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At least 217 records · Page 12

Robot arm dynamics and control

Variations in total inertia and gravity loads at the joint outputs are treated along with the relative importance of gravity and acceleration-generated reaction torques or forces versus inertia torques or forces. The relation between the dynamical state equations in explicit terms and servoing the manipulator is briefly discussed in the framework of state variable feedback control which also forms the basis of adaptive manipulator control. Exact state equations were determined for total inertia and gravity loads at the joint outputs as a function of joint variables, using the constant inertial and geometric parameters of the individual links defined in the respective link coordinate frames. The range of maximum variations in total inertia and gravity loads at the joint outputs was calculated for both no load and load in the hand. The main result is the construction of a set of greatly simplified state equations which describe the total inertia and gravity load variations at the output of the six joints with an average error of less than 5%.

Bejczy, A. K.↗

Pictorial communication in virtual and real environments

Papers about the communication between human users and machines in real and synthetic environments are presented. Individual topics addressed include: pictorial communication, distortions in memory for visual displays, cartography and map displays, efficiency of graphical perception, volumetric visualization of 3D data, spatial displays to increase pilot situational awareness, teleoperation of land vehicles, computer graphics system for visualizing spacecraft in orbit, visual display aid for orbital maneuvering, multiaxis control in telemanipulation and vehicle guidance, visual enhancements in pick-and-place tasks, target axis effects under transformed visual-motor mappings, adapting to variable prismatic displacement. Also discussed are: spatial vision within egocentric and exocentric frames of reference, sensory conflict in motion sickness, interactions of form and orientation, perception of geometrical structure from congruence, prediction of three-dimensionality across continuous surfaces, effects of viewpoint in the virtual space of pictures, visual slant underestimation, spatial constraints of stereopsis in video displays, stereoscopic stance perception, paradoxical monocular stereopsis and perspective vergence. (No individual items are abstracted in this volume)

Ellis, Stephen R.↗

Nano-ADEPT Aeroloads Wind Tunnel Test

A wind tunnel test of the Adaptable Deployable Entry and Placement Technology (ADEPT) was conducted in April 2015 at the US Army's 7 by10 Foot Wind Tunnel located at NASA Ames Research Center. Key geometric features of the fabric test article were a 0.7 meter deployed base diameter, a 70 degree half-angle forebody cone angle, eight ribs, and a nose-to-base radius ratio of 0.7. The primary objective of this wind tunnel test was to obtain static deflected shape and pressure distributions while varying pretension at dynamic pressures and angles of attack relevant to entry conditions at Earth, Mars, and Venus. Other objectives included obtaining aerodynamic force and moment data and determining the presence and magnitude of any dynamic aeroelastic behavior (buzz/flutter) in the fabric trailing edge. All instrumentation systems worked as planned and a rich data set was obtained. This paper describes the test articles, instrumentation systems, data products, and test results. Four notable conclusions are drawn. First, test data support adopting a pre-tension lower bound of 10 foot pounds per inch for Nano-ADEPT mission applications in order to minimize the impact of static deflection. Second, test results indicate that the fabric conditioning process needs to be reevaluated. Third, no flutter/buzz of the fabric was observed for any test condition and should also not occur at hypersonic speeds. Fourth, translating one of the gores caused ADEPT to generate lift without the need for a center of gravity offset. At hypersonic speeds, the lift generated by actuating ADEPT gores could be used for vehicle control.

