Stresses and fluid flow in lamina cribrosa through anisotropic poroelasticty

TL;DR

The paper develops a transversely isotropic poroelastic model of the Lamina Cribrosa (LC) using Reissner–Mindlin plate theory to study how intraocular pressure (IOP) variations couple solid deformation with fluid transport. By formulating and solving the TI poroelastic equations with physiologic and pathologic boundary conditions, the authors quantify how stress measures (Von Mises) and shear strain peak in the LC periphery, while fluid content monotonically decreases with rising $IOP$. The work demonstrates that isotropic assumptions underestimate fluid content and overestimate shear, underscoring the importance of anisotropy in LC biomechanics and perfusion. It also shows that the central retinal vessels canal stiffness significantly affects stress distribution and displacements, suggesting avenues for inverse parameter estimation and personalized glaucoma assessment. Overall, the model provides a rigorous framework to explore the coupled mechanical and hemodynamic behavior of the LC under glaucomatous conditions and to infer otherwise inaccessible mechanical properties from observable data.

Abstract

To explore the possible mechanical correlations between intraocular pressure (IOP) variations and glaucoma, this study presents a transversely isotropic poroelastic model of the Lamina Cribrosa (LC) based on Reissner Mindlin plate theory, ultimately highlighting the interplay between solid matrix deformation and blood flow behavior under pathological conditions. Starting from poroelasticity theory, the equilibrium equations governing the LC were formulated and analytically solved by applying appropriate mechanical and hydraulic boundary conditions. The results indicate that both strain and stress measures (in the form of shear strain and von Mises stress) peak in the peripheral region of the LC, which is currently suspected to be the initial site of glaucomatous damage. These quantities increase with IOP, suggesting a pressure-dependent mechanical insult to the retinal ganglion cell (RGC) axons. In parallel, the model predicts a monotonic reduction in fluid content as IOP rises, which may contribute to ischemic phenomena and disc haemorrhages. The influence of material anisotropy was also examined, revealing that isotropic assumptions tend to underestimate the fluid content while overestimating shear strain. Given the current experimental challenges in measuring blood flow within the LC, the proposed model provides a valuable framework for exploring the coupled mechanical hemodynamic behavior of the tissue and for inverse estimation of its mechanical parameters, such as the stiffness of the opening for the central retinal vessels.

Figures (4)

• Figure 1: Sketch of the boundary conditions applied to the proposed model.
• Figure 2: Variation of blood content $\zeta$ (first row), hydrostatic effective stress (which is the vascular pressure) $\sigma'_{hyd}$ (second row), Von Mises stress $\sigma'_{VM}$ (third row), and shear strain (fourth row), for three IOP conditions: ocular hypotension ($p_{IOP}=5\ \textup{mmHg}$, red, left column), baseline ($p_{IOP}=15$ mmHg, green, centre column), and ocular hypertension ($p_{IOP}=30$ mmHg, blue, right column). Stresses are normalized with respect to the baseline IOP. Mechanical and hydraulic quantities are plotted against the normalized radial coordinate in the LC. Owing to the dominant bending behavior of the lamina, through-thickness variations are significant and are reported using readings at the intraocular and retrobulbar surfaces.
• Figure 3: Comparison between transversely isotropic model (TI) and isotropic one (I), reported in terms of variation of blood content $\zeta$ (on the left), Von Mises stress $\sigma_{VM}$ (centrally) and shear strain $\gamma_{rz}$ (on the right). Readings are reported for different values of the through-thickness coordinate.
• Figure 4: Analyses of the effects of the central LC canal stiffness on the poromechanics of the LC. On the left, the variation of blood content for the basal condition $p_{IOP}=15$mmHg, given at three different heights ($z=\{-h/2,0,h/2\}$), for a soft (in red), hard (in blue) and a situation in the middle (in green) central LC canal stiffness. In the middle, the Von Mises stress is presented for the same situation of baseline inter-ocular pressure and at three different heights of the lamina for the various combination of stiffness specified above. Lastly, on the right, the effects of the central LC canal on the vertical displacements of the middle plane of the LC ($z=0$) are depicted for all three pressure-related conditions (baseline, ocular hypotension and ocular hypertension).