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.

Diffusion- and perfusion-weighted MRI response to thrombolysis in stroke

Diffusion- and perfusion-weighted magnetic resonance imaging provides important pathophysiological information in acute bra-in ischemia. We performed a prospective study in 19 sub-6-hour stroke patients using serial diffusion- and perfusion-weighted imaging before intravenous thrombolysis, with repeat studies, both subacutely and at outcome. For comparison of ischemic lesion evolution and clinical outcome, we used a historical control group of 21 sub-6-hour ischemic stroke patients studied serially with diffusion- and perfusion-weighted imaging. The two groups were well matched for the baseline National Institutes of Health Stroke Scale and magnetic resonance parameters. Perfusion-weighted imaging-diffusion-weighted imaging mismatch was present in 16 of 19 patients treated with tissue plasminogen activator, and 16 of 21 controls. Perfusion-weighted imaging-diffusion-weighted imaging mismatch patients treated with tissue plaminogen activator had higher recanalization rates and enhanced reperfusion at day 3 (81% vs 47% in controls), and a greater proportion of severely hypoperfused acute mismatch tissue not progressing to infarction (82% vs -25% in controls). Despite similar baseline diffusion-weighted imaging lesions, infarct expansion was less in the recombinant tissue plaminogen activator group (14cm(3) vs 56cm(3) in controls). The positive effect of thrombolysis on lesion growth in mismatch patients translated into a greater improvement in baseline to outcome National Institutes of Health Stroke Scale in the group treated with recombinant tissue plaminogen activator, and a significantly larger proportion of patients treated with recombinant tissue plaminogen activator having a clinically meaningful improvement in National Institutes of Health Stroke Scale of;2:7 points. The natural evolution of acute perfusion-weighted imaging-diffusion-weighted imaging mismatch tissue may be altered by thrombolysis, with improved stroke outcome. This has implications for the use of diffusion- and perfusion-weighted imaging in selecting and monitoring patients for thrombolytic therapy.

Myb-binding protein 1a augments AhR-dependent gene expression

We have studied the mechanism by which an acidic domain (amino acids 515-583) of the aromatic hydrocarbon receptor (AhR) transactivates a target gene. Studies with glutathione S-transferase fusion proteins demonstrate that the wild-type acidic domain associates in vitro with Myb-binding protein la, whereas a mutant domain (F542A, 1569A) does not. AhR-defective cells reconstituted with an AhR containing the wild-type acidic domain exhibit normal AhR function; however, cells reconstituted with an AhR containing the mutant acidic domain do not function normally. Transient transfection of Myb-binding protein la into mouse hepatoma cells is associated with augmentation of AhR-dependent gene expression. Such augmentation does not occur when Myb-binding protein la is transfected into AhR-defective cells that have been reconstituted with an AhR that lacks the acidic domain. We infer that 1) Myb-binding protein la associates with AhR, thereby enhancing transactivation, and 2) the presence of AhR's acidic domain is both necessary and sufficient for Myb-binding protein la to increase AhR-dependent gene expression.

Spatial data mining for enhanced soil map modelling

The principle of using induction rules based on spatial environmental data to model a soil map has previously been demonstrated Whilst the general pattern of classes of large spatial extent and those with close association with geology were delineated small classes and the detailed spatial pattern of the map were less well rendered Here we examine several strategies to improve the quality of the soil map models generated by rule induction Terrain attributes that are better suited to landscape description at a resolution of 250 m are introduced as predictors of soil type A map sampling strategy is developed Classification error is reduced by using boosting rather than cross validation to improve the model Further the benefit of incorporating the local spatial context for each environmental variable into the rule induction is examined The best model was achieved by sampling in proportion to the spatial extent of the mapped classes boosting the decision trees and using spatial contextual information extracted from the environmental variables.

A strategy to fill gaps in soil survey over large spatial extents: an example from the Murray-Darling basin of Australia

We re-mapped the soils of the Murray-Darling Basin (MDB) in 1995-1998 with a minimum of new fieldwork, making the most out of existing data. We collated existing digital soil maps and used inductive spatial modelling to predict soil types from those maps combined with environmental predictor variables. Lithology, Landsat Multi Spectral Scanner (Landsat MSS), the 9-s digital elevation model (DEM) of Australia and derived terrain attributes, all gridded to 250-m pixels, were the predictor variables. Because the basin-wide datasets were very large data mining software was used for modelling. Rule induction by data mining was also used to define the spatial domain of extrapolation for the extension of soil-landscape models from existing soil maps. Procedures to estimate the uncertainty associated with the predictions and quality of information for the new soil-landforms map of the MDB are described. (C) 2002 Elsevier Science B.V. All rights reserved.

Local-global processing in early-onset schizophrenia: Evidence for an impairment in shifting the spatial scale of attention

In this study we report the results of two experiments on visual attention conducted with patients with early-onset schizophrenia. These experiments investigated the effect of irrelevant spatial-scale information upon the processing of relevant spatial-scale information, and the ability to shift the spatial scale of attention, across consecutive trials, between different levels of the hierarchical stimulus. Twelve patients with early-onset schizophrenia and matched controls performed local-global tasks under: (1) directed attention conditions with a consistency manipulation and (2) divided-attention conditions. In the directed-attention paradigm, the early-onset patients exhibited the normal patterns of global advantage and interference, and were not unduly affected by the consistency manipulation. Under divided-attention conditions, however, the early-onset patients exhibited a local-processing deficit. The source of this local processing deficit lay in the prolonged reaction time to local targets, when these had been preceded by a global target, but not when preceded by a local target. These findings suggest an impaired ability to shift the spatial scale of attention from a global to a local spatial scale in early-onset schizophrenia. (C) 2003 Elsevier Science (USA). All rights reserved.

