Respiratory pacing devices are used to regulate respiratory rhythm during times of reduced respiratory drive by delivering stimulation through electrodes placed on phrenic nerve motor points in the diaphragm muscle. These devices mostly operate in an openloop fashion, and provide rhythmic stimulation without sensing the intrinsic parameters that affect breathing. This paper develops a model driven approach for the design of closed-loop pacing devices for the treatment of illnesses that affect respiratory drive. Respiratory gas exchange and pacing systems are abstracted into high-level mathematical models that are validated through formal analysis with a focus on the overall timing behaviour. Using a network of timed automata we model normal and abnormal breathing through a lung model. This model is then composed in closed loop with a pacemaker model that paces the diaphragm when abnormal breathing is detected. We then verify and express a set of safety properties in Uppaal, which establishes that the designed pacemaker may fail to maintain the correct breathing rate for certain values of the timing parameters.