Modelling skin penetration using the Laplace transform technique.

The Laplace transform is a convenient mathematical tool for solving ordinary and partial differential equations. The application of this technique to problems arising in drug penetration through the skin is reviewed in this paper.

Iontophoresis-mediated transdermal permeation of peptide dendrimers across human epidermis.

PURPOSE OF THE STUDY: The overall aim of the present work was to elucidate the effects of iontophoresis on assisting permeation/deposition of peptide dendrimers across/within human skin. PROCEDURES: A series of peptide dendrimers containing arginine and histidine as terminal acids were synthesized and characterized. These dendrimers were subjected to passive and iontophoretic permeation studies across human epidermis. RESULTS: The synthesized peptide dendrimers were found to be stable in epidermal, dermal and skin extracts up to 6 h. Passive diffusion studies revealed that none of the synthesized peptide dendrimers permeated human epidermis up to 6 h, although minute concentrations of low molecular weight dendrimers were detected in receptor medium at the end of 24 h. Application of iontophoresis significantly increased the permeation of all the tested peptide dendrimers across human skin in a molecular weight-dependent manner compared to simple passive diffusion. Electromigration was found to be the dominant mechanism behind the iontophoretic permeation of peptide dendrimers across human skin. CONCLUSIONS: The present study demonstrates that iontophoresis is an effective technique in enhancing the transdermal permeation of peptide dendrimers. MESSAGE OF THE PAPER: This study foresees the possibility of applying peptide dendrimers in iontophoretic delivery of drugs and macromolecules across/within the skin.

Compartmental modeling of skin absorption and desorption kinetics: Donor solvent evaporation, variable diffusion/partition coefficients, and slow equilibration process within stratum corneum.

This work expands the recently developed compartmental model for skin transport to model variable diffusion and/or partition coefficients, and the presence of slow equilibration/slow binding kinetics within stratum corneum. The model was validated by comparing it with the diffusion model which was solved numerically using the finite element method. It was found that the new compartmental model predictions agreed well with that of the diffusion model, providing a sufficient number of compartments was used. The compartmental model was applied to two previously published experimental data sets: water penetration and desorption data and the finite dose dermal penetration of testosterone. Significant improvement of the fitting quality for all these data sets was achieved using the compartmental model.

Using Compartments to Model Drug Delivery from Biodegradable Polymers.

Polymeric drug delivery systems can improve patient compliance, decrease toxicity and prolong therapeutic effects for a wide range of therapeutic treatments, by controlling drug release. Polymer delivery system development can be facilitated by mathematical models. We present here a new compartmental model that will be more familiar to pharmaceutical professionals and equally as effective as common diffusion equation-based models. The compartmental model considers both polymer degradation and drug diffusion to predict drug release. The model is adapted into three different geometries for different polymer delivery scenarios: membranes, fibres and particles. Model parameters are derived in terms of diffusion coefficients. Polymer-drug binding interactions and distributions of fibre/particle diameters are incorporated to the model. The model is validated by comparison to common diffusion equation-based solutions and fitting to experimental data. It is shown how the model for drug release can be incorporated into existing distribution models to predict plasma concentrations of an in vivo administration. A user-friendly Python implementation of the model is available on Github, at https://github.com/spirt-t/compartments_model.

Flexible intramedullary nails for limb lengthening: a comprehensive comparative study of three nails types.

This study aims to investigate the comparative study of calcium phosphate coatings for flexible intramedullary nails (FINs) used to lengthen long tubular bones. The presence of a calcium phosphate coating deposited by micro-arc oxidation (MAO) or a composite coating based on a co-polymer of vinylidene fluoride with tetrafluoroethylene (VDF-TeFE) and hydroxyapatite (HA) on the surface of the FIN significantly enhanced the regeneration of bone in the area of osteotomy during limb lengthening by combined osteosynthesis. The investigation of the physico-chemical properties of the FIN coated with calcium phosphate via MAO demonstrated that the improved bone tissue formation resulted from favourable conditions for adhesion, proliferation and differentiation of multipotent stem cells into osteoblasts on the coating surface. The composite coatings only stimulated the formation of bone tissue in vivo, primarily because of the piezoelectric properties of the VDF-TeFE co-polymer.

Compartmental modeling of skin transport.

The primary objective of this study is to introduce a simple and flexible mathematical approach which models transport processes in skin using compartments. The main feature of the presented approach is that the rate constants for exchange between compartments are derived from physiologically relevant diffusional transport parameters. This allows for better physical interpretation of the rate constants, and limits the number of parameters for the compartmental model. The resulting compartmental solution is in good agreement with previously published solutions for the diffusion model of skin when ten or more compartments are used. It was found that the new compartmental model with three compartments provided a better fit of the previously publish water penetration data than the diffusion model. Two special cases for which it is difficult to implement the diffusion model were considered using our compartmental approach. In both cases the compartmental model predictions agreed well with the diffusion model.

