Finite element modeling of coupled diffusion with partitioning in transdermal drug delivery

Exploring the thermally-controlled fentanyl transdermal therapy to provide constant drug delivery by physics-based digital twins

Transdermal drug delivery is suitable for low-molecular-weight drugs with specific lipophilicity, like fentanyl, which is widely used for cancer-induced pain management. However, fentanyl's transdermal therapy displays high intra-individual variability. Factors like skin characteristics at application sites and ambient temperature contribute to this variation. In this study, we developed a physics-based digital twin of the human body to cope with this variability and propose better adapted setups. This twin includes an in-silico skin model for drug penetration, a pharmacokinetic model, and a pharmacodynamic model. Based on the results of our simulations, applying the patch on the flank (side abdominal area) showed a 15.3 % higher maximum fentanyl concentration in the plasma than on the chest. Additionally, the time to reach this maximum concentration when delivered through the flank was 19.8 h, which was 10.3 h earlier than via the upper arm. Finally, this variation led to an 18 % lower minimum pain intensity for delivery via the flank than the chest. Moreover, the impact of seasonal changes on ambient temperature and skin temperature by considering the activity level was investigated. Based on our result, the fentanyl uptake flux by capillaries increased by up to 11.8 % from an inactive state in winter to an active state in summer. We also evaluated the effect of controlling fentanyl delivery by adjusting the temperature of the patch to alleviate the pain to reach a mild pain intensity (rated three on the VAS scale). By implementing this strategy, the average pain intensity decreased by 1.1 points, and the standard deviation for fentanyl concentration in plasma and average pain intensity reduced by 37.5 % and 33.3 %, respectively. Therefore, our digital twin demonstrated the efficacy of controlled drug release through temperature regulation, ensuring the therapy toward the intended target outcome and reducing therapy outcome variability. This holds promise as a potentially useful tool for physicians.

Implementing physics-based digital patient twins to tailor the switch of oral morphine to transdermal fentanyl patches based on patient physiology

Fentanyl transdermal patches are widely implemented for cancer-induced pain treatment due to the high potency of fentanyl and gradual drug release. However, transdermal fentanyl up-titration for opioid-naïve patients is difficult, which is why opioid treatment is often started with oral/iv morphine. Based on the daily dose of morphine, the initial dose of the fentanyl patch is decided upon. After reaching a stable level of pain, the switch is made from oral/iv morphine to transdermal fentanyl. There are standard calculation tools for transferring from oral/iv morphine to transdermal fentanyl, which is the same for all patients. By considering the variations in the physiology of the patients, a unique switching strategy cannot meet the needs of different patients. This study explores the outcome in terms of pain relief and minute ventilation during opioid therapy. For this, we used physics-based simulations on a virtually-generated population of patients, and we applied the same therapy to all patients. We could show that patients' physiology, such as gender, age, and weight, greatly impact the outcome of the therapy; as such, the correlation coefficient between pain intensity and age is 0.89, and the correlation coefficient between patient's weight and maximum plasma concentration of morphine and fentanyl is -0.98 and -0.97. Additionally, a different combination of the duration of overlap between morphine and fentanyl therapy with different doses of fentanyl was considered for the virtual patients to find the best opioid-switching strategy for each patient. We explored the impact of combining physiological features to determine the best-suited strategy for virtual patients. Our findings suggest that tailoring morphine and fentanyl therapy only based on a limited number of features is insufficient, and increasing the number of impactful physiological features positively influences the outcome of the therapy.

Transdermal Drug Delivery: Determining Permeation Parameters Using Tape Stripping and Numerical Modeling

The function of transdermal drug delivery (TDD) systems is complex due to the multiple layers necessary for controlling the rate of drug release and the interaction with the patient’s skin. In this work, we study a particular aspect of a TDD system, that is, the parameters that describe the drug permeation through the skin layers. Studies of the diffusion of two compounds were carried out and supported by tape stripping and numerical modeling. The experimental studies are carried out for porcine skin in a Franz diffusion cell and tape stripping is used to quantify the concentration of drug in the stratum corneum. A multi-layered numerical model, based on Fickian diffusion, is used to determine the unknown parameters that define the skin’s permeability, such as the partition between layers and the mass transfer coefficients due to the surface barrier. A significant correlation was found between the numerical modeling and experimental results, indicating that the partition and mass transfer effects at the interlayer boundary are accurately represented in the numerical model. We find that numerical modeling is essential to fully describe the diffusion characteristics.

