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.

Physiological role of calcium-activated potassium currents in the rat lateral amygdala

Principal neurons in the lateral nucleus of the amygdala (LA) exhibit a continuum of firing properties in response to prolonged current injections ranging from those that accommodate fully to those that fire repetitively. In most cells, trains of action potentials are followed by a slow after hyperpolarization (AHP) lasting several seconds. Reducing calcium influx either by lowering concentrations of extracellular calcium or by applying nickel abolished the AHP, confirming it is mediated by calcium influx. Blockade of large conductance calcium-activated potassium channel (BK) channels with paxilline, iberiotoxin, or TEA revealed that BK channels are involved in action potential repolarization but only make a small contribution to the fast AHP that follows action potentials. The fast AHP was, however, markedly reduced by low concentrations of 4-aminopyridine and alpha-dendrotoxin, indicating the involvement of voltage-gated potassium channels in the fast AHP. The medium AHP was blocked by apamin and UCL1848, indicating it was mediated by small conductance calcium-activated potassium channel (SK) channels. Blockade of these channels had no effect on instantaneous firing. However, enhancement of the SK-mediated current by 1-ethyl-2-benzimidazolinone or paxilline increased the early interspike interval, showing that under physiological conditions activation of SK channels is insufficient to control firing frequency. The slow AHP, mediated by non-SK BK channels, was apamin-insensitive but was modulated by carbachol and noradrenaline. Tetanic stimulation of cholinergic afferents to the LA depressed the slow AHP and led to an increase in firing. These results show that BK, SK, and non-BK SK-mediated calcium-activated potassium currents are present in principal LA neurons and play distinct physiological roles.

The role of the church in developing the law: response to commentators

Three of the four commentators endorse our concerns about intervention by the Roman Catholic church as an omicus curiae in civil litigation, with few reservations. One commentary rejects our arguments in We deal first with the three commentaries that support our arguments; secondly, with the reservations and qualifications in those commentaries, and thirdly, with the commentary that totally rejects our arguments.

Mantle convection modeling with viscoelastic/brittle lithosphere: Numerical methodology and plate tectonic modeling

The earth's tectonic plates are strong, viscoelastic shells which make up the outermost part of a thermally convecting, predominantly viscous layer. Brittle failure of the lithosphere occurs when stresses are high. In order to build a realistic simulation of the planet's evolution, the complete viscoelastic/brittle convection system needs to be considered. A particle-in-cell finite element method is demonstrated which can simulate very large deformation viscoelasticity with a strain-dependent yield stress. This is applied to a plate-deformation problem. Numerical accuracy is demonstrated relative to analytic benchmarks, and the characteristics of the method are discussed.

Epidemiological modelling (including economic modelling) and its role in preventive drug therapy

In contrast to curative therapies, preventive therapies are administered to largely healthy individuals over long periods. The risk-benefit and cost-benefit ratios are more likely to be unfavourable, making treatment decisions difficult. Drug trials provide insufficient information for treatment decisions, as they are conducted on highly selected populations over short durations, estimate only relative benefits of treatment and offer little information on risks and costs. Epidemiological modelling is a method of combining evidence from observational epidemiology and clinical trials to assist in clinical and health policy decision-making. It can estimate absolute benefits, risks and costs of long-term preventive strategies, and thus allow their precise targeting to individuals for whom they are safest and most cost-effective. Epidemiological modelling also allows explicit information about risks and benefits of therapy to be presented to patients, facilitating informed decision-making.

Is there a role for axillary dissection for patients with operable breast cancer in this era of conservatism?

