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.

Spontaneous and UV radiation-induced multiple metastatic melanomas in Cdk4(R24C/R24C)/TPras mice

Human melanoma susceptibility is often characterized by germ-line inactivating CDKN2A (INK4A/ARF) mutations, or mutations that activate CDK4 by preventing its binding to and inhibition by INK4A. We have previously shown that a single neonatal UV radiation (UVR) dose delivered to mice that carry melanocyte-specific activation of Hras (TPras) increases melanoma penetrance from 0% to 57%. Here, we report that activated Cdk4 cooperates with activated Hras to enhance susceptibility to melanoma in mice. Whereas UVR treatment failed to induce melanomas in Cdk4(R24C/R24C) mice, it greatly increased the penetrance and decreased the age of onset of melanoma development in Cdk4(R24C/R24C)/TPras animals compared with TPras alone. This increased penetrance was dependent on the threshold of Cdk4 activation as Cdk4(R24C/+)/TPras animals did not show an increase in UVR-induced melanoma penetrance compared with TPras alone. In addition, Cdk4(R24C/R24C)/TPras mice invariably developed multiple lesions, which occurred rarely in TPras mice. These results indicate that germ-line defects abrogating the pRb pathway may enhance UVR-induced melanoma. TPras and Cdk4(R24C/R24C)/TPras tumors were comparable histopathologically but the latter were larger and more aggressive and cultured cells derived from such melanomas were also larger and had higher levels of nuclear atypia. Moreover, the melanomas in Cdk4(R24C/R24C)/TPras mice, but not in TPras mice, readily metastasized to regional lymph nodes. Thus, it seems that in the mouse, Hras activation initiates UVR-induced melanoma development whereas the cell cycle defect introduced by mutant Cdk4 contributes to tumor progression, producing more aggressive, metastatic tumors.

A simulation model for analysing patient activity in dermatology

We developed a general model to assess patient activity within the primary and secondary health-care sectors following a dermatology outpatient consultation. Based on observed variables from the UK teledermatology trial, the model showed that up to 11 doctor-patient interactions occurred before a patient was ultimately discharged from care. In a cohort of 1000 patients, the average number of health-care visits was 2.4 (range 1-11). Simulation analysis suggested that the most important parameter affecting the total number of doctor-patient Interactions is patient discharge from care following the initial consultation. This implies that resources should be concentrated in this area. The introduction of teledermatology (either realtime or store and forward) changes the values of the model parameters. The model provides a quantitative tool for planning the future provision of dermatology health-care.

A novel mutation in the L12 domain of keratin 5 in the Kobner variant of epidermolysis bullosa simplex

We have identified a novel mutation within the linker L12 region of keratin 5 (K5) in a family with the Kobner variant of epidermolysis bullosa simplex. The pattern of inheritance of the disorder in this family is consistent with an autosomal dominant mode of transmission. Affected individuals develop extensive and generalized blistering at birth or early infancy but in later years clinical manifestations are largely confined to palmo-plantar surfaces. Direct sequencing of polymerase chain reaction products revealed a T to C transition within codon 323 of K5 in affected individuals, resulting in a valine to alanine substitution of the seventh residue within the L12 linker domain. This mutation was not observed in unaffected family members or in 100 K5 alleles of unrelated individuals with normal skin. The other critical regions of K5 and K14 were unremarkable in this family except for common polymorphisms that have been previously described. The valine at position 7 of the L12 domain is absolutely conserved in all type II keratins, and in other intermediate filament subunits as well, which suggests that this residue makes an important contribution to filament integrity. Secondary structure analysis revealed that alanine at this position markedly reduces both the hydrophobicity and the beta-sheet nature of the L12 domain. This is the first report of a mutation at this position in an intermediate filament subunit and reinforces the importance of this region to filament biology.

Simplifying the molecular mechanisms of human papillomavirus

The human papillomaviruses (HPVs) are associated with several human epithelial diseases. These diseases are confined to cutaneous and mucosal epithelia and comprise papillomas (warts) and benign or malignant neoplasms. Globally, infection by HPVs presents a considerable health problem given that at any one time approximately 10% of the population may have warts of one form or another. Of more serious concern is the prevalence of HPV-associated cervical carcinoma. It is estimated that 500,000 new cases of cervical neoplasia are diagnosed per year (primarily squamous carcinomas). Thus, HPV-associated cancer represents one of the most common cancers afflicting women and is one of the three most common causes of cancer death among women globally.(15) Although some genotypes of human papillomaviruses are clearly associated with the development of cancer (in particular, HPVs 16 and 18) these viruses share significant structural and functional similarity to the nononcogenic genotypes, and one of the puzzles of HPV biology is why essentially similar viruses vary so widely in their oncogenic potential.