The Finite Element Analysis Research on Microneedle Design Strategy and Transdermal Drug Delivery System

Microneedles (MNs) as a novel transdermal drug delivery system have shown great potential for therapeutic and disease diagnosis applications by continually providing minimally invasive, portable, cost-effective, high bioavailability, and easy-to-use tools compared to traditional parenteral administrations. However, microneedle transdermal drug delivery is still in its infancy. Many research studies need further in-depth exploration, such as safety, structural characteristics, and drug loading performance evaluation. Finite element analysis (FEA) uses mathematical approximations to simulate real physical systems (geometry and load conditions). It can simplify complex engineering problems to guide the precise preparation and potential industrialization of microneedles, which has attracted extensive attention. This article introduces FEA research for microneedle transdermal drug delivery systems, focusing on microneedle design strategy, skin mechanics models, skin permeability, and the FEA research on drug delivery by MNs.

Predicting transdermal fentanyl delivery using physics-based simulations for tailored therapy based on the age

Transdermal fentanyl patches are an effective alternative to the sustained release of oral morphine for chronic pain management. Due to the narrow therapeutic range of fentanyl, the concentration of fentanyl in the blood needs to be carefully monitored. Only then can effective pain relief be achieved while avoiding adverse effects such as respiratory depression. This study developed a physics-based digital twin of a patient by implementing drug uptake, pharmacokinetics, and pharmacodynamics models. The twin was employed to predict the in-silico effect of conventional fentanyl transdermal in a 20–80-year-old virtual patient. The results show that, with increasing age, the maximum transdermal fentanyl flux and maximum concentration of fentanyl in the blood decreased by 11.4% and 7.0%, respectively. However, the results also show that as the patient's age increases, the pain relief increases by 45.2%. Furthermore, the digital twin was used to propose a tailored therapy based on the patient's age. This predesigned therapy customized the duration of applying the commercialized fentanyl patches. According to this therapy, a 20-year-old patient needs to change the patch 2.1 times more frequently than conventional therapy, which leads to 30% more pain relief and 315% more time without pain. In addition, the digital twin was updated by the patient's pain intensity feedback. Such therapy increased the patient's breathing rate while providing effective pain relief, so a safer treatment. We quantified the added value of a patient's physics-based digital twin and sketched the future roadmap for implementing such twin-assisted treatment into the clinics.

Needle-Free Jet Injectors' Geometry Design and Drug Diffusion Process Analysis

In order to study the injection and diffusion process of the drug in the subcutaneous tissue of a needle-free jet injectors (NFJIs) in detail and understand the influence of different nozzle geometry on the diffusion process of the drug, in this paper, numerical simulations were performed to study the diffusion process of the drug in the subcutaneous tissue of NFJIs with cylindrical nozzle. On this basis, the differences of the drug diffusion process with different nozzle geometries were analyzed. The results show that the drug diffused in the shape of ellipsoid in the subcutaneous tissue. The penetration of the drug into the subcutaneous tissue is deeper under the condition of conical nozzle and conical cylindrical nozzle at the same time. However, it takes longer to spread to the interface between skin and subcutaneous tissue in reverse.

Mathematical modelling of drug-diffusion from multi-layered capsules/tablets and other drug delivery devices

In this paper, two mathematical models have been formulated by extending the basic reaction-diffusion model, along with suitable initial and boundary conditions to study the drug delivery and its diffusion in biological tissues from multi-layered capsules/tablets and other drug delivery devices (DDDs), respectively. These devices are either taken orally or through other drug-administration routes. The formulated models are solved using the variational finite element method followed by the fundamental matrix method, to study the drug delivery and its diffusion more efficiently. The main aim of this work is to provide an effective model, using optimal mathematical techniques to help researchers and biologists in medicine in decreasing the endeavours and expenses in designing DDDs. The outcomes obtained are compared with the experimental data to demonstrate the validity and the feasibility of the proposed work.

