arXiv subjects

Rayanne A. Luke

Publications and source records attributed to Rayanne A. Luke.

10 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↗

arXiv2026

A geometry-dependent, force balance-driven model of Staphylococcus epidermidis biofilm cell cluster detachment

Biofilms, bacteria cells surrounded by a self-produced polymeric matrix, are common on medical devices and lead to many hospital infections. The biofilm lifecycle includes disassembly and dispersion, where bacteria clusters detach from the biofilm, circulate in the bloodstream, and potentially colonize secondary infection sites. Existing models often simplify detachment to a function of biofilm thickness or extracellular polymeric substance (EPS) density, without tracking properties of detached clusters that impact their biological fate, including cluster size and morphology. Addressing this gap, our detachment model accounts for drag and adhesion in tagged sections of the biofilm determined by the cluster geometry and local arrangement of bacteria and EPS. A stickiness parameter controls local EPS adhesion strength, which is modulated to disrupt (or compromise) EPS biomass. We specifically model the detachment of clusters from a Staphylococcus epidermidis biofilm grown for 24 hours. Experimental data for biofilm microstructural features are utilized to benchmark the simulated biofilm, which is then subjected to different EPS disruption levels. We examine parameters that influence detached biofilm cell cluster frequency, size, and shape, providing mechanistic insights into how compromised EPS influences detachment dynamics. This integrated modeling framework is a significant advance in the predictive capabilities for biofilm detachment processes.

q-bio.QM↗

arXiv2025

Probabilistic Modeling of Antibody Kinetics Post Infection and Vaccination: A Markov Chain Approach

Understanding the dynamics of antibody levels is crucial for characterizing the time-dependent response to immune events: either infections or vaccinations. The sequence and timing of these events significantly influence antibody level changes. Despite extensive interest in the topic in the recent years and many experimental studies, the effect of immune event sequences on antibody levels is not well understood. Moreover, disease or vaccination prevalence in the population are time-dependent. This, alongside the complexities of personal antibody kinetics, makes it difficult to analyze a sample immune measurement from a population. As a solution, we design a rigorous mathematical characterization in terms of a time-inhomogeneous Markov chain model for event-to-event transitions coupled with a probabilistic framework for the post-event antibody kinetics of multiple immune events. We demonstrate that this is an ideal model for immune event sequences, referred to as personal trajectories. This novel modeling framework surpasses the susceptible-infected-recovered (SIR) characterizations by rigorously tracking the probability distribution of population antibody response across time. To illustrate our ideas, we apply our mathematical framework to longitudinal severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) data from individuals with multiple documented infection and vaccination events. Our work is an important step towards a comprehensive understanding of antibody kinetics that could lead to an effective way to analyze the protective power of natural immunity or vaccination, predict missed immune events at an individual level, and inform booster timing recommendations.

q-bio.PE↗

arXiv2024

Prevalence estimation methods for time-dependent antibody kinetics of infected and vaccinated individuals: a graph-theoretic approach

Immune events such as infection, vaccination, and a combination of the two result in distinct time-dependent antibody responses in affected individuals. These responses and event prevalences combine non-trivially to govern antibody levels sampled from a population. Time-dependence and disease prevalence pose considerable modeling challenges that need to be addressed to provide a rigorous mathematical underpinning of the underlying biology. We propose a time-inhomogeneous Markov chain model for event-to-event transitions coupled with a probabilistic framework for anti-body kinetics and demonstrate its use in a setting in which individuals can be infected or vaccinated but not both. We prove the equivalency of this approach to the framework developed in our previous work. Synthetic data are used to demonstrate the modeling process and conduct prevalence estimation via transition probability matrices. This approach is ideal to model sequences of infections and vaccinations, or personal trajectories in a population, making it an important first step towards a mathematical characterization of reinfection, vaccination boosting, and cross-events of infection after vaccination or vice versa.

q-bio.PE↗

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

Modeling in higher dimensions to improve diagnostic testing accuracy: theory and examples for multiplex saliva-based SARS-CoV-2 antibody assays

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic has emphasized the importance and challenges of correctly interpreting antibody test results. Identification of positive and negative samples requires a classification strategy with low error rates, which is hard to achieve when the corresponding measurement values overlap. Additional uncertainty arises when classification schemes fail to account for complicated structure in data. We address these problems through a mathematical framework that combines high dimensional data modeling and optimal decision theory. Specifically, we show that appropriately increasing the dimension of data better separates positive and negative populations and reveals nuanced structure that can be described in terms of mathematical models. We combine these models with optimal decision theory to yield a classification scheme that better separates positive and negative samples relative to traditional methods such as confidence intervals (CIs) and receiver operating characteristics. We validate the usefulness of this approach in the context of a multiplex salivary SARS-CoV-2 immunoglobulin G assay dataset. This example illustrates how our analysis: (i) improves the assay accuracy (e.g. lowers classification errors by up to 42 % compared to CI methods); (ii) reduces the number of indeterminate samples when an inconclusive class is permissible (e.g. by 40 % compared to the original analysis of the example multiplex dataset); and (iii) decreases the number of antigens needed to classify samples. Our work showcases the power of mathematical modeling in diagnostic classification and highlights a method that can be adopted broadly in public health and clinical settings.

