Diffusion Limit Research Articles

Reducing Dead Species by Electrochemically‐Densified Cathode‐Interface‐Reaction Layer towards High‐Rate‐Endurable Zn||I‐Br Batteries

Interhalogen‐involved aqueous Zn||halogen batteries (AZHBs) are latent high‐energy systems for grid‐level energy storage, yet usually suffer from poor high‐rate endurability caused by the formation of “dead species”. Herein, via an electrochemically‐densified cathode‐interface‐reaction layer (CIRL), Zn||I‐Br batteries involving interhalogen reactions between the I2 cathode and Br‐ from the electrolytes are initially achieved with excellent high‐rate endurability. Different from that in diluted electrolytes, the CIRL formed in Br‐‐concentrated electrolyte is denser and water‐lean, which enables halogen species conversion with a more rapid charge transfer and lower activation energy. More importantly, the CIRL robustly affords a decent I2 conservation by accelerated conversion kinetics and limited species diffusion, thereby endowing the Zn||I‐Br batteries with an ultralong high‐rate lifespan. The electrochemical mechanism is sufficiently verified by multiple spectral characterizations. Consequently, Zn||I‐Br batteries in Br‐‐concentrated (20 m) electrolytes exhibit an overwhelming rate capability and lifespan to those in Br‐‐diluted (2 m) electrolytes. Typically, when cycled at a large current density of 10 A g‐1, an ultralong lifespan of over 25,000 cycles is achieved with a high retention of 98.3%. This study provides new insight into the CIRL‐dictated active species conservation for high‐rate endurable AZHBs, which could apply to other high‐energy interhalogen batteries.

Diffusive Limit of the Boltzmann Equation in Bounded Domains

Diffusive Limit of the Boltzmann Equation in Bounded Domains

Study on the Mechanism of Temperature Effect on SO2 Electrochemical Gas Sensor

Abstract Temperature can affect the measurement values of electrochemical gas sensors, increasing measurement errors. The influence mechanism of temperature on electrochemical gas sensors was studied based on Fick's first law and the limit diffusion current formula. Temperature affects the sensitive characteristics of sensor by changing the diffusion coefficient Dl1 of SO2 in air, the Henry's coefficient KH of SO2 dissolved in water and the water content of the electrolyte solution. When the temperature increases, the degree of influence of Henry's coefficient KH and the reduction of water content is greater than the degree of influence on the increase in diffusion coefficient, which decreases the sensor measurement value. The results of the temperature experiments show that the optimal temperature range for the sensor is -25 °C to 50 °C, and the average measurement error in this temperature range is less than 20%. When the temperature exceeds 50 ℃, it will cause a reduction in the evaporation of water in the electrolyte solution, leading to a rapid increase in the measurement error. The structure of the sensor can be improved by adding a water retention layer inside the sensor to supplement the electrolyte solution with water, so as to reduce the measurement error.

Boosted performance of thin-film nanocomposite membranes based on phytic acid functionalized Zr-MOF for nanofiltration

Endowed with designable pore structure and intrinsically interconnected channels, metal-organic frameworks (MOFs) offer immense potential as functional nanofillers to boost the performance of nanocomposite membranes. However, achieving optimal pore size matching between MOFs and the polymer matrix while maintaining robust interfacial affinity remains a significant challenge in fabricating high-performance nanocomposite membranes. Herein, natural organic polyphosphate phytic acid was utilized to functionalize PCN-224 to narrow its pore size and enhance the polymer affinity. Thin-film nanocomposites containing mPCN-224 were afterward synthesized on the polysulfone support through a combined approach of anodic electrophoretic deposition (EPD) and vacuum filtration-assisted interfacial polymerization (VF-IP). The incorporation of mPCN-224 nanoparticles not only enhanced the hydrophilicity and electronegativity of the polyamide film but also led to a substantial reduction in film thickness. This is likely attributed to lessened piperazine supply at the interface, related to its limited diffusion at the presence of negatively charged mPCN-224. The additional nanochannels provided by mPCN-224, coupled with the loose PA layer, resulted in a substantial 56.3 % increase in the water permeance of the TFN-mPCN-224 membrane, reaching 20.0 L m−2 h−1 bar−1. Additionally, the post-synthesis modification with phytic acid led to an improved Cl−/SO42− selectivity coefficient of 44, substantially higher than that of the TFN-PCN-224 membrane. This improvement was primarily attributed to the narrowed pore size of mPCN-224 and the enhanced surface electronegativity. This study introduces a pathway for developing high-performance TFN membranes based on post-synthetic modification of MOF nanofillers with phytic acid molecules.

