While glaucoma is a leading cause of preventable blindness around the world, medical professionals still do not know how the most common forms of the disease develop. Glaucoma is a progressive condition that causes irreversible damage to the optic nerve, which transmits visual signals to the brain. The condition involves abnormally high pressure of intraocular fluids inside the eye, which can compress the nerves of each eye and lead to vision loss. While this mechanism is relatively well understood, clinicians cannot always identify the underlying causes of an increase in intraocular pressure or how these changes in pressure can actually affect blood velocity in the eye.

Mechanisms Affecting Blood Flow

At the September 2019  American Physiological Society Interface of Mathematical Models and Experimental Biology: Role of the Microvasculature Conference, scientist Lucia Carichino, PhD, of the Rochester Institute of Technology, presented research on a mathematical model that could shed some light on these unanswered questions. The research focused on how the effect of retinal microvasculature on ocular hemodynamics might be adequately modeled. The team behind the research used measurements on the thickness, diameter and elasticity of vessel walls found within the eye, along with scientific literature about intraocular pressure, to develop the mathematical model.

Researchers created a reduced-dimension model, meaning it uses points, lines and geometric shapes to approximate physiological structures such as blood vessels. This sort of modeling could provide a solution to a question that could otherwise prove difficult—if not impossible—to answer. These solutions could be integrated easily into the clinical setting. The clinical solutions can be quickly computed by an application using the algorithm. However, the researchers behind this new model imagined a use beyond clinical applications.

Mathematical Model to Explain Pathophysiology

One of the primary applications of the mathematical model could be as a sort of virtual toolbox to learn more about the pathophysiology of glaucoma. Researchers at the Rochester Institute of Technology in New York imagine the model is a sort of virtual toolbox that eye clinicians can use to explore the mechanisms contributing to the progression of glaucoma, as well as potentially other ophthalmologic conditions. The model shows that venules, the tiniest of blood vessels in the eye, become even smaller as intraocular pressure increases. The reduced venule diameter in turn decreases circulation to the central retinal artery, which is responsible for providing much of the nutrients to the eye. The central retinal artery is often used to measure overall ocular blood flow. The model could help to better translate those measurements into blood flow elsewhere in the eye.

Over the years, a significant amount of clinical data about the development and progression of glaucoma has been obtained, although it is not always clear what physiological processes underlie these results. The new mathematical model provides a way of understanding blood flow in the eye and how it contributes to blindness among patients with glaucoma. The model points to the particular importance of retinal venules, as well as other parts of the microvasculature, in the disease progression of glaucoma. Since studying the microvasculature may prove difficult, the model could help researchers better pinpoint the questions they need to answer and the likely physiology behind the disease.

Another Mathematical Model to Explain Glaucoma Changes

Prior to this study, Carichino participated in research efforts to try to develop a mathematical model for blood flow within the eye that could be used to discern the mechanisms behind glaucoma. In 2016, she led a team at Purdue University in Indiana  that developed a mathematical model to describe deformations in ocular structures and eye blood flow. The model was a reduced-order, fluid-structure interaction model that clinicians could use to explore the relevance of both mechanical and vascular factors contributing to glaucoma. To move the model further, the team used a new energy-based technique that coupled both partial and ordinary differential equations in blood flow through operator splitting.

Afterward, the team used clinical data and model predictions to obtain a better sense of why venous oxygen saturation increases in patients with advanced forms of glaucoma. The researchers eventually used color Doppler images to extract waveform parameters in blood flow to differentiate healthy individuals from those with glaucoma. Ultimately, the team hypothesized that an increase in resistance in retinal microcirculation contributes to the overall effect of increased intraocular pressure on hemodynamics in the eye and an increase in venous oxygen saturation is dependent on the intraocular pressure in a given patient. Also, the model found the normalized velocity difference in the descending and ascending limbs of the ophthalmic artery is much higher in patients with glaucoma than in those patients without the condition.

Understanding Glaucoma Pathophysiology

Researchers still have a lot of work to do in terms of understanding the mechanisms behind the development and progression of glaucoma. However, this goal is extremely important for the future treatment of the disease. Achieving a greater understanding of what occurs physiologically in the eye could lead to new approaches to treatment to prevent the development of the disease or potentially halt its progression. Treating the changes in microvasculature that occur due to increased intraocular pressure could help to mitigate the effects of the disease and ultimately protect individuals from losing vision.