Embedded Files
My work involves optimal decision theory, uncertainty quantification, fluid mechanics, optimization, and image analysis, among other topics, and I collaborate with immunologists, epidemiologists, and optometrists.
Current research topics include (but are not limited to): (1) contact lens drug delivery modeling and comparison to experimental data (joint work with D. Anderson at GMU), (2) probabilistic and Markov chain modeling of time-dependent antibody kinetics (joint work with P. Bedekar at BITS Hyderabad and A. Kearsley at NIST, and with experimental collaborators L. Muehling and G. Canderan at UVA and P. Pannaraj, Y. Lee, and W. Cheng at UCSD), and (3) modeling and agent-based simulation of biofilm matrix breakoff and enzymatic disruption (joint work with S. Olsen at WPI, J. Kreig at LANL, Y. Yu at IUI, and Z. Wang at UK).
I am passionate about science communication. I value presenting my work in an understandable format to stakeholders (immunologists, eye doctors, etc.) and I enjoy attending both mathematics and non-mathematics conferences.
Antibody kinetics of infection and vaccination
Antibody kinetics of infection and vaccination
In a recent paper published in the Bulletin of Mathematical Biology, we designed the first known system to capture immune state transitions and track antibody response over time simultaneously, via a coupled probabilistic and Markov chain model. We also developed an unbiased prevalence estimation scheme to track the fraction of the population that is infected or vaccinated across time. A continuation of the project is funded in part by a collaborative research grant from 4-VA (see below for more).
This work has been presented at several conferences, including at the SIAM Conference on Computational Science and Engineering in Ft. Worth, TX in March 2025 and as a keynote address at the SIAM DMV Conference on Applied Mathematics in Baltimore, MD in April 2025.
Figure to the right: Prevalence estimates for infection (top) and vaccination (bottom) over time for various sample sizes with confidence interval bands. The true prevalence is shown in pink, which is related to the true incidence rate (inset in each subfigure). The estimates are generated using synthetic data that assumes a wave of infections and a constant rate of vaccination.
4-VA funded collaborative research
4-VA funded collaborative research
From July 2024 -- June 2025, I led a team including immunologists (L. Muehling and G. Canderan, UVA), a graduate student (K. Ellis), and undergraduate students (J. O'Hanlon, K. Sullivan) on a project entitled "Data-Driven Modeling of the Time-Dependent Immune Response to Infection and Vaccination." The project was funded by a collaborative research grant from 4-VA, a collaborative partnership for advancing the Commonwealth of Virginia.
Sightseeing at Monticello after a visit to UVA. L-R: R. Luke, K. Ellis, L. Muehling, G. Canderan, K. Sullivan, J. O'Hanlon
Contact lens drug delivery
Contact lens drug delivery
In an invited paper recently published in a special collection of La Matematica, we describe models for drug release by a contact lens during wear over 24 hours of blinking. The model considers pathways of drug release to the pre- and post-lens tear films, and loss from those regions by absorption into the eyelid, sweep out due to blinking, and slide or squeeze out by the motion of the lens. Using physically realistic parameter values, we find good agreement between our solutions and experimental data from an in vitro eye model.
This work has been presented at several conferences including the Association for Research in Vision and Ophthalmology (ARVO) Annual Meeting in Seattle, WA in May 2024 and the American Physical Society Division of Fluid Dynamics (APS DFD) Annual Meeting in Washington, D.C. in November 2023.
Schematic that describes the mechanisms/processes between and during blinks. Red and blue ink denote processes affecting tear film thickness and drug concentration, respectively
We also mention this work in our recent SIAM News blog post on parameter estimation for tear film thinning and breakup, a cause of dry eye disease.
Top: A plot showing the decrease in variance of prevalence estimates from their true values as the number of samples is increased.
Bottom: A GIF from our paper: Modeling in higher dimensions to improve diagnostic testing accuracy: theory and examples for multiplex saliva-based SARS-CoV-2 assays.
Diagnostic testing of more than two classes
Diagnostic testing of more than two classes
Our paper on modeling in higher dimensions to improve diagnostic testing accuracy was highlighted on Kudos.
In a 2023 paper, we solve the multiclass diagnostic classification problem and provide a prevalence estimation framework for settings with more than two classes.
This work has been presented at several conferences including the Seronet Investigators Meeting in Bethesda, MD in March 2023 that gathered researchers studying immune and vaccine responses to SARS-CoV-2, the Joint Mathematics Meetings in Boston, MA in January 2023, and ECMTB (European Conference on Mathematical and Theoretical Biology) in Heidelberg, Germany in September 2022 that was jointly organized with SMB (Society for Mathematical Biology). More recent work has been presented at the SIAM Life Sciences meeting in Portland, OR in June 2024.
