57 resultados para mathematical content
Resumo:
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.
Resumo:
Perceived depth was measured for three-types of stereograms with the colour/texture of half-occluded (monocular) regions either similar to or dissimilar to that of binocular regions or background. In a two-panel random dot stereogram the monocular region was filled with texture either similar or different to the far panel or left blank. In unpaired background stereograms the monocular region either matched the background or was different in colour or texture and in phantom stereograms the monocular region matched the partially occluded object or was a different colour or texture. In all three cases depth was considerably impaired when the monocular texture did not match either the background or the more distant surface. The content and context of monocular regions as well as their position are important in determining their role as occlusion cues and thus in three-dimensional layout. We compare coincidence and accidental view accounts of these effects. (C) 2002 Elsevier Science Ltd. All rights reserved.
Resumo:
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.
Resumo:
The aim of this work was to exemplify the specific contribution of both two- and three-dimensional (31)) X-ray computed tomography to characterise earthworm burrow systems. To achieve this purpose we used 3D mathematical morphology operators to characterise burrow systems resulting from the activity of an anecic (Aporrectodea noctunia), and an endogeic species (Allolobophora chlorotica), when both species were introduced either separately or together into artificial soil cores. Images of these soil cores were obtained using a medical X-ray tomography scanner. Three-dimensional reconstructions of burrow systems were obtained using a specifically developed segmentation algorithm. To study the differences between burrow systems, a set of classical tools of mathematical morphology (granulometries) were used. So-called granulometries based on different structuring elements clearly separated the different burrow systems. They enabled us to show that burrows made by the anecic species were fatter, longer, more vertical, more continuous but less sinuous than burrows of the endogeic species. The granulometry transform of the soil matrix showed that burrows made by A. nocturna were more evenly distributed than those of A. chlorotica. Although a good discrimination was possible when only one species was introduced into the soil cores, it was not possible to separate burrows of the two species from each other in cases where species were introduced into the same soil core. This limitation, partly due to the insufficient spatial resolution of the medical scanner, precluded the use of the morphological operators to study putative interactions between the two species.
Resumo:
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.
Resumo:
Al-3-11% Si alloys have been high-pressure die-cast and characterized microstructurally. Alstruc was used to calculate the solidification characteristics and fraction of eutectic. Defect bands were observed at all Si contents, although their constitution, position and distinctiveness were a function of Si content. The defect bands contain a higher fraction Al-Si eutectic than the surroundings in all alloys, and porosity was additionally found in the band in AlSi3. With decreasing Si content, the defect bands formed closer to the casting surface, became more prevalent and also the width of the bands decreased. These differences are discussed by considering the effect of Si content on the distribution of solid in the mushy wall layers and on the feeding potentials of the alloys. The observations are consistent with the mechanism proposed by Gourlay et al. in which bands form due to deformation within the solidifying mushy wall layers. (c) 2005 Elsevier B.V. All rights reserved.
Resumo:
Colonius suggests that, in using standard set theory as the language in which to express our computational-level theory of human memory, we would need to violate the axiom of foundation in order to express meaningful memory bindings in which a context is identical to an item in the list. We circumvent Colonius's objection by allowing that a list item may serve as a label for a context without being identical to that context. This debate serves to highlight the value of specifying memory operations in set theoretic notation, as it would have been difficult if not impossible to formulate such an objection at the algorithmic level.
Resumo:
The fatty acid composition of 11 species of fish caught off the northeast coast of Australia was determined. No fatty acid profiles have been previously published for fish from this area nor for nine of these species. Although the percentage of polyunsaturated fatty acid (PU FA) was the same as the calculated average for Australian fish (42.3%), the percentage of n-3 fatty acids was lower (24.4 +/- 5.4% vs. 30.7 +/- 10.1%) and the n-6 fatty acids higher (16.5 +/- 4.5% vs. 11.2 +/- 5.9%), P < 0.001 in each case. The major n-3 PUFA were docosahexaenoic (15.6 +/- 6.3%) and eicosapentaenoic acid (4.3 +/- 1.1%) while the major n-6 PUFA were arachidonic (8.3 +/- 3.2%) and n-6 docosatetraenoic acid (3.1 +/- 1.3%). The second-most abundant class of fatty acid was the saturates (31.6 +/- 3.5%) while the monounsaturates accounted for 17.4 +/- 4.3% of the total fatty acids. The monounsaturate with the highest concentration was octadecenoic acid (11.8 +/- 2.6%). There was a positive correlation between the total lipid content and saturated and monounsaturated fatty acids (r = 0.675 and 0.567, respectively) and a negative correlation between the total lipid content and PUFA(r = 0.774).
Resumo:
Experimental data for E. coli debris size reduction during high-pressure homogenisation at 55 MPa are presented. A mathematical model based on grinding theory is developed to describe the data. The model is based on first-order breakage and compensation conditions. It does not require any assumption of a specified distribution for debris size and can be used given information on the initial size distribution of whole cells and the disruption efficiency during homogenisation. The number of homogeniser passes is incorporated into the model and used to describe the size reduction of non-induced stationary and induced E. coil cells during homogenisation. Regressing the results to the model equations gave an excellent fit to experimental data ( > 98.7% of variance explained for both fermentations), confirming the model's potential for predicting size reduction during high-pressure homogenisation. This study provides a means to optimise both homogenisation and disc-stack centrifugation conditions for recombinant product recovery. (C) 1997 Elsevier Science Ltd.
Resumo:
Rms1 is one of the series of five ramosus loci in pea (Pisum sativum L.) in which recessive mutant alleles confer increased branching at basal and aerial vegetative nodes. Shoots of the nonallelic rms1 and rms2 mutants are phenotypically similar in most respects. However, we found an up to 40-fold difference in root-sap zeatin riboside ([9R]Z) concentration between rms1 and rms2 plants. Compared with wild-type (WT) plants, the concentration of [9R]Z in rms1 root sap was very low and the concentration in rms2 root sap was slightly elevated. To our knowledge, the rms1 mutant is therefore the second ramosus mutant (rms4 being the first) to be characterized with low root-sap [9R]Z content. Like rms2, the apical bud and upper nodes of rms1 plants contain elevated indole-3-acetic acid levels compared with WT shoots. Therefore, the rms1 mutant demonstrates that high shoot auxin levels and low root-sap cytokinin levels are not necessarily correlated with increased apical dominance in pea. A graft-transmissible basis of action has been demonstrated for both mutants from reciprocal grafts between mutant and WT plants. Branching was also largely inhibited in rms1 shoots when grafted to rms2 rootstocks, but was not inhibited in rms2 shoots grafted to rms1 rootstocks. These grafting results are discussed, along with the conclusion that hormone-like signals other than auxin and cytokinin are also involved.