Using the level set method to model endogenous lava dome growth

Modeling volcanic phenomena is complicated by free-surfaces often supporting large rheological gradients. Analytical solutions and analogue models provide explanations for fundamental characteristics of lava flows. But more sophisticated models are needed, incorporating improved physics and rheology to capture realistic events. To advance our understanding of the flow dynamics of highly viscous lava in Peléean lava dome formation, axi-symmetrical Finite Element Method (FEM) models of generic endogenous dome growth have been developed. We use a novel technique, the level-set method, which tracks a moving interface, leaving the mesh unaltered. The model equations are formulated in an Eulerian framework. In this paper we test the quality of this technique in our numerical scheme by considering existing analytical and experimental models of lava dome growth which assume a constant Newtonian viscosity. We then compare our model against analytical solutions for real lava domes extruded on Soufrière, St. Vincent, W.I. in 1979 and Mount St. Helens, USA in October 1980 using an effective viscosity. The level-set method is found to be computationally light and robust enough to model the free-surface of a growing lava dome. Also, by modeling the extruded lava with a constant pressure head this naturally results in a drop in extrusion rate with increasing dome height, which can explain lava dome growth observables more appropriately than when using a fixed extrusion rate. From the modeling point of view, the level-set method will ultimately provide an opportunity to capture more of the physics while benefiting from the numerical robustness of regular grids.

Investigation of the antinociceptive efficacy and relative potency of extended duration injectable 3-acylmorphine-6-sulfate prodrugs in rats

This investigation was designed to examine the antinociceptive activity in rats of 3-O-acyl prodrugs of M6S relative to the parent drug, after intravenous and intramuscular injection, using the tail flick latency test of antinociception. M6S, 3-acetylmorphine-6-sulfate (3AcM6S), 3-propionylmorphine-6-sulfate (3PrM6S), 3-butanoylmorphine-6-sulfate (3BuM6S) and 3-heptanoylmorphine-6-sulfate (3HpM6S) were administered by the IV route in a dose of 4.10 mu mol/kg. Relatively high levels of antinociception (>40% Maximum Possible Effect) were achieved following administration of M6S, 3AcM6S and 3PrM6S, whereas insignificant antinociception (<20%MPE) was achieved following administration of 3BuM6S or 3HpM6S. Although the mean duration of action for 3AcM6S (6 h) was longer than for M6S or 3PrM6S (4 h), the mean area (+/- S.E.M.) under the degree of antinociception versus time curve (AUG) for 3AcM6S (151.6 +/- 6.9%MPE h) was not significantly different (p <0.05) from that for M6S (120.8 +/- 32.7%MPE h) or for 3PrM6S (106.0 +/- 21.3%MPE h). The mean ED50 (range) doses for M6S, 3AcM6S and 3PrM6S were calculated to be 4.16 (3.61-4.48), 4.32 (3.55-5.09) and 4.54 (4.21-4.79) mu mol/kg, respectively. Preliminary studies were conducted on potential long-acting formulations containing 8 x ED50 doses of M6S and the 3-acetyl and 3-propionyl esters suspended in soybean oil. These showed that 3PrM6S gave a greater AUC (mean + S.E.M.) (1087.4 +/- 97.4%MPE h) and longer duration of action (20 h) than did M6S (613.1 +/- 155.9%MPE h; 10 h duration) or 3AcM6S (379.3 + 114.2%MPE h: 8 h duration). Further studies are needed to more fully investigate these findings. (C) 1998 Elsevier Science B.V. All rights reserved.