Background: The trend in breast cancer surgery is toward more conservative operative procedures. The new staging technique of sentinel node biopsy facilitates the identification of pathological node-negative patients in whom axillary dissection may be avoided. However, patients with a positive sentinel node biopsy would require a thorough examination of their nodal status. An axillary dissection provides good local control, and accurate staging and prognostic information to inform decisions about adjuvant therapy. In addition, the survival benefit of axillary treatment is still debated. The objectives of the present study were to examine the pattern of lymph node metastases in the axilla, and evaluate the merits of a level III axillary dissection. Methods : Between June 1997 and May 2000, 308 patients underwent a total of 320 level III dissections as part of their treatment for operable invasive breast cancer. The three axillary levels were marked intraoperatively, and the contents in each level were submitted and examined separately. The patterns of axillary lymph node (ALN) metastases were examined, and factors associated with 4 positive nodes, and level III ALN metastases were evaluated by univariate and multivariate analyses. Results: An average of 25 lymph nodes were examined per case (range: 8-54), and using strict anatomical criteria, the mean numbers of ALN found in levels I, II and III were 18 (range: 2-43), 4 (range: 0 19), and 3 ( range: 0-11), respectively. Axillary lymph node involvement was found in 45% of the cases (143/320). Of the 143 cases, 78% (n = 111) had involvement of level I nodes only, and 21% (n = 30) had positive ALN in levels II and, or, III, in addition to level I. Involvement of lymph nodes in level II or III without a level I metastasis was found in two cases only (0.6%). By including level II, in addition to level I, in the dissection, four cases (1%) were converted from one to three positive nodes to 4 positive nodes (P = 0.64). By the inclusion of level III to a level I and II dissection, three cases (1%) were converted from one to three positive nodes to 4 positive nodes (P = 0.74). Involvement of lymph nodes in level III was found in 22 cases (7%), and 51 cases (16%) had 4 positive nodes. Palpability of ALN, pathological tumour size, and lymphovascular invasion (LVI), were significantly associated with level III involvement and 4 positive nodes by univariate and multivariate analyses. The frequencies of level III involvement and 4 positive nodes in patients with palpable ALN were 22% and 42%, respectively. The corresponding frequencies in patients with a clinically negative axilla, and a primary tumour which was >20 mm and LVI positive, were over 14% and 31%, respectively. Conclusion: Level III axillary dissection is appropriate for patients with palpable ALN, and in those with a tumour which is >20 mm and LVI positive, principally to reduce the risk of axillary recurrence. Staging accuracy is achieved with a level II dissection, or even a level I dissection alone based on strict anatomical criteria. Sentinel node biopsy is a promising technique in identifying pathological node-positive patients in whom an axillary clearance provides optimal local control and staging information.

Human response to environmental noise: The role of perceived control

Negative impacts of noise exposure on health and performance may result in part from learned helplessness, the syndrome of deficits typically produced by exposure to uncontrollable events. People may perceive environmental noise to be uncontrollable, and several effects of noise exposure appear to parallel learned helplessness deficits. In the present socioacoustic survey (N = 1,015), perceived control over aircraft noise correlated negatively with some effects of noise (though not others). Furthermore, these effects were better predicted by perceived control than by noise level. These observational data support the claim that learned helplessness contributes to the effects of noise exposure.

The role of dogs in transmission of gastrointestinal parasites in a remote tea-growing community in northeastern India

The prevalence and risk factors associated with canine gastrointestinal parasitic zoonoses and the role of dogs in the mechanical transmission of human Ascaris infection was examined in three tea estates in Assam, India. Nearly all (99%) dogs harbored one or more zoonotic species of gastrointestinal parasites, with hookworm infection being most common (94%). Parasitic stages presumed to be host-specific for humans such as Ascaris spp. (31%), Trichuris trichiura (25%), and Isospora belli (2%) were also recovered from dog feces. A polymerase chain reaction-linked restriction fragment length polymorphism technique was used to differentiate the species of Ascaris eggs in dog feces. The results of this study demonstrate the role of the dog as a significant disseminator and environmental contaminator of Ascaris lumbricoides in communities where promiscuous defecation by humans occurs.

To fix or not to fix: The role of 2-phenoxyethanol in rabbit, Oryctolagus cuniculus, chin gland secretion

The European rabbit (Oryctolagus cuniculus) uses the secretion of the chin gland to maintain dominance hierarchies in the wild. Recent work has investigated changes in the secretion when social status is manipulated in the rabbit. When a rabbit becomes dominant, a new compound appears in his secretion, 2-phenoxyethanol. This compound is used as a fixative in the perfume industry. This study investigates whether the compound performs a similar function in the secretion of the rabbit. 2-Phenoxyethanol is not detected olfactorially by rabbits, and slows the release rate of some of the compounds that occur naturally in rabbit chin gland secretion. We suggest that when a rabbit becomes dominant, he adds a fixative to his secretion so that his scent will persist in the environment and not dissipate. He will thus come to dominate the olfactory environment, in much the same way as he does the physical environment.