The impact of chemical engineering and technological advances on managing diabetes: present and future concepts

Monitoring blood glucose levels for diabetic patients is critical to achieve tight glycaemic control. As none of the current antidiabetic treatments restore lost functional β-cell mass in diabetic patients, insulin injections and the use of insulin pumps are most widely used in the management of glycaemia. The use of advanced and intelligent chemical engineering, together with the incorporation of micro- and nanotechnological-based processes have lately revolutionized diabetic management. The start of this concept goes back to 1974 with the description of an electrode that repeatedly measures the level of blood glucose and triggers insulin release from an infusion pump to enter the blood stream from a small reservoir upon need. Next to the insulin pumps, other drug delivery routes, including nasal, transdermal and buccal, are currently investigated. These processes necessitate competences from chemists, engineers-alike and innovative views of pharmacologists and diabetologists. Engineered micro and nanostructures hold a unique potential when it comes to drug delivery applications required for the treatment of diabetic patients. As the technical aspects of chemistry, biology and informatics on medicine are expanding fast, time has come to step back and to evaluate the impact of technology-driven chemistry on diabetics and how the bridges from research laboratories to market products are established. In this review, the large variety of therapeutic approaches proposed in the last five years for diabetic patients are discussed in an applied context. A survey of the state of the art of closed-loop insulin delivery strategies in response to blood glucose level fluctuation is provided together with insights into the emerging key technologies for diagnosis and drug development. Chemical engineering strategies centered on preserving and regenerating functional pancreatic β-cell mass are evoked in addition as they represent a permanent solution for diabetic patients.

Inverse Mechanistic Modeling of Transdermal Drug Delivery for Fast Identification of Optimal Model Parameters

Transdermal drug delivery systems are a key technology to administer drugs with a high first-pass effect in a non-invasive and controlled way. Physics-based modeling and simulation are on their way to become a cornerstone in the engineering of these healthcare devices since it provides a unique complementarity to experimental data and additional insights. Simulations enable to virtually probe the drug transport inside the skin at each point in time and space. However, the tedious experimental or numerical determination of material properties currently forms a bottleneck in the modeling workflow. We show that multiparameter inverse modeling to determine the drug diffusion and partition coefficients is a fast and reliable alternative. We demonstrate this strategy for transdermal delivery of fentanyl. We found that inverse modeling reduced the normalized root mean square deviation of the measured drug uptake flux from 26 to 9%, when compared to the experimental measurement of all skin properties. We found that this improved agreement with experiments was only possible if the diffusion in the reservoir holding the drug was smaller than the experimentally measured diffusion coefficients suggested. For indirect inverse modeling, which systematically explores the entire parametric space, 30,000 simulations were required. By relying on direct inverse modeling, we reduced the number of simulations to be performed to only 300, so a factor 100 difference. The modeling approach's added value is that it can be calibrated once in-silico for all model parameters simultaneously by solely relying on a single measurement of the drug uptake flux evolution over time. We showed that this calibrated model could accurately be used to simulate transdermal patches with other drug doses. We showed that inverse modeling is a fast way to build up an accurate mechanistic model for drug delivery. This strategy opens the door to clinically ready therapy that is tailored to patients.

Challenges and opportunities for small volumes delivery into the skin

Each individual's skin has its own features, such as strength, elasticity, or permeability to drugs, which limits the effectiveness of one-size-fits-all approaches typically found in medical treatments. Therefore, understanding the transport mechanisms of substances across the skin is instrumental for the development of novel minimal invasive transdermal therapies. However, the large difference between transport timescales and length scales of disparate molecules needed for medical therapies makes it difficult to address fundamental questions. Thus, this lack of fundamental knowledge has limited the efficacy of bioengineering equipment and medical treatments. In this article, we provide an overview of the most important microfluidics-related transport phenomena through the skin and versatile tools to study them. Moreover, we provide a summary of challenges and opportunities faced by advanced transdermal delivery methods, such as needle-free jet injectors, microneedles, and tattooing, which could pave the way to the implementation of better therapies and new methods.

