Fitting ODE models of tear film breakup

Tobin A. Driscoll; Richard J. Braun; Rayanne A. Luke; Dominick Sinopoli; Aashish Phatak; Julianna Dorsch; Carolyn G. Begley; Deborah Awisi-Gyau

doi:10.35119/maio.v5i1.128

arXiv · 2210.03593

Fitting ODE models of tear film breakup

Tobin A. Driscoll·Richard J. Braun·Rayanne A. Luke·Dominick Sinopoli·Aashish Phatak·Julianna Dorsch·Carolyn G. Begley·Deborah Awisi-Gyau

View original source ↗Read source document ↗Export metadata ↓

Abstract

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.

Explore related subjects

math.NA cs.NA

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Tobin A. Driscoll, Richard J. Braun, Rayanne A. Luke, Dominick Sinopoli, Aashish Phatak, Julianna Dorsch, Carolyn G. Begley, Deborah Awisi-Gyau. 2023-02-21. Fitting ODE models of tear film breakup. https://doi.org/10.35119/maio.v5i1.128

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A Stabilized Finite Element Method for a Morpho-Visco-Poroelastic Model

Studying the structure of soft tissues is important and relevant in biology, particularly in some diseases, such as tumor growth and dermal contraction after burn injury. Based on the complicated characteristics of the tissue and for the sake of a better understanding of the underlying biomechanics, we propose a mathematical model that combines elastic, viscous, and porous effects with growth or shrinkage due to microstructural changes. The framework is referred to as morpho-visco-poroelasticity. Although the existence results of the solution to the problem are not given in this study, we assess the stability of the equilibria for both the continuous and semi-discrete versions of the model, and the key features of this modelling framework have been discussed. To obtain reliable numerical solutions, a stabilized finite element (FE) scheme is proposed for the morpho-visco-poroelasticity equations to avoid spurious oscillations in the pressure profile; the success of this FE scheme is verified by numerical simulations and convergence investigation in both spatial and temporal aspects. For a more quantitative assessment, the total variation of the pressure profile is evaluated as a function of the stabilization parameter.

math.NA↗

arXiv2026

Efficient third-order iterative algorithms for computing zeros of special functions

This manuscript presents a novel and reliable third-order iterative procedure for computing the zeros of solutions to second-order ordinary differential equations. By approximating the solution of the related Riccati differential equation using the trapezoidal rule, this study has derived the proposed third-order method. This work establishes sufficient conditions to ensure the theoretical non-local convergence of the proposed method. This study provides suitable initial guesses for the proposed third-order iterative procedure to compute all zeros in a given interval of the solutions to second-order ordinary differential equations. The orthogonal polynomials like Legendre and Hermite, as well as the special functions like Bessel, Coulomb wave, confluent hypergeometric, and cylinder functions, satisfy the proposed conditions for convergence. Numerical simulations demonstrate the effectiveness of the proposed theory. This work also presents a comparative analysis with recent studies.

math.NA↗

arXiv2026

Machine-Learning-Enhanced Discretize-then-Project Reduced-Order Modeling of Turbulent Flows on Collocated Grids

This study presents a hybrid reduced-order modeling (ROM) framework for incompressible flows on collocated finite-volume grids, combining a discretize-then-project consistent-flux formulation for velocity and pressure with a non-intrusive neural-network closure for turbulent viscosity. The intrusive formulation preserves discrete mass conservation and pressure-velocity coupling, while a reduced pressure reference-cell constraint fixes pressure gauge ambiguity. We evaluate Multilayer Perceptron (MLP), Transformer, and Long Short-Term Memory (LSTM) closures. For a three-dimensional lid-driven cavity at $Re=100$, the LSTM-based ROM achieves relative errors of 0.7% in velocity and 4% in turbulent viscosity. At $Re=3200$, a mode-sensitivity study identifies $N=15$ POD modes as the best overall configuration, balancing accuracy, dimension, robustness, and cost. It yields a final relative velocity error of approximately 12.3% and an online wall-clock speedup of approximately $50\times$ over the full-order model; energy and enstrophy errors remain below 11% for all three architectures. This regime requires case-specific neural-network retraining and pressure reference-cell parameter retuning. In a time-extrapolation test trained on $t\in[0,3]$,s and rolled out to $t=6$,s, the ROM remains bounded, although velocity and pressure errors increase beyond the training window. The LSTM turbulent-viscosity closure remains robust, identifying long-horizon pressure accuracy as the main limitation. These results demonstrate the potential of consistent projection-based modeling combined with data-driven turbulence closure for efficient reduced-order simulation.

math.NA↗