Influence of tissue viscoelasticity on the optic nerve head perfusion: a mathematical model

Abstract

Purpose : Proper perfusion of the optic nerve head (ONH) tissue is vital to visual function. Alterations in material properties of ONH structures, such as the lamina cribrosa (LC), have been associated with many pathologies, including glaucoma. We hypothesize that changes in LC viscoelasticity may compromise LC perfusion in response to sudden variations of intraocular pressure (IOP), possibly leading to disc hemorrhages. Due to the difficulty of isolating these factors experimentally, we utilized a mathematical model as virtual lab to investigate IOP’s influence on LC perfusion.

Methods : The LC is modeled as a poro-visco-elastic material, where blood vessels are viewed as pores in a solid matrix. LC vascular porosity (ratio between blood volume and LC total volume) and LC permeability (ability of the porous material to allow fluid passing through it) depend on the local state of stress and strain. Blood flow is driven by the pressure difference between the short posterior ciliary arteries and the central retinal vein. The LC is subject to scleral tension, retrolaminar tissue pressure and IOP. A finite element method is used to simulate and compare the behavior of the integrated time rate of change of the blood kinetic energy (W) in response to sudden temporal IOP variations (Fig1) with and without LC viscoelasticity (d=1 and d=0, respectively) (Fig2).

Results : If d=0, W exhibits two sharp peaks at the IOP switch-on and switch off times (Fig2). These peaks represent sharp and acute local changes in blood flow and pressure, with consequent perfusion instability and irregularity, in response to sharp changes in IOP. If d=1, these peaks are not present and W remains bounded at lower values (Fig2). These findings suggest that the lack of viscoelasticity may increase the LC susceptibility to localized damage due to peaks in the integrated time rate of change of the blood kinetic energy as IOP experiences sudden changes in time, as they normally occur during the day.

Conclusions : Our theoretical results suggest that even physiological changes in IOP may induce pathological changes in LC perfusion if the LC viscoelasticity provided by the collagen fibers is not intact (due, e.g., to ageing or disease). The clinical implications of LC perfusion deficits during IOP variation should be further investigated to elucidate their impact on glaucoma pathophysiology.

This is an abstract that was submitted for the 2016 ARVO Annual Meeting, held in Seattle, Wash., May 1-5, 2016.