The asymptotic preserving unified gas kinetic scheme for the multi-scale kinetic SIR epidemic model

In this paper, we present an asymptotic preserving scheme for the two-dimensional space-dependent and multi-scale kinetic SIR epidemic model which is widely used to model the spread of infectious diseases in populations. The scheme combines a discrete ordinate method for the velocity variables and finite volume method for the spatial and time variables. The idea of unified gas kinetic scheme (UGKS) is used to construct the numerical boundary fluxes which needs the formal integral solutions of the model. Due to the coupling of the three transfer equations in the SIR model, it is difficult to obtain these integral solutions dependently. We decouple the system by constructing the fluxes in a separate way. Then following the framework of UGKS we can obtain the macro auxiliary quantities which is needed in the scheme. Thus the SIR model can be solved in the sequential way. In addition, we can show numerically that the scheme is second-order accurate both in space and time. Moreover, it can not only capture the solution of the diffusion limit equations without requiring the cell size and time step being related to the smallness of the scaling parameters, but also resolve the solution in hyperbolic regime in a natural way. Furthermore, the positive property of the UGKS is analyzed in detail, and through adding time step constraint conditions and applying nodal limiters together, the positive UGKS, called PPUGKS2−order, is obtained. Moreover, in order release the time step constraints in the diffusion regime, a temporal first-order accuracy positive preserving UGKS, called PPUGKS1−order, is proposed. Finally, several numerical tests are included to validate the performance of the proposed schemes.

Diffusion Mechanism of Waste Crumb Rubber Composite Modified Asphalt Based on Molecular Dynamics Simulation

Waste crumb rubber composite modified asphalt (CRCMA), composed of base asphalt, waste rubber powder, and several additives (softener, activator, and cross-linking agent), has been shown to effectively improve asphalt properties. The interactions between the components in CRCMA are complex, involving molecular diffusion that significantly impacts its performance. The diffusion behavior in asphalt molecules will affect various properties of asphalt and the reasons for the different properties of asphalt can be explained by studying its diffusion mechanism. Therefore, understanding the diffusion mechanism of CRCMA is essential. The molecular dynamics simulation was employed to analyze the factors influencing the diffusion mechanism, using the diffusion coefficient as a key indicator of molecular mobility. The findings showed that the diffusion coefficient of the asphalt system decreased over time but increased with temperature. The rubber composition type also had a significant impact on diffusion, with butadiene rubber (BR) showing the highest coefficient, followed by natural rubber (NR), crumb rubber (CR), and styrene-butadiene rubber (SBR). The diffusion coefficient was the lowest and the diffusion rate was slowest after adding softeners. The diffusion coefficient increased slightly with the addition of CR, and the diffusion rate was slightly accelerated but not significantly. The diffusion coefficient increased rapidly with adding activator and the diffusion rate increased significantly. With the addition of cross-linking agent, the diffusion coefficient began to decrease and the diffusion rate became slower. The CRCMA microscopic performance tests indicated that the swelling effect of CR limits diffusion, while activators promote degradation and desulfurization of CR due to the large molecule structure getting smaller, enhancing diffusion. The S=O bond in the asphalt system was regenerated and re-crosslinked to create a mesh after adding the cross-linking agent. The small molecule structure was transformed into large one. The molecular diffusion was restricted partly and thus the diffusion rate was slowed down.

Fluctuating hydrodynamics of an autophoretic particle near a permeable interface

We study the autophoretic motion of a spherical active particle interacting chemically and hydrodynamically with its fluctuating environment in the limit of rapid diffusion and slow viscous flow. Then, the chemical and hydrodynamic fields can be expressed in terms of integrals. The resulting boundary-domain integral equations provide a direct way of obtaining the traction on the particle, requiring the solution of linear integral equations. An exact solution for the chemical and hydrodynamic problems is obtained for a particle in an unbounded domain. For motion near boundaries, we provide corrections to the unbounded solutions in terms of chemical and hydrodynamic Green's functions, preserving the dissipative nature of autophoresis in a viscous fluid for all physical configurations. Using this, we give the fully stochastic update equations for the Brownian trajectory of an autophoretic particle in a complex environment. First, we analyse the Brownian dynamics of particles capable of complex motion in the bulk. We then introduce a chemically permeable planar surface of two immiscible liquids in the vicinity of the particle and provide explicit solutions to the chemo-hydrodynamics of this system. Finally, we study the case of an isotropically phoretic particle hovering above an interface as a function of interfacial solute permeability and viscosity contrast.

