arXiv subjects

Daniel M. Anderson

Publications and source records attributed to Daniel M. Anderson.

4 recordsLinked to original sources

arXiv2026

Drug release dynamics from a three-layer composite contact lens in the vial, eye wear with blinking, and blister pack settings

In this work we design a multi-layer model of composite contact lens drug release. Such lenses have been designed by encapsulating drug-polymer films in contact lens hydrogels. Composite lenses can promote sustained discharge of drug and achieve near zero-order release kinetics, thus surpassing other ocular delivery methods that are limited by short residence times and an undesirable initial burst release. Our model is informed by in vivo data, and includes three coupled partial differential equation layers to simulate the composite lens. We mathematically investigate the effect of composite contact lens design characteristics on the time to $50\%$ therapeutic drug release ($t_{50}$) in the vial, eye, and blister pack settings. In the eye setting, we incorporate our prior model that considers the effect of many blinks on the pre- and post-lens tear film drug concentrations. We simulate drug cumulative release profiles and study the variability of $t_{50}$ across: (1) the ratio of the drug-polymer film to hydrogel diffusion coefficients, (2) the centerline of the polymer film within the hydrogel, and (3) the polymer film thickness. In the blister pack setting, we study storage questions that may inform future commercial design. This work may help medical professionals better understand the mechanics of contact lens drug delivery and predict targeted tissue transport of ophthalmic drugs.

physics.bio-ph↗

arXiv2024

Mathematical models of drug delivery via a contact lens during wear

In 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.

physics.bio-ph↗

arXiv2022

Mathematics of Floating 3D Printed Objects

We explore the stability of floating objects through mathematical modeling and experimentation. Our models are based on standard ideas of center of gravity, center of buoyancy, and Archimedes' Principle. We investigate a variety of floating shapes with two-dimensional cross sections and identify analytically and/or computationally a potential energy landscape that helps identify stable and unstable floating orientations. We compare our analyses and computations to experiments on floating objects designed and created through 3D printing. In addition to our results, we provide code for testing the floating configurations for new shapes, as well as giving details of the methods for 3D printing the objects. The paper includes conjectures and open problems for further study.

physics.class-ph↗

arXiv2020

Mathematical analysis and potential therapeutic implications of a novel HIV-1 model of basal and activated transcription in T-cells and macrophages

HIV-1 affects tens of millions of people worldwide. Current treatments often involve a cocktail of antiretroviral drugs, which are effective in reducing the virus and extending life spans. However, there is currently no FDA-approved HIV-1 transcription inhibitor. Furthermore, there have only been a few attempts to model the transcription process in HIV-1. In this work, we extend a novel three-state model of HIV-1 transcription introduced in DeMarino et al. (2020) that has been developed and validated against experimental data. After fitting this model to in vitro data, significant differences in the transcription process of HIV-1 in T-cells and macrophages have been observed. In particular, the activation of the HIV-1 promoter in T-cells appears to take place rapidly as the Tat protein approaches a critical threshold. In contrast, the same process occurs smoother in macrophages. In this work, we carry out systematic mathematical analyses of the model to complement experimental data fitting and sensitivity analysis performed earlier. We derive explicit solutions of the model to obtain exact transcription process decay rates for the original model and then study the effect of nonlinearity on the system behavior, including the existence and the local and global stability of the positive equilibrium. We were able to show the stability of the positive steady state in limiting cases, with the global stability in the general case remaining an open question. By modeling the effect of transcription-inhibiting drug therapy, we provide a nontrivial condition for it to be effective in reducing viral load. Moreover, our numerical simulations and analysis point out that the effect of the transcription-inhibitor can be enhanced by synchronizing with standard treatments, such as combination antiretroviral therapy, to allow the reduction of total dosages and toxicity.

q-bio.PE↗