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The inverse scattering problem for a conductive boundary condition and transmission eigenvalues
(2018)
In this paper, we consider the inverse scattering problem associated with an inhomogeneous media with a conductive boundary. In particular, we are interested in two problems that arise from this inverse problem: the inverse conductivity problem and the corresponding interior transmission eigenvalue problem. The inverse conductivity problem is to recover the conductive boundary parameter from the measured scattering data. We prove that the measured scatted data uniquely determine the conductivity parameter as well as describe a direct algorithm to recover the conductivity. The interior transmission eigenvalue problem is an eigenvalue problem associated with the inverse scattering of such materials. We investigate the convergence of the eigenvalues as the conductivity parameter tends to zero as well as prove existence and discreteness for the case of an absorbing media. Lastly, several numerical and analytical results support the theory and we show that the inside–outside duality method can be used to reconstruct the interior conductive eigenvalues.
Background
For supratentorial craniotomy, surgical access, and closure technique, including placement of subgaleal drains, may vary considerably. The influence of surgical nuances on postoperative complications such as cerebrospinal fluid leakage or impaired wound healing overall remains largely unclear. With this study, we are reporting our experiences and the impact of our clinical routines on outcome in a prospectively collected data set.
Method
We prospectively observed 150 consecutive patients undergoing supratentorial craniotomy and recorded technical variables (type/length of incision, size of craniotomy, technique of dural and skin closure, type of dressing, and placement of subgaleal drains). Outcome variables (subgaleal hematoma/CSF collection, periorbital edema, impairment of wound healing, infection, and need for operative revision) were recorded at time of discharge and at late follow-up.
Results
Early subgaleal fluid collection was observed in 36.7% (2.8% at the late follow-up), and impaired wound healing was recorded in 3.3% of all cases, with an overall need for operative revision of 6.7%. Neither usage of dural sealants, lack of watertight dural closure, and presence of subgaleal drains, nor type of skin closure or dressing influenced outcome. Curved incisions, larger craniotomy, and tumor size, however, were associated with an increase in early CSF or hematoma collection (p < 0.0001, p = 0.001, p < 0.01 resp.), and larger craniotomy size was associated with longer persistence of subgaleal fluid collections (p < 0.05).
Conclusions
Based on our setting, individual surgical nuances such as the type of dural closure and the use of subgaleal drains resulted in a comparable complication rate and outcome. Subgaleal fluid collections were frequently observed after supratentorial procedures, irrespective of the closing technique employed, and resolve spontaneously in the majority of cases without significant sequelae. Our results are limited due to the observational nature in our single-center study and need to be validated by supportive prospective randomized design.
Bonding of polymer-based microfluidics to polymer substrates still poses a challenge for Lab-On-a-Chip applications. Especially, when sensing elements are incorporated, patterned deposition of adhesives with curing at ambient conditions is required. Here, we demonstrate a fabrication method for fully printed microfluidic systems with sensing elements using inkjet and stereolithographic 3D-printing.
Plate osteosynthesis of displaced proximal phalangeal neck fractures of the hand allows early mobilization due to a stable internal fixation. Nevertheless, joint stiffness—because of soft tissue irritation—represents a common complication leading to high complication rates. Del Pinal et al. recently reported promising clinical results for a new, minimally invasive fixation technique with a cannulated headless intramedullary compression screw. Hence, the aim of this study was to compare plate fixation of proximal phalangeal neck fractures to less two less invasive techniques: Crossed k-wire fixation and intramedullary screw fixation. We hypothesized that these fixation techniques provide inferior stability when compared to plate osteosynthesis.
Surgical reconstruction of the interosseous membrane (IOM) could restore longitudinal forearm stability to avoid persisting disability due to capituloradial and ulnocarpal impingement in Essex Lopresti lesions. This biomechanical study aimed to assess longitudinal forearm stability of intact specimens, after sectioning of the IOM and after reconstruction with a TightRope construct using either a single or double bundle technique.