Surface modification of electrospun poly-(l-lactic) acid scaffolds by reactive magnetron sputtering.

In this study, we modified the surface of bioresorbable electrospun poly-(l-lactic) acid (PLLA) scaffolds by reactive magnetron sputtering of a titanium target under a nitrogen atmosphere. We examined the influence of the plasma treatment time on the structure and properties of electrospun PLLA scaffolds using SEM, XRF, FTIR, XRD, optical goniometry, and mechanical testing. It was observed that the coating formed did not change physicomechanical properties of electrospun PLLA scaffolds and simultaneously, increased their hydrophilicity. No adverse tissue reaction up to 3 months after subcutaneous implantation of the modified scaffolds was detected in in-vivo rat model. The rate of scaffold replacement by the recipient tissue in-vivo was observed to depend on the plasma treatment time.

Plasma treatment as an efficient tool for controlled drug release from polymeric materials: A review.

One of the most actively developing fields in modern medicine is controlled drug delivery, an ability to keep optimal concentration of a drug at the desired body location. In particular, the most attention for potential use as drug delivery vehicles is drawn towards biodegradable polymeric materials. This is due to the versatility of tools for their fabrication, as well as due to the need to extract them after implantation being eliminated. In order to enhance polymer characteristics in terms of biocompatibility their surface can be functionalized. Plasma treatment is a method for the modification of material surface properties, which spans a wide range of applications in tissue engineering and regenerative medicine. The main advantage of this method is its ability to modify a polymeric surface without altering the bulk properties of materials, thus preserving original mechanical characteristics. Moreover, plasma modification is well-known for its speed, excluded need for solvents, and scalability. Recently, this approach has been gaining popularity for drug delivery applications. The applications of plasma treatment during the fabrication of drug delivery vehicles include surface activation, enhanced wettability, the fabrication of hydrophobic barrier layer, induced cross-linking and improved drug loading. This review covers the variety of approaches, applied to different polymeric biomaterials, including non-woven meshes, films, microparticles, microneedles and tablets, in order to achieve a controlled drug release. The applications of drug delivery devices with an implemented plasma treatment modification are also described.

A fiber distribution model for predicting drug release rates.

Sustained drug release can be achieved by loading a drug into polymer material. The drug release can then be controlled for potential use in various biomedical applications. A model for drug release from a polymeric fibrous scaffold, which takes into account the distribution of fiber diameters within its structure, is developed here. It is demonstrated that the fiber diameter distribution significantly affects the drug release profile from electrospun scaffolds. The developed model indicates that altering the fiber distribution can be used as an additional tool to achieve an appropriate drug release profile. Using published data, it was demonstrated that an application of the model allows a more precise calculation of the drug diffusion coefficient within the polymer, which is important for predicting drug release rates from fabricated materials.

Osteoinductive composite coatings for flexible intramedullary nails.

This work presents composite coatings based on a copolymer of vinylidene fluoride with tetrafluoroethylene (VDF-TeFE) and hydroxyapatite (HA) for flexible intramedullary nails (FIN). The effect of the proportion of VDF-TeFE (100-25% wt.) on physicochemical and biological properties of the composite coatings was investigated. It was shown that a decrease of VDF-TeFE in the coating hinders its crystallization in ß and γ forms which have piezoelectric properties. The decrease also reduces an adhesive strength to 9.9±2.4MPa and a relative elongation to 5.9±1.2%, but results in increased osteogenesis. It was demonstrated that the composite coatings with 35% VDF-TeFE has the required combination of physicochemical properties and osteogenic activity. Comparative studies of composite coatings (35% VDF-TeFE) and calcium phosphate coatings produced using micro-arc oxidation, demonstrated comparable results for strength of bonding of these FINs with trabecular bones (~530MPa). It was hypothesized that the high osteoinductive properties of the composite coatings are due to their piezoelectric properties.

Dialysis-assisted fiber optic spectroscopy for in situ biomedical sensing.