system engineering↗

Adaptive Aerostructures for Revolutionary Civil Supersonic Transportation

To enable commercially viable civil supersonic transport (SST) aircraft, innovative solutions must be developed to meet noise and efficiency requirements for overland flight. This research effort consists of a multidisciplinary team of academic and industrial experts exploring for the first time the potential of small real-time geometric outer mold line (OML) reconfigurations to minimize sonic boom signatures and aircraft drag in response to changing ambient conditions, thereby enabling noise-compliant overland supersonic flight. The team utilizes recent advances in supersonic computational fluid dynamic (CFD) methods, new noise prediction tools, and new design approaches to consider embedded highly energy-dense shape memory alloy (SMA) actuators for local shape modifications to an SST aircraft leading to optimal low boom signature and low drag in different environments. This university-led program will provide strategic leadership toward technology convergence that advances NASA's Aerospace Research Mission Directorate's (ARMD) research objectives with regard to Thrust 2: “Innovation in Commercial Supersonic Aircraft” by exploring for the first time enabling low-boom operation across a range of flight conditions via structural adaptivity, and will promote education of the next generation of engineers. The overall research strategy is to pursue three critical areas: the design of configurations for reducing boom, SMA material development and modeling, and technology feasibility demonstration in a relevant environment. Initially, the team will identify potential applications where structure or geometry adaptivity provides a benefit in noise or drag across the entire flight envelope. For selected applications/structural locations, required OML geometry changes will be determined based on analysis of sonic boom ground signature and drag reduction using new design tools, trade studies, and atmospheric sensing techniques. Designs will be developed and evaluated against requirements on loading, stroke length, and operational temperature. New alloy formulations will be developed tailored for both autonomous and controlled actuation modes. As the SMA material development matures, integrated system-level factors will be investigated. Optimized designs for small-scale distributed adaptivity applications of maximum benefit will then be matured and tested, moving toward demonstration of the innovative technology approaches at a TRL 4-5 and showing that sonic booms can be reduced by reconfiguration on demand.

Koushik Datta↗

WE-B-BRD-00: MRI for Radiation Oncology

The use of MRI in radiation therapy is rapidly increasing. Applications vary from the MRI simulator, to the MRI fused with CT, and to the integrated MRI+RT system. Compared with the standard MRI QA, a broader scope of QA features has to be defined in order to maximize the benefits of using MRI in radiation therapy. These QA features include geometric fidelity, image registration, motion management, cross-system alignment, and hardware interference. Advanced MRI techniques require a specific type of QA, as they are being widely used in radiation therapy planning, dose calculations, post-implant dosimetry, and prognoses. A vigorous and adaptive QA program is crucial to defining the responsibility of the entire radiation therapy group and detecting deviations from the performance of high-quality treatment. As a drastic departure from CT simulation, MRI simulation requires changes in the work flow of treatment planning and image guidance. MRI guided radiotherapy platforms are being developed and commercialized to take the advantage of the advance in knowledge, technology and clinical experience. This symposium will from an educational perspective discuss the scope and specific issues related to MRI guided radiotherapy. Learning Objectives: Understand the difference between a standard and a radiotherapy-specific MRI QA program. Understand the effects of MRI artifacts (geometric distortion and motion) on radiotherapy. Understand advanced MRI techniques (ultrashort echo, fast MRI including dynamic MRI and 4DMRI, diffusion, perfusion, and MRS) and related QA. Understand the methods to prepare MRI for treatment planning (electron density assignment, multimodality image registration, segmentation and motion management). Current status of MRI guided treatment platforms. Dr. Jihong Wang has a research grant with Elekta-MRL project. Dr. Ke Sheng receives research grants from Varian Medical systems.

60 APPLIED LIFE SCIENCES↗

WE-B-BRD-01: MR-LINAC

The use of MRI in radiation therapy is rapidly increasing. Applications vary from the MRI simulator, to the MRI fused with CT, and to the integrated MRI+RT system. Compared with the standard MRI QA, a broader scope of QA features has to be defined in order to maximize the benefits of using MRI in radiation therapy. These QA features include geometric fidelity, image registration, motion management, cross-system alignment, and hardware interference. Advanced MRI techniques require a specific type of QA, as they are being widely used in radiation therapy planning, dose calculations, post-implant dosimetry, and prognoses. A vigorous and adaptive QA program is crucial to defining the responsibility of the entire radiation therapy group and detecting deviations from the performance of high-quality treatment. As a drastic departure from CT simulation, MRI simulation requires changes in the work flow of treatment planning and image guidance. MRI guided radiotherapy platforms are being developed and commercialized to take the advantage of the advance in knowledge, technology and clinical experience. This symposium will from an educational perspective discuss the scope and specific issues related to MRI guided radiotherapy. Learning Objectives: Understand the difference between a standard and a radiotherapy-specific MRI QA program. Understand the effects of MRI artifacts (geometric distortion and motion) on radiotherapy. Understand advanced MRI techniques (ultrashort echo, fast MRI including dynamic MRI and 4DMRI, diffusion, perfusion, and MRS) and related QA. Understand the methods to prepare MRI for treatment planning (electron density assignment, multimodality image registration, segmentation and motion management). Current status of MRI guided treatment platforms. Dr. Jihong Wang has a research grant with Elekta-MRL project. Dr. Ke Sheng receives research grants from Varian Medical systems.

