The third boundary value problem in potential theory

summary:The aim of this paper is to give a convergence proof of a numerical method for the Dirichlet problem on doubly connected plane regions using the method of reflection across the exterior boundary curve (which is analytic) combined with integral equations extended over the interior boundary curve (which may be irregular with infinitely many angular points)

Central blockade of oxytocin receptors during mid-late gestation reduces amplitude of slow afterhyperpolarization in supraoptic oxytocin neurons

The neurohypophysial hormone oxytocin (OT), synthesized in magnocellular paraventricular (PVN) and supraoptic (SON) nuclei, is well known for its effects in lactation. Our previous studies showed that central OT receptor (OTR) binding is increased during gestation and that blockade of central OTRs, specifically during mid-late gestation, causes a delay in OT release during suckling and reduces weight gain in pups, suggesting decreased milk delivery. In the present study, we tested whether central OTR blockade during late gestation disrupts the gestation-related plasticity in intrinsic membrane properties. Whole cell current-clamp recordings were performed in OT neurons from pregnant rats (19–22 days in gestation) that were infused with an OTR antagonist (OTA) or artificial cerebrospinal fluid (aCSF) and from virgin rats infused with aCSF into the third ventricle via an osmotic minipump beginning on days 12–14 of gestation. The amplitudes of both Ca2+-dependent afterhyperpolarizations (AHPs), an apamin-sensitive medium AHP (mAHP) and an apamin-insensitive slow AHP (sAHP), were significantly increased during late gestation in control pregnant animals. However, the amplitude of the sAHP from pregnant rats treated with the OTA was significantly smaller than that of pregnant control rats and similar to that of virgins. These results indicate that the diminished efficiency in lactation due to OTR blockade may be partly a result of an altered sAHP that would shape OT bursting. These findings suggest that central actions of OT during late gestation are necessary for programming the plasticity of at least some of the intrinsic membrane properties in OT neurons during lactation