Cryopreservation of Neuroectoderm on a Pillar Plate and In Situ Differentiation into Human Brain Organoids.

Cryopreservation in cryovials extends cell storage at low temperatures, and advances in organoid cryopreservation improve reproducibility and reduce generation time. However, cryopreserving human organoids presents challenges due to the limited diffusion of cryoprotective agents (CPAs) into the organoid core and the potential toxicity of these agents. To overcome these obstacles, we developed a cryopreservation technique using a pillar plate platform. To demonstrate cryopreservation application to human brain organoids (HBOs), early stage HBOs were produced by differentiating induced pluripotent stem cells (iPSCs) into neuroectoderm (NE) in an ultralow attachment (ULA) 384-well plate. The NE was transferred and encapsulated in Matrigel on the pillar plate. The NE on the pillar plate was exposed to four commercially available CPAs, including the PSC cryopreservation kit, CryoStor CS10, 3dGRO, and 10% DMSO, before being frozen overnight at -80 °C and subsequently stored in a liquid nitrogen dewar. We examined the impact of the CPA type, organoid size, and CPA exposure duration on cell viability post-thaw. Additionally, the differentiation of NE into HBOs on the pillar plate was assessed using RT-qPCR and immunofluorescence staining. The PSC cryopreservation kit proved to be the least toxic for preserving the early stage HBOs on the pillar plate. Notably, smaller HBOs showed higher cell viability postcryopreservation than larger ones. An incubation period of 80 min with the PSC kit was essential to ensure optimal CPA diffusion into HBOs with a diameter of 400-600 μm. These cryopreserved early stage HBOs successfully matured over 30 days, exhibiting gene expression patterns akin to noncryopreserved HBOs. The cryopreserved early stage HBOs on the pillar plate maintained high viability after thawing and successfully differentiated into mature HBOs. This on-chip cryopreservation method could extend to other small organoids, by integrating cryopreservation, thawing, culturing, staining, rinsing, and imaging processes within a single system, thereby preserving the 3D structure of the organoids.

Tailored 3D Agarose-Well Integrated with Human Skin Equivalents for Enhanced Skin Penetration Assessment

We developed a tailored 3D Agarose-well system integrated with reconstructed human skin equivalents to enhance skin penetration assessments. This system addresses common limitations in traditional trans-well reconstructions, such as dermal layer contraction and limited lateral diffusion, by entangling collagen fibrils within the Agarose-well. We evaluated the penetration behavior of three peptides, with and without skin-penetrating peptide (SPP) sequences, alongside adenosine, a known anti-wrinkle agent. Despite a SPP having a molecular weight approximately four times greater than that of adenosine, its kinetic constant was similar, with values of about 39 and 34, respectively. Moreover, this living skin equivalent system not only allowed for the evaluation of adenosine penetration, but also demonstrated its biological effects, with adenosine significantly enhancing procollagen synthesis by approximately 23% compared to the control. Overall, this novel strategy holds the potential for tailoring 3D Agarose-wells and advancing high-performance gel development, making it a promising approach for applications in tissue engineering, medical science, regenerative medicine, and cosmetics.

Dynamic culture of cerebral organoids using a pillar/perfusion plate for the assessment of developmental neurotoxicity

Despite the potential toxicity of commercial chemicals to the development of the nervous system (known as developmental neurotoxicity or DNT), conventionalin vitrocell models have primarily been employed for the assessment of acute neuronal toxicity. On the other hand, animal models used for the assessment of DNT are not physiologically relevant due to the heterogenic difference between humans and animals. In addition, animal models are low-throughput, time-consuming, expensive, and ethically questionable. Recently, human brain organoids have emerged as a promising alternative to assess the detrimental effects of chemicals on the developing brain. However, conventional organoid culture systems have several technical limitations including low throughput, lack of reproducibility, insufficient maturity of organoids, and the formation of the necrotic core due to limited diffusion of nutrients and oxygen. To address these issues and establish predictive DNT models, cerebral organoids were differentiated in a dynamic condition in a unique pillar/perfusion plate, which were exposed to test compounds to evaluate DNT potential. The pillar/perfusion plate facilitated uniform, dynamic culture of cerebral organoids with improved proliferation and maturity by rapid, bidirectional flow generated on a digital rocker. Day 9 cerebral organoids in the pillar/perfusion plate were exposed to ascorbic acid (DNT negative) and methylmercury (DNT positive) in a dynamic condition for 1 and 3 weeks, and changes in organoid morphology and neural gene expression were measured to determine DNT potential. As expected, ascorbic acid did not induce any changes in organoid morphology and neural gene expression. However, exposure of day 9 cerebral organoids to methylmercury resulted in significant changes in organoid morphology and neural gene expression. Interestingly, methylmercury did not induce adverse changes in cerebral organoids in a static condition, thus highlighting the importance of dynamic organoid culture in DNT assessment.

