Mathematical models in percutaneous absorption

A number of mathematical models have been used to describe percutaneous absorption kinetics. In general, most of these models have used either diffusion-based or compartmental equations. The object of any mathematical model is to a) be able to represent the processes associated with absorption accurately, b) be able to describe/summarize experimental data with parametric equations or moments, and c) predict kinetics under varying conditions. However, in describing the processes involved, some developed models often suffer from being of too complex a form to be practically useful. In this chapter, we attempt to approach the issue of mathematical modeling in percutaneous absorption from four perspectives. These are to a) describe simple practical models, b) provide an overview of the more complex models, c) summarize some of the more important/useful models used to date, and d) examine sonic practical applications of the models. The range of processes involved in percutaneous absorption and considered in developing the mathematical models in this chapter is shown in Fig. 1. We initially address in vitro skin diffusion models and consider a) constant donor concentration and receptor conditions, b) the corresponding flux, donor, skin, and receptor amount-time profiles for solutions, and c) amount- and flux-time profiles when the donor phase is removed. More complex issues, such as finite-volume donor phase, finite-volume receptor phase, the presence of an efflux. rate constant at the membrane-receptor interphase, and two-layer diffusion, are then considered. We then look at specific models and issues concerned with a) release from topical products, b) use of compartmental models as alternatives to diffusion models, c) concentration-dependent absorption, d) modeling of skin metabolism, e) role of solute-skin-vehicle interactions, f) effects of vehicle loss, a) shunt transport, and h) in vivo diffusion, compartmental, physiological, and deconvolution models. We conclude by examining topics such as a) deep tissue penetration, b) pharmacodynamics, c) iontophoresis, d) sonophoresis, and e) pitfalls in modeling.

Finite element modelling of heat transfer through permeable cracks in hydrothermal systems with upward throughflow

We use the finite element method to model the heat transfer phenomenon through permeable cracks in hydrothermal systems with upward throughflow. Since the finite element method is an approximate numerical method, the method must be validated before it is used to soh,e any new, kind of problem. However, the analytical solution, which can be used to validate the finite element method and other numerical methods, is rather limited in the literature, especially, for the problem considered here. Keeping this in mind, we have derived analytical solutions for the temperature distribution along the vertical axis of a crack in a fluid-saturated porous layer. After the finite element method is validated by comparing the numerical solution with the analytical solution for the same benchmark problem, it is used to investigate the pore-fluid flow and heat transfer in layered hydrothermal systems with vertical permeable cracks. The related analytical and numerical results have demonstrated that vertical cracks are effective and efficient members to transfer heat energy from the bottom section to the top section in hydrothermal systems with upward throughflow.

Phase and microstructural evolution during the heat treatment of Sm-Ca-alpha-sialon ceramics

The phase and microstructural evolution of multi-cation Sm-Ca-alpha-sialon ceramics was investigated. Six samples were prepared, ranging from a pure Sm-sialon to a pure Ca-sialon, with calcium replacing samarium in 20 eq% increments, thus maintaining an equivalent design composition in all samples. After pressureless sintering at 1820 degreesC for 2 It, all samples were subsequently heat treated up to 192 h at 1450 and 1300 degreesC. The amount of grain boundary glass in the samples after sintering was observed to decrease with increasing calcium levels. A M-ss' or M-ss',-gehlenite solid solution was observed to form during the 1450 degreesC heat treatment of all Sm-containing samples, and this phase forms in clusters in the high-Sm samples. The thermal stability of the alpha-sialon phase was improved in the multi-cation systems. Heat treatment at 1300 degreesC produces SmAlO3 in the high-Sm samples, a M-ss',-gehlenite solid solution in the high-Ca samples, and a Sm-Ca-apatite phase in some intermediate samples. (C) 2002 Elsevier Science Ltd. All rights reserved.