Can tissue drug concentrations be monitored by microdialysis during or after isolated limb perfusion for melanoma treatment?

Isolated limb perfusion (ILP) with melphalan is used to treat recurrent melanoma. This study aimed to develop a microdialysis technique for melphalan tissue concentration measurement during ILP. The effects of melphalan concentration (50-600 mu g/ml), microdialysis flow rate (0.55-17.5 mu l/min), probe length (5-50 mm) and temperature (25-41.5 degrees C) on in vitro recovery were studied. In addition, in vivo recovery was measured in rat hindlimbs perfused with melphalan using 50 mm microdialysis probes implanted subcutaneously and into muscle. Both dialysate and tissue sample melphalan concentrations were determined by high performance liquid chromatography. The in vitro recovery of melphalan was not affected by melphalan concentration or temperature, but increased with probe length and decreased with flow rate. The melphalan concentrations in subcutaneous and muscle dialysates were not significantly different. A linear relationship was found between tissue dialysate concentrations and actual tissue concentrations of melphalan (r(2) = 0.97). Microdialysis is a potential method for tissue drug monitoring which may assist in the efficacious use of cytotoxics in human ILP. (C) 2000 Lippincott Williams & Wilkins.

Analysis of Mouse Keratin 6a Regulatory Sequences in Transgenic Mice Reveals Constitutive, Tissue-Specific Expression by a Keratin 6a Minigene

The analysis of keratin 6 expression is complicated by the presence of multiple isoforms that are expressed constitutively in a number of internal stratified epithelia, in palmoplantar epidermis, and in the companion cell layer of the hair follicle. In addition, keratin 6 expression is inducible in interfollicular epidermis and the outer root sheath of the follicle, in response to wounding stimuli, phorbol esters, or retinoic acid. In order to establish the critical regions involved in the regulation of keratin 6a (the dominant isoform in mice), we generated transgenic mice with two different-sized mouse keratin 6a constructs containing either 1.3 kb or 0.12 kb of 5' flanking sequence linked to the lacZ reporter gene. Both constructs also contained the first intron and the 3' flanking sequence of mouse keratin 6a. Ectopic expression of either transgene was not observed. Double-label immunofluorescence analyses demonstrated expression of the reporter gene in keratin 6 expressing tissues, including the hair follicle, tongue, footpad, and nail bed, showing that both transgenes retained keratinocyte-specific expression. Quantitative analysis of beta -galactosidase activity verified that both the 1.3 and 0.12 kb keratin 6a promoter constructs produced similar levels of the reporter. Notably, both constructs were constitutively expressed in the outer root sheath and interfollicular epidermis in the absence of any activating stimulus, suggesting that they lack the regulatory elements that normally silence transcription in these cells. This study has revealed that a keratin 6a minigene contains critical cis elements that mediate tissue-specific expression and that the elements regulating keratin 6 induction lie distal to the 1.3 kb promoter region.

Screening for leprosy in immigrants: A decision analysis model

Almost all leprosy cases reported in industrialized countries occur amongst immigrants or refugees from developing countries where leprosy continues to be an important health issue. Screening for leprosy is an important question for governments in countries with immigration and refugee programmes. A decision analysis framework is used to evaluate leprosy screening. The analysis uses a set of criteria and parameters regarding leprosy screening, and available data to estimate the number of cases which would be detected by a leprosy screening programme of immigrants from countries with different leprosy prevalences, compared with a policy of waiting for immigrants who develop symptomatic clinical diseases to present for health care. In a cohort of 100,000 immigrants from high leprosy prevalence regions (3.6/10,000), screening would detect 32 of the 42 cases which would arise in the destination country over the 14 years after migration; from medium prevalence areas (0.7/10,000) 6.3 of the total 8.1 cases would be detected, and from low prevalence regions (0.2/10,600) 1.8 of 2.3 cases. Using Australian data, the migrant mix would produce 74 leprosy cases from 10 years intake; screening would detect 54, and 19 would be diagnosed subsequently after migration. Screening would only produce significant case-yield amongst immigrants from regions or social groups with high leprosy prevalence. Since the number of immigrants to Australia from countries of higher endemnicity is not large routine leprosy screening would have a small impact on case incidence.