60 APPLIED LIFE SCIENCES↗

WE-B-BRD-02: MR Simulation for Radiation Therapy

The use of MRI in radiation therapy is rapidly increasing. Applications vary from the MRI simulator, to the MRI fused with CT, and to the integrated MRI+RT system. Compared with the standard MRI QA, a broader scope of QA features has to be defined in order to maximize the benefits of using MRI in radiation therapy. These QA features include geometric fidelity, image registration, motion management, cross-system alignment, and hardware interference. Advanced MRI techniques require a specific type of QA, as they are being widely used in radiation therapy planning, dose calculations, post-implant dosimetry, and prognoses. A vigorous and adaptive QA program is crucial to defining the responsibility of the entire radiation therapy group and detecting deviations from the performance of high-quality treatment. As a drastic departure from CT simulation, MRI simulation requires changes in the work flow of treatment planning and image guidance. MRI guided radiotherapy platforms are being developed and commercialized to take the advantage of the advance in knowledge, technology and clinical experience. This symposium will from an educational perspective discuss the scope and specific issues related to MRI guided radiotherapy. Learning Objectives: Understand the difference between a standard and a radiotherapy-specific MRI QA program. Understand the effects of MRI artifacts (geometric distortion and motion) on radiotherapy. Understand advanced MRI techniques (ultrashort echo, fast MRI including dynamic MRI and 4DMRI, diffusion, perfusion, and MRS) and related QA. Understand the methods to prepare MRI for treatment planning (electron density assignment, multimodality image registration, segmentation and motion management). Current status of MRI guided treatment platforms. Dr. Jihong Wang has a research grant with Elekta-MRL project. Dr. Ke Sheng receives research grants from Varian Medical systems.

60 APPLIED LIFE SCIENCES↗

WE-B-BRD-03: MR QA/QC for MRgRT

The use of MRI in radiation therapy is rapidly increasing. Applications vary from the MRI simulator, to the MRI fused with CT, and to the integrated MRI+RT system. Compared with the standard MRI QA, a broader scope of QA features has to be defined in order to maximize the benefits of using MRI in radiation therapy. These QA features include geometric fidelity, image registration, motion management, cross-system alignment, and hardware interference. Advanced MRI techniques require a specific type of QA, as they are being widely used in radiation therapy planning, dose calculations, post-implant dosimetry, and prognoses. A vigorous and adaptive QA program is crucial to defining the responsibility of the entire radiation therapy group and detecting deviations from the performance of high-quality treatment. As a drastic departure from CT simulation, MRI simulation requires changes in the work flow of treatment planning and image guidance. MRI guided radiotherapy platforms are being developed and commercialized to take the advantage of the advance in knowledge, technology and clinical experience. This symposium will from an educational perspective discuss the scope and specific issues related to MRI guided radiotherapy. Learning Objectives: Understand the difference between a standard and a radiotherapy-specific MRI QA program. Understand the effects of MRI artifacts (geometric distortion and motion) on radiotherapy. Understand advanced MRI techniques (ultrashort echo, fast MRI including dynamic MRI and 4DMRI, diffusion, perfusion, and MRS) and related QA. Understand the methods to prepare MRI for treatment planning (electron density assignment, multimodality image registration, segmentation and motion management). Current status of MRI guided treatment platforms. Dr. Jihong Wang has a research grant with Elekta-MRL project. Dr. Ke Sheng receives research grants from Varian Medical systems.

60 APPLIED LIFE SCIENCES↗

NanoPSD: A software for automatic detection of Nano-Particle Shape Distribution in electron microscopy images

