Math Model Sees Success
A mathematical model developed by a new faculty member at Mizzou could become a tool for early detection of vascular abnormalities of the eye. Professor Giovanna Guidoboni, who holds a joint appointment in electrical engineering, computer science, and mathematics, says her research began in 2010 while she was a professor of mathematical sciences at Indiana University–Purdue University Indianapolis (IUPUI). That’s when she met her collaborator, Professor Alon Harris, director of clinical research at the university’s Eugene and Marilyn Glick Eye Institute. Harris had invited Guidoboni and 11 other colleagues from the School of Science to visit his clinic, where he demonstrated a collection of instruments that could non-invasively measure many characteristics of the physiology of the eye.
“Alon said that in spite of this huge amount of data he had been collecting for decades, he could not make sense of it because there are so many factors that are interacting with each other, and that only mathematics could tell us why a measurement in one person is okay but the same measurement in another person could lead to blindness,” Guidoboni says. “He said we need some models based on physics and the physiology of the system that can help us disentangle all of these factors, so this is how we started.”
Envisioning a New Approach
Guidoboni says her research team focused on developing a model for glaucoma because it is one of the leading causes of blindness, and there is currently no cure. However, there are some treatments capable of slowing down or arresting the progression of vision loss. She says one treatment is to lower the intraocular pressure (IOP) in the eye, but a quarter of patients do not respond. Other patients do not exhibit an elevated IOP and yet display damage to the eye that is typical of glaucoma—studies have indicated there may be a vascular contribution to the disease. Guidoboni says her team decided to try to quantify the effect of blood flow through the eyes.
“From an engineering perspective, one can see the vasculature as an electrical pipe or conduit. You have the blood pressure, which pushes the blood through the pipes, so it is the driving force,” she explains. “The intraocular pressure is a pressure acting on the outside of the pipes; if you increase the pressure the pipes will constrict, making it difficult for blood to flow through.” She says these “pipes” also have different characteristics: arteries are like garden hoses with strong walls that are difficult to compress, while veins are like thin straws that compress easily. Another factor that had to be included in the modeling was vascular regulation, or the ability of the arteries to actively change their diameter in order to accommodate changes in blood flow to ensure tissues get the amount of blood and oxygen they need.
Guidoboni says her team, which includes mathematicians, engineers, computer scientists, statisticians, ophthalmologists, and physiologists, was the first to create a mathematical model of the interaction between the blood pressure, intraocular pressure, and vascular regulation in the eye, allowing the team to change certain variables and determine theoretical outcomes. Her team also collaborated with researchers at Polytechnic University of Milan, Italy and the University of Strasbourg, France.
“I like to say we used mathematics as a virtual lab where we can explore ideas and hypotheses offline, since it is not possible to manipulate blood pressure or IOP easily in people without causing problems. And even if you could, there are so many other variables that it is not easy to isolate one factor and be sure that what you see is due to a change in that particular variable,” she says.
Verification in Sight
Her team published their findings in Investigative Ophthalmology & Visual Science in 2014 and presented their findings at a number of conferences, but Guidoboni says their work remained theoretical until it was independently verified by a paper published in the British journal Ophthalmology in 2018. She says her team found the paper, published by a research team in Singapore, by chance while they were preparing for some talks and wanted to see what was new in terms of studies relating to blood pressure, the IOP, and blood flow. She says the Singapore team analyzed data on nearly 10,000 people and performed some statistical analyses to look for correlations among the factors involved—blood pressure, IOP, and glaucoma.
“What was interesting was the last two pages where they confirmed our theoretical predictions,” Guidoboni says. “In this sense, our model generated a testable hypothesis. They found people with low blood pressure and high IOP were at higher risk for glaucoma, which is what our model predicted. The scientific arguments in support of their findings are exactly what we predicted in our model, namely that the combination of low blood pressure and high IOP leaves the patient with a reduced capability of blood flow regulation and an increased susceptibility to venous collapse.”
She says the model offers an opportunity to develop a more individualistic approach to diagnosing and treating not just glaucoma but other diseases that manifest in the eye such as diabetes, hypertension, Alzheimer’s, and other disorders that show alterations in the eye before extensively damaging other organs. Guidoboni says her team has secured a patent to develop their mathematical model into an early, individualized diagnostic tool for vascular abnormalities.
“Having these tools that can detect early pathological changes in the eye could be useful for many people suffering from these diseases, because an early diagnosis would also mean early treatment, with much better outcomes,” she says.