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.

Social structures, genetic structures and dispersal strategies in Australian rabbit (Oryctolagus cuniculus) populations

In this study, the pattern of movement of young male and female rabbits and the genetic structures present in adult male and female populations in four habitats was examined. The level of philopatry in young animals was found to vary between 18-90% for males and 32-95% for females in different populations. It was skewed, with more males dispersing than females in some but not all populations. Analysis of allozyme data using spatial autocorrelation showed that adult females from the same social group, unlike males, were significantly related in four of the five populations studied. Changes in genetic structure and rate of dispersal were measured before and during the recovery of a population that was artificially reduced in size. There were changes in the rate and distance of dispersal with density and sex. Subadults of both sexes moved further in the first year post crash (low density) than in the following years. While the level of dispersal for females was lower than that of the males for the first 3 years, thereafter (high density) both sexes showed similar, low levels of dispersal (20%). The density at which young animals switch behaviour between dispersal and philopatry differed for males and females. The level of genetic structuring in adult females was high in the precrash population, reduced in the first year post crash and undetectable in the second year. Dispersal behaviour of rabbits both affects the genetic structure of the population and changes with conditions. Over a wide range of levels of philopatry, genetic structuring is present in the adult female, but not the male population. Consequently, though genetic structuring is present, it does not lead to inbreeding. More long-distance movements are found in low-density populations, even though vacant warrens are available near birth warrens. The distances moved decreased as density increased. Calculation of the effective population size (N-e) shows that changes in dispersal distance offset changes in density, so that N-e remains constant.

Cyclic octapeptides containing thiazole. Effect of stereochemistry and degree of flexibility on calcium binding properties

Solution conformation and calcium binding properties have been investigated for the two cyclic octapeptides cyclo(-D-Thr-D-Val(Thz)-Ile-)(2) (4) and cyclo(-Thr-Gly(Thz)-Ile-Ser-Gly(Thz)-Ile-)(5) and the results are compared to those for the cyclic octapeptides previously studied; ascidiacyclamide (1), patellamide D (2), cyclo(-Thr-D-Val(Thz)-Ile-)(2) (3), and cyclo(-Thr-D-Val-alphaAbu-Ile-)2 (6). Both 4 and 5 contain two heterocyclic thiazole ring constraints but the latter has a larger degree of flexibility as a consequence of the glycine residues within the cyclic framework. The solution conformation of 4 and 5 was determined from H-1 NMR spectra and found to be a twisted figure of eight similar to that for 2. Complexation studies using H-1 NMR and CD spectroscopy yielded 1 : 1 calcium-peptide binding constants (logK) for the two peptides (2.3 (4) and 5.7 (5)). For 5 the magnitude of the binding constant was verified by a competition titration using CD. The different calcium-binding affinities of 3 (logK = 4.0) and 4 is attributed to the stereochemistry of the threonine residue. The magnitude of the binding constant for 5 compared to 3 and 4 (all peptides containing two thiazole ring constrains) demonstrates that the increase in flexibility of the cyclic peptide has a dramatic effect on the Ca2+ binding ability. The affinity for Ca2+ thus decreases in the order (6 similar to 5 > 3 > 2 similar to 1 > 4). The number of carbonyl donors available on each peptide has only a limited effect on calcium binding. The most important factor is the flexibility, which allows for a conformation of the peptide capable of binding calcium efficiently.

On entanglement and Lorentz transformations

We study the transformation of maximally entangled states under the action of Lorentz transformations in a fully relativistic setting. By explicit calculation of the Wigner rotation, we describe the relativistic analog of the Bell states as viewed from two inertial frames moving with constant velocity with respect to each other. Though the finite dimensional matrices describing the Lorentz transformations are non-unitary, each single particle state of the entangled pair undergoes an effective, momentum dependent, local unitary rotation, thereby preserving the entanglement fidelity of the bipartite state. The details of how these unitary transformations are manifested are explicitly worked out for the Bell states comprised of massive spin 1/2 particles and massless photon polarizations. The relevance of this work to non-inertial frames is briefly discussed.

Aspects of the biology of the yabby Trypea australiensis (Dana) (Decapoda : Thalassinidea) and the potential of burrow counts as an indirect measure of population density

The thalassinidean shrimp Trypea australiensis (the yabby) commonly occurs on intertidal sandflats and subtidal regions of sheltered embayments and estuaries along the east coast of Australia and is harvested commercially and recreationally for use as bait by anglers. The potential for counts of burrow openings to provide a reliable indirect estimate of the abundance of yabbies was examined on intertidal sandflats on North Stradbroke Island (Queensland, Australia). The relationship between the number of burrow openings and the abundance of yabbies was generally poor and also varied significantly through time, casting doubt on previous estimates of abundance for this species based on unvalidated hole counts. Spatial and temporal variation in population density, the size at maturity and the reproductive period of the yabby were also assessed. Except for an initial peak in abundance as a result of recruitment, the density of yabbies was constant throughout the study but considerably less than that estimated from a previous study in the same area. Ovigerous females were recorded at 3 mm carapace length (CL) which is smaller than previously recorded for this species and thalassinideans in general. Small ovigerous females were found throughout the study, including the summer months, which is unusual for thalassinideans in the intertidal zone. It was hypothesised that in the intertidal zone, small female yabbies may be able to balance the metabolic demands of reproduction and respiration at higher temperatures than can larger females allowing them to reproduce in the warmer months.

