Direct electromagnetic coupling to determine diagnostic bone fracture stiffness.

Background: Rapid prediction of adverse bone fracture healing outcome (e.g., nonunion and/or delayed union) is essential to advise adjunct therapies to reduce patient suffering and improving healing outcome. Radiographic diagnostic methods remain ineffective during early healing, resulting in average nonunion diagnosis times surpassing six months. To address this clinical deficit, we developed a novel diagnostic device to predict fracture healing outcome by noninvasive telemetric measurements of fracture bending stiffness. This study evaluated the hypothesis that our diagnostic antenna system is capable of accurately measuring temporal fracture healing stiffness, and advises the utility of this data for expedited prediction of healing outcomes during early (≤3 weeks) fracture recovery. Methods: Fracture repair was simulated, in reverse chronology, by progressively destabilizing cadaveric ovine metatarsals (n=8) stabilized via locking plate fixation. Bending stiffness of each fracture state were predicted using a novel direct electromagnetic coupling diagnostic system, and results were compared to values from material testing (MT) methods. While direct calculation of fracture stiffness in a simplistic cadaver model is possible, comparable analysis of the innumerable permutations of fracture and treatment type is not feasible. Thus, clinical feasibility of direct electromagnetic coupling was explored by parametric finite element (FE) analyses (n=1,632 simulations). Implant mechanics were simulated throughout the course of healing for cases with variations to fracture size, implant type, implant structure, and implant material. Results: For all fracture states, stiffness values predicted by the direct electromagnetic coupling system were not significantly different than those quantified by in vitro MT methods [P=0.587, P=0.985, P=0.975; for comparing intact, destabilized, and fully fractured (FF) states; respectively]. In comparable models, the total implant deflection reduction (from FF to intact states) was less than 10% different between direct electromagnetic coupling measurements (82.2 µm) and FE predictions (74.7 µm). For all treatment parameters, FE analyses predicted nonlinear reduction in bending induced implant midspan deflections for increasing callus stiffness. Conclusions: This technology demonstrates potential as a noninvasive clinical tool to accurately quantify healing fracture stiffness to augment and expedite healing outcome predictions made using radiographic imaging.

Vivaldi Antennas for Contactless Sensing of Implant Deflections and Stiffness for Orthopaedic Applications.

The implementation of novel coaxial dipole antennas has been shown to be a satisfactory diagnostic platform for the prediction of orthopaedic bone fracture healing outcomes. These techniques require mechanical deflection of implanted metallic hardware (i.e., rods and plates), which, when loaded, produce measurable changes in the resonant frequency of the adjacent antenna. Despite promising initial results, the coiled coaxial antenna design is limited by large antenna sizes and nonlinearity in the resonant frequency data. The purpose of this study was to develop two Vivaldi antennas (a.k.a., "standard" and "miniaturized") to address these challenges. Antenna behaviors were first computationally modeled prior to prototype fabrication. In subsequent benchtop tests, metallic plate segments were displaced from the prototype antennas via precision linear actuator while measuring resultant change in resonant frequency. Close agreement was observed between computational and benchtop results, where antennas were highly sensitive to small displacements of the metallic hardware, with sensitivity decreasing nonlinearly with increasing distance. Greater sensitivity was observed for the miniaturized design for both stainless steel and titanium implants. Additionally, these data demonstrated that by taking resonant frequency data during implant displacement and then again during antenna displacement from the same sample, via linear actuators, that "antenna calibration procedures" could be used to enable a clinically relevant quantification of fracture stiffness from the raw resonant frequency data. These improvements mitigate diagnostic challenges associated with nonlinear resonant frequency response seen in previous antenna designs.

Diagnostic prediction of ovine fracture healing outcomes via a novel multi-location direct electromagnetic coupling antenna.

