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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.