Endogenous Magnetic Lipid Droplet-Mediated Cascade-Targeted Sonodynamic Therapy as an Approach to Reversing Breast Cancer Multidrug Resistance.

Multidrug resistance (MDR) has emerged as a major barrier to effective breast cancer treatment, contributing to high rates of chemotherapy failure and disease recurrence. There is thus a pressing need to overcome MDR and to facilitate the efficient and precise treatment of breast cancer in a targeted manner. In this study, endogenous functional lipid droplets (IR780@LDs-Fe3O4/OA) were developed and used to effectively overcome the limited diffusion distance of reactive oxygen species owing to their amenability to cascade-targeted delivery, thereby facilitating precise and effective sonodynamic therapy (SDT) for MDR breast cancer. Initially, IR780@LDs-Fe3O4/OA was efficiently enriched within tumor sites in a static magnetic field, achieving the visualization of tumor treatment. Subsequently, the cascade-targeted SDT combined with the Fenton effect induced lysosome membrane permeabilization and relieved lysosomal sequestration, thus elevating drug concentration at the target site. This treatment approach also suppressed ATP production, thereby inhibiting P-glycoprotein-mediated chemotherapeutic drug efflux. This cascade-targeted SDT strategy significantly increased the sensitivity of MDR cells to doxorubicin, increasing the IC50 value of doxorubicin by approximately 10-fold. Moreover, the cascade-targeted SDT also altered the gene expression profiles of MDR cells and suppressed the expression of MDR-related genes. In light of these promising results, the combination of cascade-targeted SDT and conventional chemotherapy holds great clinical promise as an effective treatment modality with excellent biocompatibility that can improve MDR breast cancer patient outcomes.

An Integrated Microcurrent Delivery System Facilitates Human Parathyroid Hormone Delivery for Enhancing Osteoanabolic Effect.

Human parathyroid hormone (1-34) (PTH) exhibits osteoanabolic and osteocatabolic effects, with shorter plasma exposure times favoring bone formation. Subcutaneous injection (SCI) is the conventional delivery route for PTH but faces low delivery efficiency due to limited passive diffusion and the obstruction of the vascular endothelial barrier, leading to prolonged drug exposure times and reduced osteoanabolic effects. In this work, a microcurrent delivery system (MDS) based on multimicrochannel microneedle arrays (MMAs) is proposed, achieving high efficiency and safety for PTH transdermal delivery. The internal microchannels of the MMAs are fabricated using high-precision 3D printing technology, providing a concentrated and safe electric field that not only accelerates the movement of PTH but also reversibly increases vascular endothelial permeability by regulating the actin cytoskeleton and interendothelial junctions through Ca2+-dependent cAMP signaling, ultimately promoting PTH absorption and shortening exposure times. The MDS enhances the osteoanabolic effect of PTH in an osteoporosis model by inhibiting osteoclast differentiation on the bone surface compared to SCI. Moreover, histopathological analysis of the skin and organs demonstrated the good safety of PTH delivered by MDS in vivo. In addition to PTH, the MDS shows broad prospects for the high-efficiency transdermal delivery of macromolecular drugs.

