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1.
Adv Sci (Weinh) ; 9(10): e2105352, 2022 04.
Article in English | MEDLINE | ID: mdl-35112810

ABSTRACT

Catheters integrated with microcoils for electromagnetic steering under the high, uniform magnetic field within magnetic resonance (MR) scanners (3-7 Tesla) have enabled an alternative approach for active catheter operations. Achieving larger ranges of tip motion for Lorentz force-based steering have previously been dependent on using high power coupled with active cooling, bulkier catheter designs, or introducing additional microcoil sets along the catheter. This work proposes an alternative approach using a heat-mitigated design and actuation strategy for a magnetic resonance imaging (MRI)-driven microcatheter. A quad-configuration microcoil (QCM) design is introduced, allowing miniaturization of existing MRI-driven, Lorentz force-based catheters down to 1-mm diameters with minimal power consumption (0.44 W). Heating concerns are experimentally validated using noninvasive MRI thermometry. The Cosserat model is implemented within an MR scanner and results demonstrate a desired tip range up to 110° with 4° error. The QCM is used to validate the proposed model and power-optimized steering algorithm using an MRI-compatible neurovascular phantom and ex vivo kidney tissue. The power-optimized tip orientation controller conserves as much as 25% power regardless of the catheter's initial orientation. These results demonstrate the implementation of an MRI-driven, electromagnetic catheter steering platform for minimally invasive surgical applications without the need for camera feedback or manual advancement via guidewires. The incorporation of such system in clinics using the proposed design and actuation strategy can further improve the safety and reliability of future MRI-driven active catheter operations.


Subject(s)
Hot Temperature , Magnetic Resonance Imaging , Equipment Design , Magnetic Resonance Imaging/methods , Minimally Invasive Surgical Procedures , Reproducibility of Results
2.
Sci Adv ; 8(2): eabk0685, 2022 Jan 14.
Article in English | MEDLINE | ID: mdl-35030013

ABSTRACT

The application of the Shannon entropy to study the relationship between information and structures has yielded insights into molecular and material systems. However, the difficulty in directly observing and manipulating atoms and molecules hampers the ability of these systems to serve as model systems for further exploring the links between information and structures. Here, we use, as a model experimental system, hundreds of spinning magnetic micro-disks self-organizing at the air-water interface to generate various spatiotemporal patterns with varying degrees of order. Using the neighbor distance as the information-bearing variable, we demonstrate the links among information, structure, and interactions. We establish a direct link between information and structure without using explicit knowledge of interactions. Last, we show that the Shannon entropy by neighbor distances is a powerful observable in characterizing structural changes. Our findings are relevant for analyzing natural self-organizing systems and for designing collective robots.

3.
Front Robot AI ; 8: 732643, 2021.
Article in English | MEDLINE | ID: mdl-34676248

ABSTRACT

The passive, mechanical adaptation of slender, deformable robots to their environment, whether the robot be made of hard materials or soft ones, makes them desirable as tools for medical procedures. Their reduced physical compliance can provide a form of embodied intelligence that allows the natural dynamics of interaction between the robot and its environment to guide the evolution of the combined robot-environment system. To design these systems, the problems of analysis, design optimization, control, and motion planning remain of great importance because, in general, the advantages afforded by increased mechanical compliance must be balanced against penalties such as slower dynamics, increased difficulty in the design of control systems, and greater kinematic uncertainty. The models that form the basis of these problems should be reasonably accurate yet not prohibitively expensive to formulate and solve. In this article, the state-of-the-art modeling techniques for continuum robots are reviewed and cast in a common language. Classical theories of mechanics are used to outline formal guidelines for the selection of appropriate degrees of freedom in models of continuum robots, both in terms of number and of quality, for geometrically nonlinear models built from the general family of one-dimensional rod models of continuum mechanics. Consideration is also given to the variety of actuators found in existing designs, the types of interaction that occur between continuum robots and their biomedical environments, the imposition of constraints on degrees of freedom, and to the numerical solution of the family of models under study. Finally, some open problems of modeling are discussed and future challenges are identified.