Multi-region finite element modelling of drug release from hydrogel based ophthalmic lenses

Understanding the way in which drug is released from drug carrying hydrogel based ophthalmic lenses aids in the development of efficient ophthalmic drug delivery. Various solute-polymer interactions affect solute diffusion within hydrogels as well as hydrogel-bulk partitioning. Additionally, surface modifications or coatings may add to resistance of mass transfer across the hydrogel interface. It is necessary to consider both interfacial resistances as well as the appropriate driving force when characterizing interface flux. Such a driving force is induced by a difference in concentration which deviates from equilibrium conditions. We present a Galerkin finite element approach for solute transport in hydrogels which accounts for diffusion within the gel, storage effects due to polymer-solute interaction, as well as partitioning and mass transfer resistance effects at the interface. The approach is formulated using a rotational symmetric model to account for realistic geometry. We show that although the resulting global system is not symmetric in the case of partitioning, it is similar to a symmetric negative semidefinite system. Thus, it has non-positive real eigenvalues and is coercive, ensuring the validity of the finite element formulation as well as the numerical stability of the implicit backward Euler time integration method employed. Two models demonstrating this approach are presented and verified with release experimental data. The first is the release of moxifloxacin from intraocular lenses (IOLs) plasma grafted with different polyacrylates. The second accounts for both loading as well as the release of diclofenac from disc shaped IOL material loaded for varied time periods and temperature.

Predicting Transdermal Fentanyl Delivery Using Mechanistic Simulations for Tailored Therapy

Transdermal drug delivery is a key technology for administering drugs. However, most devices are “one-size-fits-all”, even though drug diffusion through the skin varies significantly from person-to-person. For next-generation devices, personalization for optimal drug release would benefit from an augmented insight into the drug release and percutaneous uptake kinetics. Our objective was to quantify the changes in transdermal fentanyl uptake with regards to the patient’s age and the anatomical location where the patch was placed. We also explored to which extent the drug flux from the patch could be altered by miniaturizing the contact surface area of the patch reservoir with the skin. To this end, we used validated mechanistic modeling of fentanyl diffusion, storage, and partitioning in the epidermis to quantify drug release from the patch and the uptake within the skin. A superior spatiotemporal resolution compared to experimental methods enabled in-silico identification of peak concentrations and fluxes, and the amount of stored drug and bioavailability. The patients’ drug uptake showed a 36% difference between different anatomical locations after 72 h, but there was a strong interpatient variability. With aging, the drug uptake from the transdermal patch became slower and less potent. A 70-year-old patient received 26% less drug over the 72-h application period, compared to an 18-year-old patient. Additionally, a novel concept of using micron-sized drug reservoirs was explored in silico. These reservoirs induced a much higher local flux (µg cm^-2 h^-1) than conventional patches. Up to a 200-fold increase in the drug flux was obtained from these small reservoirs. This effect was mainly caused by transverse diffusion in the stratum corneum, which is not relevant for much larger conventional patches. These micron-sized drug reservoirs open new ways to individualize reservoir design and thus transdermal therapy. Such computer-aided engineering tools also have great potential for in-silico design and precise control of drug delivery systems. Here, the validated mechanistic models can serve as a key building block for developing digital twins for transdermal drug delivery systems.

Finite Element Analysis for Predicting Skin Pharmacokinetics of Nano Transdermal Drug Delivery System Based on the Multilayer Geometry Model

Background

Skin pharmacokinetics is an indispensable indication for studying the drug fate after administration of transdermal drug delivery systems (TDDS). However, the heterogeneity and complex skin structured with stratum corneum, viable epidermis, dermis, and subcutaneous tissue inevitably leads the drug diffusion coefficient (Kp) to vary depending on the skin depth, which seriously limits the development of TDDS pharmacokinetics in full thickness skin.

Methods

A multilayer geometry skin model was established and the Kp of drug in SC, viable epidermis, and dermis was obtained using the technologies of molecular dynamics simulation, in vitro permeation experiments, and in vivo microdialysis, respectively. Besides, finite element analysis (FEA) based on drug Kps in different skin layers was applied to simulate the paeonol nanoemulsion (PAE-NEs) percutaneous dynamic penetration process in two and three dimensions. In addition, PAE-NEs skin pharmacokinetics profile obtained by the simulation was verified by in vivo experiment.

