SIAM News Blog

Mathematically Modeling Retinal Hemodynamics

By Karthika Swamy Cohen

Lucia Carichino of Worcester Polytechnic Institute presented a multiscale mathematical model to help understand retinal hemodynamics.
The eye has a complex multi-layered structure: the sclera—also called the white of the eye—forms the outer layer; the choroid is the middle vascular layer receiving roughly 80% of the total ocular blood flow; and the retina, which is light sensitive, forms the inner layer. Retinal ganglion cells, types of neurons located near the inner surface of the retina, send signals from the eye to the brain, transmitting visual information via the optic nerve.

The primary source of blood to the eye is the ophthalmic artery, which is located close to the optic nerve. It gives rise to the central retinal artery (CRA), which runs within the central portion of the optic nerve canal and parallel to the central retina vein (CRV); the latter, in turn, drains blood from the eye. 

The dynamics of blood flow in the retina, or retinal hemodynamics, plays an important role in ocular diseases such as glaucoma. At a minisymposium at the SIAM Annual Meeting being held in Pittsburgh, Pa. this week, Lucia Carichino of Worcester Polytechnic Institute presented a multiscale mathematical model that can help us understand the mechanisms leading to these correlations.

Central retinal artery and central retinal vein represent the only input and output of retinal circulation

“We are trying to create a model that is able to describe the fundamental physics governing blood flow in the eye,” Carichino said. 

The nerve fibers that form the optic nerve exit the eye through a hole in the sclera in the posterior region of the eye, which is occupied by the lamina cribrosa. The lamina cribrosa is a collagen-like structure that helps maintain the pressure between the inside of the eye and the surrounding tissue, that is, between the intraocular pressure (IOP) inside the eye globe and the cerebrospinal fluid pressure (CSFp) in the retrobulbar region.

"There are lots of interesting features when studying the eye, and one of them is pressure,” Carichino said. The optic nerve tissue and the eye globe are a pressurized system. The combined action of the IOP, CSFp, and scleral tension cause deformations in the lamina, which is modeled as a nonlinear, homogeneous, isotropic, elastic circular plate of finite thickness.

Carichino’s model analyzes the velocity profile in the eye: the peak systolic and diastolic velocities, which represent the max and the mean are dependent on intraocular pressure. The velocities are seen to decrease with increase in pressure.

The model assumes that the lamina is made of a homogenous isotopic material and exhibits axial symmetry. It is a weakly nonlinear elastic circular plate. This allows Carichino’s group to reduce it to a two-dimensional model rather than solving for a three-dimensional model. It also assumes steady state

Overview of multiscale model for retinal hemodynamics.

Stokes flow is used to model blood flow in the central retinal vessels, which in turn deform under external pressure.

Carichino’s mathematical model couples retinal blood flow in the CRA and CRV with the lamina cribrosa deformation via a fluid-structure interaction problem. The CRA, which is connected to the arterial system, and the CRV, which is connected to the venous system, are modeled as a network of resistances. 

“We assume that as IOP changes we actually change the resistance depending on the pressure inside the eye,” Carichino explained. “And then we impose conservation of flow.”

Carichino compared her model results to clinical data; this comparison helps estimate and quantify the mechanical factors that influence IOP and CSFp on retinal hemodynamics. "We use the model to interpret clinical data and understand the mechanisms behind it."

The model shows that regions of compressive stresses in the lamina cribrosa become more pronounced as IOP is elevated. It also demonstrates that IOP changes have a greater effect on retinal hemodynamics than changes in CSFp. Carichino speculates that this may be due to the fact that intraocular pressure acts directly on the intraocular retinal vessels, as opposed to cerebrospinal fluid pressure, which does not. 

The model suggests that reduction of CRA blood velocity induced by elevation of IOP elevation, which is seen in vivo in humans may be caused by IOP-induced increase in vascular resistance of the retinal venules. Indeed, regions of radial compressive stress in the lamina cribrosa are seen to cause an increase in the vascular resistance of the CRA in the model. This increase, however, is minimal compared to the IOP-induced increase in resistance of the retinal venules.

Click here for more coverage of the 2017 SIAM Annual Meeting.

Karthika Swamy Cohen is the managing editor of SIAM News.
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