Modeling R$^3$ Needle Steering in Uppaal

TL;DR

This paper presents a verifiable model for medical needle steering in soft tissue using Uppaal, balancing model accuracy and data precision to enable safe, online navigation in complex environments.

Contribution

It introduces a bounded, discrete model of needle motion in Uppaal and an online steering framework, addressing the challenge of verification in safety-critical medical systems.

Findings

Successfully applied static and dynamic models in various scenarios

Achieved up to 100% target reachability in experiments

Demonstrated real-time needle steering in virtual and physical setups

Abstract

Medical cyber-physical systems are safety-critical, and as such, require ongoing verification of their correct behavior, as system failure during run time may cause severe (or even fatal) personal damage. However, creating a verifiable model often conflicts with other application requirements, most notably regarding data precision and model accuracy, as efficient model checking promotes discrete data (over continuous) and abstract models to reduce the state space. In this paper, we approach the task of medical needle steering in soft tissue around potential obstacles. We design a verifiable model of needle motion (implemented in Uppaal Stratego) and a framework embedding the model for online needle steering. We mitigate the conflict by imposing boundedness on both the data types, reducing from R^3 to Z^3 when needed, and the motion and environment models, reducing the set of allowed local actions and global paths. In experiments, we successfully apply the static model alone, as well as the dynamic framework in scenarios with varying environment complexity and both a virtual and real needle setting, where up to 100% of targets were reached depending on the scenario and needle.