Results

Coarse-grained modeling of molecular dynamic simulation was successfully established and the Kp of PAE in SC was 2.00×10⁻⁶ cm²/h. The Kp of PAE-NE in viable epidermis and in dermis detected using penetration test and microdialysis probe technology, was 1.58×10⁻⁵ cm²/h and 3.20×10⁻⁵ cm²/h, respectively. In addition, the results of verification indicated that PAE-NEs skin pharmacokinetics profile obtained by the simulation was consistent with that by in vivo experiment.

Discussion

This study demonstrated that the FEA combined with the established multilayer geometry skin model could accurately predict the skin pharmacokinetics of TDDS.

Regular Solution Theory for Polymer Permeation Transients: A Toolkit for Understanding Experimental Waveshapes

The accurate measurement of permeation is important at the product design stage for a variety of industries as diverse as conveyance methods for oil and gas produced fluids, such as mixtures of carbon dioxide, methane, hydrogen sulfide, water, and hydrocarbons, and in polymer-lined, unbonded flexible risers and flow lines through connectors and valves, hydrogen and methane gas carrying domestic lines, hydrogen storage tanks, sulfur hexafluoride circuit breakers for high power-carrying lines, oxygen through display technology, and drug delivery. It would also be appropriate to monitor the permeation rate through the polymer, composite, and elastomeric layers during the in-service times where applications allow. In the future, any alteration in the short term and long-term transport rates could be analyzed in terms of an initial alteration or degradation of the polymeric materials and, in some cases, metallic components. Crucially, such measurements would serve as an early warning system of any change in a polymeric material that could result in the loss of function of the fluid of a gas containing barrier material. Most experimental determinations are made through recording flux transients (varying flux) through permeation cells in which a polymer membrane or film separates a donor compartment (usually an infinite supply) and an acceptor compartment and in which membrane transport is considered to be slow. Treatment of the resulting experimental data is usually, but not always, undertaken through comparison with a steady-state model based on Fickian diffusion through the membrane, so as to extract the membrane permeability, the diffusion coefficient of the permeant, and the solubility of the permeant in the membrane phase. However, in spite of these measurements being undertaken routinely using closed cell manometric or continuous flow methods, there is a lack of literature in which experimental flux transients are provided, and in several cases, it is clear that the experimental data do not conform to the expected model of slow, Fickian diffusion through the membrane, even though experiments are performed at temperatures much higher than the glass transition temperature of the polymer membrane. In this paper, we first re-examine the classical model for an infinite source and extend it to account for (1) molecular interactions between membrane and permeant, using regular solution theory, (2) slow transport in the acceptor phase, and (3) slow kinetics across the membrane|acceptor interface. We demonstrate that all three aspects can cause permeation flux transients to exhibit unusual, nonclassical waveshapes, which have nevertheless been experimentally realized without rationalization. This enables the development of an algorithmic toolkit for the interpretation of permeation flux transients, so as to provide reliable and accurate data analysis for experimentalists.

Predicting drug delivery efficiency into tumor tissues through molecular simulation of transport in complex vascular networks

Efficient delivery of anticancer drugs into tumor tissues at maximally effective and minimally toxic concentrations is vital for therapeutic success. At present, no method exists that can predict the spatial and temporal distribution of drugs into a target tissue after administration of a specific dose. This prevents accurate estimation of optimal dosage regimens for cancer therapy. Here we present a new method that predicts quantitatively the time-dependent spatial distribution of drugs in tumor tissues at sub-micrometer resolution. This is achieved by modeling the diffusive flow of individual drug molecules through the three-dimensional network of blood-vessels that vascularize the tumor, and into surrounding tissues, using molecular mechanics techniques. By evaluating delivery into tumors supplied by a series of blood-vessel networks with varying degrees of complexity, we show that the optimal dose depends critically on the precise vascular structure. Finally, we apply our method to calculate the optimal dosage of the cancer drug doxil into a section of a mouse ovarian tumor, and demonstrate the enhanced delivery of liposomally administered doxorubicin when compared to free doxorubicin. Comparison with experimental data and a multiple-compartment model show that the model accurately recapitulates known pharmacokinetics and drug-load predictions. In addition, it provides, for the first time, a detailed picture of the spatial dependence of drug uptake into tissues surrounding tumor vasculatures. This approach is fundamentally different to current continuum models, and reveals that the target tumor vascular topology is as important for therapeutic success as the transport properties of the drug delivery platform itself. This sets the stage for revisiting drug dosage calculations.