Spatial and temporal variation in distribution of mangroves in Moreton Bay, subtropical Australia: a comparison of pattern metrics and change detection analyses based on aerial photographs

An assessment of the changes in the distribution and extent of mangroves within Moreton Bay, southeast Queensland, Australia, was carried out. Two assessment methods were evaluated: spatial and temporal pattern metrics analysis, and change detection analysis. Currently, about 15,000 ha of mangroves are present in Moreton Bay. These mangroves are important ecosystems, but are subject to disturbance from a number of sources. Over the past 25 years, there has been a loss of more than 3800 ha, as a result of natural losses and mangrove clearing (e.g. for urban and industrial development, agriculture and aquaculture). However, areas of new mangroves have become established over the same time period, offsetting these losses to create a net loss of about 200 ha. These new mangroves have mainly appeared in the southern bay region and the bay islands, particularly on the landward edge of existing mangroves. In addition, spatial patterns and species composition of mangrove patches have changed. The pattern metrics analysis provided an overview of mangrove distribution and change in the form of single metric values, while the change detection analysis gave a more detailed and spatially explicit description of change. An analysis of the effects of spatial scales on the pattern metrics indicated that they were relatively insensitive to scale at spatial resolutions less than 50 m, but that most metrics became sensitive at coarser resolutions, a finding which has implications for mapping of mangroves based on remotely sensed data. (C) 2003 Elsevier Science B.V. All rights reserved.

Myb-binding Protein 1a is a Nucleocytoplasmic Shuttling Protein that Utilizes CRM1-dependent and Independent Nuclear Export Pathways

Myb-binding protein 1a (Mybbp1a) is a novel nuclear protein localized predominantly, but not exclusively, in nucleoli. Although initially isolated as a c-Myb interacting protein, Mybbp1a is expressed ubiquitously, associates with a number of different transcription factors, and may play a role in both RNA polymerase I- and II-mediated transcriptional regulation. However, its precise function remains unclear. In this study we show that Mybbp1a is a nucleocytoplasmic shuttling protein and investigate the mechanisms responsible for both nuclear import and export. The carboxyl terminus of Mybbp1a, which contains seven short basic amino acid repeat sequences, is responsible for both nuclear and nucleolar localization, and this activity can be transferred to a heterologous protein. Deletion mapping demonstrated that these repeat sequences appear to act incrementally, with successive deletions resulting in a corresponding increase in the proportion of protein localized in the cytoplasm. Glutathione S-transferase pulldown experiments showed that the nuclear receptor importin-alpha/beta mediates Mybbp1a nuclear import. Interspecies heterokaryons were used to demonstrate that Mybbp1a was capable of shuttling between the nucleus and the cytoplasm. Deletion analysis and in vivo export studies using a heterologous assay system identified several nuclear export sequences which facilitate Mybbp1a nuclear export of Mybbp1a by CRM1-dependent and -independent pathways. (C) 2003 Elsevier Science (USA). All rights reserved.

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.

Multiresolution spatial databases: Making web-based spatial applications faster

Spatial data has now been used extensively in the Web environment, providing online customized maps and supporting map-based applications. The full potential of Web-based spatial applications, however, has yet to be achieved due to performance issues related to the large sizes and high complexity of spatial data. In this paper, we introduce a multiresolution approach to spatial data management and query processing such that the database server can choose spatial data at the right resolution level for different Web applications. One highly desirable property of the proposed approach is that the server-side processing cost and network traffic can be reduced when the level of resolution required by applications are low. Another advantage is that our approach pushes complex multiresolution structures and algorithms into the spatial database engine. That is, the developer of spatial Web applications needs not to be concerned with such complexity. This paper explains the basic idea, technical feasibility and applications of multiresolution spatial databases.

Proteasomal degradation of N-acetyltransferase 1 is prevented by acetylation of the active site cysteine - A mechanism for the slow acetylator phenotype and substrate-dependent down-regulation

Many drugs and chemicals found in the environment are either detoxified by N-acetyltransferase 1 (NAT1, EC 2.3.1.5) and eliminated from the body or bioactivated to metabolites that have the potential to cause toxicity and/or cancer. NAT1 activity in the body is regulated by genetic polymorphisms as well as environmental factors such as substrate-dependent down-regulation and oxidative stress. Here we report the molecular mechanism for the low protein expression from mutant NAT1 alleles that gives rise to the slow acetylator phenotype and show that a similar process accounts for enzyme down-regulation by NAT1 substrates. NAT1 allozymes NAT1 14, NAT1 15, NAT1 17, and NAT1 22 are devoid of enzyme activity and have short intracellular half-lives (similar to4 h) compared with wild-type NAT1 4 and the active allozyme NAT1 24. The inactive allozymes are unable to be acetylated by cofactor, resulting in ubiquitination and rapid degradation by the 26 S proteasome. This was confirmed by site-directed mutagenesis of the active site cysteine 68. The NAT1 substrate p-aminobenzoic acid induced ubiquitination of the usually stable NAT1 4, leading to its rapid degradation. From this study, we conclude that NAT1 exists in the cell in either a stable acetylated state or an unstable non-acetylated state and that mutations in the NAT1 gene that prevent protein acetylation produce a slow acetylator phenotype.