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Math modeling may provide greater understanding of glaucoma risk


Low perfusion pressure is a risk factor for glaucoma. However, understanding the role of perfusion pressure in the disease must be clarified.


Take-home message: Low perfusion pressure is a risk factor for glaucoma. However, understanding the role of perfusion pressure in the disease must be clarified. 


By Lynda Charters; Reviewed by Alon Harris, MS, PhD, FARVO

Bloomington, IN-The understanding of the etiology of glaucoma has come a long way since the time that IOP was considered the sole determinant of glaucomatous damage.

Investigators currently are on the threshold of uncovering the complex relationships in the eye that govern the development and progression of glaucoma. 

For instance, perfusion pressure has recently come under closer scrutiny. Ocular perfusion pressure can be calculated by the formula two-thirds of the mean arterial pressure minus the IOP, according to Alon Harris, MS, PhD, FARVO.

“The difference between IOP and blood pressure is critical when talking about the driving force of the perfusion pressure,” said Dr. Harris, director of clinical research, Lois Letzter Professor of Ophthalmology, Professor of Cellular and Integrative Physiology, within the Department of Ophthalmology, Indiana University School of Medicine, Bloomington, IN. 

Dr. Harris discussed the relationship among different variables that affect the perfusion pressure-specifically, IOP, blood pressure, and the combination of the two, or in other words, the weight of each variable and whether it the same across the entire IOP spectrum.

He and his colleagues have embarked upon the development and evaluation of mathematical models to answer questions about the relevance of these factors in the development and progression of glaucoma.

Numerous studies have suggested that low diastolic perfusion pressure is an important risk factor for the prevalence of glaucoma, beginning with the Baltimore Study up to the recent South India Study, Dr. Harris noted.

Some studies-such as the Barbados Eye Study and the Rotterdam Study-have suggested perfusion pressure is a risk factor for the glaucoma incidence and progression. On the other hand, studies such as the Early Manifest Glaucoma Study have suggested the perfusion pressure is an important factor in glaucoma progression.

The Thessalonika Study, in which Dr. Harris is an investigator, evaluated progression models for diastolic blood pressure as a continuous variable and determined that low diastolic blood pressure and anti-hypertensive treatment are independently associated with the structure of the optic disc, he explained.

Changing course

The researchers reconsidered their approach, however, because of misinterpretations of the original data.

“When we analyzed the data and stratified it by the level of blood pressure and treatment, we found that only in subjects with low diastolic blood pressure and treated with anti-hypertensive drugs that structure was associated with ocular perfusion pressure,” he said.

In the Thessalonika Study, they hypothesized that the status of the perfusion pressure-that is, ocular perfusion pressure with or without anti-hypertensive treatment-may be more related to the pathogenesis of glaucoma than the ocular perfusion pressure by itself. 

“After subgroup analysis based on the status of the ocular perfusion pressure, we found that diastolic perfusion pressure was significantly associated with glaucoma in those treated with anti-hypertensive medications, and this was not the case in patients not treated with anti-hypertensive drugs,” Dr. Harris noted.

This suggested that perfusion pressure status may be more clinically relevant than just the level of the perfusion pressure. The findings were published in the American Journal of Ophthalmology (2013;155:843-851. doi: 10.1016/j.ajo.2012.12.007. Epub 2013 Feb 6).

One explanation for this finding is related to the treated patients having more decreases in nocturnal blood pressure with consequent variations in the perfusion pressure. A second explanation is that the anti-hypertensive drugs may disrupt the ability of the blood vessels to autoregulate.

The mathematical model

When conducting research in this area, it is difficult to isolate all factors that affect perfusion pressure and isolate their effect on the system, he noted.

“There are anatomic and physiologic variations among species and among individual patients,” Dr. Harris said.

This has led to the exploration of mathematical modeling.

“Basically, this model calculates stresses and strains in the lamina cribosa, which becomes deformed based on the action of the IOP and the retrolaminar pressure,” he said. “We look at fluid/structure interactions. The model describes the relationship between stresses and strains in the lamina cribosa and the blood flow in the vessels.”

This model also considers blood pressure and simulates a relationship between an increase in IOP and venous collapse, i.e., the Starling resistor effect.

Collaborators on the model include Dr. Harris and Giovanna Guidoboni, PhD, associate professor, Department of Mathematical Sciences, Indiana University and Purdue University at Indianapolis, and adjunct professor, Department of Ophthalmology, Indiana University School of Medicine.


A final factor evaluated is autoregulation, which, Dr. Harris said, it can turn on, off, or keep constant.

He provided an example of how this model works to interpret clinical data. In this example, three theoretical patients had three different blood pressure levels: low, high, and normal. Among the three patients, IOP was changed in the model from 15 mm Hg up to 45 mm Hg in correspondence with a mean arterial pressure and IOP level. With this information, the model predicts blood flow, of which perfusion pressure is a surrogate.

“We saw that at an IOP of <26 mm Hg, the blood flow plateaus for high blood pressure and normal blood pressure,” Dr. Harris said. “There is no plateau in a patient with low blood pressure. At IOPs of 26 to 36 mm Hg, the same decreasing slope is seen for all three patients. Over 36 mm Hg, a steeper slope is seen due to what we think is partial venous collapse, which begins earlier in patients with lower blood pressure.”

The data correspond to some data from the previously mentioned population-based studies, and offer an explanation of those data, he noted.

“Patients with low blood pressure that lack the ability to autoregulate have lower blood flow levels at any given level of IOP, and, we believe, may have early venous collapse,” Dr. Harris said. “We concluded that high IOP values are likely to be the dominant factor in ocular perfusion pressure causing inadequate or dysfunctional autoregulation.”

What understanding means for future

Dr. Harris summarized that previous studies are consistent on the finding that low perfusion pressure is a risk factor for glaucoma. In theory, ocular perfusion pressure can be incorporated into glaucoma management as a risk factor or a treatment target.

However, based on current knowledge, clinicians must first improve understanding of the role of perfusion pressure in glaucoma.

The complexity of perfusion pressure in and of itself and its interaction with potential risk factors for glaucoma still need to be determined. Synergy between math models and clinical studies can help weigh the contributions of different factors and mechanisms that influence autoregulation of blood flow in the eye and in the clinical interpretation of data, he explained.

This understanding may lead in the future to patient-specific evaluations elucidating the complex relationship between IOP, blood pressure, cerebrospinal fluid pressure, and optic nerve blood flow, according to Dr. Harris.



Alon Harris, MS, PhD, FARVO

E: alharris@indiana.edu

This article was adapted from Dr. Harris’ presentation at the 2015 meeting of the American Glaucoma Society. Dr. Harris has no financial interest in any aspect of this report.


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