In-Silico Skin Model: A Multiscale Simulation Study of Drug Transport

Accurate in-silico models are required to predict the release of drug molecules through skin in order to supplement the in-vivo experiments for faster development/testing of drugs. The upper most layer of the skin, stratum corneum (SC), offers the main resistance for permeation of actives. Most of the SC's molecular level models comprise cholesterol and phospholipids only, which is far from reality. In this study we have implemented a multiscale modeling framework to obtain the release profile of three drugs, namely, caffeine, fentanyl, and naphthol, through skin SC. We report for the first time diffusion of drugs through a realistic skin molecular model comprised of ceramides, cholesterol, and free fatty acid. The diffusion coefficients of drugs in the SC lipid matrix were determined from multiple constrained molecular dynamics simulations. The calculated diffusion coefficients were then used in the macroscopic models to predict the release profiles of drugs through the SC. The obtained release profiles were in good agreement with available experimental data. The partition coefficient exhibits a greater effect on the release profiles. The reported multiscale modeling framework would provide insight into the delivery mechanisms of the drugs through the skin and shall act as a guiding tool in performing targeted experiments to come up with a suitable delivery system.

Surging footprints of mathematical modeling for prediction of transdermal permeability

In vivo skin permeation studies are considered gold standard but are difficult to perform and evaluate due to ethical issues and complexity of process involved. In recent past, a useful tool has been developed by combining the computational modeling and experimental data for expounding biological complexity. Modeling of percutaneous permeation studies provides an ethical and viable alternative to laboratory experimentation. Scientists are exploring complex models in magnificent details with advancement in computational power and technology. Mathematical models of skin permeability are highly relevant with respect to transdermal drug delivery, assessment of dermal exposure to industrial and environmental hazards as well as in developing fundamental understanding of biotransport processes. Present review focuses on various mathematical models developed till now for the transdermal drug delivery along with their applications.

A Theoretical Study on Inhibition of Melanoma with Controlled and Targeted Delivery of siRNA via Skin Using SPACE-EGF

Melanoma is a potentially lethal skin cancer with high mortality rate. Recently, the peptide-mediated transdermal delivery of small interference RNA (siRNA) emerges as a promising strategy to treat melanoma by inducing the apoptosis of tumor cells, but the related theoretical model describing the delivery of siRNA under the effect of SPACE-EGF, the growth inhibition of melanoma and the dynamic expanding of the bump on the skin due to the growth of melanoma has not been reported yet. In this article, a theoretical model is developed to describe the percutaneous siRNA delivery mediated by SPACE-EGF to melanoma and the growth inhibition of melanoma. The results present the spatial-temporal distribution of siRNA and the growth of melanoma under the inhibition of siRNA, which shows a good consistency with the experimental results. In addition, this model represents the uplift process of tumors on the skin surface. The model presented here is a useful tool to understand the whole process of the SPACE-EGF-mediated delivery of the siRNA to melanoma through skin, to predict the therapeutic effect, and to optimize the therapeutic strategy, providing valuable references for the treatment of melanoma.

Mass partitioning effects in diffusion transport

Frequent mass exchange takes place in a heterogeneous environment among several phases, where mass partitioning may occur at the interface of phases. Analytical and computational methods for diffusion do not usually incorporate molecule partitioning masking the true picture of mass transport. Here we present a computational finite element methodology to calculate diffusion mass transport with a partitioning phenomenon included and the analysis of the effects of partitioning. Our numerical results showed that partitioning controls equilibrated mass distribution as expected from analytical solutions. The experimental validation of mass release from drug-loaded nanoparticles showed that partitioning might even dominate in some cases with respect to diffusion itself. The analysis of diffusion kinetics in the parameter space of partitioning and diffusivity showed that partitioning is an extremely important parameter in systems, where mass diffusivity is fast and that the concentration of nanoparticles can control payload retention inside nanoparticles. The computational and experimental results suggest that partitioning and physiochemical properties of phases play an important, if not crucial, role in diffusion transport and should be included in the studies of mass transport processes.