Dormancy release in Lolium rigidum seeds is a function of thermal after-ripening time and seed water content

Dormancy release in seeds of Lolium rigidum Gaud. (annual ryegrass) was investigated in relation to temperature and seed water content. Freshly matured seeds were collected from cropping fields at Wongan Hills and Merredin, Western Australia. Seeds from Wongan Hills were equilibrated to water contents between 6 and 18% dry weight and after-ripened at constant temperatures between 9 and 50degreesC for up to 23 weeks. Wongan Hills and Merredin seeds at water contents between 7 and 17% were also after-ripened in full sun or shade conditions. Dormancy was tested at regular intervals during after-ripening by germinating seeds on agar at 12-h alternating 15degreesC (dark) and 25degreesC (light) periods. Rate of dormancy release for Wongan Hills seeds was a positive linear function of after-ripening temperature above a base temperature (T-b) of 5.4degreesC. A thermal after-ripening time model for dormancy loss accounting for seed moisture in the range 6-18% was developed using germination data for Wongan Hills seeds after-ripened at constant temperatures. The model accurately predicted dormancy release for Wongan Hills seeds after-ripened under naturally fluctuating temperatures. Seeds from Merredin responded similarly but had lower dormancy at collection and a faster rate of dormancy release in seeds below 9% water content.

Quantum error correction for continuously detected errors

We show that quantum feedback control can be used as a quantum-error-correction process for errors induced by a weak continuous measurement. In particular, when the error model is restricted to one, perfectly measured, error channel per physical qubit, quantum feedback can act to perfectly protect a stabilizer codespace. Using the stabilizer formalism we derive an explicit scheme, involving feedback and an additional constant Hamiltonian, to protect an (n-1)-qubit logical state encoded in n physical qubits. This works for both Poisson (jump) and white-noise (diffusion) measurement processes. Universal quantum computation is also possible in this scheme. As an example, we show that detected-spontaneous emission error correction with a driving Hamiltonian can greatly reduce the amount of redundancy required to protect a state from that which has been previously postulated [e.g., Alber , Phys. Rev. Lett. 86, 4402 (2001)].

Background risk in generalized expected utility theory

In this paper, it is shown that, for a wide range of risk-averse generalized expected utility preferences, independent risks are complementary, contrary to the results for expected utility preferences satisfying conditions such as proper and standard risk aversion.

Theoretical and numerical analyses of convective instability in porous media with temperature-dependent viscosity

Exact analytical solutions of the critical Rayleigh numbers have been obtained for a hydrothermal system consisting of a horizontal porous layer with temperature-dependent viscosity. The boundary conditions considered are constant temperature and zero vertical Darcy velocity at both the top and bottom of the layer. Not only can the derived analytical solutions be readily used to examine the effect of the temperature-dependent viscosity on the temperature-gradient driven convective flow, but also they can be used to validate the numerical methods such as the finite-element method and finite-difference method for dealing with the same kind of problem. The related analytical and numerical results demonstrated that the temperature-dependent viscosity destabilizes the temperature-gradient driven convective flow and therefore, may affect the ore body formation and mineralization in the upper crust of the Earth. Copyright (C) 2003 John Wiley Sons, Ltd.

Field assessment of thermal after-ripening time for dormancy release prediction in Lolium rigidum seeds

Dormancy release was studied in four populations of annual ryegrass (Lolium rigidum) seeds to determine whether loss of dormancy in the field can be predicted from temperature alone or whether seed water content (WC) must also be considered. Freshly matured seeds were after-ripened at the northern and southern extremes of the Western Australian cereal cropping region and at constant 37degreesC. Seed WC was allowed to fluctuate with prevailing humidity, but full hydration was avoided by excluding rainfall. Dormancy was measured regularly during after-ripening by germinating seeds with 12-hourly light or in darkness. Germination was lower in darkness than in light/dark and dormancy release was slower when germination was tested in darkness. Seeds were consistently drier, and dormancy release was slower, during after-ripening at 37degreesC than under field conditions. However, within each population, the rate of dormancy release in the field (north and south) in terms of thermal time was unaffected by after-ripening site. While low seed WC slowed dormancy release in seeds held at 37degreesC, dormancy release in seeds after-ripened under Western Australian field conditions was adequately described by thermal after-ripening time, without the need to account for changes in WC elicited by fluctuating environmental humidity.