4.
Med Image Anal ; 71: 102058, 2021 07.
Article in English | MEDLINE | ID: mdl-33930829

ABSTRACT

Deep learning techniques hold promise to develop dense topography reconstruction and pose estimation methods for endoscopic videos. However, currently available datasets do not support effective quantitative benchmarking. In this paper, we introduce a comprehensive endoscopic SLAM dataset consisting of 3D point cloud data for six porcine organs, capsule and standard endoscopy recordings, synthetically generated data as well as clinically in use conventional endoscope recording of the phantom colon with computed tomography(CT) scan ground truth. A Panda robotic arm, two commercially available capsule endoscopes, three conventional endoscopes with different camera properties, two high precision 3D scanners, and a CT scanner were employed to collect data from eight ex-vivo porcine gastrointestinal (GI)-tract organs and a silicone colon phantom model. In total, 35 sub-datasets are provided with 6D pose ground truth for the ex-vivo part: 18 sub-datasets for colon, 12 sub-datasets for stomach, and 5 sub-datasets for small intestine, while four of these contain polyp-mimicking elevations carried out by an expert gastroenterologist. To verify the applicability of this data for use with real clinical systems, we recorded a video sequence with a state-of-the-art colonoscope from a full representation silicon colon phantom. Synthetic capsule endoscopy frames from stomach, colon, and small intestine with both depth and pose annotations are included to facilitate the study of simulation-to-real transfer learning algorithms. Additionally, we propound Endo-SfMLearner, an unsupervised monocular depth and pose estimation method that combines residual networks with a spatial attention module in order to dictate the network to focus on distinguishable and highly textured tissue regions. The proposed approach makes use of a brightness-aware photometric loss to improve the robustness under fast frame-to-frame illumination changes that are commonly seen in endoscopic videos. To exemplify the use-case of the EndoSLAM dataset, the performance of Endo-SfMLearner is extensively compared with the state-of-the-art: SC-SfMLearner, Monodepth2, and SfMLearner. The codes and the link for the dataset are publicly available at https://github.com/CapsuleEndoscope/EndoSLAM. A video demonstrating the experimental setup and procedure is accessible as Supplementary Video 1.


Subject(s)
Algorithms , Capsule Endoscopy , Animals , Computer Simulation , Phantoms, Imaging , Swine , Tomography, X-Ray Computed
5.
Med Image Anal ; 70: 101990, 2021 05.
Article in English | MEDLINE | ID: mdl-33609920

ABSTRACT

Current capsule endoscopes and next-generation robotic capsules for diagnosis and treatment of gastrointestinal diseases are complex cyber-physical platforms that must orchestrate complex software and hardware functions. The desired tasks for these systems include visual localization, depth estimation, 3D mapping, disease detection and segmentation, automated navigation, active control, path realization and optional therapeutic modules such as targeted drug delivery and biopsy sampling. Data-driven algorithms promise to enable many advanced functionalities for capsule endoscopes, but real-world data is challenging to obtain. Physically-realistic simulations providing synthetic data have emerged as a solution to the development of data-driven algorithms. In this work, we present a comprehensive simulation platform for capsule endoscopy operations and introduce VR-Caps, a virtual active capsule environment that simulates a range of normal and abnormal tissue conditions (e.g., inflated, dry, wet etc.) and varied organ types, capsule endoscope designs (e.g., mono, stereo, dual and 360∘ camera), and the type, number, strength, and placement of internal and external magnetic sources that enable active locomotion. VR-Caps makes it possible to both independently or jointly develop, optimize, and test medical imaging and analysis software for the current and next-generation endoscopic capsule systems. To validate this approach, we train state-of-the-art deep neural networks to accomplish various medical image analysis tasks using simulated data from VR-Caps and evaluate the performance of these models on real medical data. Results demonstrate the usefulness and effectiveness of the proposed virtual platform in developing algorithms that quantify fractional coverage, camera trajectory, 3D map reconstruction, and disease classification. All of the code, pre-trained weights and created 3D organ models of the virtual environment with detailed instructions how to setup and use the environment are made publicly available at https://github.com/CapsuleEndoscope/VirtualCapsuleEndoscopy and a video demonstration can be seen in the supplementary videos (Video-I).