Numerical modelling of transdermal delivery from matrix systems: parametric study and experimental validation with silicone matrices

A model is presented for transdermal drug delivery from single-layered silicone matrix systems. The work is based on our previous results that, in particular, extend the well-known Higuchi model. Recently, we have introduced a numerical transient model describing matrix systems where the drug dissolution can be non-instantaneous. Furthermore, our model can describe complex interactions within a multi-layered matrix and the matrix to skin boundary. The power of the modelling approach presented here is further illustrated by allowing the possibility of a donor solution. The model is validated by a comparison with experimental data, as well as validating the parameter values against each other, using various configurations with donor solution, silicone matrix and skin. Our results show that the model is a good approximation to real multi-layered delivery systems. The model offers the ability of comparing drug release for ibuprofen and diclofenac, which cannot be analysed by the Higuchi model because the dissolution in the latter case turns out to be limited. The experiments and numerical model outlined in this study could also be adjusted to more general formulations, which enhances the utility of the numerical model as a design tool for the development of drug-loaded matrices for trans-membrane and transdermal delivery.

A two-phase two-layer model for transdermal drug delivery and percutaneous absorption

One of the promising frontiers of bioengineering is the controlled release of a therapeutic drug from a vehicle across the skin (transdermal drug delivery). In order to study the complete process, a two-phase mathematical model describing the dynamics of a substance between two coupled media of different properties and dimensions is presented. A system of partial differential equations describes the diffusion and the binding/unbinding processes in both layers. Additional flux continuity at the interface and clearance conditions into systemic circulation are imposed. An eigenvalue problem with discontinuous coefficients is solved and an analytical solution is given in the form of an infinite series expansion. The model points out the role of the diffusion and reaction parameters, which control the complex transfer mechanism and the drug kinetics across the two layers. Drug masses are given and their dependence on the physical parameters is discussed.

Application of numerical methods for diffusion-based modeling of skin permeation

The application of numerical methods for mechanistic, diffusion-based modeling of skin permeation is reviewed. Methods considered here are finite difference, method of lines, finite element, finite volume, random walk, cellular automata, and smoothed particle hydrodynamics. First the methods are briefly explained with rudimentary mathematical underpinnings. Current state of the art numerical models are described, and then a chronological overview of published models is provided. Key findings and insights of reviewed models are highlighted. Model results support a primarily transcellular pathway with anisotropic lipid transport. Future endeavors would benefit from a fundamental analysis of drug/vehicle/skin interactions.

Improved input parameters for diffusion models of skin absorption

To use a diffusion model for predicting skin absorption requires accurate estimates of input parameters on model geometry, affinity and transport characteristics. This review summarizes methods to obtain input parameters for diffusion models of skin absorption focusing on partition and diffusion coefficients. These include experimental methods, extrapolation approaches, and correlations that relate partition and diffusion coefficients to tabulated physico-chemical solute properties. Exhaustive databases on lipid-water and corneocyte protein-water partition coefficients are presented and analyzed to provide improved approximations to estimate lipid-water and corneocyte protein-water partition coefficients. The most commonly used estimates of lipid and corneocyte diffusion coefficients are also reviewed. In order to improve modeling of skin absorption in the future diffusion models should include the vertical stratum corneum heterogeneity, slow equilibration processes, the absorption from complex non-aqueous formulations, and an improved representation of dermal absorption processes. This will require input parameters for which no suitable estimates are yet available.

Detailed modeling of skin penetration--an overview

In recent years, the combination of computational modeling and experiments has become a useful tool that is proving increasingly powerful for explaining biological complexity. As computational power is increasing, scientists are able to explore ever more complex models in finer detail and to explain very complex real world data. This work provides an overview of one-, two- and three-dimensional diffusion models for penetration into mammalian skin. Besides diffusive transport this includes also binding of substances to skin proteins and metabolism. These models are based on partial differential equations that describe the spatial evolution of the transport process through the biological barrier skin. Furthermore, the work focuses on analytical and numerical techniques for this type of equations such as discretization schemes or homogenization (upscaling) techniques. Finally, the work compares different geometry models with respect to the permeability.

Simulating intravitreal injections in anatomically accurate models for rabbit, monkey, and human eyes

Purpose

To develop models for rabbit, monkey, and human that enable prediction of the clearance after intravitreal (IVT) injections in one species from experimental results obtained in another species.

