Eye2Heart: A reduced mathematical model bridging cardiovascular and ocular hemodynamics

Lorenzo Sala; Mohamed Zaid; Faith Hughes; Marcela Szopos; Virginia H. Huxley; Alon Harris; Giovanna Guidoboni; Sergey Lapin; Lorenzo Sala; Mohamed Zaid; Faith Hughes; Marcela Szopos; Virginia H. Huxley; Alon Harris; Giovanna Guidoboni; Sergey Lapin

doi:10.3934/mbe.2026017

Mathematical Biosciences and Engineering

2026, Volume 23, Issue 2: 421-448. doi: 10.3934/mbe.2026017

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Eye2Heart: A reduced mathematical model bridging cardiovascular and ocular hemodynamics

1.
Université Paris-Saclay, INRAE, MaIAGE, 78350, Jouy-en-Josas, France
2.
Foresite Healthcare LLC, Maryland Heights, Missouri 63043, USA
3.
Electrical and Computer Engineering, University of Maine, Maine, USA
4.
Université Paris Cité, CNRS, MAP5, F-75006 Paris, France
5.
Department of Medical Pharmacology and Physiology, School of Medicine, University of Missouri, Columbia, MO, United States
6.
Department of Ophthalmology, Icahn School of Medicine at Mount Sinai, New York City, NY, 10029, USA
7.
Department of Mathematics and Statistics, Program in Data Analytics, Washington State University Everett, Everett (WA), USA

Received: 23 July 2025 Revised: 18 November 2025 Accepted: 27 November 2025 Published: 07 January 2026

The cardiovascular and ocular systems are intricately connected, with hemodynamic interactions playing a crucial role in both physiological regulation and pathological conditions. However, existing models often treat these systems separately, thus limiting the understanding of their interdependence. In this study, we present the Eye2Heart model, which is a novel closed-loop mathematical framework that integrates cardiovascular and ocular dynamics. Using an electrical-hydraulic analogy, the model describes the interactions between the heart and retinal circulation through a nonlinear system of ordinary differential equations. The model is tested against clinical and experimental data, thus demonstrating its ability to reproduce key cardiovascular parameters (e.g., stroke volume, cardiac output) and ocular hemodynamics (e.g., retinal blood flow). Additionally, we explore in silico the effects of intraocular pressure and left ventricular compliance on both local ocular and global systemic circulation, thus revealing critical dependencies between cardiovascular and ocular health. The results highlight the model's potential for studying cardiovascular diseases with ocular manifestations and support emerging research in oculomics by providing a mechanistic basis to interpret ocular biomarkers within a systemic context. This paves the way for patient-specific data integration and broader applications in personalized medicine.
- Cardiovascular system,
- ocular hemodynamics,
- oculomics,
- lumped-parameter model,
- ordinary differential equations,
- in silico experimentation,
- left ventricular compliance,
- intraocular pressure
Citation: Lorenzo Sala, Mohamed Zaid, Faith Hughes, Marcela Szopos, Virginia H. Huxley, Alon Harris, Giovanna Guidoboni, Sergey Lapin. Eye2Heart: A reduced mathematical model bridging cardiovascular and ocular hemodynamics[J]. Mathematical Biosciences and Engineering, 2026, 23(2): 421-448. doi: 10.3934/mbe.2026017

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Abstract

The cardiovascular and ocular systems are intricately connected, with hemodynamic interactions playing a crucial role in both physiological regulation and pathological conditions. However, existing models often treat these systems separately, thus limiting the understanding of their interdependence. In this study, we present the Eye2Heart model, which is a novel closed-loop mathematical framework that integrates cardiovascular and ocular dynamics. Using an electrical-hydraulic analogy, the model describes the interactions between the heart and retinal circulation through a nonlinear system of ordinary differential equations. The model is tested against clinical and experimental data, thus demonstrating its ability to reproduce key cardiovascular parameters (e.g., stroke volume, cardiac output) and ocular hemodynamics (e.g., retinal blood flow). Additionally, we explore in silico the effects of intraocular pressure and left ventricular compliance on both local ocular and global systemic circulation, thus revealing critical dependencies between cardiovascular and ocular health. The results highlight the model's potential for studying cardiovascular diseases with ocular manifestations and support emerging research in oculomics by providing a mechanistic basis to interpret ocular biomarkers within a systemic context. This paves the way for patient-specific data integration and broader applications in personalized medicine.

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