Top: Presenting a talk in a session at SIAM Life Sciences in Portland, OR in June 2024.
Bottom: Presenting a poster at the AWM Research Symposium in Minneapolis, MN in June 2022.
Attending the 2019 Association for Research in Vision and Ophthalmology (ARVO) Annual Meeting in Vancouver, BC. I presented a poster.
PhD Thesis
PhD Thesis
My dissertation research focused on fitting models for extreme thinning of the tear film (TBU) to patient data under the advisement of Dr. Richard Braun and in collaboration with Dr. Carolyn Begley and Deborah Antwi (School of Optometry, Indiana University). I extracted meaningful parameters and analyzed quantities that cannot be measured in vivo.
In the final year of my dissertation, I won the Wenbo Li Scholarship for Graduate Research that recognizes an outstanding research paper in the mathematical sciences. The paper is #8 below in Recent Publications.
My PhD thesis was entitled Parameter Identification for Tear Film Thinning and Breakup.
Pitching a poster at the High Performance Computing Symposium in Newark, DE in 2020.
Recent Publications
Recent Publications
Bedekar P*, Luke RA*, Kearsley AJ (2025) Prevalence estimation methods for time-dependent antibody kinetics of infected and vaccinated individuals: a Markov chain approach. Bulletin of Mathematical Biology, 87(26). https://link.springer.com/article/10.1007/s11538-024-01402-0 (*: contributed equally)
Anderson DM, Luke RA (2024) Mathematical models of drug delivery via a contact lens during wear. La Matematica. In special collection Mathematical Modeling of the Eye (invited article). https://link.springer.com/article/10.1007/s44007-024-00136-8
Luke RA, Shaw GJ, Clarke GS, Mollalo A (2024) Identifying long COVID definitions, predictors, and risk factors in the United States: a scoping review of data sources utilizing electronic health records. Informatics, 11(41). https://www.mdpi.com/2227-9709/11/2/41
Luke RA, Kelly N, Stoner M, Esplin O’Brien J, Ellwein Fix L, Lubkin S (2024) Towards a mathematical understanding of ventilator-induced lung injury in preterm rat pups. Mathematical Modeling for Women’s Health. The IMA Volumes in Mathematics and its Applications, 166:167-211. https://link.springer.com/chapter/10.1007/978-3-031-58516-6_6
Driscoll TA, Braun RJ, Luke RA, Sinopoli S, Phatak A, Dorsch J, Begley CG, Awisi-Gyau D (2023) Fitting ODE models of tear film breakup. Modeling and Artificial Intelligence in Ophthalmology 5(1):1-36. https://www.maio-journal.com/index.php/MAIO/article/view/128
Luke RA, Kearsley AJ, Pisanic N, Manabe YC, Thomas DL, Heaney C, Patrone PN (2023) Modeling in higher dimensions to improve diagnostic testing accuracy: theory and examples for multiplex saliva-based SARS-CoV-2 assays. PLoS ONE 18(3): e0280823. https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0280823
Access the supplemental figures HERE
Luke RA, Kearsley AJ, Patrone PN (2023) Optimal classification and generalized prevalence estimates for diagnostic settings with more than two classes. Mathematical Biosciences 358:108982. https://www.sciencedirect.com/science/article/pii/S0025556423000238
Luke RA, Braun RJ, Begley CG (2021) Mechanistic determination of tear film thinning via fitting simplified models to tear breakup. Modeling and Artificial Intelligence in Ophthalmology, 3(1):71-100. https://doi.org/10.35119/maio.v3i1.114
Braun RJ, Luke RA, Driscoll TA, Begley CG (2021) Dynamics and mechanisms for tear breakup (TBU) on the ocular surface. Mathematical Biosciences and Engineering, 18(5):5146-5175. http://aimspress.com/article/doi/10.3934/mbe.2021262
Luke RA, Braun RJ, Driscoll TA, Awisi-Gyau D, Begley CG (2021) Parameter estimation for mixed- mechanism tear film thinning. Bulletin of Mathematical Biology, 83(56). https://link.springer.com/article/10.1007/s11538-021-00871-x
Luke RA, Braun RJ, Driscoll TA, Begley CG, Awisi-Gyau D (2020) Parameter estimation for evaporation-driven tear film thinning. Bulletin of Mathematical Biology, 82(71). https://link.springer.com/article/10.1007/s11538-020-00745-8
For more detailed information, see Dr. Luke's CV and Google Scholar.
Page updated
Google Sites
Report abuse