A poroelastic model for the perfusion of the lamina cribrosa in the optic nerve head

Abstract

In this work we present a mathematical model for the coupling between biomechanics and hemodynamics in the lamina cribrosa, a thin porous tissue at the base of the optic nerve head which is thought to be the site of injury in ocular neurodegenerative diseases such as glaucoma. In this exploratory two-dimensional investigation, the lamina cribrosa is modeled as a poroelastic material where blood vessels are viewed as pores in a solid elastic matrix. The model is used to investigate the influence on the distributions of stress, blood volume fraction (or vascular porosity) and blood velocity within the lamina cribrosa due to the application of different levels of the intraocular pressure (IOP) and the enforcement of different mechanical constraints at the lamina's boundary. The model simulations suggest that the degree of fixity of the boundary constraint strongly influences the lamina's response to IOP elevation. Specifically, when the boundary is mechanically clamped, IOP elevation leads to an increase in stress close to the lamina's boundary, making it more susceptible to tissue damage. On the other hand, when rotations are allowed at the boundary, the most vulnerable region appears to be located at the lamina's central axis, in proximity of the eye globe, where increased stress and reduced vascular porosity and blood velocity are predicted for increased levels of IOP.

Factors Influencing Lamina Cribrosa Microcapillary Hemodynamics and Oxygen Concentrations

“…This is not biologically accurate as the LC has a thickness of approximately 270 lm. 58 Considering that the LC may exhibit highly heterogeneous stresses (induced by IOP, the retrolaminar pressure, or during eye movements 59 ), it would be logical to observe variations in LC hemodynamics and oxygen concentrations through the thickness of the LC, as predicted by Causin et al 20 LC thickness has also been shown to change with glaucoma progression, which may in turn compromise blood flow further in glaucoma subjects. 8 While using 'surface-like' LCs (as performed herein) should provide a first degree of understanding of LC hemodynamics, future improvements to our models should prioritize on incorporating LC thickness and interactions with LC stresses.…”

“…It should be mentioned that a computational study on LC hemodynamics was previously conducted by Causin et al 20 The authors used a poroelastic model, whereby blood capillaries were modeled as homogeneous pores in an elastic matrix. The work accounted for the biomechanical action of IOP, retrolaminar tissue pressure, and scleral tension on hemodynamics, but it did not take into account complex capillary networks and oxygen transport.…”

“…A CFD study by Carichino et al 19 revealed that IOP-induced LC deformation could reduce the lumen size of the central retinal artery (CRA), and thus the overall ocular blood flow volume. A computational study by Causin et al 20 also suggested that an increase in IOP could disrupt LC hemodynamics through biomechanical interactions. However, no CFD studies have yet modeled the LC as a detailed capillary network and studied how changes in ONH morphology could affect hemodynamics and oxygen concentrations within such a capillary network.…”

A poroelastic mixture model of mechanobiological processes in biomass growth: theory and application to tissue engineering

“…[53], Chapt. 9), because in the present model the variable p is not a Lagrange multiplier (as in the Stokes system), rather, it is the solution of an elliptic Darcy problem (for a similar treatment see [12]). In the case of the ADR equation we employ for the approximation of the concentration and of the cellular volume fractions the primal-mixed finite element discretization scheme with exponential fitting stabilization proposed and investigated in [62].…”

Effect of ocular shape and vascular geometry on retinal hemodynamics: a computational model

“…We utilize the theory of capillary models for porous media [6,28] and we write the porosity at each hierarchical level as…”