Subject(s)
Capsule Endoscopy , Robotics , Algorithms , Computer Simulation , Endoscopy , Humans , Neural Networks, Computer
6.
Soft Robot ; 7(1): 10-21, 2020 02.
Article in English | MEDLINE | ID: mdl-31418640

ABSTRACT

Wireless capsule endoscopes have revolutionized diagnostic procedures in the gastrointestinal (GI) tract by minimizing discomfort and trauma. Biopsy procedures, which are often necessary for a confirmed diagnosis of an illness, have been incorporated recently into robotic capsule endoscopes to improve their diagnostic functionality beyond only imaging. However, capsule robots to date have only been able to acquire biopsy samples of superficial tissues of the GI tract, which could generate false-negative diagnostic results if the diseased tissue is under the surface of the GI tract. To improve their diagnostic accuracy for submucosal tumors/diseases, we propose a magnetically actuated soft robotic capsule robot, which takes biopsy samples in a deep tissue of a stomach using the fine-needle biopsy technique. We present the design, control, and human-machine interfacing methods for the fine-needle biopsy capsule robot. Ex vivo experiments in a porcine stomach show 85% yield for the biopsy of phantom tumors located underneath the first layers of the stomach wall.


Subject(s)
Capsule Endoscopy/instrumentation , Gastrointestinal Diseases/diagnosis , Animals , Biopsy, Fine-Needle , Equipment Design , Humans , Robotics , Sensitivity and Specificity , Swine , User-Computer Interface , Wireless Technology
7.
Annu Int Conf IEEE Eng Med Biol Soc ; 2019: 5488-5493, 2019 Jul.
Article in English | MEDLINE | ID: mdl-31947097

ABSTRACT

Recent research indicates that music-supported therapies may offer unique benefits for rehabilitation of motor function after stroke. We designed an adapted guitar and training task aimed to improve coordination between rhythmic and discrete movements because individuals recovering from stroke have greater difficulty performing discrete vs. rhythmic movements. In this paper, we report a feasibility study on training to play this adapted guitar in healthy young adults. Subjects (N = 10) practiced two rhythmic strumming patterns over three consecutive days using their non-dominant hand guided by an audiovisual metronome (60 bpm). They were also instructed to press a foot pedal while maintaining the strumming movement. Elbow and wrist kinematics were estimated using wireless inertial measurement units. Results showed positive mean asynchrony between strum onsets and metronome onsets, and a decrease in the standard deviation of mean asynchrony over practice. In early practice, participants slowed the strumming movement when they pressed the foot pedal, but this interference decreased on days two and three. Smoothness of the elbow movement during the strum phase, which includes the contact with the strings, increased over practice, while smoothness of the return phase did not change over practice. The predominant joint coordination pattern used for the strum phase consisted of elbow extension coupled with elbow pronation, wrist extension, and ulnar deviation. We discuss how these results fit into current music-based rehabilitation literature and outline directions for future applications of this music-supported intervention.


Subject(s)
Stroke Rehabilitation , Stroke , Feasibility Studies , Humans , Motor Skills , Movement , Music , Stroke Rehabilitation/instrumentation , Wrist , Young Adult
8.
Oper Neurosurg (Hagerstown) ; 13(1): 15-22, 2017 02.
Article in English | MEDLINE | ID: mdl-28580377

ABSTRACT

BACKGROUND: The recent development of MRI-guided laser-induced thermal therapy (LITT) offers a minimally invasive alternative to craniotomies performed for tumor resection or for amygdalohippocampectomy to control seizure disorders. Current LITT therapies rely on linear stereotactic trajectories that mandate twist-drill entry into the skull and potentially long approaches traversing healthy brain. The use of robotically-driven, telescoping, curved needles has the potential to reduce procedure invasiveness by tailoring trajectories to the curved shape of the ablated structure and by enabling access through natural orifices. OBJECTIVE: To investigate the feasibility of using a concentric tube robot to access the hippocampus through the foramen ovale to deliver thermal therapy and thereby provide a percutaneous treatment for epilepsy without drilling the skull. METHODS: The skull and both hippocampi were segmented from dual CT/MR image volumes for 10 patients. For each of the 20 hippocampi, a concentric tube robot was designed and optimized to traverse a trajectory from the foramen ovale to and through the hippocampus from head to tail. RESULTS: Across all 20 cases, the mean distances (error) between hippocampus medial axis and backbone of the needle were 0.55 mm, 1.11 mm, and 1.66 mm for best, mean, and worst case, respectively. CONCLUSION: These curvilinear trajectories would provide accurate transforamenal delivery of an ablation probe to typical hippocampus volumes. This strategy has the potential to both decrease the invasiveness of the procedure and increase the completeness of hippocampal ablation.