On the self-similarity of unbounded viscous Marangoni flows

The Marangoni flow induced by an insoluble surfactant on a fluid–fluid interface is a fundamental problem investigated extensively due to its implications in colloid science, biology, the environment and industrial applications. Here, we study the limit of a deep liquid subphase with negligible inertia (low Reynolds number, $Re\ll {1}$ ), where the two-dimensional problem has been shown to be described by the complex Burgers equation. We analyse the problem through a self-similar formulation, providing further insights into its structure and revealing its universal features. Six different similarity solutions are found. One of the solutions includes surfactant diffusion, whereas the other five, which are identified through a phase-plane formalism, hold only in the limit of negligible diffusion (high surface Péclet number $Pe_s\gg {1}$ ). Surfactant ‘pulses’, with a locally higher concentration that spreads outward, lead to two similarity solutions of the first kind with a similarity exponent $\beta =1/2$ . On the other hand, distributions that are locally depleted and flow inwards lead to similarity of the second kind, with two different exponents that we obtain exactly using stability arguments. We distinguish between ‘dimple’ solutions, where the surfactant has a quadratic minimum and $\beta =2$ , from ‘hole’ solutions, where the concentration profile is flatter than quadratic and $\beta =3/2$ . Each of these two cases exhibits two similarity solutions, one valid prior to a critical time $t_*$ when the derivative of the concentration is singular, and another one valid after $t_*$ . We obtain all six solutions in closed form, and discuss predictions that can be extracted from these results.

Nonlinear effects of partitioning and diffusion limitation on the efficiency of three-layer enzyme bioreactors and potentiometric biosensors

The nonlinear effects of the partitioning and diffusion limitation on the efficiency of enzyme-based bioreactors and potentiometric biosensors are investigated analytically and numerically using a three-layer mathematical model involving the Michaelis–Menten type reaction in the transient and steady states. Analytical expressions of the steady state substrate and reaction product concentrations and the bioreactor effectiveness as well as biosensor output potential are presented for the first and zero-order reaction rates. Mathematical modelling of the diffusion limiting membrane and the conditions under which the same values of the steady state characteristics are obtained when simulating the treated system at different values of the diffusion and distribution coefficients are investigated. The effective diffusion coefficients in the total diffusion layer consisting of the diffusion limiting membrane and the outer diffusion (Nernst) layer are applied to reduce the three-layer model to the corresponding two-layer model. The dynamics and behaviour of the substrate consumption rate, product emission rate, effectiveness factor and the output potential are numerically investigated.

Fast simulation strategy for capacitively-coupled plasmas based on fluid model

Fluid simulations are widely used in optimizing the reactor geometry and improving the performance of capacitively coupled plasma (CCP) sources in industry, so high computation speed is very important. In this work, a fast method for CCP fluid simulation based on the framework of Multi-physics Analysis of Plasma Sources (MAPS) is developed, which includes a multi-time-step explicit upwind scheme to solve electron fluid equations, a semi-implicit scheme and an iterative method with in-phase initial value to solve Poisson's equation, an explicit upwind scheme with limited artificial diffusion to solve heavy particle fluid equations, and an acceleration method based on fluid equation modification to reduce the periods required to reach equilibrium. In order to prove the validity and efficiency of the newly developed method, benchmarking against COMSOL and comparison with experimental data have been performed in argon discharges on the Gaseous Electronics Conference (GEC) reactor. Besides, the performance of each acceleration method is tested, and the results indicated that the multi-time-step explicit Euler scheme can effectively decline the computational burden in the bulk plasma and reduce the time cost on the electron fluid equations by half. The in-phase initial value method can greatly decrease the iteration times required to solve linear equations and lower the computational time of Poisson's equation by 77 %. The acceleration method based on equation modification can reduce the periods required to reach equilibrium by two-thirds.

Simulated hydrogen diffusion in diamond grain boundaries

To evaluate hydrogen diffusion within diamond, a series of molecular dynamics simulations have been carried out in which diffusion coefficients and activation energies were determined. Diamond grown via chemical vapour deposition (CVD) contains a high hydrogen concentration within grain boundaries, because of this, common tilt grain boundaries were recreated from transmission electron microscopy images taken from literature. Diffusion coefficients of hydrogen placed within the grain boundary were estimated and compared to the bulk diffusion. Unlike many crystalline structures, some grain boundaries presented limited diffusion when compared to the bulk. Diffusion characteristics of grain boundaries are thought to be a result of channelling effects combined with the formation of sp3C-H bonds with sp2 carbon present within some grain boundaries - increasing and decreasing diffusion rates respectively. Potential wells were observed across some but not all the grain boundaries resulting in hydrogen trapping and anisotropic diffusion.

