  Tendon-driven robotic catheters are capable of precise execution of minimally
invasive cardiac procedures including ablations and imaging. These procedures
require accurate mathematical models of not only the catheter and tendons but
also their interactions with surrounding tissue and vasculature in order to
control the robot path and interaction. This paper presents a mechanical model
of a tendon-driven robotic catheter system based on Cosserat rods and
integrated with a stable, implicit Euler scheme. We implement the Cosserat rod
as a model for a simple catheter centerline and validate its physical accuracy
against a large deformation analytical model and experimental data. The
catheter model is then supplemented by adding a second Cosserat rod to model a
single tendon, using penalty forces to define the constraints of the
tendon-catheter system. All the model parameters are defined by the catheter
properties established by the design. The combined model is validated against
experimental data to confirm 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 mechanical Cosserat rods and
fully-validated against experimental data in the case of the single rod system.