BACKGROUND: Expedient prediction of adverse bone fracture healing (delayed- or non-union) is necessary to advise secondary treatments for improving healing outcome to minimize patient suffering. Radiographic imaging, the current standard diagnostic, remains largely ineffective at predicting nonunions during the early stages of fracture healing resulting in mean nonunion diagnosis times exceeding six months. Thus, there remains a clinical deficit necessitating improved diagnostic techniques. It was hypothesized that adverse fracture healing expresses impaired biological progression at the fracture site, thus resulting in reduced temporal progression of fracture site stiffness which may be quantified prior to the appearance of radiographic indicators of fracture healing (i.e., calcified tissue). METHODS: A novel multi-location direct electromagnetic coupling antenna was developed to diagnose relative changes in the stiffness of fractures treated by metallic orthopaedic hardware. The efficacy of this diagnostic was evaluated during fracture healing simulated by progressive destabilization of cadaveric ovine metatarsals treated by locking plate fixation (n=8). An ovine in vivo comparative fracture study (n=8) was then utilized to better characterize the performance of the developed diagnostic in a clinically translatable setting. In vivo measurements using the developed diagnostic were compared to weekly radiographic images and postmortem biomechanical, histological, and micro computed tomography analyses. RESULTS: For all cadaveric samples, the novel direct electromagnetic coupling antenna displayed significant differences at the fracture site (P<0.05) when measuring a fully fractured sample versus partially intact and fully intact fracture states. In subsequent in vivo fracture models, this technology detected significant differences (P<0.001) in fractures trending towards delayed healing during the first 30 days post-fracture. CONCLUSIONS: This technology, relative to traditional X-ray imaging, exhibits potential to greatly expedite clinical diagnosis of fracture nonunion, thus warranting additional technological development.

Direct electromagnetic coupling for non-invasive measurements of stability in simulated fracture healing.

Diagnostic monitoring and prediction of bone fracture healing is critical for the detection of delayed union or non-union and provides the requisite information as to whether therapeutic intervention or timely revision are warranted. A promising approach to monitor fracture healing is to measure the mechanical load-sharing between the healing callus and the implanted hardware used for internal fixation. The objectives of this study were to evaluate a non-invasive measurement system in which an antenna electromagnetically couples with the implanted hardware to sense deflections of the hardware due to an applied load and to investigate the efficacy of the system to detect changes in mechanical load-sharing in an ex vivo fracture healing model. The measurement system was applied to ovine metatarsal bones treated with osteotomies, resulting in four different levels of bone stability which simulated various degrees of fracture healing. Computational finite element simulations supplemented these ex vivo experiments to compare the osteotomy model of fracture healing to a more clinically applicable callus stiffening model of healing. In the ex vivo experiments, the electromagnetic coupling system detected significant differences between the four simulated degrees of healing with good repeatability. Computational simulations indicated that the experimental model of fracture healing provided a good surrogate for studying healing during the early time period as the callus stiffness is increasing as well as when diagnostic monitoring of the healing process is most critical. Based upon the data reported herein, the direct electromagnetic coupling method holds strong potential for clinical assessments and predictions of fracture healing. © 2019 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res.

Characterization of gain and directivity of exponential horn receivers.

It is difficult and expensive to match the sensitivity of the most sensitive vertebrate ears with off-the-shelf microphones due to the self-noise of the sensor. The extremely small apertures of microelectromechanical microphones create options to use horn waveguides to amplify sound prior to transduction without resulting in an unacceptably narrow directivity. Substantial gain can be achieved at wavelengths larger than the horn. An analytical model of an exponential horn embedded in a rigid spherical housing was formulated to describe the gain relative to a free-field receiver as a function of frequency and angle of arrival. For waves incident on-axis, the analytical model provided an accurate estimate of gain at high frequencies as validated by experimental measurement. Numerical models, using the equivalent source method, can account for higher order modes and comprehensively describe the acoustic scattering within and around the horn for waves arriving from any direction. Results show the directivity of horn receivers were adequately described by the analytical model up to a critical wavelength, and the mechanisms of deviation in gain at high frequencies and large angles of arrival were identified.

Conformal cubical 3D transformation-based metamaterial invisibility cloak: Erratum.

A correction to the definition of the constant a introduced after Eq. (4) in [J. Opt. Soc. Am. A30, 7-12 (2013)JOAOD60740-323210.1364/JOSAA.30.000007] is given.

Conformal cubical 3D transformation-based metamaterial invisibility cloak.

A conformal cubical transformation-based metamaterial invisibility cloak is presented and verified, in the near and the far field, by a rigorous full-wave numerical technique based on a higher-order, large-domain finite element method, employing large anisotropic, continuously inhomogeneous generalized hexahedral finite elements, with no need for discretization of the permittivity and permeability profiles of the cloak. The analysis requires about 30 times fewer unknowns than with commercial software. To our knowledge, this is the first conformal cubical cloak and the first full-wave computational characterization of such a structure with sharp edges. The presented methodology can also be used in development of conformal, transformation-based perfectly matched layers.