Quantitative regular expressions for arrhythmia detection

Implantable medical devices are safety-critical systems whose incorrect operation can jeopardize a patient's health, and whose algorithms must meet tight platform constraints like memory consumption and runtime. In particular, we consider here the case of implantable cardioverter defibrillators, where peak detection algorithms and various others discrimination algorithms serve to distinguish fatal from non-fatal arrhythmias in a cardiac signal. Motivated by the need for powerful formal methods to reason about the performance of arrhythmia detection algorithms, we show how to specify all these algorithms using Quantitative Regular Expressions QREs. QRE is a formal language to express complex numerical queries over data streams, with provable runtime and memory consumption guarantees. We show that QREs are more suitable than classical temporal logics to express in a concise and easy way a range of peak detectors in both the time and wavelet domains and various discriminators at the heart of today's arrhythmia detection devices. The proposed formalization also opens the way to formal analysis and rigorous testing of these detectors' correctness and performance, alleviating the regulatory burden on device developers when modifying their algorithms. We demonstrate the effectiveness of our approach by executing QRE-based monitors on real patient data on which they yield results on par with the results reported in the medical literature.