Accurate quantification of the size and morphology of nanoparticles from electron microscopy (EM) images is essential to understand growth mechanisms, surface reactivity, and functional behavior in nanoscale materials. Manual analysis remains slow, subjective, and difficult to reproduce in large datasets. We introduce NanoPSD (Nano-Particle Shape Distribution), an open-source and fully automated framework for quantitative particle detection and morphology analysis from EM images. NanoPSD integrates adaptive contrast enhancement, polarity-agnostic scale-bar detection, Optical Character Recognition (OCR)-based calibration, and classical segmentation via Otsu thresholding with morphological refinement. Particle contours are used to extract geometric descriptors, including equivalent circular diameter, aspect ratio, circularity, and solidity, enabling automated classification into spherical, rod-like, and aggregate morphologies. The framework supports both single-image and batch processing, generating publication-quality visualizations, LaTeX-ready tables, and structured comma-separated values (CSV) datasets. As a demonstration, we applied NanoPSD to plasma-synthesized nanoparticle samples diagnosed via transmission electron microscopy (TEM). The code produced statistically robust size and morphology distributions spanning a few to tens of nanometers with minimal user supervision. The pipeline demonstrates high reproducibility and scalability, processing large image collections with consistent calibration and output formatting. Its modular design enables seamless integration of future deep-learning-based segmentation models, providing a pathway toward intelligent, data-driven electron microscopy analysis.

36 MATERIALS SCIENCE↗

One-photon mass-analyzed threshold ionization (MATI) spectroscopy of pyridine: Determination of accurate ionization energy and cationic structure

Ionization energies and cationic structures of pyridine were intensively investigated utilizing one-photon mass-analyzed threshold ionization (MATI) spectroscopy with vacuum ultraviolet radiation generated by four-wave difference frequency mixing in Kr. The present one-photon high-resolution MATI spectrum of pyridine demonstrated a much finer and richer vibrational structure than that of the previously reported two-photon MATI spectrum. From the MATI spectrum and photoionization efficiency curve, the accurate ionization energy of the ionic ground state of pyridine was confidently determined to be 73 570 ± 6 cm{sup −1} (9.1215 ± 0.0007 eV). The observed spectrum was almost completely assigned by utilizing Franck-Condon factors and vibrational frequencies calculated through adjustments of the geometrical parameters of cationic pyridine at the B3LYP/cc-pVTZ level. A unique feature unveiled through rigorous analysis was the prominent progression of the 10 vibrational mode, which corresponds to in-plane ring bending, and the combination of other totally symmetric fundamentals with the ring bending overtones, which contribute to the geometrical change upon ionization. Notably, the remaining peaks originate from the upper electronic state ({sup 2}A{sub 2}), as predicted by high-resolution photoelectron spectroscopy studies and symmetry-adapted cluster configuration interaction calculations. Based on the quantitatively good agreement between the experimental and calculated results, it was concluded that upon ionization the pyridine cation in the ground electronic state should have a planar structure of C{sub 2v} symmetry through the C-N axis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Passive mapping and intermittent exploration for mobile robots

An adaptive state space architecture is combined with diktiometric representation to provide the framework for designing a robot mapping system with flexible navigation planning tasks. This involves indexing waypoints described as expectations, geometric indexing, and perceptual indexing. Matching and updating the robot's projected position and sensory inputs with indexing waypoints involves matchers, dynamic priorities, transients, and waypoint restructuring. The robot's map learning can be opganized around the principles of passive mapping.

Engleson, Sean P.↗

Surface stress tensor and junction conditions on a rotating null horizon

The general form of the surface stress tensor of an infinitesimally thin shell located on a rotating null horizon is derived, when different interior and exterior geometries are joined there. Even though the induced metric on the surface must be the same approached from either side, the first derivatives of the metric need not be. Such discontinuities lead to a Dirac δ-distribution in the Einstein tensor localized on the horizon. For a general stationary axisymmetric geometry the surface stress tensor can be expressed in terms of two geometric invariants that characterize the surface, namely the discontinuities [κ] and [J] of the surface gravity κ and angular momentum density J. The Komar energy and angular momentum are given in coordinates adapted to the Killing symmetries, and the surface contributions to each determined in terms of [κ] and [J] . Guided by these, a simple modification of the original Israel junction conditions is verified directly from the Einstein tensor density to give the correct finite result for the surface stress, when the normal n to the surface is allowed to tend continuously to a null vector. The relation to Israel’s original junction conditions, which fail on null surfaces, is given. The modified junction conditions are suitable to the matching of a rotating “black hole” exterior to any interior geometry joined at the Kerr null horizon surface, even when the surface normal is itself discontinuous and the Barrabès-Israel formalism is also inapplicable. This joining on a rotating null horizon is purely of the matter shell type and does not contain a propagating gravitational shock wave.

