Computational study of retinal blood flow coupled to a global circulation model

This work focuses on the study of retinal blood flow, using computational models to simulate the interactions between ocular circulation and global systemic dynamics. The primary aim of this work is to develop a comprehensive multiscale mathematical model that can accurately represent the blood flow dynamics in the retina, considering the complex interplay between retinal circulation, intraocular pressure, and systemic factors such as cerebrospinal fluid pressure. These interactions are essential for gaining deeper insights into the regulation and behavior of retinal blood flow under normal and pathological conditions. The first chapter provides the physiological background necessary for understanding the intricacies of ocular circulation. It explains the structure and function of the visual apparatus, with particular focus on the vascular system. Detailed descriptions are provided for the retinal and choroidal circulations, both of which are responsible for supplying the retina with oxygen and nutrients, while also facilitating the removal of waste products. The chapter further explores the relationship between ocular circulation and systemic circulation, particularly in the context of intraocular pressure (IOP), which plays a critical role in maintaining the shape of the eye and preventing damage. The dynamics of retinal vein pulsation, influenced by both IOP and intracranial pressure, are also discussed, as well as pathological conditions related to disturbances in retinal circulation. The second chapter reviews the mathematical models that have been developed to simulate retinal blood flow. These models vary in their complexity, from simplified lumpedparameter models to more advanced 1D, 2D, and 3D models. Each model offers a different approach to representing the retinal vascular system and its hemodynamic behavior. The chapter critically examines the strengths and limitations of each. For example, lumped-parameter models provide a global representation of blood flow, but lack spatial resolution, while 1D models offer a more detailed representation of blood flow along the length of vessels, and 3D models capture the full complexity of retinal vasculature but at the cost of higher computational demand. The chapter discusses how advancements in computational power and imaging technologies have contributed to the development of these models, enabling a more accurate understanding of retinal circulation. The third chapter presents the global multiscale mathematical model developed by Müller and Toro, as detailed in their foundational works . This comprehensive model integrates the circulatory system with CSF dynamics, combining one-dimensional (1D) representations of major vessels with zero-dimensional (0D) models for microcirculation, heart and pulmonary circulation, and CSF compartments. This chapter provides a detailed explanation of the model’s structure, formulation, the physical laws and numerical techniques it incorporates. Chapter 4 builds upon the global circulation model described in Chapter 3, focusing on the integration of the retinal vascular network and IOP dynamics. This chapter details how the model is adapted to simulate blood flow specifically in the retina, incorporating both the IOP and the Starling Resistor (SR) model to represent retinal perfusion. The process begins with the segmentation and correction of the retinal vessels, ensuring accurate representation of the arterial and venous networks within the eye. Once the vasculature is properly defined, the IOP model is incorporated to simulate how intraocular pressure influences blood flow through the retinal vessels. Additionally, the SR model is applied to simulate retinal vein pulsation, accounting for changes in vessel diameter and pressure during the cardiac cycle, and reflecting the dynamic nature of retinal blood flow. Chapter 5 presents the results of the simulations performed using the models developed in the previous chapters. The chapter begins with an analysis of mass conservation across the different numerical methods employed in the simulations. This analysis ensures that the models accurately preserve mass throughout the system, which is critical for the validity of the simulation results. Following this, the results primarily focus on the validation of the model’s predictions against experimental and clinical data, with a particular emphasis on systemic and cerebral hemodynamics. The model’s blood flow predictions are compared with data from the literature to validate the accuracy of the simulations. For the retinal circulation, the chapter includes a comparison of the simulated curves and values with those available in the literature. This comparison helps to validate the model’s representation of retinal blood flow dynamics, particularly in terms of pressure and flow. Additionally, the chapter compares viscoelastic and elastic models to evaluate how different vessel properties affect blood flow. Finally, the sixth chapter presents a discussion of the results, offering insights into the implications for clinical applications. The limitations of the current model will be addressed, and suggestions for future research will be provided. The chapter is concluded by a discussion how this research contributes to the understanding of retinal hemodynamics.