Quantitative Regular Expressions for Arrhythmia Detection Algorithms

TL;DR

This paper introduces Quantitative Regular Expressions (QREs) as a formal language to specify and verify arrhythmia detection algorithms, enabling rigorous analysis and testing of medical devices with real patient data.

Contribution

It formalizes arrhythmia detection algorithms using QREs, simplifying their specification, analysis, and testing compared to traditional temporal logics.

Findings

QREs effectively express peak detection and discriminators in arrhythmia algorithms.

QRE-based detectors perform comparably to cardiologists on real patient data.

The approach facilitates formal verification and potential regulatory benefits.

Abstract

Motivated by the problem of verifying the correctness of arrhythmia-detection algorithms, we present a formalization of these algorithms in the language of Quantitative Regular Expressions. QREs are a flexible formal language for specifying complex numerical queries over data streams, with provable runtime and memory consumption guarantees. The medical-device algorithms of interest include peak detection (where a peak in a cardiac signal indicates a heartbeat) and various discriminators, each of which uses a feature of the cardiac signal to distinguish fatal from non-fatal arrhythmias. Expressing these algorithms' desired output in current temporal logics, and implementing them via monitor synthesis, is cumbersome, error-prone, computationally expensive, and sometimes infeasible. In contrast, we show that a range of peak detectors (in both the time and wavelet domains) and various discriminators at the heart of today's arrhythmia-detection devices are easily expressible in QREs. The fact that one formalism (QREs) is used to describe the desired end-to-end operation of an arrhythmia detector opens the way to formal analysis and rigorous testing of these detectors' correctness and performance. Such analysis could alleviate the regulatory burden on device developers when modifying their algorithms. The performance of the peak-detection QREs is demonstrated by running them on real patient data, on which they yield results on par with those provided by a cardiologist.