By Karthika Swamy Cohen
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.
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.
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
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.
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