Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2507.13589

Quantifying Ocular Surface Changes with Contact Lens Wear

Lucia Carichino·Kara L. Maki·David S. Ross·Riley K. Supple·Evan Rysdam
View original source ↗Read source document ↗Export metadata ↓

Abstract

Over 140 million people worldwide and over 45 million people in the United States wear contact lenses; it is estimated that 12%-27.4% contact lens users stop wearing them due to discomfort. Contact lens mechanical interactions with the ocular surface have been found to affect the ocular surface itself. These mechanical interactions are difficult to measure and calculate in a clinical setting, and the research in this field is limited. This paper presents the first mathematical model that captures the interactions between the contact lens and the open eye, where the contact lens configuration, the contact lens suction pressure, and the deformed ocular shape are all emergent properties of the model. The non-linear coupling between the contact lens and the eye is achieved by assuming that the suction pressure under the lens is applied directly to the ocular surface through the post-lens tear film layer. The contact lens mechanics are modeled using a previous published model. We consider homogeneous and heterogeneous linear elastic eye models, different ocular shapes, different lens shapes and thickness profiles, and extract lens deformations, suction pressure profiles, and ocular deformations and stresses for all the considered scenarios. The model predicts higher ocular deformations and stresses at the center of the eye and in the limbal/scleral regions. Accounting for heterogeneous material eye parameters increases the magnitude of such deformations and stresses. The ocular displacements and stresses non-linearly increase as we increase the stiffness of the contact lens. Inserting a steeper contact lens on the eye results in a reduction of the ocular displacement at the center of the eye and a larger displacement at the edge of the contact lens. The model predictions are compared with experimental data and previously developed mathematical models.

Explore related subjects

math.NAcs.NAphysics.bio-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Lucia Carichino, Kara L. Maki, David S. Ross, Riley K. Supple, Evan Rysdam. 2025-12-10. Quantifying Ocular Surface Changes with Contact Lens Wear. https://doi.org/10.3934/mbe.2026008

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

KEEP EXPLORING

Related papers

arXiv2026

How many continuous measurements are needed to learn a vector?

One can recover vectors from $\mathbb{R}^m$ with arbitrary precision, using only $\lceil \log_2(m)\rceil +1$ continuous measurements that are chosen adaptively. This surprising result is explained and discussed, and we present applications to infinite-dimensional approximation problems.

math.NA↗
arXiv2026

IterativeCUR: Large Rank-Adaptive Approximation From a Small Recycled Sketch

The computation of accurate low-rank matrix approximations is central to improving the scalability of various techniques in machine learning, uncertainty quantification, and control. Traditionally, low-rank approximations are constructed using SVD-based approaches such as truncated SVD or Randomized SVD. Although these SVD approaches---especially Randomized SVD---have proven to be very computationally efficient, other low-rank approximation methods can offer even greater performance. One such approach is the CUR decomposition, which forms a low-rank approximation using direct row and column subsets of a matrix. Because CUR uses direct matrix subsets, it is also often better able to preserve native matrix structures like sparsity or non-negativity than SVD-based approaches and can facilitate data interpretation in many contexts. This paper introduces IterativeCUR, which draws on previous work in randomized numerical linear algebra to build a new algorithm that is highly competitive compared to prior work. IterativeCUR is adaptive in the sense that it takes as an input parameter the desired tolerance $ε$ and outputs (with arbitrarily high probability) an approximation of error bounded by $ε$, rather than requiring an a priori guess of the numerical rank. IterativeCUR typically runs significantly faster than both existing CUR algorithms and techniques such as Randomized SVD. Its asymptotic complexity is $\mathcal{O}(mn + (m+n)r^2)$ for an $m\times n$ matrix of output rank $r$. IterativeCUR relies on a single small sketch from the matrix that is successively downdated as the algorithm proceeds. We demonstrate through extensive experiments that IterativeCUR achieves up to $4\times$ speed-up over state-of-the-art pivoting-on-sketch approaches with no loss of accuracy, and up to $40\times$ speed-up over rank-adaptive randomized SVD approaches.

math.NA↗
arXiv2026

Multigrid with Linear Storage Complexity

As the discretization error for the solution of a partial differential equation (PDE) decreases, the precision required to store the corresponding coefficients naturally increases. Storing the solution's finite element coefficients explicitly requires $\mathcal O(n \log n)$ bits of storage, where $n$ is the number of degrees of freedom (DoFs). This paper presents a full multigrid method to compute the solution in a compressed format that reduces the storage complexity of the solution and intermediate vectors to $\mathcal O(n)$ bits. This reduction allows a matrix-free implementation to solve elliptic PDEs with an overall linear space complexity. For problems limited by the memory capacity of current supercomputers, we expect a memory footprint reduction of about an order of magnitude compared to state-of-the-art mixed-precision methods. We demonstrate the applicability of our algorithm by solving two model problems. Depending on the PDE and polynomial degree, but irrespective of the problem size, the solution vector on the finest grid requires between 4 and 12 bits per DoF, and the residual and correction require 3 to 6 bits each. Additional data is stored on the coarse grids with modestly increasing bit widths toward coarser grids.

math.NA↗