Antibacterial cationic porous organic polymer coatings via an adsorption-contact-photodynamic inactivation strategy for treatment of drug-resistant bacteria

Although photodynamic therapy (PDT) has great potential for treating severely infected wounds, it is restricted by the short lifetime, limited diffusion distance of reactive oxygen species (ROS), and incomplete contact with bacteria. Herein, we report a novel nanosized ionic porous organic polymer (TPAPy-IPOP) based on the triphenylamine (TPA) moiety. Strong electron-deficient cationic groups were introduced into TPA to construct the donor–acceptor (D–A) system, in which the photoelectric effect of TPAPy-IPOP was greatly enhanced, and it was easily excited to produce ROS under irradiation with visible light. The introduction of cations not only facilitated bacterial adsorption by TPAPy-IPOP via electrostatic attraction, which was more conducive to killing bacteria by ROS, but also inactivated bacteria by the cations directly. The nanosized TPAPy-IPOP remained suspended in water for several months and could be sprayed onto various substrates to form a durable coating with excellent antibacterial properties. The in vivo results proved that the silk fibroin/polyvinyl alcohol non-woven fabric (SF/PVA) coated with TPAPy-IPOP could create and maintain a sterile microenvironment at a wound site. The rapid reduction in inflammation resulting from its bactericidal action accelerated the wound healing rate. Collectively, this design is expected to offer a generalizable approach for developing novel antibacterial therapeutic photosensitizers, especially for infected wound treatment.

Linking the spatiotemporal distribution of static stress drops to source faults in a fluid-driven earthquake swarm, northeastern Noto Peninsula, central Japan

We investigated stress drops during an earthquake swarm in northeastern Noto Peninsula, central Japan, which is characterized by ongoing seismic activity in four clusters. We focused on the spatiotemporal distribution of the static stress drop and its relationship with the source faults of the earthquake swarm. Employing the empirical Green’s function method, we estimated static stress drops for 90 earthquakes of MJMA 3.0–5.4. We obtained logarithmic mean stress drops of 13 MPa and 19 MPa from P-wave and S-wave analyses, respectively, which were typical values for crustal earthquakes. We comprehensively analyzed the spatiotemporal distribution of static stress drops in the northern cluster due to the abundance of available data and clarity of fault structures there. We observed larger static stress drops for earthquakes along shallow portions of the source faults, as defined by the hypocentral distribution during a given period. Conversely, we observed smaller static stress drops for earthquakes at medial parts along the faults. These results suggest higher fault strength at shallower parts along the faults and reduced fault strength at medial parts. We attribute the high fault strength at shallow parts to low pore fluid pressure after only limited fluid diffusion near the fault terminus. In contrast, we attribute the reduction in fault strength at medial parts to high pore fluid pressure within the fault following penetration by migrating fluids.Graphical

Low-Temperature Selective Si:As Epitaxy

A selective low-temperature Si:As (LT-SiAs) process is presented which utilizes cyclic deposition-etch (CDE) at <450oC. Selectivity against SiN and SiOx dielectrics and crystallinity are confirmed on gate-all-around (GAA) patterned structures. Hall measurements on blanket wafers show a resistivity minimum of 0.42 mΩ-cm at ~1.7% As for selective LT-SiAs. Secondary-ion mass spectroscopy (SIMS) profiles of P and As diffusion into intrinsic Si (i-Si) for LT-SiP/LT-SiAs/i-Si and LT-SiP/i-Si stacks show >2× benefit of using LT-SiAs spacers to minimize dopant diffusion for as-deposited, soak-annealed and spike-annealed samples. Improvement is attributed to relatively limited diffusivity of As in Si versus P and the lower As concentration needed for LT-SiAs layer to achieve minimum resistivity relative to LT-SiP (~3%). Lastly, a comparison of LT-SiAs and high-temperature Si:As (HT-SiAs) shows a ~2× reduction of As diffusion into i-Si for LT-SiAs at length scales of >10nm.

Mathematical Models of Drug Delivery via a Contact Lens During Wear

AbstractIn this work we develop and investigate mathematical and computational models that describe drug delivery from a contact lens during wear. Our models are designed to predict the dynamics of drug release from the contact lens and subsequent transport into the adjacent pre-lens tear film and post-lens tear film as well as into the ocular tissue (e.g. cornea), into the eyelid, and out of these regions. These processes are modeled by one dimensional diffusion out of the lens coupled to compartment-type models for drug concentrations in the various accompanying regions. In addition to numerical solutions that are compared with experimental data on drug release in an in vitro eye model, we also identify a large diffusion limit model for which analytical solutions can be written down for all quantities of interest, such as cumulative release of the drug from the contact lens. We use our models to make assessments about possible mechanisms and drug transport pathways through the pre-lens and post-lens tear films and provide interpretation of experimental observations. We discuss successes and limitations of our models as well as their potential to guide further research to help understand the dynamics of ophthalmic drug delivery via drug-eluting contact lenses.