A miniature fiber optic spectrometer enclosed within a semipermeable (dialysis) membrane is proposed for in vivo interstitial sensing applications. The semipermeable membrane acts as a molecular filter, allowing only small molecules to pass through to the sampling volume. This filtering, in principle, should enable continuous in vivo drug sensing, removing the necessity for complex microdialysis systems. We use a biological phantom to examine the reliable detection of a fluorescence signal from small dye molecules in the presence of large fluorophores and scatterers. We find that spectral artefacts arising from scatterers and large fluorophores are substantially suppressed, simplifying the spectral analysis. In addition, the measured sampling rate of 157 s is superior to existing in vivo tissue assaying techniques such as microdialysis, which can take tens of minutes.

Hepatic structure-pharmacokinetic relationships: the hepatic disposition and metabolite kinetics of a homologous series of O-acyl derivatives of salicylic acid.

1. The hepatic disposition and metabolite kinetics of a homologous series of O-acyl (acetyl, propionyl, butanoyl, pentanoyl, hexanoyl and octanoyl) esters of salicylic acid (C2SA, C3SA, C4SA, C5SA, C6SA and C8SA, respectively) was determined using a single-pass, in-situ rat liver preparation. 2. The hepatic venous outflow profiles for the parent esters and the generated metabolite, salicylic acid (SA) were analysed by HPLC. Non-parametric moments analysis was used to determine the area under the curve (AUC'), mean transit time (MTT) and normalized variance (CV2) for the parent esters and generated SA. 3. Pregenerated SA ([14C]-salicylic acid) was injected into each liver with the parent ester to determine its distribution characteristics. 4. The overall recovery of ester plus metabolite was 89% of the ester dose injected and independent of the ester carbon number, suggesting that ester extraction was due to hepatic metabolism to salicylic acid. 5. The metabolite AUC' value increased directly with the lipophilicity of the parent ester (from 0.12 for C2SA to 0.95 for C8SA). By contrast, the parent AUC' decreased with the lipophilicity (from 0.85 for C2SA to zero for C8SA). The metabolite MTT value also showed a trend to increase with the lipophilicity of the parent ester (from 15.72 s for C3SA to 61.97 s for C8SA). However, the parent MTT value shows no significant change across the series. 6. The two-compartment dispersion model was used to derive the kinetic parameters for parent ester, pregenerated SA and generated SA. Consequently, these parameters were used to estimate the values of AUC', MTT and CV2 for the parent ester and metabolite. The moments values obtained using the two-compartment dispersion model show similar trends to the corresponding moments values obtained from the outflow profiles using a non-parametric approach. 7. The more lipophilic aspirin analogues are more confined to the portal circulation after oral administration than aspirin due to their more extensive hepatic elimination avoiding systemic prostacyclin inhibition. Given that aspirin's selectivity as an anti-thrombotic agent has been postulated to be due to selective anti-platelet effects in the portal circulation, the more lipophilic and highly extracted analogues are potentially more selective anti-thrombotic agents than aspirin.

Pharmacokinetics and pharmacodynamics of melphalan in isolated limb infusion for recurrent localized limb malignancy.

Isolated limb infusion (ILI) is an attractive, less complex alternative to isolated limb perfusion (ILP). It has a lower morbidity in treating localized recurrences and in transit metastases of the limb for tumours such as melanoma, Merkel cell tumour and Kaposi's sarcoma, allowing administration of high concentrations of cytotoxic agent to the affected limb under hypoxic conditions. Melphalan is the preferred cytotoxic agent for the treatment of melanoma by ILP or ILI. We report pharmacokinetic data from 12 patients treated by ILI for tumours of the limb in Brisbane. The kinetics of drug distribution in the limb was calculated using a two-compartment vascular model, where both tissue and infusate act as well-stirred compartments. Analysis of melphalan concentrations in the perfusate during ILI showed good agreement between the values measured and the concentrations predicted by the model. Recirculation and wash-out flow rates, tissue concentrations and the permeability surface area product (PS) were calculated. Correlations between the PS value and the drug concentrations in the perfusate and tissue were supported by the results. These data contribute to a better understanding of the distribution of melphalan during ILI in the limb, and offer the opportunity to optimize the drug regimen for patients undergoing ILI.

Diffusion modeling of percutaneous absorption kinetics. 1. Effects of flow rate, receptor sampling rate, and viable epidermal resistance for a constant donor concentration.

A diffusion model for the percutaneous absorption of a solute through the skin is developed for the specific case of a constant donor concentration with a finite removal rate from the receptor due to either perfusion rate or sampling. The model has been developed to include a viable epidermal resistance and a donor-stratum corneum interfacial resistance. Numerical inversion of the Laplace domain solutions were used for simulations of solute flux and cumulative amount absorbed and to model specific examples of percutaneous absorption. Limits of the Laplace domain solutions were used to define the steady-state flux, lag time, and receptor concentration. Steady-state approximations obtained from the solutions were used to relate the steady-state flux and the effective permeability coefficient to the viable epidermis resistance, a donor-stratum corneum interfacial resistance, receptor removal rate, and partitioning between the receptor and donor phases. The lag time was shown to be dependent on these parameters and on the volume of the receptor phase. It is concluded that curvilinear cumulative amount and flux-time profiles are dependent on the processes affecting percutaneous absorption, the shapes of the profiles reflecting the processes most determining transport.

