A mathematical model for fluid-glucose-albumin transport in peritoneal dialysis

A mathematical model for fluid and solute transport in peritoneal dialysis is constructed. The model is based on a three-component nonlinear system of two-dimensional partial differential equations for fluid, glucose and albumin transport with the relevant boundary and initial conditions. Its aim is to model ultrafiltration of water combined with inflow of glucose to the tissue and removal of albumin from the body during dialysis, and it does this by finding the spatial distributions of glucose and albumin concentrations and hydrostatic pressure. The model is developed in one spatial dimension approximation and a governing equation for each of the variables is derived from physical principles. Under certain assumptions the model are simplified with the aim of obtaining exact formulae for spatially non-uniform steady-state solutions. As the result, the exact formulae for the fluid fluxes from blood to tissue and across the tissue are constructed together with two linear autonomous ODEs for glucose and albumin concentrations in the tissue. The obtained analytical results are checked for their applicability for the description of fluid-glucose-albumin transport during peritoneal dialysis.Comment: 28 pages, 8 figures. arXiv admin note: text overlap with arXiv:1110.128

Exact Solutions of a Mathematical Model for Fluid Transport in Peritoneal Dialysis

A mathematical model for fluid transport in peritoneal dialysis is constructed. The model is based on a nonlinear system of two-dimensional partial differential equations with corresponding boundary and initial conditions. Using the classical Lie scheme, we establish that the base system of partial differential equations (under some restrictions on coefficients) is invariant under the infinite-dimensional Lie algebra, which enables us to construct families of exact solutions. Moreover, exact solutions with a more general structure are found using another (non-Lie) technique. Finally, it is shown that some of the solutions obtained describe the hydrostatic pressure and the glucose concentration in peritoneal dialysis.Побудовано математичну модель переносу рідини при очеревинному діалізі, яка базується на нелінійній системі двовимірних диференціальних рівнянь з частинними похідними (ДРЧП) з відповідними крайовими та початковими умовами. Шляхом застосування класичного методу Лі встановлено, що базова система ДРЧП (при певних обмеженнях на коефіцієнти) інваріантна відносно нескінченновимірної алгебри Лі, що дозволило побудувати сім'ї точних розв'язків. Крім того, точні розв'язки більш загальної структури знайдено за допомогою іншого неліївського методу. Також встановлено, що деякі з отриманих розв'язків описують гідростатичний тиск та концентрацію глюкози при очеревинному діалізі

Flow patterns in nappe flow regime down low gradient stepped chutes

Although modern gravity dam spillways include often steep chutes operating in skimming flow regime, succession of free-falling nappes (i.e. nappe flow regime) are more common on low gradient chutes and cascades, and this flow situation received little attention to date. New experiments were conducted in nappe flows without hydraulic jump in two large-size facilities with flat slopes. The flow on the stepped cascade displayed complex, three-dimensional patterns. Detailed air-water flow measurements were performed in the jet, at nappe impact and in the downstream flow region. Key results demonstrated that the flow on each step was rapidly varied (RVF), highly three-dimensional and strongly aerated

The short-chain fatty acid acetate reduces appetite via a central homeostatic mechanism

Increased intake of dietary carbohydrate that is fermented in the colon by the microbiota has been reported to decrease body weight, although the mechanism remains unclear. Here we use in vivo11C-acetate and PET-CT scanning to show that colonic acetate crosses the blood–brain barrier and is taken up by the brain. Intraperitoneal acetate results in appetite suppression and hypothalamic neuronal activation patterning. We also show that acetate administration is associated with activation of acetyl-CoA carboxylase and changes in the expression profiles of regulatory neuropeptides that favour appetite suppression. Furthermore, we demonstrate through 13C high-resolution magic-angle-spinning that 13C acetate from fermentation of 13C-labelled carbohydrate in the colon increases hypothalamic 13C acetate above baseline levels. Hypothalamic 13C acetate regionally increases the 13C labelling of the glutamate–glutamine and GABA neuroglial cycles, with hypothalamic 13C lactate reaching higher levels than the ‘remaining brain’. These observations suggest that acetate has a direct role in central appetite regulation