Subject(s)
Hippocampus/surgery , Laser Therapy/methods , Needles , Robotic Surgical Procedures/methods , Combined Modality Therapy , Computer Simulation , Epilepsy, Temporal Lobe/surgery , Equipment Design , Hippocampus/diagnostic imaging , Humans , Imaging, Three-Dimensional , Laser Therapy/instrumentation , Magnetic Resonance Imaging, Interventional , Robotic Surgical Procedures/instrumentation , Skull Base/diagnostic imaging , Skull Base/surgery , Tomography, X-Ray Computed
9.
J Med Device ; 11(1): 0145011-145019, 2017 Mar.
Article in English | MEDLINE | ID: mdl-28070228

ABSTRACT

This paper presents a miniature wrist that can be integrated into needle-sized surgical instruments. The wrist consists of a nitinol tube with asymmetric cutouts that is actuated by a single tendon to provide high distal curvature. We derive and experimentally validate kinematic and static models for the wrist and describe several prototype wrists, illustrating the straightforward fabrication and scalability of the design. We experimentally investigate fatigue life, the concept of tip-first bending, and practical use of the wrist with a concentric tube robot in an endonasal surgical scenario.

10.
IEEE Robot Autom Lett ; 1(1): 98-105, 2016.
Article in English | MEDLINE | ID: mdl-27648473

ABSTRACT

Shape setting Nitinol tubes and wires in a typical laboratory setting for use in superelastic robots is challenging. Obtaining samples that remain superelastic and exhibit desired precurvatures currently requires many iterations, which is time consuming and consumes a substantial amount of Nitinol. To provide a more accurate and reliable method of shape setting, in this paper we propose an electrical technique that uses Joule heating to attain the necessary shape setting temperatures. The resulting high power heating prevents unintended aging of the material and yields consistent and accurate results for the rapid creation of prototypes. We present a complete algorithm and system together with an experimental analysis of temperature regulation. We experimentally validate the approach on Nitinol tubes that are shape set into planar curves. We also demonstrate the feasibility of creating general space curves by shape setting a helical tube. The system demonstrates a mean absolute temperature error of 10°C.

11.
IEEE Trans Robot ; 32(1): 20-35, 2016 Feb.
Article in English | MEDLINE | ID: mdl-27042170

ABSTRACT

Concentric tube robots are needle-sized manipulators which have been investigated for use in minimally invasive surgeries. It was noted early in the development of these devices that elastic energy storage can lead to rapid snapping motion for designs with moderate to high tube curvatures. Substantial progress has recently been made in the concentric tube robot community in designing snap-free robots, planning stable paths, and characterizing conditions that result in snapping for specific classes of concentric tube robots. However, a general measure for how stable a given robot configuration is has yet to be proposed. In this paper, we use bifurcation and elastic stability theory to provide such a measure, as well as to produce a test for determining whether a given design is snap-free (i.e. whether snapping can occur anywhere in the unloaded robot's workspace). These results are useful in designing, planning motions for, and controlling concentric tube robots with high curvatures.

12.
IEEE Trans Robot ; 31(2): 246-258, 2015 Apr.
Article in English | MEDLINE | ID: mdl-26622208

ABSTRACT

Concentric tube robots can enable new clinical interventions if they are able to pass through soft tissue, deploy along desired paths through open cavities, or travel along winding lumens. These behaviors require the robot to deploy in such a way that the curved shape of its shaft remains unchanged as the tip progresses forward (i.e., "follow-the-leader" deployment). Follow-the-leader deployment is challenging for concentric tube robots due to elastic (and particularly torsional) coupling between the tubes that form the robot. However, as we show in this paper, follow-the-leader deployment is possible, provided that tube precurvatures and deployment sequences are appropriately selected. We begin by defining follow-the-leader deployment and providing conditions that must be satisfied for a concentric tube robot to achieve it. We then examine several useful special cases of follow-the-leader deployment, showing that both circular and helical precurvatures can be employed, and provide an experimental illustration of the helical case. We also explore approximate follow-the-leader behavior and provide a metric for the similarity of a general deployment to a follow-the-leader deployment. Finally, we consider access to the hippocampus in the brain to treat epilepsy, as a motivating clinical example for follow-the-leader deployment.