q-bio.QM↗

arXiv2022

Fitting ODE models of tear film breakup

The contribution of different physical effects to tear breakup (TBU) in subjects with no self-reported history of dry eye are quantified. An automated system using a convolutional neural network is deployed on fluorescence (FL) imaging videos to identify multiple likely TBU instances in each trial. Once identified, extracted FL intensity data was fit by mathematical models that included tangential flow along the eye, evaporation, osmosis and FL intensity of emission from the tear film. The mathematical models consisted of systems of ordinary differential equations for the aqueous layer thickness, osmolarity, and the FL concentration. Optimizing the fit of the models to the FL intensity data determined the mechanism(s) driving each instance of TBU and produced an estimate of the osmolarity within TBU. Fits were produced for 467 instances of potential TBU from 15 non-DED subjects. The results showed a distribution of causes of TBU in these healthy subjects, as reflected by estimated flow and evaporation rates, which appear to agree well with previously published data. Final osmolarity depended strongly on the TBU mechanism, generally increasing with evaporation rate but complicated by the dependence on flow. The results suggest that it might be possible to classify individual subjects and provide a baseline for comparison and potential classification of dry eye disease subjects.

math.NA↗

arXiv2022

Optimal classification and generalized prevalence estimates for diagnostic settings with more than two classes

An accurate multiclass classification strategy is crucial to interpreting antibody tests. However, traditional methods based on confidence intervals or receiver operating characteristics lack clear extensions to settings with more than two classes. We address this problem by developing a multiclass classification based on probabilistic modeling and optimal decision theory that minimizes the convex combination of false classification rates. The classification process is challenging when the relative fraction of the population in each class, or generalized prevalence, is unknown. Thus, we also develop a method for estimating the generalized prevalence of test data that is independent of classification. We validate our approach on serological data with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) naïve, previously infected, and vaccinated classes. Synthetic data are used to demonstrate that (i) prevalence estimates are unbiased and converge to true values and (ii) our procedure applies to arbitrary measurement dimensions. In contrast to the binary problem, the multiclass setting offers wide-reaching utility as the most general framework and provides new insight into prevalence estimation best practices.

q-bio.QM↗

arXiv2021

Mechanistic determination of tear film thinning via fitting simplified models to tear breakup

Purpose: To determine whether evaporation, tangential flow, or a combination of the two cause tear film breakup in a variety of instances; to estimate related breakup parameters that cannot be measured in breakup during subject trials; and to validate our procedure against previous work. Methods: Five ordinary differential equation models for tear film thinning were designed that model evaporation, osmosis, and various types of flow. Eight tear film breakup instances of five healthy subjects that were identified in fluorescence images in previous work were fit with these five models. The fitting procedure used a nonlinear least squares optimization that minimized the difference of the computed theoretical fluorescent intensity from the models and the experimental fluorescent intensity from the images. The optimization was conducted over the evaporation rate and up to three flow rate parameters. The smallest norm of the difference was determined to correspond to the model that best explained the tear film dynamics. Results: All of the breakup instances were best fit by models with time-dependent flow. Our optimal parameter values and thinning rate and fluid flow profiles compare well with previous partial differential equation model results in most instances. Conclusion: Our fitting procedure suggests that the combination of the Marangoni effect and evaporation cause most of the breakup instances. Comparison with results from previous work suggests that the simplified models can capture the essential tear film dynamics in most cases, thereby validating this procedure as one that could be used on many other instances.

physics.flu-dyn↗

arXiv2020

Parameter Estimation for Mixed-Mechanism Tear Film Thinning

Etiologies of tear breakup include evaporation-driven, divergent flow-driven, and a combination of these two. A mathematical model incorporating evaporation and lipid-driven tangential flow is fit to fluorescence imaging data. The lipid-driven motion is hypothesized to be caused by localized excess lipid, or "globs." Tear breakup quantities such as evaporation rates and tangential flow rates cannot currently be directly measured during breakup. We determine such variables by fitting mathematical models for tear breakup and the computed fluorescent intensity to experimental intensity data gathered in vivo. Parameter estimation is conducted via least squares minimization of the difference between experimental data and computed answers using either the trust-region-reflective or Levenberg-Marquardt algorithm. Best-fit determination of tear breakup parameters supports the notion that evaporation and divergent tangential flow can cooperate to drive breakup. The resulting tear breakup is typically faster than purely evaporative cases. Many instances of tear breakup may have similar causes, which suggests that interpretation of experimental results may benefit from considering multiple mechanisms.

physics.flu-dyn↗