| Abstract: | Insecticide penetration studies are usually done by applying a finite dose of material to a finite area of the integument in a solvent, such as acetone, that evaporates very quickly. The time-course of penetration is then measured either as the buildup of material inside the insect or as the decline of material recoverable in a surface wash. Pharmacokinetic models are often used to describe such experiments, but identical models can be formulated from diffusion theory. Diffusion theory was applied to obtain equations that describe the steady-state behavior of a single-layer integument with partitioning between integument and solutions, and a double-layer integument with partitioning between layers and between each layer and the adjacent solution. The steady-state flux equations for both models were first-order, and it was shown that this would be the case for steady-state flux through any number of layers. The steady-state analysis has two limitations. First, the assumption of a steady state implies that the concentration gradient across each layer of the integument is linear, and that this could not occur instantaneously. Second, the analysis assumes that material diffuses from a pool on the surface at some external concentration, whereas, ideally, it is applied as a plane source of infinite concentration. If the steady-state assumption is rejected, the diffusion equation can be solved exactly, using Green's function, for diffusion of a topically applied dose across the integument modeled as a homogeneous plate, if the concentration at the internal face is assumed to remain zero. An analytical expression is obtained for concentration as a function of time and position in the integument, and from it are calculated flux into the insect and disappearance of material recoverable in a solvent wash, where material is assumed to be recoverable to an arbitrary depth. For small values of recovery depth, recovery falls precipitously following application, then progressively more slowly as the experiment proceeds. This phenomenon has been seen in much published data, and is explained adequately for the first time by the theory presented here. Predicted flux into the insect rises with a delay and then falls, but its fall is not exponential, as is often assumed. Peak flux is predicted to be directly related to the diffusion coeficient. The impact of these results on the design of penetration experiments is discussed. |
