An internal crack problem for an infinite elastic layer

The elastostatic plane problem of an infinite elastic layer with an internal crack is considered. The elastic layer is subjected to two different loadings, (a) the elastic layer is loaded by a symmetric transverse pair of compressive concentrated forces P/2, (b) it is loaded by a symmetric transverse pair of tensile concentrated forces P/2. The crack is opened by an uniform internal pressure p ₀ along its surface and located halfway between and parallel to the surfaces of the elastic layer. It is assumed that the effect of the gravity force is neglected. Using an appropriate integral transform technique, the mixed boundary value problem is reduced to a singular integral equation. The singular integral equation is solved numerically by making use of an appropriate Gauss–Chebyshev integration formula and the stress-intensity factors and the crack opening displacements are determined according to two different loading cases for various dimensionless quantities.     

A layered composite containing a crack in its lower layer loaded by a rigid stamp

The elastostatic plane problem of a layered composite containing an internal or edge crack perpendicular to its boundaries in its lower layer is considered. The layered composite consists of two elastic layers having different elastic constants and heights and rests on two simple supports. Solution of the problem is obtained by superposition of solutions for the following two problems: The layered composite subjected to a concentrated load through a rigid rectangular stamp without a crack and the layered composite having a crack whose surface is subjected to the opposite of the stress distribution obtained from the solution of the first problem. Using theory of Elasticity and Fourier transform technique, the problem is formulated in terms of two singular integral equations. Solving these integral equations numerically by making use of Gauss–Chebyshev integration, numerical results related to the normal stress σ_x(0,y), the stress-intensity factors, and the crack opening displacements are presented and shown graphically for various dimensionless quantities.     

Integration of cell phone imaging with microchip ELISA to detect ovarian cancer HE4 biomarker in urine at the point-of-care

Ovarian cancer is asymptomatic in the early stages and most patients present with advanced levels of disease. The lack of cost-effective methods that can achieve frequent, simple and non-invasive testing hinders early detection and causes high mortality in ovarian cancer patients. Here, we report a simple and inexpensive microchip ELISA-based detection module that employs a portable detection system, i.e., a cell phone/charge-coupled device (CCD) to quantify an ovarian cancer biomarker, HE4, in urine. Integration of a mobile application with a cell phone enabled immediate processing of microchip ELISA results, which eliminated the need for a bulky, expensive spectrophotometer. The HE4 level detected by a cell phone or a lensless CCD system was significantly elevated in urine samples from cancer patients (n = 19) than healthy controls (n = 20) (p < 0.001). Receiver operating characteristic (ROC) analyses showed that the microchip ELISA coupled with a cell phone running an automated analysis mobile application had a sensitivity of 89.5% at a specificity of 90%. Under the same specificity, the microchip ELISA coupled with a CCD had a sensitivity of 84.2%. In conclusion, integration of microchip ELISA with cell phone/CCD-based colorimetric measurement technology can be used to detect HE4 biomarker at the point-of-care (POC), paving the way to create bedside technologies for diagnostics and treatment monitoring.