Diffusion modeling of percutaneous absorption kinetics: 2. Finite vehicle volume and solvent deposited solids.

The diffusion model for percutaneous absorption is developed for the specific case of delivery to the skin being limited by the application of a finite amount of solute. Two cases are considered; in the first, there is an application of a finite donor (vehicle) volume, and in the second, there are solvent-deposited solids and a thin vehicle with a high partition coefficient. In both cases, the potential effect of an interfacial resistance at the stratum corneum surface is also considered. As in the previous paper, which was concerned with the application of a constant donor concentration, clearance limitations due to the viable eqidermis, the in vitro sampling rate, or perfusion rate in vivo are included. Numerical inversion of the Laplace domain solutions was used for simulations of solute flux and cumulative amount absorbed and to model specific examples of percutaneous absorption of solvent-deposited solids. It was concluded that numerical inversions of the Laplace domain solutions for a diffusion model of the percutaneous absorption, using standard scientific software (such as SCIENTIST, MicroMath Scientific software) on modern personal computers, is a practical alternative to computation of infinite series solutions. Limits of the Laplace domain solutions were used to define the moments of the flux-time profiles for finite donor volumes and the slope of the terminal log flux-time profile. The mean transit time could be related to the diffusion time through stratum corneum, viable epidermal, and donor diffusion layer resistances and clearance from the receptor phase. Approximate expressions for the time to reach maximum flux (peak time) and maximum flux were also derived. The model was then validated using reported amount-time and flux-time profiles for finite doses applied to the skin. It was concluded that for very small donor phase volume or for very large stratum corneum-vehicle partitioning coefficients (e.g., for solvent deposited solids), the flux and amount of solute absorbed are affected by receptor conditions to a lesser extent than is obvious for a constant donor constant donor concentrations.

Commentary: using the convection-dispersion model and transit time density functions in the analysis of organ distribution kinetics.

The convection-dispersion model and its extended form have been used to describe solute disposition in organs and to predict hepatic availabilities. A range of empirical transit-time density functions has also been used for a similar purpose. The use of the dispersion model with mixed boundary conditions and transit-time density functions has been queried recently by Hisaka and Sugiyama in this journal. We suggest that, consistent with soil science and chemical engineering literature, the mixed boundary conditions are appropriate providing concentrations are defined in terms of flux to ensure continuity at the boundaries and mass balance. It is suggested that the use of the inverse Gaussian or other functions as empirical transit-time densities is independent of any boundary condition consideration. The mixed boundary condition solutions of the convection-dispersion model are the easiest to use when linear kinetics applies. In contrast, the closed conditions are easier to apply in a numerical analysis of nonlinear disposition of solutes in organs. We therefore argue that the use of hepatic elimination models should be based on pragmatic considerations, giving emphasis to using the simplest or easiest solution that will give a sufficiently accurate prediction of hepatic pharmacokinetics for a particular application.

Hepatic disposition and metabolite kinetics of a homologous series of diflunisal esters.

The hepatic disposition and metabolite kinetics of a homologous series of diflunisal O-acyl esters (acetyl, butanoyl, pentanoyl, and hexanoyl) were determined using a single-pass perfused in situ rat liver preparation. The experiments were conducted using 2% BSA Krebs-Henseleit buffer (pH 7.4), and perfusions were performed at 30 mL/min in each liver. O-Acyl esters of diflunisal and pregenerated diflunisal were injected separately into the portal vein. The venous outflow samples containing the esters and metabolite diflunisal were analyzed by high performance liquid chromatography (HPLC). The normalized outflow concentration-time profiles for each parent ester and the formed metabolite, diflunisal, were analyzed using statistical moments analysis and the two-compartment dispersion model. Data (presented as mean +/- standard error for triplicate experiments) was compared using ANOVA repeated measures, significance level P < 0.05. The hepatic availability (AUC'), the fraction of the injected dose recovered in the outflowing perfusate, for O-acetyldiflunisal (C2D = 0.21 +/- 0.03) was significantly lower than the other esters (0.34-0.38). However, RN/fu, the removal efficiency number RN divided by the unbound fraction in perfusate fu, which represents the removal efficiency of unbound ester by the liver, was significantly higher for the most lipophilic ester (O-hexanoyldiflunisal, C6D = 16.50 +/- 0.22) compared to the other members of the series (9.57 to 11.17). The most lipophilic ester, C6D, had the largest permeability surface area (PS) product (94.52 +/- 38.20 mL min-1 g-1 liver) and tissue distribution value VT (35. 62 +/- 11.33 mL g-1 liver) in this series. The MTT of these O-acyl esters of diflunisal were not significantly different from one another. However, the metabolite diflunisal MTTs tended to increase with the increase in the parent ester lipophilicity (11.41 +/- 2.19 s for C2D to 38.63 +/- 9.81 s for C6D). The two-compartment dispersion model equations adequately described the outflow profiles for the parent esters and the metabolite diflunisal formed from the O-acyl esters of diflunisal in the liver.