Treatment of posttraumatic osteoarthritis of the radial column of the elbow joint remains a challenging yet common issue.
While partial joint replacement leads to high revision rates, radial head excision has shown to severely increase joint instability. Shortening osteotomy of the radius could be an option to decrease the contact pressure of the radiohumeral joint and thereby pain levels without causing valgus instability. Hence, the aim of this biomechanical study was to evaluate the effects of radial shortening on axial load distribution and valgus stability of the elbow joint.
Many applications in computational science and engineering require the computation of eigenvalues and vectors of dense symmetric or Hermitian matrices. For example, in DFT (density functional theory) calculations on modern supercomputers 10% to 30% of the eigenvalues and eigenvectors of huge dense matrices have to be calculated. Therefore, performance and parallel scaling of the used eigensolvers is of upmost interest. In this article different routines of the linear algebra packages ScaLAPACK and Elemental for parallel solution of the symmetric eigenvalue problem are compared concerning their performance on the BlueGene/P supercomputer. Parameters for performance optimization are adjusted for the different data distribution methods used in the two libraries. It is found that for all test cases the new library Elemental which uses a two-dimensional element by element distribution of the matrices to the processors shows better performance than the old ScaLAPACK library which uses a block-cyclic distribution.
A novel photoexcitation method for the light-addressable potentiometric sensor (LAPS) is proposed to achieve a higher spatial resolution of chemical images. The proposed method employs a combined light source that consists of a modulated light probe, which generates the alternating photocurrent signal, and a ring of constant illumination surrounding it. The constant illumination generates a sheath of carriers with increased concentration which suppresses the spread of photocarriers by enhanced recombination. A device simulation was carried out to verify the effect of constant illumination on the spatial resolution, which demonstrated that a higher spatial resolution can be obtained.
A novel photoexcitation method for the light-addressable potentiometric sensor (LAPS) realized a higher spatial resolution of chemical imaging. In this method, a modulated light probe, which generates the alternating photocurrent signal, is surrounded by a ring of constant light, which suppresses the lateral diffusion of photocarriers by enhancing recombination. A device simulation verified that a higher spatial resolution could be obtained by adjusting the gap between the modulated and constant light. It was also found that a higher intensity and a longer wavelength of constant light was more effective. However, there exists a tradeoff between the spatial resolution and the amplitude of the photocurrent, and thus, the signal-to-noise ratio. A tilted incidence of constant light was applied, which could achieve even higher resolution with a smaller loss of photocurrent.
As a semiconductor-based electrochemical sensor, the light-addressable potentiometric sensor (LAPS) can realize two dimensional visualization of (bio-)chemical reactions at the sensor surface addressed by localized illumination. Thanks to this imaging capability, various applications in biochemical and biomedical fields are expected, for which the spatial resolution is critically significant. In this study, therefore, the spatial resolution of the LAPS was investigated in detail based on the device simulation. By calculating the spatiotemporal change of the distributions of electrons and holes inside the semiconductor layer in response to a modulated illumination, the photocurrent response as well as the spatial resolution was obtained as a function of various parameters such as the thickness of the Si substrate, the doping concentration, the wavelength and the intensity of illumination.
The simulation results verified that both thinning the semiconductor substrate and increasing the doping concentration could improve the spatial resolution, which were in good agreement with known experimental results and theoretical analysis. More importantly, new findings of interests were also obtained. As for the dependence on the wavelength of illumination, it was found that the known dependence was not always the case. When the Si substrate was thick, a longer wavelength resulted in a higher spatial resolution which was known by experiments. When the Si substrate was thin, however, a longer wavelength of light resulted in a lower spatial resolution. This finding was explained as an effect of raised concentration of carriers, which reduced the thickness of the space charge region.
The device simulation was found to be helpful to understand the relationship between the spatial resolution and device parameters, to understand the physics behind it, and to optimize the device structure and measurement conditions for realizing higher performance of chemical imaging systems.