Doris Hettlich and Family to Mister Meredith (14 October 1962)

https://egrove.olemiss.edu/mercorr_pro/2166/thumbnail.jp

The domain derivate in inverse obstacle scattering with nonlinear impedance boundary condition

In this paper an inverse obstacle scattering problem for the Helmholtz equation with nonlinear impedance boundary condition is considered. For a certain class of nonlinearities, well-posedness of the direct scattering problem is proven. Furthermore, differentiability of solutions with respect to the boundary is shown by the variational method. A characterization of the derivative allows for iterative regularization schemes in solving the inverse problem, which consists in reconstructing the scattering obstacle from the far field pattern of a scattered wave. An all-at-once Newton-type regularization method is developed to illustrate the use of the domain derivative by some numerical examples

The domain derivative in inverse obstacle scattering with nonlinear impedance boundary condition

In this paper an inverse obstacle scattering problem for the Helmholtz equation with nonlinear impedance boundary condition is considered. For a certain class of nonlinearities, well-posedness of the direct scattering problem is proven. Furthermore, differentiability of solutions with respect to the boundary is shown by the variational method. A characterization of the derivative allows for iterative regularization schemes in solving the inverse problem, which consists in reconstructing the scattering obstacle from the far field pattern of a scattered wave. An all-at-once Newton-type regularization method is developed to illustrate the use of the domain derivative by some numerical examples

Application of the second domain derivative in inverse electromagnetic scattering

We consider the inverse scattering problem of reconstructing a perfect conductor from the far field pattern of a scattered time harmonic electromagnetic wave generated by one incident plane wave. In view of iterative regularization schemes for the severely ill-posed problem the first and the second domain derivative of the far field pattern with respect to variations of the domain are established. Charaterizations of the derivatives by boundary value problems allow for an application of second degree regularization methods to the inverse problem. A numerical implementation based on integral equations is presented and its performance is illustrated by a selection of examples

On potential-based shape derivatives of the electromagnetic transmission problem

Domain derivatives are an important tool to characterize and compute shape derivatives. If some quantity of interest depends on the shape of an object such as the obstacle in a scattering problem, shape derivatives are used to describe the effect of variations of the shape on that quantity. We here consider the scattering of time-harmonic electromagnetic waves by a penetrable obstacle. As an alternative to the formulation using the Maxwell system, the problem may be posed as a coupled system of Helmholtz equations with complicated transmission conditions. We prove equivalence of the two formulations and then proceed to characterize the domain derivatives of the scattered fields in the potential formulation. Our main result is the equivalence of the characterizations of such derivatives in the Maxwell and in the potential based problem formulation

The Domain Derivative of Time-Harmonic Electromagnetic Waves at Interfaces

We consider the scattering of time harmonic electromagnetic waves by a penetrable obstacle. In view of shape optimization or inverse reconstruction problems the domain derivative of the scattering problem is investigated. Existence of the derivative in the sense of a Fr´echet derivative and a characterization by a transmission boundary value problem are shown

Accuracy of Conventional Radiography and Computed Tomography in Predicting Implant Position in Relation to the Vertebral Canal in Dogs