Ferroelectric polymer scaffolds based on a copolymer of tetrafluoroethylene with vinylidene fluoride: fabrication and properties.

A solution blow spinning technique is a method developed recently for making nonwoven webs of micro- and nanofibres. The principal advantage of this method compared to a more traditional electrospinning process is its significantly higher production rate. In this work, the solution blow spinning method was further developed to produce nonwoven polymeric scaffolds based on a copolymer of tetrafluoroethylene with vinylidene fluoride solution in acetone. A crucial feature of the proposed method is that high-voltage equipment is not required, which further improves the method's economics. Scanning electron microscopy analysis of the samples demonstrated that the surface morphology of the nonwoven materials is dependent on the polymer concentration in the spinning solution. It was concluded that an optimum morphology of the nonwoven scaffolds for medical applications is achieved by using a 5% solution of the copolymer. It was established that the scaffolds produced from the 5% solution have a fractal structure and anisotropic mechanical properties. X-ray diffraction, infrared spectroscopy, Raman spectroscopy and differential scanning calorimetry demonstrated that the fabricated nonwoven materials have crystal structures that exhibit ferroelectric properties. Gas chromatography has shown that the amount of acetone in the nonwoven material does not exceed the maximum allowable concentration of 0.5%. In vitro analysis, using the culture of motile cells, confirmed that the nonwoven material is non-toxic and does not alter the morpho-functional status of stem cells for short-term cultivation, and therefore can potentially be used in medical applications.

Development and validation of a reversed-phase high-performance liquid chromatographic method for quantification of peptide dendrimers in human skin permeation experiments.

The aim of the present work was to develop and validate a simple RP-HPLC method with UV detection to quantify peptide dendrimers in skin permeation experiments. Six dendrimers of varying positive charges (4(+), 8(+) and 16(+)) containing either histidine or arginine as terminal aminoacids were prepared by solid phase peptide synthesis. Mobile phase containing 0.02% (v/v) heptafluorobutyric acid in 90% acetonitrile-water was capable of separating all dendrimers from interfering peaks of receptor fluid. For the calibration of each dendrimer, a different dendrimer from the same class was selected as the internal standard. The results of preliminary human skin permeation studies showed that the developed analytical method can be successfully used for the quantification of cationic poly(aminoacid)-based dendrimers in skin permeation experiments.

An integrated pharmacokinetic and imaging evaluation of vehicle effects on solute human epidermal flux and, retention characteristics.

OBJECTIVE: Our understanding of the differential effects of topically applied vehicles on solute partitioning and diffusion within the skin is presently limited. In this work, in vitro epidermal partitioning, penetration and multiphoton laser scanning microscopy (MPLSM) imaging studies were used to assess the distribution of 2-naphthol across human epidermis. MATERIALS AND METHODS: Four commonly used liquid vehicles (100% water, 20% propylene glycol (PG)/water, 50% ethanol (EtOH)/water and 100% isopropyl myristate (IPM)) were used. RESULTS AND DISCUSSION: The maximum flux and membrane retention of 2-naphthol from 50% EtOH/water was almost an order of magnitude or larger than from the other vehicles evaluated whereas IPM resulted in the highest membrane retention and lowest membrane penetration for 2-naphthol than other vehicles. MPLSM studies showed that 2-naphthol solute partitioned favourably into the intercellular lipids and that there was a vehicle-dependent uptake of 2-naphthol into corneocytes. CONCLUSIONS: The integrated evaluation using in vitro penetration, epidermal retention and MPLSM imaging has shown that vehicle effects on skin penetration occurs by an alteration in the distribution of solutes between the corneocytes and intercellular lipids in addition to the well known mechanisms of altered partitioning into the stratum corneum and enhanced epidermal diffusion.