for this workshop
Multiscale modeling of ocular and cardiovascular systems
at the
American Institute of Mathematics, Pasadena, California
organized by
Virginia Huxley, Sergey Lapin, Lorenzo Sala, Marcela Szopos, and Mohamed Zaid
This workshop, sponsored by AIM and the NSF, will bring together experts in mathematical modeling, biomedical engineering, and clinical research to advance multiscale modeling approaches that bridge ocular, cardiovascular, and systemic dynamics. The non-invasive nature of ocular measurements, such as retinal blood flow and intraocular pressure, provides a unique opportunity for early diagnosis and monitoring of conditions such as diabetes, hypertension, heart failure, and neurological disorders. However, translating these insights into clinical practice requires a strong collaboration between clinicians and modelers to design interpretable and actionable approaches.
A key focus of the workshop will be integrating mechanistic models with data-driven approaches, balancing interpretability with predictive power. Participants will work on developing coupled models using ordinary and partial differential equations, numerical methods, and stochastic approaches to better capture physiological processes across different scales. The workshop will also address challenges in integrating clinical data into these models, exploring techniques like uncertainty quantification, data assimilation, and machine learning to improve model reliability and predictive accuracy.
Through interdisciplinary discussions, the workshop aims to ensure that mathematical models are biologically relevant and clinically useful. By combining biophysical principles with clinical data, participants will explore new ways to refine and validate diagnostic models, bridging the gap between theoretical research and real-world medical applications. Practical sessions will focus on solving computational challenges, refining existing models, and identifying key open questions in the field, with the goal of establishing new research collaborations and improving the mathematical foundation of biomedical modeling.
The main topics for the workshop are:
- Multiscale mathematical modeling: developing models that integrate ocular hemodynamics, cardiovascular function, and systemic regulation with direct relevance for non-invasive diagnostics;
- Stochastic models and uncertainty quantification: addressing biological variability using stochastic differential equations, inverse problems, and data assimilation to improve reliability in clinical predictions;
- Integrating data-driven and mechanistic approaches: exploring how statistical methods, machine learning, and hybrid modeling frameworks can enhance model calibration, improve disease prognosis, and support clinical decision-making.
- Clinically relevant modeling questions and medical impact: identifying key challenges in non-invasive diagnostics and exploring how mathematical models can improve clinical decision-making. The focus will be on developing models that provide actionable insights, enhance diagnostic accuracy, and support personalized medicine.
This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
Space and funding is available for a few more participants. If you would like to participate, please apply by filling out the on-line form no later than May 29, 2025.
Before submitting an application, please read the description of the AIM style of workshop.
For more information email workshops@aimath.org