Vertebral column stabilization is performed for dogs suffering from instability secondary to trauma, neoplasia, caudal cervical spondylomyelopathy, infection and other. A common stabilizing technique involves bicortical placement of positive profile end-threaded Steinman pins into the vertebral body and pedicles. Bicortical placement of these pins carries a high risk for iatrogenic trauma of important neurovascular structures. A clinical frustration has been the difficulty determining exact implant position based on postoperative conventional spinal survey radiographs. Implant position within the vertebral column may be better determined using a different imaging modality such as computed tomography as this would allow for evaluation of tissues in different anatomic planes. The goal of this study was to compare the accuracy of radiography and computed tomography in predicting implant position in relation to the vertebral canal in the cervical and thoracolumbar vertebral column in an in vitro imaging and anatomic study. Twelve medium-sized canine cadaver vertebral columns were utilized for this study. Steinman pins were placed into cervical and thoracolumbar vertebrae based on established landmarks but without predetermination of vertebral canal violation. Radiographs and CT exams were obtained and evaluated by 6 individuals. A random subset of pins was evaluated for ability to distinguish left from right pins on radiographs. The ability of the examiner to correctly identify vertebral canal penetration for all pins was assessed both on radiographs and CT. Spines were then anatomically prepared and visual examination of pin penetration into the canal served as the gold standard. Results revealed a left/right accuracy of 93.1%. Overall sensitivity of radiographs and CT to detect vertebral canal penetration by an implant were significantly different and estimated as 50.7% and 93.4%, respectively (P < 0.0001). Sensitivity was significantly higher for complete vs. partial penetration and for radiologists vs. non-radiologists for both imaging modalities. Overall specificity of radiographs and CT to detect vertebral canal penetration was 82.9% and 86.4%, respectively (P = 0.049). In conclusion, CT was superior to radiographic assessment and is the recommended imaging modality to assess penetration into the vertebral canal. The clinical relevance of this finding is that CT is significantly more accurate in identifying vertebral canal violation by Steinman pins and should be performed postoperatively to assess implant position

The definition and measurement of electromagnetic chirality

The notion of Electromagnetic Chirality, recently introduced in the Physics literature, is investigated in the framework of scattering of time-harmonic electromagnetic waves by bounded scatterers. This type of chirality is defined as a property of the far field operator. The relation of this novel notion of chirality to that of geometric chirality of the scatterer is explored. It is shown for several examples of scattering problems that electromagnetic achirality is a more general property than geometric chirality. On the other hand, a chiral material law, as for example given by the Drude-Born-Fedorov model, yields an electromagnetically chiral scatterer. Electromagnetic chirality also allows the definition of a measure. Scatteres invisible to fields of one helicity turn out to be maximally chiral with respect to this measure. For a certain class of electromagnetically chiral scatters, we provide numerical calculations of the measure of chirality through solutions of scattering problems computed by a boundary element method

Accuracy of end-on fluoroscopy in predicting implant position in relation to the vertebral canal in dogs.

Objective To evaluate the accuracy of end-on fluoroscopy in predicting implant position in relation to the vertebral canal in the canine thoracolumbar vertebral column. Study design In vitro imaging and anatomic study. Animals Canine cadaveric thoracolumbar vertebral columns (n = 5). Methods Smooth Steinmann pins were inserted bicortically into the thoracolumbar vertebral columns between T10 and L7 using recommended insertion angles. Penetration of the spinal canal was not strictly avoided. After pin placement, end-on fluoroscopy images were obtained of each pin. Pin position was subsequently assessed by four evaluators and determined to either being out of the vertebral canal or in, with the latter being additionally divided into partially or completely penetrating the canal. To assess potential differences in modalities, fluoroscopy images were gray-scale inverted and evaluated again later by the same four individuals. Correct identification of pin position in relationship to the vertebral canal was assessed for both fluoroscopy images. Anatomic preparation of the spines was used for verification of pin position in relation to the spinal canal. Some data from this study were compared with historical data on accuracy using orthogonal radiography and computed tomography (CT). Results Overall sensitivity and specificity of F to detect vertebral canal penetration was 98.8 % (95% confidence interval (CI), 96.0-99.6) and 98.0% (95% CI, 77.0-99.9), respectively. For Fi, sensitivity and specificity were 97.0% (95% CI, 91.5-99.0) and 98.5% (95% CI, 81.5-99.9) respectively. F exceeded Fi for the sensitivity of detecting pin penetration into the vertebral canal (p = 0.039) but specificities were not different (p = 0.585). When comparing to historical data, the overall accuracy of end-on fluoroscopy (F) and inverted fluoroscopy (Fi) was statistical better than conventional radiographic assessment (p < 0.001). Conclusion End-on fluoroscopy is a highly accurate method for the assessment of pin position in relationship to the thoracolumbar spinal canal in cadaveric dogs. Clinical significance End-on fluoroscopy, with or without inversion, is accurate in identifying vertebral canal violation by bicortically placed Steinmann pins. When CT is not available, end-on fluoroscopy might be a valuable imaging modality to determine pin position in the canine vertebral column