79 ASTRONOMY AND ASTROPHYSICS↗

A conceptual study of the potential for automotive-derived and free-piston Stirling engines in 30- to 400-kilowatt stationary power applications

The technical feasibility of applying automotive-derived kinematic and free-piston Stirling engine concepts for stationary applications was explored. Automotive-derived engines offer cost advantages by providing a mature and developd engine technology base with downrating and parts commonality options for specific applications. Two engine sizes (30 and 400 kW), two Stirling engine configurations (kinematic and free-piston), and two output systems (crankshaft and hydraulic pump) were studied. The study includes the influences of using either hydrogen or helium as the working gas. The first kinematic configuration selects an existing Stirling engine design from an automotive application and adapts it to stationary requirements. A 50,000-hour life requirement was established by downrating the engine to 40 kW and reducing auxiliary loads. Efficiency improvements were gained by selective material and geometric variations and peak brake efficiency of 36.8 percent using helium gas was achieved. The second design was a four-cylinder, 400 kW engine, utilizing a new output drive system known as the z-crank, which provides lower friction losses and variable stroke power control. Three different material and working gas combinations were considered. Brake efficiency levels varied from 40.5 percent to 45.6 percent. A 37.5 kW single-cycle, free-piston hydraulic output design was generated by scaling one cylinder of the original automotive engine and mating it to a counterbalanced reciprocal hydraulic pump. Metallic diaphragms were utilized to transmit power.

Vatsky, A.↗

A failure mechanism in adaptive arrays

The steady-state behavior of an adaptive array is considered and the degradation of its output SNR in the presence of jammers is analyzed. It is shown that for given incident powers (of jammers and signal), there are geometric configurations of the sources exciting the array for which the SNR degradation is much more pronounced than for other configurations. This result is proved for the case where the thermal noise power of each array receiver is negligible compared to the total power intercepted by the array from each jammer. The result is general, being valid for an array of n arbitrary antennae in an arbitrary three-dimensional configuration. It is stated in terms of linear dependence relationships among the n-dimensional vectors that describe the effects of the sources on the array.

Zohar, S.↗

Crack Growth Simulation and Residual Strength Prediction in Airplane Fuselages

This is the final report for the NASA funded project entitled "Crack Growth Prediction Methodology for Multi-Site Damage." The primary objective of the project was to create a capability to simulate curvilinear fatigue crack growth and ductile tearing in aircraft fuselages subjected to widespread fatigue damage. The second objective was to validate the capability by way of comparisons to experimental results. Both objectives have been achieved and the results are detailed herein. In the first part of the report, the crack tip opening angle (CTOA) fracture criterion, obtained and correlated from coupon tests to predict fracture behavior and residual strength of built-up aircraft fuselages, is discussed. Geometrically nonlinear, elastic-plastic, thin shell finite element analyses are used to simulate stable crack growth and to predict residual strength. Both measured and predicted results of laboratory flat panel tests and full-scale fuselage panel tests show substantial reduction of residual strength due to the occurrence of multi-site damage (MSD). Detailed comparisons of n stable crack growth history, and residual strength between the predicted and experimental results are used to assess the validity of the analysis methodology. In the second part of the report, issues related to crack trajectory prediction in thin shells; an evolving methodology uses the crack turning phenomenon to improve the structural integrity of aircraft structures are discussed, A directional criterion is developed based on the maximum tangential stress theory, but taking into account the effect of T-stress and fracture toughness orthotropy. Possible extensions of the current crack growth directional criterion to handle geometrically and materially nonlinear problems are discussed. The path independent contour integral method for T-stress evaluation is derived and its accuracy is assessed using a p- and hp-version adaptive finite element method. Curvilinear crack growth is simulated in coupon tests and in full-scale fuselage panel tests. Both T-stress and fracture toughness orthotropy are found to be essential to predict the observed crack paths. The analysis methodology and software program (FRANC3D/STAGS) developed herein allows engineers to maintain aging aircraft economically while insuring continuous airworthiness. Consequently, it will improve the technology to support the safe operation of the current aircraft fleet as well as the design of more damage-tolerant aircraft for the next generation fleet.