Analysis of steady-state heat transfer through mid-crustal vertical cracks with upward throughflow in hydrothermal systems

We conduct a theoretical analysis of steady-state heat transfer problems through mid-crustal vertical cracks with upward throughflow in hydrothermal systems. In particular, we derive analytical solutions for both the far field and near field of the system. In order to investigate the contribution of the forced advection to the total temperature of the system, two concepts, namely the critical Peclet number and the critical permeability of the system, have been presented and discussed in this paper. The analytical solution for the far field of the system indicates that if the pore-fluid pressure gradient in the crust is lithostatic, the critical permeability of the system can be used to determine whether or not the contribution of the forced advection to the total temperature of the system is negligible. Otherwise, the critical Peclet number should be used. For a crust of moderate thickness, the critical permeability is of the order of magnitude of 10(-20) m(2), under which heat conduction is the overwhelming mechanism to transfer heat energy, even though the pore-fluid pressure gradient in the crust is lithostatic. Furthermore, the lower bound analytical solution for the near field of the system demonstrates that the permeable vertical cracks in the middle crust can efficiently transfer heat energy from the lower crust to the upper crust of the Earth. Copyright (C) 2002 John Wiley Sons, Ltd.

Polydnavirus particle proteins with similarities to molecular chaperones, heat-shock protein 70 and calreticulin

Multipartite nucleic acid-containing virus-like particles, known as polydnaviruses, are special structures produced by female parasitoid wasps to deliver wasp components into the body of their host at oviposition. The particles confer protection for the developing parasitoid by passive and active means. Although several genes expressed from the circular DNA of these particles have been identified from various host-parasitoid systems, there is not much known about the structural proteins of these particles. Here we report on two genes encoding Cotesia rubecula particle proteins with similarities to molecular chaperones, calreticulin and heat-shock protein 70.

Effects of hot intrusions on pore-fluid flow and heat transfer in fluid-saturated rocks

We use the finite element method to solve coupled problems between pore-fluid flow and heat transfer in fluid-saturated porous rocks. In particular, we investigate the effects of both the hot pluton intrusion and topographically driven horizontal flow on the distributions of the pore-flow velocity and temperature in large-scale hydrothermal systems. Since general mineralization patterns are strongly dependent on distributions of both the pore-fluid velocity and temperature fields, the modern mineralization theory has been used to predict the general mineralization patterns in several realistic hydrothermal systems. The related numerical results have demonstrated that: (1) The existence of a hot intrusion can cause an increase in the maximum value of the pore-fluid velocity in the hydrothermal system. (2) The permeability of an intruded pluton is one of the sensitive parameters to control the pore-fluid flow, heat transfer and ore body formation in hydrothermal systems. (3) The maximum value of the pore-fluid velocity increases when the bottom temperature of the hydrothermal system is increased. (4) The topographically driven flow has significant effects on the pore-fluid flow, temperature distribution and precipitation pattern of minerals in hydrothermal systems. (5) The size of the computational domain may have some effects on the pore-fluid flow and heat transfer, indicating that the size of a hydrothermal system may affect the pore-fluid flow and heat transfer within the system. (C) 2003 Elsevier Science B.V. All rights reserved.

Dormancy release in Australian fire ephemeral seeds during burial increases germination response to smoke water or heat

Fire ephemerals are short-lived plants that primarily germinate after fire. Fresh and laboratory-stored seeds are difficult to germinate ex situ, even in response to fire-related cues such as heat and smoke. Seeds of eight Australian fire ephemeral species were buried in unburnt and recently burnt sites of natural bushland during autumn. Seeds were exhumed after 6 and 12 months and incubated in water and smoke water, either with or without a heat treatment at 70 degrees C for 1 h. Generally, germination did not increase after 6 months of burial, but after 12 months of burial germination was enhanced in seven of the eight species. Actinotus leucocephalus produced higher germination following 12 months of burial without any further treatment, and smoke water and heat further improved germination. The four Gyrostemonaceae species, Codonocarpus cotinifolius, Gyrostemon racemiger, Gyrostemon ramulosus and Tersonia cyathiflora, only germinated in the presence of smoke water, and their germination was enhanced by burial. Burial improved germination in response to a heat treatment in Grevillea scapigera and Alyogyne huegelii seeds, but did not enhance Alyogyne hakeifolia germination. During concurrent dry laboratory storage of seeds at 15 degrees C, only Actinotus leucocephalus produced increased germination in response to smoke water and heat over time. In summary, soil burial can alter the dormancy status of a number of Australian fire ephemeral seeds, rendering them more responsive to germination cues such as smoke water and heat. The requirement for a period of burial before seeds become responsive to smoke and/or heat would ensure that seeds persist in the soil until a subsequent fire, when there is an increase in nutrients available for growth and reduced competition from other plants.

