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Concentric tube robots, which are comprised of pre-curved elastic tubes that are concentrically arranged, are being developed for many medical interventions. The shape of the robot is determined by the rotation and translation of the tubes relative to each other, and also by any external forces applied by the environment. As the tubes rotate and translate relative to each other, elastic potential energy caused by tube bending and twisting can accumulate; if a configuration is not locally elastically stable, then a dangerous snapping motion may occur as energy is suddenly released. External loads on the robot also influence elastic stability. In this paper we provide a second-order sufficient condition, and also a separate necessary condition, for elastic stability. Using methods of optimal control theory, we show that these conditions apply to general concentric tube robot designs subject to arbitrary conservative external loads. They can be used to assess the stability of candidate robot configurations. Our results are validated via comparison with other known stability criteria, and their utility is demonstrated by an application to stable path planning.

The goal was to develop a pediatric airway stent for treating tracheobronchomalacia that could be used as an alternative to positive pressure ventilation. The design goals were for the stent to allow mucus flow and to resist migration inside the airways, while also enabling easy insertion and removal. Methods: A helical stent design, together with insertion and removal tools, is presented. A mechanics model of stent compression is derived to assist in selecting stent design parameters (pitch and wire diameter) that provide the desired amount of tracheal support, while introducing the minimal amount of foreign material into the airway. Worst-case airway area reduction with stent support is investigated experimentally using a pressurized tracheal phantom matched to porcine tracheal tissue properties. The stent design is then evaluated in a porcine in vivo experiment. Results: Phantom testing validated the mechanics model of stent compression. In vivo testing demonstrated that the stent was well tolerated by the animal. Since the helical design covers only a small portion of the epithelium, mucus transport through the stented region was minimally impeded. Furthermore, the screw-like stent resisted migration, while also providing for atraumatic removal through the use of an unscrewing motion during removal. Conclusion: The proposed stent design and tools represent a promising approach to prevent airway collapse in children with tracheobronchomalacia. Significance: The proposed technology overcomes the limitations of existing airway stents and may provide an alternative to maintaining children on a ventilator. Index Terms-Tracheobronchomalacia, airway stent. I. INTRODUCTION T RACHEOBRONCHOMALACIA is the most common congenital defect of the central airways [1] and has been identified in up to 15% of infants and 30% of young children undergoing bronchoscopic examination for respiratory distress [2]. The condition arises due to intrinsic weakness of the wall and cartilaginous support. For these children, during dynamic expiration and coughing at low lung volume, pleural pressure exceeds intraluminal pressure resulting in airway collapse [3],