Mathematical analysis of a model of river channel formation.

The study of overland flow of water over an erodible sediment leads to a coupled model describing the evolution of the topographic elevation and the depth of the overland water film. The spatially uniform solution of this model is unstable, and this instability corresponds to the formation of rills, which in reality then grow and coalesce to form large-scale river channels. In this paper we consider the deduction and mathematical analysis of a deterministic model describing river channel formation and the evolution of its depth. The model involves a degenerate nonlinear parabolic equation (satisfied on the interior of the support of the solution) with a super-linear source term and a prescribed constant mass. We propose here a global formulation of the problem (formulated in the whole space, beyond the support of the solution) which allows us to show the existence of a solution and leads to a suitable numerical scheme for its approximation. A particular novelty of the model is that the evolving channel self-determines its own width, without the need to pose any extra conditions at the channel margin

Determination of no-observed effect level (NOEL)-biomarker equivalents to interpret biomonitoring data for organophosphorus pesticides in children

<p>Abstract</p> <p>Background</p> <p>Environmental exposure to organophosphorus pesticides has been characterized in various populations, but interpretation of these data from a health risk perspective remains an issue. The current paper proposes biological reference values to help interpret biomonitoring data related to an exposure to organophosphorus pesticides in children for which measurements of alkylphosphate metabolites are available.</p> <p>Methods</p> <p>Published models describing the kinetics of malathion and chlorpyrifos in humans were used to determine no-observed effect level – biomarker equivalents for methylphosphates and ethylphosphates, respectively. These were expressed in the form of cumulative urinary amounts of alkylphosphates over specified time periods corresponding to an absorbed no-observed effect level dose (derived from a published human exposure dose) and assuming various plausible exposure scenarios. Cumulative amounts of methylphosphate and ethylphosphate metabolites measured in the urine of a group of Quebec children were then compared to the proposed biological reference values.</p> <p>Results</p> <p>From a published no-observed effect level dose for malathion and chlorpyrifos, the model predicts corresponding oral biological reference values for methylphosphate and ethylphosphate derivatives of 106 and 52 nmol/kg of body weight, respectively, in 12-h nighttime urine collections, and dermal biological reference values of 40 and 32 nmol/kg of body weight. Out of the 442 available urine samples, only one presented a methylphosphate excretion exceeding the biological reference value established on the basis of a dermal exposure scenario and none of the methylphosphate and ethylphosphate excretion values were above the obtained oral biological reference values, which reflect the main exposure route in children.</p> <p>Conclusion</p> <p>This study is a first step towards the development of biological guidelines for organophophorus pesticides using a toxicokinetic modeling approach, which can be used to provide a health-based interpretation of biomonitoring data in the general population.</p