13.
IEEE Int Conf Robot Autom ; 2015: 1776-1781, 2015 May.
Article in English | MEDLINE | ID: mdl-26405562

ABSTRACT

The needle-sized surgical tools used in arthroscopy, otolaryngology, and other surgical fields could become even more valuable to surgeons if endowed with the ability to navigate around sharp corners to manipulate or visualize tissue. We present a needle-sized wrist design that grants this ability. It can be easily interfaced with manual tools or concentric tube robots and is straightforward and inexpensive to manufacture. The wrist consists of a nitinol tube with several asymmetric cutouts, actuated by a tendon. Perhaps counter-intuitively, within this seemingly simple design concept, design optimization is challenging due to the number of parameters available and nonlinearities in material properties. In this paper, we examine a subset of possible geometries and derive kinematic and static models. Experimental results with a 1.16 mm diameter prototype validate the models. Lastly, we provide a discussion summarizing the lessons learned in our early experience designing and fabricating wrists of this type.

14.
IEEE Int Conf Robot Autom ; 2015: 2361-2367, 2015 May.
Article in English | MEDLINE | ID: mdl-26413381

ABSTRACT

Concentric tube robots are thin, tentacle-like devices that can move along curved paths and can potentially enable new, less invasive surgical procedures. Safe and effective operation of this type of robot requires that the robot's shaft avoid sensitive anatomical structures (e.g., critical vessels and organs) while the surgeon teleoperates the robot's tip. However, the robot's unintuitive kinematics makes it difficult for a human user to manually ensure obstacle avoidance along the entire tentacle-like shape of the robot's shaft. We present a motion planning approach for concentric tube robot teleoperation that enables the robot to interactively maneuver its tip to points selected by a user while automatically avoiding obstacles along its shaft. We achieve automatic collision avoidance by precomputing a roadmap of collision-free robot configurations based on a description of the anatomical obstacles, which are attainable via volumetric medical imaging. We also mitigate the effects of kinematic modeling error in reaching the goal positions by adjusting motions based on robot tip position sensing. We evaluate our motion planner on a teleoperated concentric tube robot and demonstrate its obstacle avoidance and accuracy in environments with tubular obstacles.

15.
Neurosurgery ; 76(4): 479-84; discussion 484, 2015 Apr.
Article in English | MEDLINE | ID: mdl-25599203

ABSTRACT

BACKGROUND: Novel robots have recently been developed specifically for endonasal surgery. They can deliver several thin, tentacle-like surgical instruments through a single nostril. Among the many potential advantages of such a robotic system is the prospect of telesurgery over long distances. OBJECTIVE: To describe a phantom pituitary tumor removal done by a surgeon in Nashville, Tennessee, controlling a robot located approximately 800 km away in Chapel Hill, North Carolina, the first remote telesurgery experiment involving tentacle-like concentric tube manipulators. METHODS: A phantom pituitary tumor removal experiment was conducted twice, once locally and once remotely, with the robotic system. Robot commands and video were transmitted across the Internet. The latency of the system was evaluated quantitatively in both local and remote cases to determine the effect of the 800-km distance between the surgeon and robot. RESULTS: We measured a control and video latency of < 100 milliseconds in the remote case. Qualitatively, the surgeon was able to carry out the experiment easily and observed no discernable difference between the remote and local cases. CONCLUSION: Telesurgery over long distances is feasible with this robotic system. In the longer term, this may enable expert skull base surgeons to help many more patients by performing surgeries remotely over long distances.


Subject(s)
Neuroendoscopy/instrumentation , Neuroendoscopy/methods , Robotics/instrumentation , Robotics/methods , Telemedicine/instrumentation , Telemedicine/methods , Aged , Feasibility Studies , Female , Humans , Male , Nose , Phantoms, Imaging , Pituitary Neoplasms/surgery , Skull Base/surgery
16.
J Neurol Surg B Skull Base ; 76(2): 145-9, 2015 Mar.
Article in English | MEDLINE | ID: mdl-27054057

ABSTRACT

Objectives The purpose of this study is to experimentally evaluate the use of concentric tube continuum robots in endonasal skull base tumor removal. This new type of surgical robot offers many advantages over existing straight and rigid surgical tools including added dexterity, the ability to scale movements, and the ability to rotate the end effector while leaving the robot fixed in space. In this study, a concentric tube continuum robot was used to remove simulated pituitary tumors from a skull phantom. Design The robot was teleoperated by experienced skull base surgeons to remove a phantom pituitary tumor within a skull. Percentage resection was measured by weight. Resection duration was timed. Setting Academic research laboratory. Main Outcome Measures Percentage removal of tumor material and procedure duration. Results Average removal percentage of 79.8 ± 5.9% and average time to complete procedure of 12.5 ± 4.1 minutes (n = 20). Conclusions The robotic system presented here for use in endonasal skull base surgery shows promise in improving the dexterity, tool motion, and end effector capabilities currently available with straight and rigid tools while remaining an effective tool for resecting the tumor.

