Models for Formal Analysis of Real Systems
(MARS)

In medicine, needles are frequently used to deliver treatments to subsurface targets or to take tissue samples from the inside of an organ. Current clinical practice is to insert needles under image guidance or haptic feedback, although that may involve reinsertions and adjustments since the needle and its interaction with the tissue during insertion cannot be completely controlled. (Automated) needle steering could in theory improve the accuracy with which a target is reached and thus reduce surgical traumata especially for minimally invasive procedures, e.g., brachytherapy or biopsy. Yet, flexible needles and needle-tissue interaction are both complex and expensive to model and can often be computed approximatively only.
We propose to employ timed games to navigate flexible needles with a bevel tip to reach a fixed target in tissue. We use a simple non-holonomic model of needle-tissue interaction, which abstracts in particular from the various physical forces involved and appears to be simplistic compared to related models from medical robotics. Based on a model, we synthesize strategies from which we can derive sufficiently precise motion plans to steer the needle in soft tissue. However, applying those strategies in practice, one is faced with the problem of an unpredictable behavior of the needle at the initial insertion point.
We design a second 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.