Infiltration from surface and buried point sources: The average wetting water content

The assumption in analytical solutions for flow from surface and buried point sources of an average water content, (θ) over bar, behind the wetting front is examined. Some recent work has shown that this assumption fitted some field data well. Here we calculated (θ) over bar using a steady state solution based on the work by Raats [1971] and an exponential dependence of the diffusivity upon the water content. This is compared with a constant value of (θ) over bar calculated from an assumption of a hydraulic conductivity at the wetting front of 1 mm day(-1) and the water content at saturation. This comparison was made for a wide range of soils. The constant (θ) over bar generally underestimated (θ) over bar at small wetted radii and overestimated (θ) over bar at large radii. The crossover point between under and overestimation changed with both soil properties and flow rate. The largest variance occurred for coarser texture soils at low-flow rates. At high-flow rates in finer-textured soils the use of a constant (θ) over bar results in underestimation of the time for the wetting front to reach a particular radius. The value of (θ) over bar is related to the time at which the wetting front reaches a given radius. In coarse-textured soils the use of a constant value of (θ) over bar can result in an error of the time when the wetting front reaches a particular radius, as large as 80% at low-flow rates and large radii.

Spatial aspects of trade liberalization in Colombia: A general equilibrium approach

This paper offers some preliminary steps in the marriage of some of the theoretical foundations of new economic geography with spatial computable general equilibrium models. Modelling the spatial economy of Colombia using the traditional assumptions of computable general equilibrium (CGE) models makes little sense when one territorial unit, Bogota, accounts for over one quarter of GDP and where transportation costs are high and accessibility low compared to European or North American standards. Hence, handling market imperfections becomes imperative as does the need to address internal spatial issues from the perspective of Colombia`s increasing involvement with external markets. The paper builds on the Centro de Estudios de Economia Regional (CEER) model, a spatial CGE model of the Colombian economy; non-constant returns and non-iceberg transportation costs are introduced and some simulation exercises carried out. The results confirm the asymmetric impacts that trade liberalization has on a spatial economy in which one region, Bogota, is able to more fully exploit scale economies vis--vis the rest of Colombia. The analysis also reveals the importance of different hypotheses on factor mobility and the role of price effects to better understand the consequences of trade opening in a developing economy.

Optimal reserve management and sovereign debt

Most models currently used to determine optimal foreign reserve holdings take the level of international debt as given. However, given the sovereign`s willingness-to-pay incentive problems, reserve accumulation may reduce sustainable debt levels. In addition, assuming constant debt levels does not allow addressing one of the puzzles behind using reserves as a means to avoid the negative effects of crisis: why do not sovereign countries reduce their sovereign debt instead? To study the joint decision of holding sovereign debt and reserves, we construct a stochastic dynamic equilibrium model calibrated to a sample of emerging markets. We obtain that the reserve accumulation does not play a quantitatively important role in this model. In fact, we find the optimal policy is not to hold reserves at all. This finding is robust to considering interest rate shocks, sudden stops, contingent reserves and reserve dependent output costs. (c) 2008 Elsevier B.V. All rights reserved.

When the going gets rough: effect of maternal size manipulation on larval quality

Variation in larval size has been shown to be an important factor for the post-metamorphic performance of marine invertebrates but, despite its importance, few sources of this variation have been identified. For a range of taxa, offspring size is positively correlated with maternal size but the reasons for this correlation remain unclear. We halved the size of colonies in the bryozoan Bugula neritina 1 wk prior to reproduction (but during embryogenesis) to determine if larval size is a fixed or plastic trait. We manipulated colonies in such a way that the ratio of feeding zooids to reproductive zooids was constant between treatment and control colonies. We found that manipulating colony size strongly affects larval size; halved colonies produced larvae that were similar to13% smaller than those produced by intact colonies. We entered these data into a simple model based on previous work to estimate the likely post-metamorphic consequences of this reduction in larval size. The model predicted that larvae that came from manipulated colonies would suffer similar to300% higher post-metamorphic mortality and similar to50% lower fecundity as adults. Colonies that are faced with a stress appear to be trading off current offspring fitness to maximize their own long-term fitness and this may explain previous observations of compensatory growth in colonial organisms. This study demonstrates that larval size is a surprisingly dynamic trait and strong links exist between the maternal phenotype and the fitness of the offspring. The performance of settling larvae may be determined not only by their larval experience but also by the experience of their mothers.

Slant or occlusion: global factors resolve stereoscopic ambiguity in sets of horizontal lines

Perceived slant was measured for horizontal lines aligned on one side and of varying lengths whose length disparity was either a constant linear amount for all lines (consistent with uniocular occlusion) or proportional to line length (consistent with global slant). Although the disparity of any line was ambiguous with respect to these two possibilities, slant of individual lines did not occur in the former case, but a subjective contour in depth was reported along the alignment. For proportional disparity of the set, global slant was seen. Adding a constant length to each line on the invalid eye for occlusion resulted in multiple slants. Smooth uniocular variations in alignment shape elicited subjective contours slanting or curving in depth. Global context can disambiguate the depth status of individual disparate lines. (C) 2004 Elsevier Ltd. All rights reserved.