Carbamazepine can induce kidney water absorption by increasing aquaporin 2 expression

Background. Carbamazepine (Carba) is an anticonvulsant and psychotropic drug used widely for the treatment of intellectual disability and severe pains, but the incidence of hyponatremia is a common related occurrence. This hyponatremia is frequently attributed to a SIADH induced by this drug. It is also known that Carba is used to decrease the urinary volume in Diabetes Insipidus (DI) because it has an antidiuretic effect. Lithium (Li) is one of the most important drugs used to treat bipolar mood disorders. However Li has the undesirable capacity to induce DI. Nowadays, the association of these drugs is used in the treatment of patients with psychiatric and neurological problems. Methods. In vivo and in vitro (microperfusion) experiments were developed to investigate the effect of Carba in the rat Inner Medullary Collecting Duct (IMCD). Results. The results revealed that Carba was able to stimulate the V2 vasopressin receptor-Protein G complex increasing the water permeability (Pf) and water absorption. In vivo studies showed that in rats with lithium-induced DI, Carba decreased the urinary volume and increased the urinary osmolality. AQP2 expression was increased both in normal IMCD incubated with Carba and in IMCD from lithium-induced DI after Carba addition to the diet, when compared with the control. Conclusion. These results showed that the hyponatremia observed in patients using this anticonvulsant drug, at least in part, is due to the Carba capacity to increase IMCD`s Pf and that the Lithium-Carbamazepine association is beneficial to the patient.

Acute Pancreatitis Hypertonic Saline Increases Heat Shock Proteins 70 and 90 and Reduces Neutrophil Infiltration in Lung Injury

Objectives: Acute pancreatitis (AP) protease release induces lung parenchymal destruction via matrix metalloproteinases (MMPs), a neutrophil (polymorphonuclear leukocyte)-dependent process. Recent studies in hemorrhagic shock revealed that hypertonic saline (HTS) has an anti-inflammatory effect and can inhibit a variety of neutrophil functions. The aim of this study was to determine whether HTS and its actions in the pathway of neutrophil migration, MMPs, and heat shock proteins (HSPs) are effective in protecting the lung from injury associated with AP. Methods: We determined neutrophil infiltration and expressions of MMPs and HSPs in the lung tissue after AP induced by retrograde infusion of 2.5% of sodium taurocholate. Results: Animals submitted to AP that received HTS compared with those who received normal saline presented with increased HSP70 and HSP90 expressions and reduced myeloperoxidase levels and MMP-9 expression and activity. Conclusions: Our data raised the hypothesis that a sequence of HTS lung protection events increases HSP70 and HSP90, inhibiting infiltration of neutrophils and their protease actions in the lung.