Chen, Chuin-Shan↗

SU-F-J-89: Assessment of Delivered Dose in Understanding HCC Tumor Progression Following SBRT

Purpose: It is well documented that the delivered dose to patients undergoing radiotherapy (RT) is often different from the planned dose due to geometric variability and uncertainties in patient positioning. Recent work suggests that accumulated dose to the GTV is a better predictor of progression compared to the minimum planned dose to the PTV. The purpose of this study is to evaluate if deviations from the planned dose can contributed to tumor progression. Methods: From 2010 to 2014 an in-house Phase II clinical trial of adaptive stereotactic body RT was completed. Of the 90 patients enrolled, 7 patients had a local recurrence defined on contrast enhanced CT or MR imaging 3–21 months after completion of RT. Retrospective dose accumulation was performed using a biomechanical model-based deformable image registration algorithm (DIR) to accumulate the dose based on the kV CBCT acquired prior to each fraction for soft tissue alignment of the patient. The DIR algorithm was previously validated for geometric accuracy in the liver (target registration error = 2.0 mm) and dose accumulation in a homogeneous image, similar to a liver CBCT (gamma index = 91%). Following dose accumulation, the minimum dose to 0.5 cc of the GTV was compared between the planned and accumulated dose. Work is ongoing to evaluate the tumor control probability based on the planned and accumulated dose. Results: DIR and dose accumulation was performed on all fractions for 6 patients with local recurrence. The difference in minimum dose to 0.5 cc of the GTV ranged from −0.3–2.3 Gy over 3–5 fractions. One patient had a potentially significant difference in minimum dose of 2.3 Gy. Conclusion: Dose accumulation can reveal tumor underdosage, improving our ability to understand recurrence and tumor progression patterns, and could aid in adaptive re-planning during therapy to correct for this. This work was supported in part by NIH P01CA059827.

60 APPLIED LIFE SCIENCES↗

Analyzing the Effects of Geometric Lane Constraints on Radar-Based Sensing of Available Vehicle Headway Using Mapped Lane Geometry and Camera Registration of Lane Position

Commercial trucks are currently equipped with a single front-facing RADAR mounted on the front bumper, as this is a sensor useful for Cooperative Adaptive Cruise Control, Emergency Braking Systems, and many similar Connected and Automated vehicle functions that require longitudinal vehicle control. This paper investigates the use of a bumper-mounted RADAR to perform traffic characterization around the ego-vehicle to obtain an estimate of the furthest headway that can be considered as a reliable estimate of open maneuvering space, such that there are no vehicles within the same lane as the ego-vehicle. This available headway in front of a vehicle is an important parameter in an ongoing study whose goal is to obtain improvements in fuel economy for highway driving of a tractor-trailer. But headway availability depends on the correct attribution of RADAR measured vehicles to be either within the ego-lane, or outside the lane. The attribution of lane designations to specific RADAR targets depend strongly on lane geometry and the ability to align RADAR measurements to the ego-lane. This work investigates how knowledge of lane geometries, as well as sensor performance characteristics, may improve the trust in a RADAR measurement of open headway distance in front of a vehicle. Specifically, several strategies for associating local traffic either within or excluded from the ego lane are considered, and the possible sources of error in headway calculations are investigated for each strategy. The strategies differ by the availability of lane geometry information and RADAR target association to lane constraints, which in turn is assumed to be supplied by the use of map data and secondary camera measurements. It is observed that combining RADAR with lane-geometry maps help detect headway up to and beyond RADAR range limit with exceptions tied to a particular road. These errors can further be minimized by using camera measurements, and this reduction in error is analyzed assuming errors associated with registering images to lane markers. Here, the results, based on actual highway routes measured with our test vehicle, reveal: that RADAR data without lane geometry strongly limits the trusted headway measurement from this sensor; that lane geometry maps can greatly increase the trusted range, usually beyond the RADAR’s range limits; and that image-based registration of lane markers to lane geometry should have accuracies allowing full-range trust in the RADAR target measurements of headway.

33 ADVANCED PROPULSION SYSTEMS↗

Preventing stent failure using adaptive shear responsive endovascular implant

A stent apparatus, system, and method that senses wall shear stress by measuring fluid flow at localized areas within the stent, that processes measured information through an integrated circuit, and selectively sends power to mechanically controllable stent surfaces which results in localized geometric changes. In various embodiments the stent apparatus, system, and method sends data to outside the body in real time.

Mukerjee, Erik V.↗