Cosserat Model for Robotic Catheter Systems

Abstract

Tendon-driven robotic catheters are capable of precise execution of minimally invasive cardiac procedures including ablations and imaging. However, these procedures require accurate modeling of not only the catheter and tendons but also their interactions with surrounding tissue and vasculature. For this reason, mechanically-derived models provide a clear advantage over geometric models, given the ease with which mechanical models handle contact fores and friction. As a solution, we present a fully-mechanical model of a tendon-driven robotic catheter system based on Cosserat rods and integrated with a stable, implicit scheme. We first validate the physical accuracy of the Cosserat rod as a model for a simple catheter centerline against an analytical model for large deformations and experimental data. We then expand the system by adding a second Cosserat rod to model a single tendon in addition to the catheter, and define the constraints of the tendon-catheter system with penalty forces. We then validate the resulting tendon-catheter system against experimental data to prove its physical accuracy. This model represents a new contribution to the field of robotic catheter modeling in which both the tendons and catheter are modeled by fully-mechanical Cosserat rods and fully validated against experimental data.