HDL-C concentration is related to markers of absorption and of cholesterol synthesis: Study in subjects with low vs. high HDL-C

Background: The antiatherogenic functions of high density lipoprotein (HDL-C) include its role in reverse cholesterol transport, but to what extent the concentration of HDL-C interferes with the whole-body cholesterol metabolism is unknown. Therefore, we measured markers of body cholesterol synthesis (desmosterol and lathosterol) and of intestinal cholesterol absorption (campesterol and beta-sitosterol) in healthy subjects that differ according to their plasma HDL-C concentrations. Methods: Healthy participants presented either low HDL-C (<40 mg/dl, n = 33,17 male and 16 female) or high HDL-C (>60 mg/dl, n = 33, 17 male and 16 female), BMI <30 kg/m(2), were paired according to age and gender, without secondary factors that might interfere with their plasma lipid concentrations. Plasma concentrations of non-cholesterol sterols were measured by the combined GC-MS analysis. Results: Plasma desmosterol did not differ between the two groups; however, as compared with the high HDL-C participants, the low HDL-C participants presented higher concentration of lathosterol and lower concentration of the intestinal cholesterol absorption markers campesterol and beta-sitosterol. Conclusion: Plasma concentrations of HDL, and not the activities of LCAT and CETP that regulate the reverse cholesterol transport system, correlate with plasma sterol markers of intestinal cholesterol absorption directly, and of cholesterol synthesis reciprocally. (C) 2010 Elsevier B.V. All rights reserved.

Percutaneous absorption of sunscreen agents from liquid paraffin: Self-association of octyl salicylate and effects on skin flux

This study provides an investigation of the availability of octyl salicylate (OS), a common sunscreen agent, from liquid paraffin and the effect of OS on skin permeability. A model membrane system to isolate the vehicle effect from membrane permeability has been developed. Partitioning of OS between liquid paraffin and aqueous receptor phases was conducted. Partition coefficients increased with increase in OS concentration. A range of OS concentrations in liquid paraffin was diffused across human epidermis and synthetic membranes into 4% bovine serum albumin in phosphate-buffered saline and 50% ethanol. Absorption profiles of OS obtained from silicone and low-density polyethylene (LDPE) membranes were similar to each other but higher than for the high-density polyethylene [HDPE (3 times)] membrane and human epidermis (15 times). The steady state fluxes and apparent permeability coefficients (K-p') obtained from the diffusion studies showed the same trends with all membranes, except for the HDPE membrane which showed greater increase in flux and K-p' at concentrations above 30%. IR spectra showed that several bands of OS were shifted with concentrations, and the molecular models further suggested that the main contribution to the self-association is from non-1,4 van der Waals interactions.

Modeling of subcutaneous absorption kinetics of infusion solutions in the elderly using technetium

Absorption kinetics of solutes given with the subcutaneous administration of fluids is ill-defined. The gamma emitter, technitium pertechnetate, enabled estimates of absorption rate to be estimated independently using two approaches. In the first approach, the counts remaining at the site were estimated by imaging above the subcutaneous administration site, whereas in the second approach, the plasma technetium concentration-time profiles were monitored up to 8 hr after technetium administration. Boluses of technetium pertechnetate were given both intravenously and subcutaneously on separate occasions with a multiple dosing regimen using three doses on each occasion. The disposition of technetium after iv administration was best described by biexponential kinetics with a V-ss of 0.30 +/- 0.11 L/kg and a clearance of 30.0 +/- 13.1 ml/min. The subcutaneous absorption kinetics was best described as a single exponential process with a half-life of 18.16 +/- 3.97 min by image analysis and a half-life of 11.58 +/- 2.48 min using plasma technetium time data. The bioavailability of technetium by the subcutaneous route was estimated to be 0.96 +/- 0.12. The absorption half-life showed no consistent change with the duration of the subcutaneous infusion. The amount remaining at the absorption site with time was similar when analyzed using image analysis, and plasma concentrations assuming multiexponential disposition kinetics and a first-order absorption process. Profiles of fraction remaining at the absorption sire generated by deconvolution analysis, image analysis, and assumption of a constant first-order absorption process were similar. Slowing of absorption from the subcutaneous administration site is apparent after the last bolus dose in three of the subjects and can De associated with the stopping of the infusion. In a fourth subject, the retention of technetium at the subcutaneous site is more consistent with accumulation of technetium near the absorption site as a result of systemic recirculation.