17.
Expert Rev Med Devices ; 11(1): 5-7, 2014 Jan.
Article in English | MEDLINE | ID: mdl-24308740

ABSTRACT

This paper discusses a new class of robots known as concentric tube robots and their application to transnasal skull base surgery. The endonasal approach has clear benefits for patients, but the surgery presents challenges that strongly motivate the use of robotic tools. In this paper, the concentric tube robot concept is described, and preliminary experimental results for transnasal skull base surgery are reviewed. Just as the da Vinci robot has revolutionized many laparoscopic surgeries, we expect concentric tube robots will enable the advancement of skull base surgery and the development of other minimally invasive procedures that require access through constrained paths.


Subject(s)
Nose/surgery , Robotics/instrumentation , Surgery, Computer-Assisted/instrumentation , Clinical Trials as Topic , Humans , Needles , Pituitary Neoplasms/surgery , Skull Base/surgery
18.
IEEE Trans Biomed Eng ; 60(4): 906-9, 2013 Apr.
Article in English | MEDLINE | ID: mdl-23204267

ABSTRACT

In the quest to design higher curvature bevel-steered needles, kinked bevel-tips have been one of the most successful approaches yet proposed. However, the price to be paid for enhancing steerability in this way has been increased tissue damage, since the prebent tip cuts a local helical path into tissue when axially rotated. This is problematic when closed-loop control is desired, because the controller will typically require the needle to rotate rapidly, and it is particularly problematic when duty cycling (i.e., continual needle spinning) is used to adjust curvature. In this paper, we propose a new flexure-based needle tip design that provides the enhanced steerability of kinked bevel-tip needles, while simultaneously minimizing tissue damage.


Subject(s)
Needles , Surgery, Computer-Assisted/instrumentation , Animals , Equipment Design , Models, Biological , Muscle, Skeletal/surgery , Phantoms, Imaging , Pliability , Robotics/instrumentation , Swine
19.
IEEE ASME Trans Mechatron ; 19(3): 996-1006, 2013 Jun 19.
Article in English | MEDLINE | ID: mdl-25089086

ABSTRACT

Mechanics-based models of concentric tube continuum robots have recently achieved a level of sophistication that makes it possible to begin to apply these robots to a variety of real-world clinical scenarios. Endonasal skull base surgery is one such application, where their small diameter and tentacle like dexterity are particularly advantageous. In this paper we provide the medical motivation for an endonasal surgical robot featuring concentric tube manipulators, and describe our model-based design and teleoperation methods, as well as a complete system incorporating image-guidance. Experimental demonstrations using a laparoscopic training task, a cadaver reachability study, and a phantom tumor resection experiment illustrate that both novice and expert users can effectively teleoperate the system, and that skull base surgeons can use the robot to achieve their objectives in a realistic surgical scenario.

20.
IEEE Trans Robot ; 29(5): 1289-1299, 2013 Oct.
Article in English | MEDLINE | ID: mdl-25400527

ABSTRACT

Steerable needles can potentially increase the accuracy of needle-based diagnosis and therapy delivery, provided they can be adequately controlled based on medical image information. We propose a novel sliding mode control law that can be used to deliver the tip of a flexible asymmetric-tipped needle to a desired point, or to track a desired trajectory within tissue. The proposed control strategy requires no a priori knowledge of model parameters, has bounded input speeds, and requires little computational resources. We show that if the standard nonholonomic model for tip-steered needles holds, then the control law will converge to desired targets in a reachable workspace, within a tolerance that can be defined by the control parameters. Experimental results validate the control law for target points and trajectory following in phantom tissue and ex vivo liver. Experiments with targets that move during insertion illustrate robustness to disturbances caused by tissue deformation.

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