Effective Cell-Centred Time-Domain Maxwell's Equations Numerical Solvers

This research work analyses techniques for implementing a cell-centred finite-volume time-domain (ccFV-TD) computational methodology for the purpose of studying microwave heating. Various state-of-the-art spatial and temporal discretisation methods employed to solve Maxwell's equations on multidimensional structured grid networks are investigated, and the dispersive and dissipative errors inherent in those techniques examined. Both staggered and unstaggered grid approaches are considered. Upwind schemes using a Riemann solver and intensity vector splitting are studied and evaluated. Staggered and unstaggered Leapfrog and Runge-Kutta time integration methods are analysed in terms of phase and amplitude error to identify which method is the most accurate and efficient for simulating microwave heating processes. The implementation and migration of typical electromagnetic boundary conditions. from staggered in space to cell-centred approaches also is deliberated. In particular, an existing perfectly matched layer absorbing boundary methodology is adapted to formulate a new cell-centred boundary implementation for the ccFV-TD solvers. Finally for microwave heating purposes, a comparison of analytical and numerical results for standard case studies in rectangular waveguides allows the accuracy of the developed methods to be assessed.

Elevated concentration of TNF-a induces trophoblast differentiation in mouse blastocyst outgrowths

Elevated expression of tumour necrosis factora (TNF-a) is associated with adverse pregnancy outcome. This study has examined the expression of TNF-a and its receptors (TNF-Rs) by mouse blastocysts and blastocyst outgrowths from day 4 to 9.5 of pregnancy and investigated the effects of elevated TNF-a on the inner cell mass (ICM) and trophoblast cells of blastocyst outgrowths. RTPCR demonstrated TNF-a mRNA expression from day 7.5 to 9.5, TNF-R1 from day 6.5 to 9.5 and TNF-R2 from day 5.5 to 7.5 of pregnancy, and in situ hybridisation revealed the trophoblast giant cells (TGCs) of the early placenta as the site of TNF-a expression. Day 4 blastocysts were cultured in a physiologically high concentration of TNF-a (100 ng/ml) for 72 h to the outgrowth stage and then compared to blastocysts cultured in media alone. TNF-a-treated blastocyst outgrowths exhibited a significant reduction in ICM cells (mean € SD 23.90€10.42 vs 9.37€7.45, t-test, P<0.0001) with no significant change in the numbers of trophoblast cells (19.97€8.14 vs 21.73€7.79, t-test, P=0.39). Within the trophoblast cell population, the TNF-a-treated outgrowths exhibited a significant increase in multinucleated cells (14.10€5.53 vs 6.37€5.80, t-test, P<0.0001) and a corresponding significant decrease in mononucleated cells (5.87€3.60 vs 15.37€5.87, t-test, P<0.0001). In summary, this study describes the expression of TNF-a and its receptors during the peri-implantation period in the mouse. It also reports that elevated TNF-a restricts ICM proliferation in the blastocyst and changes the ratio of mononucleated to multinucleated trophoblast cells. These findings suggest a mechanism by which increased