Methods

Anatomically accurate geometric models were constructed for rabbit, monkey, and human that enabled computational fluid dynamic simulation of clearance of an IVT injected bolus. Models were constructed with and without the retrozonular space of Petit. Literature data on clearance after IVT injection of substances spanning a range of molecular weight up to 157 kDa were used to validate the rabbit model.

Results

The space of Petit had a significant increase on the clearance of slowly diffusing substances cleared by the anterior pathway by reducing the bottleneck for drug efflux. Models that did not include this zone could not accurately predict the clearance of slowly diffusing substances whose clearance was accelerated by intraocular pressure-driven convection.

Conclusions

The ocular anatomy must be carefully reconstructed in the model to enable accurate predictions of clearance. This method offers an alternative means for scaling experimental data from one species to another that may be more appropriate than other simple approaches based entirely upon scaling of compartment volumes and flow rates.

Computational modeling of the skin barrier

A simulation environment for the numerical calculation of permeation processes through human skin has been developed. In geometry models that represent the actual cell morphology of stratum corneum (SC) and deeper skin layers, the diffusive transport is simulated by a finite volume method. As reference elements for the corneocyte cells and lipid matrix, both three-dimensional tetrakaidecahedra and cuboids as well as two-dimensional brick-and-mortar models have been investigated. The central finding is that permeability and lag time of the different membranes can be represented in a closed form depending on model parameters and geometry. This allows a comparison of the models in terms of their barrier effectiveness at comparable cell sizes. The influence of the cell shape on the barrier properties has been numerically demonstrated and quantified. It is shown that tetrakaidecahedra in addition to an almost optimal surface-to-volume ratio also has a very favorable barrier-to-volume ratio. A simulation experiment was successfully validated with two representative test substances, the hydrophilic caffeine and the lipophilic flufenamic acid, which were applied in an aqueous vehicle with a constant dose. The input parameters for the simulation were determined in a companion study by experimental collaborators.

Multiscale modeling framework of transdermal drug delivery

This study addresses the modeling of transdermal diffusion of drugs to better understand the permeation of molecules through the skin, especially the stratum corneum, which forms the main permeation barrier to percutaneous permeation. In order to ensure reproducibility and predictability of drug permeation through the skin and into the body, a quantitative understanding of the permeation barrier properties of the stratum corneum (SC) is crucial. We propose a multiscale framework of modeling the multicomponent transdermal diffusion of molecules. The problem is divided into subproblems of increasing length scale: microscopic, mesoscopic, and macroscopic. First, the microscopic diffusion coefficient in the lipid bilayers of the SC is found through molecular dynamics (MD) simulations. Then, a homogenization procedure is performed over a model unit cell of the heterogeneous SC, resulting in effective diffusion parameters. These effective parameters are the macroscopic diffusion coefficients for the homogeneous medium that is "equivalent" to the heterogeneous SC, and thus can be used in finite element simulations of the macroscopic diffusion process. The resulting drug flux through the skin shows very reasonable agreement to experimental data.

A theoretical model for transdermal drug delivery from emulsions and its dependence upon formulation

This article presents a theoretical model of transdermal drug delivery from an emulsion-type vehicle that addresses the vehicle heterogeneity and incorporates the prediction of drug transport parameters as function of the vehicle composition. The basic mass transfer model considers interfacial and diffusion resistances within the emulsion and partition/diffusion phenomena across two skin compartments in series. Drug transport parameters are predicted as follows: partition coefficients are derived from regular solutions theory, drug diffusivity in the continuous phase is computed from a free volume theory with segmental motion, and permeability of the surfactant layer around droplets is estimated based on a free surface area model. These relationships are incorporated within the basic mass transfer model, so that the overall model is able to predict temporal profiles of drug release from the vehicle and of drug concentration in plasma, as a function of vehicle composition. In this way, the proposed model provides a sound physicochemical basis to support the development of new formulations and the planning of experiments. A simulated case study regarding a nitroglycerin ointment is presented in detail, illustrating how thermodynamic and kinetic factors inherent to the emulsion vehicle can modulate drug release and subsequent systemic absorption.